Atmospheric turbulence significantly affects electromagnetic (EM) wave propagation, especially at millimeter-wave (mmWave) frequencies, resulting in scintillation. Developing a statistical channel model to characterize these effects is crucial for accurate prediction and mitigation across various applications. In radar and satellite systems, turbulence can degrade signal quality and reduce accuracy. As telecommunications advance toward higher EM frequencies, turbulence will significantly influence signal performance. Moreover, statistical analysis of a propagating EM wave provides a unique opportunity for the remote sensing of atmospheric turbulence dynamics. The push towards an improved understanding of the planetary boundary layer on a global scale motivates the development of next generation measurement techniques.
\r\n\r\nThis thesis presents a novel approach for studying and characterizing the physical effects of atmospheric turbulence on mmWave propagation in a controlled laboratory environment. The method combines theoretical modeling and experimental validation to link meteorological parameters and turbulence dynamics to the scintillation effects on the power spectrum of a radio frequency (RF) signal. The experimental setup employs a versatile fan array wind tunnel to generate repeatable and controllable turbulent flows. A W-band (95GHz) transceiver is used to propagate EM energy through the turbulent flow, with the received signal analyzed to characterize the effects of turbulence-induced scintillation. Additional components include utility heaters for generating strong temperature gradients, a thermal screen and infrared camera to measure the temperature profile of the flow with high spatial resolution, a high-speed anemometer for turbulence spectrum characterization, and barometers and hygrometers for pressure and humidity measurements.
\r\n\r\nThe effects of temperature gradients and wind speeds are shown to increase and shift the power spectrum of the RF signal across multiple turbulent scales. Meteorological and RF measurements are directly linked through an empirical model that builds upon existing theoretical frameworks to accurately determine flow dynamics based on the characteristics of the received signal. The results are shown to be consistent and repeatable across multiple days, ambient conditions, and experimental configurations. Improvements and future directions are discussed, including extending this experimental setup to practical applications and leveraging the controllability to develop more sophisticated models that advance the understanding of scintillation.
", "doi": "10.7907/7sbc-5v10", "publication_date": "2026", "thesis_type": "phd", "thesis_year": "2026" }, { "id": "thesis:18782", "collection": "thesis", "collection_id": "18782", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06032026-191806044", "type": "thesis", "title": "Integrated Transceivers from Microwave to Optical: Signals, Systems and Silicon for Sensing and Communications", "author": [ { "family_name": "Nooshabadi", "given_name": "Samir Vahdat", "orcid": "0000-0003-1645-0009", "clpid": "Nooshabadi-Samir-Vahdat" } ], "thesis_advisor": [ { "family_name": "Hajimiri", "given_name": "Ali", "orcid": "0000-0001-6736-8019", "clpid": "Hajimiri-A" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" }, { "family_name": "Hajimiri", "given_name": "Ali", "orcid": "0000-0001-6736-8019", "clpid": "Hajimiri-A" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Marandi", "given_name": "Alireza", "orcid": "0000-0002-0470-0050", "clpid": "Marandi-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The enormous complexity to size ratio of integrated circuits is one of the great technological accomplishments. The proliferation of integrated circuits into all aspects of daily life has ushered in an era where the line between circuit and system designers has become increasingly blurred. This thesis explores new systems in sensing and connectivity and the design of the integrated circuits that can empower them. The first part of this thesis focuses on the quest for a low-cost, LiDAR-like imaging radar for automotive applications. Novel signals, systems, analytical frameworks and custom silicon transceivers are presented. The second part of this thesis explores decentralized relay architectures for communications, monolithic electro-optic systems for sensing, flexible arrays for wireless power transfer, and the novel integrated circuits that enable them all.", "doi": "10.7907/zke2-7t12", "publication_date": "2026", "thesis_type": "phd", "thesis_year": "2026" }, { "id": "thesis:17300", "collection": "thesis", "collection_id": "17300", "cite_using_url": "https://resolver.caltech.edu/CaltechThesis:05292025-205908563", "primary_object_url": { "basename": "Kulkarni_Pranav_Dhananjay_2025.pdf", "content": "final", "filesize": 9065719, "license": "other", "mime_type": "application/pdf", "url": "/17300/1/Kulkarni_Pranav_Dhananjay_2025.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Signal Processing for Line Spectra: New Sensor Arrays, Algorithms, and Theoretical Results", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav Dhananjay", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-Dhananjay" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Kostina", "given_name": "Victoria", "orcid": "0000-0002-2406-7440", "clpid": "Kostina-V" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Line spectrum signals appear in diverse application areas such as molecular dynamics, power electronics, speech processing, and target localization. They are composed of sums of complex exponentials with distinct frequencies. Identifying the parameters of these constituent complex exponentials has been a prominent research topic in signal processing for over four decades. In this thesis, we focus on two specific applications involving line spectrum signals: direction of arrival (DOA) estimation using sensor arrays, and denoising of discrete-time periodic signals.
\r\n\r\nThe main contribution of this thesis on the topic of DOA estimation is to propose unconventional sensor array geometries and algorithms in the presence of aperture constraints. In the first part, we demonstrate that under an aperture constraint, the traditional integer arrays (defined as arrays with sensors placed at integer multiples of the half-wavelength distance \u03bb/2) can perform only suboptimally because of the restrictive sensor placement at integer locations. To address this, we propose to use 'rational arrays' that can have sensors located at rational multiples of \u03bb/2. This offers greater flexibility in sensor placement under aperture constraints. In particular, we propose rational coprime arrays that can approach the Cram\u00e9r-Rao bound (CRB) even at low signal-to-noise ratio (SNR) and with a limited number of snapshots, and can outperform the integer arrays. Numerical simulations show that rational arrays are also better equipped to resolve closely separated DOAs. To enable the derivation of the theoretical results and identifiability guarantees for rational coprime arrays, we extend the number-theoretic concepts such as greatest common divisor and coprimality to the case of rational numbers, and prove several number-theoretic properties. Rational arrays are also demonstrated to have important advantages when the DOAs are known to lie in a sector of the space, and for identifying O(N2) uncorrelated sources using N sensors under aperture constraint.
\r\n\r\nIn the second part of the thesis, we propose modifications to the traditionally used sparse (integer) array design criteria. These modifications are aimed at mitigating the impact of mutual coupling on DOA estimation and reducing the required aperture. To reduce the impact of mutual coupling, we propose two types of sparse arrays that have either double or triple minimum inter-element spacing compared to the traditionally used \u03bb/2 spacing. This introduces 'holes' at lags 1 and 2 in the difference coarrays (defined as the set of differences in sensor locations). The first type of arrays, called weight-constrained sparse arrays, have O(N) aperture, making them suitable when the available aperture is constrained and the number of DOAs is small. A general array construction, to further reduce the weights at other coarray lags, is also proposed. The second type of arrays, called weight-constrained nested arrays, have O(N2) degrees of freedom and are suitable when there are no aperture restrictions. Extensive Monte-Carlo simulations demonstrate that the proposed arrays have significantly smaller DOA estimation errors compared to the well-known sparse arrays from the literature, in the presence of high mutual coupling.
\r\n\r\nBecause of the central holes in the difference coarrays of the weight-constrained arrays, there are two segments of consecutive entries in their coarrays: one on the positive side and the other on the negative side. To leverage these both, we propose to use an augmented coarray covariance matrix for the subspace-based algorithms such as multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance (ESPRIT). This further reduces the DOA estimation error for the weight-constrained arrays, and the computation time of augmented-MUSIC is significantly less than that of optimization-based methods, such as coarray interpolation and dictionary-based methods. We also develop methods to algorithmically interpolate the missing entries in the coarray at lags 1 and 2, to generate a larger coarray matrix. This approach demonstrates the capability to identify up to twice as many DOAs compared to what can be achieved using only the one-sided segment of consecutive lags in the coarray. This mitigates the main disadvantage of having central holes in the coarrays of weight-constrained arrays, while still benefiting from their advantage in reducing the impact of mutual coupling.
\r\n\r\nOne major drawback of using coarray-MUSIC for DOA estimation is its inefficiency (i.e., the mean squared error (MSE) does not approach CRB, even asymptotically). We conduct several experiments to provide new insights into the complex relationship of coarray-MUSIC MSE on several parameters, such as array geometry, DOA separation, and accuracy of the estimated array output correlations. Furthermore, we demonstrate that an alternative way of constructing the Toeplitz covariance matrix can greatly improve the MSE compared to coarray-MUSIC, and can lead to efficient DOA estimation. This approach is based on solving an optimization problem whose objective is derived using the asymptotic error distribution of the known entries from the covariance matrix. We also propose a modification to the Toeplitz covariance matrix construction approach to account for the presence of mutual coupling and provide simulations with different sparse arrays.
\r\n\r\nThe third part of the thesis is focused on developing a periodicity-aware signal denoising framework using Capon-optimized Ramanujan filter banks and pruned Ramanujan dictionaries. The signal reconstruction (synthesis) is done by solving a regularized optimization problem, based on the outputs of the analysis filter bank. This hybrid analysis-synthesis framework ensures that the denoised output is necessarily composed of discrete-time periodic components. Capon beamforming principles from array signal processing are utilized to optimize the Ramanujan filters to the incoming data. A computationally efficient way of obtaining the inverses of the required autocorrelation matrices is derived using Levinson\u2019s recursion. The proposed denoising method is observed to be effective even when the signal length is small and demonstrates a high SNR gain across a wide range of input signal SNRs. Furthermore, we derive several decimation properties of Ramanujan subspace signals, which help in reducing the required computations by appropriately downsampling the filter outputs without any loss of information.
\r\n\r\nTowards the end of the thesis, we theoretically investigate the locations of zeros of Ramanujan filters. Additionally, we propose an ideal interpolation filter model for Ramanujan subspace signals, which has potential application in developing a synthesis filter bank counterpart to the Ramanujan analysis filter bank for perfect signal reconstruction. We also explore the use of dictionary learning to represent periodic signals, and adapt a convolutional neural network based DOA estimation method to sparse arrays.
", "doi": "10.7907/n6dp-p089", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:17300", "collection": "thesis", "collection_id": "17300", "cite_using_url": "https://resolver.caltech.edu/CaltechThesis:05292025-205908563", "primary_object_url": { "basename": "Kulkarni_Pranav_Dhananjay_2025.pdf", "content": "final", "filesize": 9065719, "license": "other", "mime_type": "application/pdf", "url": "/17300/1/Kulkarni_Pranav_Dhananjay_2025.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Signal Processing for Line Spectra: New Sensor Arrays, Algorithms, and Theoretical Results", "author": [ { "family_name": "Kulkarni", "given_name": "Pranav Dhananjay", "orcid": "0000-0002-1461-0948", "clpid": "Kulkarni-Pranav-Dhananjay" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Kostina", "given_name": "Victoria", "orcid": "0000-0002-2406-7440", "clpid": "Kostina-V" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Line spectrum signals appear in diverse application areas such as molecular dynamics, power electronics, speech processing, and target localization. They are composed of sums of complex exponentials with distinct frequencies. Identifying the parameters of these constituent complex exponentials has been a prominent research topic in signal processing for over four decades. In this thesis, we focus on two specific applications involving line spectrum signals: direction of arrival (DOA) estimation using sensor arrays, and denoising of discrete-time periodic signals.
\r\n\r\nThe main contribution of this thesis on the topic of DOA estimation is to propose unconventional sensor array geometries and algorithms in the presence of aperture constraints. In the first part, we demonstrate that under an aperture constraint, the traditional integer arrays (defined as arrays with sensors placed at integer multiples of the half-wavelength distance \u03bb/2) can perform only suboptimally because of the restrictive sensor placement at integer locations. To address this, we propose to use 'rational arrays' that can have sensors located at rational multiples of \u03bb/2. This offers greater flexibility in sensor placement under aperture constraints. In particular, we propose rational coprime arrays that can approach the Cram\u00e9r-Rao bound (CRB) even at low signal-to-noise ratio (SNR) and with a limited number of snapshots, and can outperform the integer arrays. Numerical simulations show that rational arrays are also better equipped to resolve closely separated DOAs. To enable the derivation of the theoretical results and identifiability guarantees for rational coprime arrays, we extend the number-theoretic concepts such as greatest common divisor and coprimality to the case of rational numbers, and prove several number-theoretic properties. Rational arrays are also demonstrated to have important advantages when the DOAs are known to lie in a sector of the space, and for identifying O(N2) uncorrelated sources using N sensors under aperture constraint.
\r\n\r\nIn the second part of the thesis, we propose modifications to the traditionally used sparse (integer) array design criteria. These modifications are aimed at mitigating the impact of mutual coupling on DOA estimation and reducing the required aperture. To reduce the impact of mutual coupling, we propose two types of sparse arrays that have either double or triple minimum inter-element spacing compared to the traditionally used \u03bb/2 spacing. This introduces 'holes' at lags 1 and 2 in the difference coarrays (defined as the set of differences in sensor locations). The first type of arrays, called weight-constrained sparse arrays, have O(N) aperture, making them suitable when the available aperture is constrained and the number of DOAs is small. A general array construction, to further reduce the weights at other coarray lags, is also proposed. The second type of arrays, called weight-constrained nested arrays, have O(N2) degrees of freedom and are suitable when there are no aperture restrictions. Extensive Monte-Carlo simulations demonstrate that the proposed arrays have significantly smaller DOA estimation errors compared to the well-known sparse arrays from the literature, in the presence of high mutual coupling.
\r\n\r\nBecause of the central holes in the difference coarrays of the weight-constrained arrays, there are two segments of consecutive entries in their coarrays: one on the positive side and the other on the negative side. To leverage these both, we propose to use an augmented coarray covariance matrix for the subspace-based algorithms such as multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance (ESPRIT). This further reduces the DOA estimation error for the weight-constrained arrays, and the computation time of augmented-MUSIC is significantly less than that of optimization-based methods, such as coarray interpolation and dictionary-based methods. We also develop methods to algorithmically interpolate the missing entries in the coarray at lags 1 and 2, to generate a larger coarray matrix. This approach demonstrates the capability to identify up to twice as many DOAs compared to what can be achieved using only the one-sided segment of consecutive lags in the coarray. This mitigates the main disadvantage of having central holes in the coarrays of weight-constrained arrays, while still benefiting from their advantage in reducing the impact of mutual coupling.
\r\n\r\nOne major drawback of using coarray-MUSIC for DOA estimation is its inefficiency (i.e., the mean squared error (MSE) does not approach CRB, even asymptotically). We conduct several experiments to provide new insights into the complex relationship of coarray-MUSIC MSE on several parameters, such as array geometry, DOA separation, and accuracy of the estimated array output correlations. Furthermore, we demonstrate that an alternative way of constructing the Toeplitz covariance matrix can greatly improve the MSE compared to coarray-MUSIC, and can lead to efficient DOA estimation. This approach is based on solving an optimization problem whose objective is derived using the asymptotic error distribution of the known entries from the covariance matrix. We also propose a modification to the Toeplitz covariance matrix construction approach to account for the presence of mutual coupling and provide simulations with different sparse arrays.
\r\n\r\nThe third part of the thesis is focused on developing a periodicity-aware signal denoising framework using Capon-optimized Ramanujan filter banks and pruned Ramanujan dictionaries. The signal reconstruction (synthesis) is done by solving a regularized optimization problem, based on the outputs of the analysis filter bank. This hybrid analysis-synthesis framework ensures that the denoised output is necessarily composed of discrete-time periodic components. Capon beamforming principles from array signal processing are utilized to optimize the Ramanujan filters to the incoming data. A computationally efficient way of obtaining the inverses of the required autocorrelation matrices is derived using Levinson\u2019s recursion. The proposed denoising method is observed to be effective even when the signal length is small and demonstrates a high SNR gain across a wide range of input signal SNRs. Furthermore, we derive several decimation properties of Ramanujan subspace signals, which help in reducing the required computations by appropriately downsampling the filter outputs without any loss of information.
\r\n\r\nTowards the end of the thesis, we theoretically investigate the locations of zeros of Ramanujan filters. Additionally, we propose an ideal interpolation filter model for Ramanujan subspace signals, which has potential application in developing a synthesis filter bank counterpart to the Ramanujan analysis filter bank for perfect signal reconstruction. We also explore the use of dictionary learning to represent periodic signals, and adapt a convolutional neural network based DOA estimation method to sparse arrays.
", "doi": "10.7907/n6dp-p089", "publication_date": "2025", "thesis_type": "phd", "thesis_year": "2025" }, { "id": "thesis:16398", "collection": "thesis", "collection_id": "16398", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05202024-212313617", "primary_object_url": { "basename": "Caltech_thesis_20240521_submitted.pdf", "content": "final", "filesize": 2356609, "license": "other", "mime_type": "application/pdf", "url": "/16398/1/Caltech_thesis_20240521_submitted.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Signal Processing for Large Arrays: Convolutional Beamspace, Hybrid Analog and Digital Processing, and Distributed Algorithms", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Kostina", "given_name": "Victoria", "orcid": "0000-0002-2406-7440", "clpid": "Kostina-V" }, { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The estimation of the directions of arrival (DOAs) of incoming waves for a passive antenna array has long been an important topic in array signal processing. Meanwhile, the estimation of the MIMO channel between a transmit antenna array and a receive antenna array is a key problem in wireless communications. In many recent works on these array processing tasks, people consider millimeter waves (mmWaves) due to their potential to offer more bandwidth than the already highly occupied lower-frequency bands. However, new challenges like strong path loss at the high frequencies of mmWaves arise. To compensate for the path loss, large arrays, or massive MIMO, are used to get large beamforming gain. It is practical due to the small sizes of mmWave antennas. When large arrays are used, it is important to develop efficient estimation algorithms with low computational and hardware complexity.
\r\n\r\nThe main contribution of this thesis is to propose low-complexity DOA and channel estimation methods that are especially effective for large arrays. To achieve low complexity, three main aspects are explored: beamspace methods, hybrid analog and digital processing, and distributed algorithms. First, a new beamspace method, convolutional beamspace (CBS), is proposed for DOA estimation based on passive arrays. In CBS, the array output is spatially filtered, followed by uniform decimation (downsampling) to achieve dimensionality reduction. No DOA ambiguity occurs since the filter output is represented only by the passband sources. CBS enjoys the advantages of classical beamspace such as lower computational complexity, increased parallelism of subband processing, and improved resolution threshold for DOA estimation. Moreover, unlike classical beamspace methods, it allows root-MUSIC and ESPRIT to be performed directly for uniform linear arrays without additional preparation since the Vandermonde structure is preserved under the CBS transformation. The method produces more accurate DOA estimates than classical beamspace, and for correlated sources, better estimates than element-space.
\r\n\r\nThe idea of hybrid analog and digital processing is then incorporated into CBS, leading to hybrid CBS for DOA estimation. In hybrid processing, an analog combiner is used to reduce the number of radio frequency (RF) chains and thus hardware complexity. Also for lowering hardware cost, the analog combiner is designed as a phase shifter network with unit-modulus entries. It is shown that any general (arbitrary coefficient) CBS filter can be implemented despite the unit-modulus constraints. Moreover, a new scheme of CBS is proposed based on nonuniform decimation and difference coarray method. This allows us to identify more sources than RF chains. The retained samples correspond to the sensor locations of a virtual sparse array, dilated by an integer factor, which results in larger coarray aperture and thus better estimation performance. Besides, with the use of random or deterministic filter delays that vary with snapshots, a new method is proposed to decorrelate sources for the coarray method to work.
\r\n\r\nNext, a 2-dimensional (2-D) hybrid CBS method is developed for mmWave MIMO channel estimation. Since mmWave channel estimation problems can be formulated as 2-D direction-of-departure (DOD) and DOA estimation, benefits of CBS such as low complexity are applicable here. The receiver operation is again filtering followed by decimation. A key novelty is the use of a proper counterpart of CBS at the transmitter\u2014expansion (upsampling) followed by filtering\u2014to reduce RF chains. The expansion and decimation can be either uniform or nonuniform. The nonuniform scheme is used with 2-D coarray method and requires fewer RF chains to achieve the same estimation performance as the uniform scheme. A method based on the introduction of filter delays is also proposed to decorrelate path gains, which is crucial to the success of coarray methods. It is shown that given fixed pilot overhead, 2-D hybrid CBS can yield more accurate channel estimates than previous methods.
\r\n\r\nFinally, distributed (decentralized) algorithms for array signal processing are studied. With the potential of reducing computation and communication complexity, distributed estimation of covariance, and distributed principal component analysis have been introduced and studied in the signal processing community in recent years. Applications in array processing have been also indicated in some detail. In this thesis, distributed algorithms are further developed for several well-known methods for DOA estimation and beamforming. New distributed algorithms are proposed for DOA estimation methods like root-MUSIC, total least squares ESPRIT, and FOCUSS. Other contributions include distributed design of the Capon beamformer from data, distributed implementation of the spatial smoothing method for coherent sources, and distributed realization of CBS. The proposed algorithms are fully distributed since average consensus (AC) is used to avoid the need for a fusion center. The algorithms are based on a finite-time version of AC which converges to the exact solution in a finite number of iterations. This enables the proposed distributed algorithms to achieve the same performance as the centralized counterparts, as demonstrated by simulations.
", "doi": "10.7907/m5ys-t440", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:16344", "collection": "thesis", "collection_id": "16344", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04072024-202335451", "type": "thesis", "title": "Energy-Efficient and Robust Algorithms for Biomedical Applications", "author": [ { "family_name": "Haghi", "given_name": "Benyamin Allahgholizadeh", "orcid": "0000-0002-4839-7647", "clpid": "Haghi-Benyamin-Allahgholizadeh" } ], "thesis_advisor": [ { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" } ], "thesis_committee": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Andersen", "given_name": "Richard A.", "orcid": "0000-0002-7947-0472", "clpid": "Andersen-R-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Medical devices play a critical role in improving the quality of life for patients and assisting physicians by monitoring, detecting, and helping manage chronic conditions such as epilepsy and spinal cord injuries. To perform these functions effectively, these devices must extract the most relevant information from complex medical data. However, the functionality of these medical devices has been limited by the existing challenges in medical applications. Some of these challenges include the complexity in the analysis of raw medical data, adaptability, non-stationarity, noise, large data volumes, real-time processing, limited resources, and high accuracy demands. Moreover, considering factors such as individual differences, environmental influences, and genetic variations, medical data will cause numerous variations and uncertainties in analyzing and interpreting the medical conditions in different biomedical applications. Medical data analysis is already complex and is further complicated by issues like non-stationarity and noise, especially when using traditional and manual methods. When it comes to the designing, implementation, and utilization of wearable and implantable medical devices, efficiency, accuracy, and adaptability become crucial. Particularly, applications that require fast control of equipment, such as brain-machine interfaces (BMIs), make the need for fast decision-making evident. Medical data have been conventionally managed by reliance on extensive manual labor. However, such manual data management techniques are not scalable, have inefficient procedures, and are more likely to produce errors. Therefore, more advanced, automated methods are required immediately considering the existing challenges of the current medical data analysis techniques.
\r\n\r\nSuch a shift in data processing and management will lead to more trustable procedures that can significantly improve the accuracy and efficiency of medical data analysis. Other than being just an improvement, such transformation signifies a noteworthy point in the development of medical devices. In this view, it is essential to introduce advanced technology and novel methods for medical data processing as well as automation. Therefore, it becomes critical that these high-performance and advanced techniques can efficiently be implemented with minimum effects on hardware for clinical applications. Currently, artificial intelligence (AI) and its subfield machine learning (ML) has led to major transformations in designing and utilization of various medical devices. Among all these biomedical applications, three major area are addressed in this thesis: Brain Machine Interfaces (BMIs), seizure detection, and classification of arrhythmias in cardiac rhythms. We selected these three applications due to their significance and ability to improve patient treatment further. Additionally, we showed how we used machine learning algorithms for each of these applications to address their current challenges.
\r\n\r\nIn our work related to Brain-Machine Interfaces (BMIs), we have been focused on improving the quality of life for individuals with spinal cord injury (SCI) through two studies. In our initial study, we have designed and implemented a deep multi-state Dynamic Recurrent Neural Network (DRNN) decoder for BMI applications. This algorithm decodes neural data recorded from the posterior parietal cortex (PPC) and the motor cortex (M1) of human participants to appropriate control signals to predict computer cursor kinematics on the computer screen. By reducing the amount of history used in predicting the movement kinematics from the recorded neural data, we have demonstrated that improved performance and robustness are preserved while memory and power consumption are reduced. We then compared the performance of DRNN with other decoding techniques to demonstrate that when operating on wavelet-based neural features, our proposed DRNN-based decoder outperforms other decoding techniques. Therefore, DRNN have the potential to be used for more efficient and effective BMIs. After developing DRNN as a decoding technique for BMI applications, we have implemented an efficient feature extraction technique, referred to as Feature Extraction Network (FENet), which has been designed by using convolutional neural networks for optimizing feature extraction and decoding to ensure consistency across electrodes when decoding the recorded neural data to the movement kinematics in BMI systems. After being tested with data recorded from the posterior parietal and motor cortices of three human participants, FENet outperformed existing feature extraction techniques such as threshold crossings and wavelet transforms, and it significantly enhanced both closed- and open-loop cursor controls. We have also evaluated the generalizability of FENet when applied to different datasets, brain regions, and participants. Therefore, the results of our research in BMI technology have the potential to promise the improvement of the quality of life for spinal cord injury (SCI) patients.
\r\n\r\nSecond, we co-designed EKGNet, a convolutional network that combines analog computing and deep learning for detecting heartbeat arrhythmia. EKGNet demonstrated high accuracy while minimizing power consumption, effectively overcoming challenges related to analog circuitry and real-time processing. The experimental findings, using PhysionNet\u2019s MIT-BIH and PTB Diagnostics datasets, showed an average balanced accuracy of 95% for intra-patient arrhythmia classification and 94.25% for myocardial infarction (MI) classification.
\r\n\r\nFinally, we designed a real-time seizure detector by using XGboost as a technique relies on gradient boosted trees, which can help with the fast and accurate diagnosis of seizure for epileptic patients. With an averaged detection latency of 1.1 seconds, this design attained average F1 scores of 99.23% and 87.86% under various data splitting methods. The energy-area-latency product was 27\u00d7 lower than the current state-of-the-art solutions, which allowed for adjustments that were specific to each patient and significantly reduced energy consumption.
\r\n\r\nThe results presented in this dissertation demonstrate the potential of AI in addressing the existing challenges in three biomedical applications: brain-machine interfaces (BMI), seizure detection, and heartbeat arrhythmia detection. By addressing these existing challenges including complex biological data management, real-time processing constraints, and limited resources in biomedical applications, AI has the potential to improve the quality of life for patients suffering from neurological disorders and medical conditions. Moreover, the improved precision, operational efficiency, and flexibility caused by the integration of AI into the design of the future biomedical systems will potentially assist healthcare providers to offer enhanced support and treatment to patients. While we have focused on the three above-mentioned biomedical applications, the principles learned from our analysis may be relevant and can be extended to other biomedical applications.
", "doi": "10.7907/gkx4-s019", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:16398", "collection": "thesis", "collection_id": "16398", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05202024-212313617", "primary_object_url": { "basename": "Caltech_thesis_20240521_submitted.pdf", "content": "final", "filesize": 2356609, "license": "other", "mime_type": "application/pdf", "url": "/16398/1/Caltech_thesis_20240521_submitted.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Signal Processing for Large Arrays: Convolutional Beamspace, Hybrid Analog and Digital Processing, and Distributed Algorithms", "author": [ { "family_name": "Chen", "given_name": "Po-Chih", "orcid": "0000-0003-1637-9329", "clpid": "Chen-Po-Chih" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Kostina", "given_name": "Victoria", "orcid": "0000-0002-2406-7440", "clpid": "Kostina-V" }, { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The estimation of the directions of arrival (DOAs) of incoming waves for a passive antenna array has long been an important topic in array signal processing. Meanwhile, the estimation of the MIMO channel between a transmit antenna array and a receive antenna array is a key problem in wireless communications. In many recent works on these array processing tasks, people consider millimeter waves (mmWaves) due to their potential to offer more bandwidth than the already highly occupied lower-frequency bands. However, new challenges like strong path loss at the high frequencies of mmWaves arise. To compensate for the path loss, large arrays, or massive MIMO, are used to get large beamforming gain. It is practical due to the small sizes of mmWave antennas. When large arrays are used, it is important to develop efficient estimation algorithms with low computational and hardware complexity.
\r\n\r\nThe main contribution of this thesis is to propose low-complexity DOA and channel estimation methods that are especially effective for large arrays. To achieve low complexity, three main aspects are explored: beamspace methods, hybrid analog and digital processing, and distributed algorithms. First, a new beamspace method, convolutional beamspace (CBS), is proposed for DOA estimation based on passive arrays. In CBS, the array output is spatially filtered, followed by uniform decimation (downsampling) to achieve dimensionality reduction. No DOA ambiguity occurs since the filter output is represented only by the passband sources. CBS enjoys the advantages of classical beamspace such as lower computational complexity, increased parallelism of subband processing, and improved resolution threshold for DOA estimation. Moreover, unlike classical beamspace methods, it allows root-MUSIC and ESPRIT to be performed directly for uniform linear arrays without additional preparation since the Vandermonde structure is preserved under the CBS transformation. The method produces more accurate DOA estimates than classical beamspace, and for correlated sources, better estimates than element-space.
\r\n\r\nThe idea of hybrid analog and digital processing is then incorporated into CBS, leading to hybrid CBS for DOA estimation. In hybrid processing, an analog combiner is used to reduce the number of radio frequency (RF) chains and thus hardware complexity. Also for lowering hardware cost, the analog combiner is designed as a phase shifter network with unit-modulus entries. It is shown that any general (arbitrary coefficient) CBS filter can be implemented despite the unit-modulus constraints. Moreover, a new scheme of CBS is proposed based on nonuniform decimation and difference coarray method. This allows us to identify more sources than RF chains. The retained samples correspond to the sensor locations of a virtual sparse array, dilated by an integer factor, which results in larger coarray aperture and thus better estimation performance. Besides, with the use of random or deterministic filter delays that vary with snapshots, a new method is proposed to decorrelate sources for the coarray method to work.
\r\n\r\nNext, a 2-dimensional (2-D) hybrid CBS method is developed for mmWave MIMO channel estimation. Since mmWave channel estimation problems can be formulated as 2-D direction-of-departure (DOD) and DOA estimation, benefits of CBS such as low complexity are applicable here. The receiver operation is again filtering followed by decimation. A key novelty is the use of a proper counterpart of CBS at the transmitter\u2014expansion (upsampling) followed by filtering\u2014to reduce RF chains. The expansion and decimation can be either uniform or nonuniform. The nonuniform scheme is used with 2-D coarray method and requires fewer RF chains to achieve the same estimation performance as the uniform scheme. A method based on the introduction of filter delays is also proposed to decorrelate path gains, which is crucial to the success of coarray methods. It is shown that given fixed pilot overhead, 2-D hybrid CBS can yield more accurate channel estimates than previous methods.
\r\n\r\nFinally, distributed (decentralized) algorithms for array signal processing are studied. With the potential of reducing computation and communication complexity, distributed estimation of covariance, and distributed principal component analysis have been introduced and studied in the signal processing community in recent years. Applications in array processing have been also indicated in some detail. In this thesis, distributed algorithms are further developed for several well-known methods for DOA estimation and beamforming. New distributed algorithms are proposed for DOA estimation methods like root-MUSIC, total least squares ESPRIT, and FOCUSS. Other contributions include distributed design of the Capon beamformer from data, distributed implementation of the spatial smoothing method for coherent sources, and distributed realization of CBS. The proposed algorithms are fully distributed since average consensus (AC) is used to avoid the need for a fusion center. The algorithms are based on a finite-time version of AC which converges to the exact solution in a finite number of iterations. This enables the proposed distributed algorithms to achieve the same performance as the centralized counterparts, as demonstrated by simulations.
", "doi": "10.7907/m5ys-t440", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:16344", "collection": "thesis", "collection_id": "16344", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04072024-202335451", "type": "thesis", "title": "Energy-Efficient and Robust Algorithms for Biomedical Applications", "author": [ { "family_name": "Haghi", "given_name": "Benyamin Allahgholizadeh", "orcid": "0000-0002-4839-7647", "clpid": "Haghi-Benyamin-Allahgholizadeh" } ], "thesis_advisor": [ { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" } ], "thesis_committee": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Andersen", "given_name": "Richard A.", "orcid": "0000-0002-7947-0472", "clpid": "Andersen-R-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Medical devices play a critical role in improving the quality of life for patients and assisting physicians by monitoring, detecting, and helping manage chronic conditions such as epilepsy and spinal cord injuries. To perform these functions effectively, these devices must extract the most relevant information from complex medical data. However, the functionality of these medical devices has been limited by the existing challenges in medical applications. Some of these challenges include the complexity in the analysis of raw medical data, adaptability, non-stationarity, noise, large data volumes, real-time processing, limited resources, and high accuracy demands. Moreover, considering factors such as individual differences, environmental influences, and genetic variations, medical data will cause numerous variations and uncertainties in analyzing and interpreting the medical conditions in different biomedical applications. Medical data analysis is already complex and is further complicated by issues like non-stationarity and noise, especially when using traditional and manual methods. When it comes to the designing, implementation, and utilization of wearable and implantable medical devices, efficiency, accuracy, and adaptability become crucial. Particularly, applications that require fast control of equipment, such as brain-machine interfaces (BMIs), make the need for fast decision-making evident. Medical data have been conventionally managed by reliance on extensive manual labor. However, such manual data management techniques are not scalable, have inefficient procedures, and are more likely to produce errors. Therefore, more advanced, automated methods are required immediately considering the existing challenges of the current medical data analysis techniques.
\r\n\r\nSuch a shift in data processing and management will lead to more trustable procedures that can significantly improve the accuracy and efficiency of medical data analysis. Other than being just an improvement, such transformation signifies a noteworthy point in the development of medical devices. In this view, it is essential to introduce advanced technology and novel methods for medical data processing as well as automation. Therefore, it becomes critical that these high-performance and advanced techniques can efficiently be implemented with minimum effects on hardware for clinical applications. Currently, artificial intelligence (AI) and its subfield machine learning (ML) has led to major transformations in designing and utilization of various medical devices. Among all these biomedical applications, three major area are addressed in this thesis: Brain Machine Interfaces (BMIs), seizure detection, and classification of arrhythmias in cardiac rhythms. We selected these three applications due to their significance and ability to improve patient treatment further. Additionally, we showed how we used machine learning algorithms for each of these applications to address their current challenges.
\r\n\r\nIn our work related to Brain-Machine Interfaces (BMIs), we have been focused on improving the quality of life for individuals with spinal cord injury (SCI) through two studies. In our initial study, we have designed and implemented a deep multi-state Dynamic Recurrent Neural Network (DRNN) decoder for BMI applications. This algorithm decodes neural data recorded from the posterior parietal cortex (PPC) and the motor cortex (M1) of human participants to appropriate control signals to predict computer cursor kinematics on the computer screen. By reducing the amount of history used in predicting the movement kinematics from the recorded neural data, we have demonstrated that improved performance and robustness are preserved while memory and power consumption are reduced. We then compared the performance of DRNN with other decoding techniques to demonstrate that when operating on wavelet-based neural features, our proposed DRNN-based decoder outperforms other decoding techniques. Therefore, DRNN have the potential to be used for more efficient and effective BMIs. After developing DRNN as a decoding technique for BMI applications, we have implemented an efficient feature extraction technique, referred to as Feature Extraction Network (FENet), which has been designed by using convolutional neural networks for optimizing feature extraction and decoding to ensure consistency across electrodes when decoding the recorded neural data to the movement kinematics in BMI systems. After being tested with data recorded from the posterior parietal and motor cortices of three human participants, FENet outperformed existing feature extraction techniques such as threshold crossings and wavelet transforms, and it significantly enhanced both closed- and open-loop cursor controls. We have also evaluated the generalizability of FENet when applied to different datasets, brain regions, and participants. Therefore, the results of our research in BMI technology have the potential to promise the improvement of the quality of life for spinal cord injury (SCI) patients.
\r\n\r\nSecond, we co-designed EKGNet, a convolutional network that combines analog computing and deep learning for detecting heartbeat arrhythmia. EKGNet demonstrated high accuracy while minimizing power consumption, effectively overcoming challenges related to analog circuitry and real-time processing. The experimental findings, using PhysionNet\u2019s MIT-BIH and PTB Diagnostics datasets, showed an average balanced accuracy of 95% for intra-patient arrhythmia classification and 94.25% for myocardial infarction (MI) classification.
\r\n\r\nFinally, we designed a real-time seizure detector by using XGboost as a technique relies on gradient boosted trees, which can help with the fast and accurate diagnosis of seizure for epileptic patients. With an averaged detection latency of 1.1 seconds, this design attained average F1 scores of 99.23% and 87.86% under various data splitting methods. The energy-area-latency product was 27\u00d7 lower than the current state-of-the-art solutions, which allowed for adjustments that were specific to each patient and significantly reduced energy consumption.
\r\n\r\nThe results presented in this dissertation demonstrate the potential of AI in addressing the existing challenges in three biomedical applications: brain-machine interfaces (BMI), seizure detection, and heartbeat arrhythmia detection. By addressing these existing challenges including complex biological data management, real-time processing constraints, and limited resources in biomedical applications, AI has the potential to improve the quality of life for patients suffering from neurological disorders and medical conditions. Moreover, the improved precision, operational efficiency, and flexibility caused by the integration of AI into the design of the future biomedical systems will potentially assist healthcare providers to offer enhanced support and treatment to patients. While we have focused on the three above-mentioned biomedical applications, the principles learned from our analysis may be relevant and can be extended to other biomedical applications.
", "doi": "10.7907/gkx4-s019", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:16294", "collection": "thesis", "collection_id": "16294", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02152024-233300684", "primary_object_url": { "basename": "Ruizhi_Cao_2023_thesis_v2.pdf", "content": "final", "filesize": 33398694, "license": "other", "mime_type": "application/pdf", "url": "/16294/1/Ruizhi_Cao_2023_thesis_v2.pdf", "version": "v6.0.0" }, "type": "thesis", "title": "Dealing with Imperfections: From Aberration to Scattering", "author": [ { "family_name": "Cao", "given_name": "Ruizhi", "orcid": "0000-0003-3385-446X", "clpid": "Ruizhi-Cao" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "orcid": "0000-0001-8791-0354", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Wang", "given_name": "Lihong", "orcid": "0000-0001-9783-4383", "clpid": "Wang-Lihong" }, { "family_name": "Yang", "given_name": "Changhuei", "orcid": "0000-0001-8791-0354", "clpid": "Yang-Changhuei" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Marandi", "given_name": "Alireza", "orcid": "0000-0002-0470-0050", "clpid": "Marandi-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Optical imaging has gained popularity in life science, biomedical imaging, fundamental physics research, and various other fields due to its non-invasive nature. In a carefully designed optical instrument operating in an ideal environment, the resolution of the optical imaging system is defined by its numerical aperture. However, practical manufacturing issues and inaccurate lens models make it challenging to achieve high resolution across a large area. High magnification lenses introduce aberrations that degrade image quality, prompting the use of complex lens systems dedicated to mitigating such aberrations. Furthermore, when a scattering medium is introduced into the imaging system, image formation becomes infeasible as light follows a complicated trajectory. These challenges pose great obstacles to the use of optical imaging methods in various scenarios. This thesis primarily consists of two parts, one aims to deal with aberration and the other tries to solve scattering induced imaging problems.
\r\n\r\nIn the first part of my thesis, I will discuss a technique called APIC (Angular Ptychographic Imaging with Closed-form method), which enables high-resolution imaging across a large field of view. To make APIC applicable in many non-ideal cases where aberrations (such as defocus) degrade image quality, we equip APIC with a closed-form aberration correction algorithm. We will demonstrate that APIC is unprecedentedly robust against aberrations and can retrieve high-resolution complex light fields using low magnification objectives.
\r\n\r\nIn the second part, we move on to dealing with scattering induced imaging problems. To form images where a scattering medium is present, we first explore the application of ultrasound modulation in optical imaging. We show that, by using ultrasound, we can image a hidden object in a highly scattering medium with ultrasonic resolution. Although this technique helps obtain clear images in the presence of a scattering medium, its resolution is limited. We then demonstrate a method in addressing another scattering problem, namely the non-line-of-sight (NLOS) imaging problem. In a general NLOS problem, modulation mechanisms such as the aforementioned ultrasound modulation are infeasible. We demonstrate that light can be directly focused on the hidden target with an optical diffraction-limited resolution by exploring the properties of the hidden target itself. We will show that this active focusing method possess remarkably improved resolution compared to existing methods and is able to image objects with large reflectance differences.
", "doi": "10.7907/adgc-g315", "publication_date": "2024", "thesis_type": "phd", "thesis_year": "2024" }, { "id": "thesis:15238", "collection": "thesis", "collection_id": "15238", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312023-034316442", "type": "thesis", "title": "Low-Power and Miniaturized Medical Electronics for In-Vivo Localization and Tracking", "author": [ { "family_name": "Sharma", "given_name": "Saransh", "orcid": "0000-0002-5052-4932", "clpid": "Sharma-Saransh" } ], "thesis_advisor": [ { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" } ], "thesis_committee": [ { "family_name": "Shapiro", "given_name": "Mikhail G.", "orcid": "0000-0002-0291-4215", "clpid": "Shapiro-M-G" }, { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Marandi", "given_name": "Alireza", "orcid": "0000-0002-0470-0050", "clpid": "Marandi-A" }, { "family_name": "Traverso", "given_name": "Giovanni", "orcid": "0000-0001-7851-4077", "clpid": "Traverso-Giovanni" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Medical electronic devices are an integral part of the healthcare system today. Significant advances have been made over the past few decades to yield highly miniaturized and low-power medical devices that are suitable for implantable, ingestible, or wearable applications. A key feature of medical devices that is central to their use in many applications is the capability to locate them precisely inside the body, and quite a lot of research effort has been expended in this direction. Location sensing is crucial for several applications: tracking pills in the GI tract, navigation during precision surgeries, endovascular procedures, robotic and minimally invasive surgery, and targeted therapy. The current gold-standard solutions for these procedures include invasive techniques such as endoscopy, or procedures that require repeated use of potentially harmful X-ray radiation such as CT scans. These techniques also require repeated evaluation in a hospital setting and are not conducive for non-clinical environments. While there are several alternative non-ionizing methods for imaging and localization based on electromagnetic tracking, radio-frequency, ultrasound, and optical tracking, none of them are able to simultaneously achieve a high field-of-view of tracking, high spatiotemporal resolution, fully wireless operation and miniaturization of the sensing devices, and system scalability with the number of devices. In this dissertation, we present a radiation-free system for high-precision localization and tracking of miniaturized wireless devices in vivo, using harmless magnetic field gradients.
\r\n\r\nFirst, we demonstrate our system for precision surgery applications. We designed highly miniaturized, wireless and battery-less microdevices, capable of measuring and transmitting their local magnetic field. One such device can be attached to an implant inside the body and another to a surgical tool, such that both can simultaneously measure and communicate the magnetic field at their respective locations to an external receiver. The relative location of the two devices on a real-time display can enable precise surgical navigation without using X-ray fluoroscopy. The prototype device consists of a micro-chip fabricated in 65nm CMOS technology, a 3D magnetic sensor and an inductor-coil. The chip performs wireless power management, wireless bi-directional data-telemetry, and I2C communication with the sensor. Planar electromagnetic coils are designed for creating monotonically varying magnetic fields in the X, Y, and Z directions, resulting in field gradients that encode each spatial point with a unique magnetic field value. The concept of gradient-based spatial encoding is inspired by MRI. The system is tested in vitro to demonstrate a localization accuracy of <100\u00b5m in 3D, the highest reported to the best of our knowledge.
\r\n\r\nSecond, we demonstrate our system for localization and tracking of ingestible microdevices in the GI tract, which is valuable for the diagnosis and treatment of GI disorders. We designed highly miniaturized, low-power, and wireless ingestible devices to sense and transmit their local magnetic field as they travel through the GI tract. These devices consist of a 3D magnetic sensor, a Bluetooth microprocessor and a 2.4GHz Bluetooth antenna for wireless communication, all packaged into a 000-size capsule. The magnetic field sensed by the devices is created by using high-efficiency planar electromagnetic coils that encode each spatial point with a distinct magnetic field magnitude, allowing us to track the location of the devices unambiguously. The system functionality is demonstrated in vivo in large animals under different chronic conditions and disease models to show 3D localization and tracking in real time and in non-clinical settings, with mm-scale spatial resolution, and without using any X-ray radiation. This has the potential for significant clinical benefit for quantitative assessment of GI transit-time, motility disorders, constipation, incontinence, medication adherence monitoring, anatomic targeting for drug delivery, and targeted stimulation therapy.
\r\n\r\nThird, in order to further miniaturize the devices developed for the above two applications and to make them even more low-power, we present a monolithic 3D magnetic sensor in 65nm CMOS technology that measures <5mm\u00b2 in area and consumes 14.8\u00b5W in power while achieving <10\u03bcTrms noise. Our novel 3D magnetic sensor overcomes the challenges faced by traditional magnetic sensors by being fully CMOS compatible and achieving high sensitivity with only \u00b5W-level power, which is in sharp contrast with Hall and Fluxgate sensors. The sensor is comprised of three orthogonal and highly dense metal coils implemented in the 65nm node, which generate a voltage signal in response to AC magnetic fields by electromagnetic induction. The EMF voltage signal is processed by on-chip circuitry that performs low-noise amplification, filtering, peak detection, and 12-bit digitization. Though the sensor can be used for a variety of applications that require AC field sensing, it is particularly useful for biomedical applications\u2014tracking catheters and guidewires during endovascular procedures, minimally invasive surgeries, targeted radiotherapy, and for use as fiducial markers during preoperative planning. The proposed magnetic sensor is demonstrated for use in 3D tracking of catheters using the magnetic-field gradient-based spatial encoding scheme, and achieves 500\u00b5m of mean 3D localization accuracy.
", "doi": "10.7907/xrw0-k789", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:16066", "collection": "thesis", "collection_id": "16066", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06022023-215651797", "type": "thesis", "title": "Advancements in Hemodynamic Measurement: Arterial Resonance, Ultrasound, and Machine Learning", "author": [ { "family_name": "Yurk", "given_name": "Dominic Jeffrey", "orcid": "0000-0002-2276-4189", "clpid": "Yurk-Dominic-Jeffrey" } ], "thesis_advisor": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Emami", "given_name": "Azita", "orcid": "0000-0002-6945-9958", "clpid": "Emami-A" }, { "family_name": "Rajagopal", "given_name": "Aditya", "orcid": "0000-0002-7768-2463", "clpid": "Rajagopal-Aditya" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "3MT Competition (Caltech)" }, { "literal": "div_eng" } ], "abstract": "This thesis covers two separate projects which both use ultrasound to measure a form of blood pressure in very different ways. The first project focuses on the noninvasive measurement of continuous arterial blood pressure via the previously unstudied phenomenon of arterial resonance. While prior research efforts have attempted many methods of noninvasive blood pressure measurement, none has been able to generate continuous, calibration-free measurements based on a first-principles physical model. This work describes the derivation of this resonance-based model, its in vitro validation, and its in vivo testing on 60 subjects. This testing resulted in robust resonance detection and accurate calculation of BP in the large majority of evaluated subjects, representing very promising performance for the first test of a new biomedical technology. The second study changes focus to the measurement of blood pressure in the right atrium of the heart, an important clinical indicator in heart disease patients. Rather than developing a new physical approach, this project used machine learning to model the existing assessments made by cardiologists. Comparison to gold standard invasive catheter measurements showed that model predictions were statistically indistinguishable from cardiologist measurements. Both of these projects represent significant advances in expanding precise blood pressure measurements beyond critical care units and expanding access to a much broader population.
", "doi": "10.7907/q7j4-vj19", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:15219", "collection": "thesis", "collection_id": "15219", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05282023-011333603", "primary_object_url": { "basename": "prxngghxkcbcwkqrvrczrmfgrnkjvwdz.pdf", "content": "final", "filesize": 7824181, "license": "other", "mime_type": "application/pdf", "url": "/15219/1/prxngghxkcbcwkqrvrczrmfgrnkjvwdz.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Learning and Control of Dynamical Systems", "author": [ { "family_name": "Lale", "given_name": "Ali Sahin", "orcid": "0000-0002-7191-346X", "clpid": "Lale-Ali-Sahin" } ], "thesis_advisor": [ { "family_name": "Anandkumar", "given_name": "Anima", "orcid": "0000-0002-6974-6797", "clpid": "Anandkumar-A" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Anandkumar", "given_name": "Anima", "orcid": "0000-0002-6974-6797", "clpid": "Anandkumar-A" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Wierman", "given_name": "Adam C.", "orcid": "0000-0002-5923-0199", "clpid": "Wierman-A-C" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Despite the remarkable success of machine learning in various domains in recent years, our understanding of its fundamental limitations remains incomplete. This knowledge gap poses a grand challenge when deploying machine learning methods in critical decision-making tasks, where incorrect decisions can have catastrophic consequences. To effectively utilize these learning-based methods in such contexts, it is crucial to explicitly characterize their performance. Over the years, significant research efforts have been dedicated to learning and control of dynamical systems where the underlying dynamics are unknown or only partially known a priori, and must be inferred from collected data. However, much of these classical results have focused on asymptotic guarantees, providing limited insights into the amount of data required to achieve desired control performance while satisfying operational constraints such as safety and stability, especially in the presence of statistical noise.
\r\n\r\nIn this thesis, we study the statistical complexity of learning and control of unknown dynamical systems. By utilizing recent advances in statistical learning theory, high-dimensional statistics, and control theoretic tools, we aim to establish a fundamental understanding of the number of samples required to achieve desired (i) accuracy in learning the unknown dynamics, (ii) performance in the control of the underlying system, and (iii) satisfaction of the operational constraints such as safety and stability. We provide finite-sample guarantees for these objectives and propose efficient learning and control algorithms that achieve the desired performance at these statistical limits in various dynamical systems. Our investigation covers a broad range of dynamical systems, starting from fully observable linear dynamical systems to partially observable linear dynamical systems, and ultimately, nonlinear systems.
\r\n\r\nWe deploy our learning and control algorithms in various adaptive control tasks in real-world control systems and demonstrate their strong empirical performance along with their learning, robustness, and stability guarantees. In particular, we implement one of our proposed methods, Fourier Adaptive Learning and Control (FALCON), on an experimental aerodynamic testbed under extreme turbulent flow dynamics in a wind tunnel. The results show that FALCON achieves state-of-the-art stabilization performance and consistently outperforms conventional and other learning-based methods by at least 37%, despite using 8 times less data. The superior performance of FALCON arises from its physically and theoretically accurate modeling of the underlying nonlinear turbulent dynamics, which yields rigorous finite-sample learning and performance guarantees. These findings underscore the importance of characterizing the statistical complexity of learning and control of unknown dynamical systems.
", "doi": "10.7907/rdhq-8a88", "publication_date": "2023", "thesis_type": "phd", "thesis_year": "2023" }, { "id": "thesis:13621", "collection": "thesis", "collection_id": "13621", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01152020-143207091", "primary_object_url": { "basename": "TzuChiehChou2022thesis.pdf", "content": "final", "filesize": 24486732, "license": "other", "mime_type": "application/pdf", "url": "/13621/2/TzuChiehChou2022thesis.pdf", "version": "v6.0.0" }, "type": "thesis", "title": "Wearable Inductive Damping Sensors for Skin Edema Quantification", "author": [ { "family_name": "Chou", "given_name": "Tzu-Chieh", "orcid": "0000-0002-6074-8286", "clpid": "Chou-Tzu-Chieh" } ], "thesis_advisor": [ { "family_name": "Tai", "given_name": "Yu-Chong", "orcid": "0000-0001-8529-106X", "clpid": "Tai-Yu-Chong" } ], "thesis_committee": [ { "family_name": "Gao", "given_name": "Wei", "orcid": "0000-0002-8503-4562", "clpid": "Gao-Wei" }, { "family_name": "Wang", "given_name": "Lihong", "orcid": "0000-0001-9783-4383", "clpid": "Wang-Lihong" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tai", "given_name": "Yu-Chong", "orcid": "0000-0001-8529-106X", "clpid": "Tai-Yu-Chong" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The electrical conductivity of human organs is closely related to the physiological or pathological changes occurring within the organ. For example, metastatic liver tumors significantly increase electrical conductivity compared to healthy liver tissues over a wide frequency range. Therefore, knowing when and where these conductivity changes happen within an organ is highly valuable for disease monitoring.
\r\n \r\nSkin is the largest human organ by surface area, and under its large surface, there are numerous tiny blood and lymphatic vessels that circulate body fluid and dissipate heat. Therefore, it contains critical information about systemic circulation. Diseases such as congestive heart failure, acute renal injury, and liver failure disturb the systemic circulation and allow extra interstitial fluid to accumulate in the form of peripheral skin edema. As the interstitial fluid is highly conductive, the overall skin conductivity significantly increases when edema occurs.
\r\n\r\nConsequently, quantification of skin edema allows us to track the progression of these diseases and is the main goal to pursue in this study. The current clinical standard uses a 0-to-4 grade system to quantify the severity of edema based on how the skin responds to a pressing force. However, it requires in-person examination and has relatively large inter-examiner variations, making it less suitable for real-time edema monitoring.
\r\n\r\nTo solve the unmet need to quantify edema in real-time, I present a skin edema model that relates skin conductivity to the interstitial fluid volume fraction. The latter is used to quantify the severity of edema. Furthermore, I developed a wearable coil sensor that provides accurate real-time conductivity measurements on subcutis, a significant portion of the skin where edema typically occurs. The coil sensor uses alternating magnetic fields to induce eddy currents in the skin and measures the skin conductivity as a function of coil resistance change. The experimental results suggested that when grade-1 edema occurs, the subcutis conductivity increases from the average value of 0.09 S/m to 0.25 S/m. This change corresponds to an increase of interstitial volume fraction from 10% to 20% in the subcutis. These quantitative results are consistent with finite element simulations and allow direct comparison with ultrasonography measurements. Due to its high accuracy and portability, the proposed wearable sensor opens a new possibility for continuous monitoring of skin edema.
", "doi": "10.7907/q77f-me73", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14506", "collection": "thesis", "collection_id": "14506", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02182022-230421298", "type": "thesis", "title": "Nanophotonic Application to Biomedical Devices", "author": [ { "family_name": "Hanania", "given_name": "Haeri Park", "orcid": "0000-0002-2206-5732", "clpid": "Hanania-Haeri-Park" } ], "thesis_advisor": [ { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "thesis_committee": [ { "family_name": "Gao", "given_name": "Wei", "orcid": "0000-0002-8503-4562", "clpid": "Gao-Wei" }, { "family_name": "Scherer", "given_name": "Axel", "orcid": "0000-0002-2160-9064", "clpid": "Scherer-A" }, { "family_name": "Burdick", "given_name": "Joel Wakeman", "orcid": "0000-0002-3091-540X", "clpid": "Burdick-J-W" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Choo", "given_name": "Hyuck", "orcid": "0000-0002-8903-7939", "clpid": "Choo-Hyuck" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Nanophotonics is the study of interactions between nanoscale structures and light. It has greatly expanded the fields of application over the past decades, taking advantage of the advancement in MEMS technology. The most common nanophotonic structures consist of either dielectrics, metals, or both. When a nanophotonic structure contains metals, it is considered as a plasmonic structure. Plasmonics is a field of light-metal interactions. Due to the negative permittivity of metals, the electromagnetic energy of light is focused at the metal-dielectric interface and creates plasmons-a collective motion of electrons in the conduction band of metals. By shaping metals into different structures to achieve a desired performance, plasmonics have been successfully applied to many fields including photovoltaics, spectroscopy, and biomedical devices.
\r\n\r\nThis thesis provides 3 different applications of biomedical devices in which nanophotonics-articularly plasmonics-was applied. Chapter 1 discusses the application of nanophotonics to molecular sensing. In this chapter, an open-top, tapered waveguide that serves as a 3-dimensional plasmon cavity is demonstrated and achieves a near or single molecular detection. Chapter 2 discusses the application of nanophotonics to an implantable intraocular pressure sensor. In this chapter, an array of gold nanodots are introduced on a flexible membrane to optimize the performance of the sensor. Chapter 3 discusses the application of nanophotonics to angle-and-polarization independent pressure or strain sensing, which reduces the need for precise alignment or a trained technician, and therefore can be easily applied to moving subjects in diverse environments. Inspired by the geometry and optical principles of butterfly corneas, an array of gold paraboloids is designed to support a surface plasmon resonance that is angle-and-polarization independent. This array is integrated onto a hermetically sealed cavity with a flexible membrane and enables angle-and-polarization independent pressure/strain sensing.
", "doi": "10.7907/tzpw-pt75", "publication_date": "2022", "thesis_type": "phd", "thesis_year": "2022" }, { "id": "thesis:14150", "collection": "thesis", "collection_id": "14150", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05172021-044724906", "type": "thesis", "title": "Structured Signal Recovery from Nonlinear Measurements with Applications in Phase Retrieval and Linear Classification", "author": [ { "family_name": "Salehi", "given_name": "Fariborz", "orcid": "0000-0002-9679-1016", "clpid": "Salehi-Fariborz" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Kostina", "given_name": "Victoria", "orcid": "0000-0002-2406-7440", "clpid": "Kostina-V" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Nonlinear models are widely used in signal processing, statistics, and machine learning to model real-world applications. A popular class of such models is the single-index model where the response variable is related to a linear combination of dependent variables through a link function. In other words, if x \u2208 Rp denotes the input signal, the posterior mean of the generated output y has the form, E[y|x] = \u03c1(xTw), where \u03c1 :R \u2192 R is a known function (referred to as the link function), and w \u2208 Rp is the vector of unknown parameters. When \u03c1(\u2022) is invertible, this class of models is called generalized linear models (GLMs). GLMs are commonly used in statistics and are often viewed as flexible generalizations of linear regression. Given n measurements (samples) from this model, D = {(xi, yi) | 1 \u2264q i \u2264 n}, the goal is to estimate the parameter vector w. While the model parameters are assumed to be unknown, in many applications these parameters follow certain structures (sparse, low-rank, group-sparse, etc.) The knowledge on this structure can be used to form more accurate estimators.
\r\n\r\nThe main contribution of this thesis is to provide a precise performance analysis for convex optimization programs that are used for parameter estimation in two important classes of single-index models. These classes are: (1) phase retrieval in signal processing, and (2) binary classification in statistical learning.
\r\n\r\nThe first class of models studied in this thesis is the phase retrieval problem, where the goal is to recover a discrete complex-valued signal from amplitudes of its linear combinations. Methods based on convex optimization have recently gained significant attentions in the literature. The conventional convex-optimization-based methods resort to the idea of lifting which makes them computationally inefficient. In addition to providing an analysis of the recovery threshold for the semidefinite-programming-based methods, this thesis studies the performance of a new convex relaxation for the phase retrieval problem, known as phasemax, which is computationally more efficient as it does not lift the signal to higher dimensions. Furthermore, to address the case of structured signals, regularized phasemax is introduced along with a precise characterization of the conditions for its perfect recovery in the asymptotic regime.
\r\n\r\nThe next important application studied in this thesis is the binary classification in statistical learning. While classification models have been studied in the literature since 1950's, the understanding of their performance has been incomplete until very recently. Inspired by the maximum likelihood (ML) estimator in logistic models, we analyze a class of optimization programs that attempts to find the model parameters by minimizing an objective that consists of a loss function (which is often inspired by the ML estimator) and an additive regularization term that enforces our knowledge on the structure. There are two operating regimes for this problem depending on the separability of the training data set D. In the asymptotic regime, where the number of samples and the number of parameters grow to infinity, a phase transition phenomenon is demonstrated that happens at a certain over-parameterization ratio. We compute this phase transition for the setting where the underlying data is drawn from a Gaussian distribution.
\r\n\r\nIn the case where the data is non-separable, the ML estimator is well-defined, and its attributes have been studied in the classical statistics. However, these classical results fail to provide reasonable estimate in the regime where the number of data points is proportional to the number of samples. One contribution of this thesis is to provide an exact analysis on the performance of the regularized logistic regression when the number of training data is proportional to the number of samples. When the data is separable (a.k.a. the interpolating regime), there exist multiple linear classifiers that perfectly fit the training data. In this regime, we introduce and analyze the performance of \"extended margin maximizers\" (EMMs). Inspired by the max-margin classifier, EMM classifiers simultaneously consider maximizing the margin and the structure of the parameter. Lastly, we discuss another generalization to the max-margin classifier, referred to as the robust max-margin classifier, that takes into account the perturbations by an adversary. It is shown that for a broad class of loss functions, gradient descent iterates (with proper step sizes) converge to the robust max-margin classifier.
", "doi": "10.7907/1c69-wq71", "publication_date": "2021-06-11", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:13843", "collection": "thesis", "collection_id": "13843", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:07242020-111050846", "type": "thesis", "title": "Bioinspired Nanostructures for Biomedical Applications", "author": [ { "family_name": "Narasimhan", "given_name": "Vinayak", "orcid": "0000-0003-4165-402X", "clpid": "Narasimhan-Vinayak" } ], "thesis_advisor": [ { "family_name": "Choo", "given_name": "Hyuck", "orcid": "0000-0002-8903-7939", "clpid": "Choo-Hyuck" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "thesis_committee": [ { "family_name": "Burdick", "given_name": "Joel Wakeman", "orcid": "0000-0002-3091-540X", "clpid": "Burdick-J-W" }, { "family_name": "Choo", "given_name": "Hyuck", "orcid": "0000-0002-8903-7939", "clpid": "Choo-Hyuck" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "Scherer", "given_name": "Axel", "orcid": "0000-0002-2160-9064", "clpid": "Scherer-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Siddique", "given_name": "Radwanul Hasan", "orcid": "0000-0001-7494-5857", "clpid": "Siddique-Radwanul-Hasan" } ], "local_group": [ { "literal": "Kavli Nanoscience Institute" }, { "literal": "div_eng" } ], "abstract": "Nature boasts a myriad examples of coloration achieved purely through the physical interaction of light with nano-scale features also known as biophotonic nanostructures. From reptiles to insects, birds to flora, structural coloration has been achieved through a variety of fascinating nano-architectures that leverage different physics. Beyond structural coloration, these nanostructures are often truly multifunctional. For instance, biophotonic nanostructures can also serve as self-cleaning and bactericidal surfaces, gas and thermal sensors, waveguides and beam splitters. With the growing need for robust and compact biomedical devices, the requirement to embed multiple functionalities towards sensing, monitoring, diagnostics and therapeutics within a diminutive device footprint becomes crucial. In this regard, inspiration from the multifunctionality of biophotonic nanostructures can prove to be greatly beneficial for medical applications. Consequently, this work attempts to showcase various examples of the utilization of nanostructures inspired from biophotonic nanostructures for biomedical applications under various overlapping themes such as ophthalmic sensors, bioinspired optics and plasmonic biosensing.
\r\n\r\nThis thesis is summarized in two parts. The first part (Chapters 2--4) introduces a proof-of-concept optical intraocular pressure (IOP) sensor implant and various challenges faced during its in vivo implementation. In Chapter 3, nanostructures inspired by light-trapping epidermal micro-/nanostructures on flower petals are proposed and embedded onto the sensor platform to improve its in vivo optical signal-to-noise ratio and biocompatibility. Chapter 4 covers nanostructures inspired by biophotonic nanostructures on longtail glasswing butterfly wings that improve the in vivo angle of acceptance and biocompatibility of the sensor.
\r\n\r\nThe second part (Chapters 5 and 6) presents the use of bioinspired nanostructures in plasmonic biosensors. Chapter 5 discusses an on-chip platform consisting of bioinspired plasmonic nanostructures to detect various nucleic acid sequences of relevance in the pathogenesis of HIV-1 via plasmon-enhanced fluorescence. Chapter 6 describes the employment of bioinspired quasi-ordered nanostructuring on flexible substrates for broadband surface-enhanced Raman spectroscopy (SERS). Here, SERS-based biosensing enabled by quasi-ordering is used to detect uric acid -- a biomarker of various pathologies in human tears.
", "doi": "10.7907/atnt-8p46", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:13946", "collection": "thesis", "collection_id": "13946", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09092020-162015646", "type": "thesis", "title": "Optical Light Manipulation and Imaging Through Scattering Media", "author": [ { "family_name": "Xu", "given_name": "Jian", "orcid": "0000-0002-4743-2471", "clpid": "Xu-Jian" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "orcid": "0000-0001-8791-0354", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Faraon", "given_name": "Andrei", "orcid": "0000-0002-8141-391X", "clpid": "Faraon-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Chen", "given_name": "Yanbei", "orcid": "0000-0002-9730-9463", "clpid": "Chen-Yanbei" }, { "family_name": "Yang", "given_name": "Changhuei", "orcid": "0000-0001-8791-0354", "clpid": "Yang-Changhuei" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Typical optical systems are designed to be implemented in free space or clean media. However, the presence of optical scattering media scrambles light waves and becomes a problem in light field control, optical imaging, and sensing.
\r\n\r\nTo address the problem caused by optical scattering media, we discuss two types of solutions in this thesis. One type of solution is active control, where active modulators are used to modulate the light wave to compensate the wave distortion caused by optical scattering. The other type of solution is computational optics, where physical and mathematical models are built to computationally reconstruct the information from the measured distorted wavefront.
\r\n\r\nIn the part of active control, we first demonstrate coherent light focusing through scattering media by transmission matrix inversion. The transmission matrix inversion approach can realize coherent light control through scattering media with higher fidelity compared to conventional transmission matrix approaches. Then, by combining the pre-designed scattering metasurface with wavefront shaping, we demonstrate a beam steering system with large angular and high angular resolution. Next, we present optical-channel-based intensity streaming (OCIS), which uses only intensity information of light fields to realize light control through scattering media. This solution can be used to control spatially incoherent light propagating through scattering media. In the part of computational optics, we first demonstrate the idea of interferometric speckle visibility spectroscopy (ISVS) to measure the information cerebral blood flow. In ISVS, a camera records the speckle frames of diffused light from the human subject interferometrically, and the speckle statistics is used to calculate the speckle decorrelation time and consequently the blood flow index. Then, we compare the two methods of decorrelation time measurements - temporal sampling methods and spatial ensemble methods - and derive unified mathematical expressions for them in terms of measurement accuracy. Based on current technology of camera sensors and single detectors, our results indicate that spatial ensemble methods can have higher decorrelation time measurement accuracy compared to commonly used temporal sampling methods.
", "doi": "10.7907/4hkq-dz43", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:13965", "collection": "thesis", "collection_id": "13965", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09242020-094028488", "primary_object_url": { "basename": "oguzhan_teke_2020.pdf", "content": "final", "filesize": 14690337, "license": "other", "mime_type": "application/pdf", "url": "/13965/1/oguzhan_teke_2020.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Signals on Networks: Random Asynchronous and Multirate Processing, and Uncertainty Principles", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-Oguzhan" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The processing of signals defined on graphs has been of interest for many years, and finds applications in a diverse set of fields such as sensor networks, social and economic networks, and biological networks. In graph signal processing applications, signals are not defined as functions on a uniform time-domain grid but they are defined as vectors indexed by the vertices of a graph, where the underlying graph is assumed to model the irregular signal domain. Although analysis of such networked models is not new (it can be traced back to the consensus problem studied more than four decades ago), such models are studied recently from the view-point of signal processing, in which the analysis is based on the \"graph operator\" whose eigenvectors serve as a Fourier basis for the graph of interest. With the help of graph Fourier basis, a number of topics from classical signal processing (such as sampling, reconstruction, filtering, etc.) are extended to the case of graphs.
\r\n\r\nThe main contribution of this thesis is to provide new directions in the field of graph signal processing and provide further extensions of topics in classical signal processing. The first part of this thesis focuses on a random and asynchronous variant of \"graph shift,\" i.e., localized communication between neighboring nodes. Since the dynamical behavior of randomized asynchronous updates is very different from standard graph shift (i.e., state-space models), this part of the thesis focuses on the convergence and stability behavior of such random asynchronous recursions. Although non-random variants of asynchronous state recursions (possibly with non-linear updates) are well-studied problems with early results dating back to the late 60's, this thesis considers the convergence (and stability) in the statistical mean-squared sense and presents the precise conditions for the stability by drawing parallels with switching systems. It is also shown that systems exhibit unexpected behavior under randomized asynchronicity: an unstable system (in the synchronous world) may be stabilized simply by the use of randomized asynchronicity. Moreover, randomized asynchronicity may result in a lower total computational complexity in certain parameter settings. The thesis presents applications of the random asynchronous model in the context of graph signal processing including an autonomous clustering of network of agents, and a node-asynchronous communication protocol that implements a given rational filter on the graph.
\r\n\r\nThe second part of the thesis focuses on extensions of the following topics in classical signal processing to the case of graph: multirate processing and filter banks, discrete uncertainty principles, and energy compaction filters for optimal filter design. The thesis also considers an application to the heat diffusion over networks.
\r\n\r\nMultirate systems and filter banks find many applications in signal processing theory and implementations. Despite the possibility of extending 2-channel filter banks to bipartite graphs, this thesis shows that this relation cannot be generalized to M-channel systems on M-partite graphs. As a result, the extension of classical multirate theory to graphs is nontrivial, and such extensions cannot be obtained without certain mathematical restrictions on the graph. The thesis provides the necessary conditions on the graph such that fundamental building blocks of multirate processing remain valid in the graph domain. In particular, it is shown that when the underlying graph satisfies a condition called M-block cyclic property, classical multirate theory can be extended to the graphs.
\r\n\r\nThe uncertainty principle is an essential mathematical concept in science and engineering, and uncertainty principles generally state that a signal cannot have an arbitrarily \"short\" description in the original basis and in the Fourier basis simultaneously. Based on the fact that graph signal processing proposes two different bases (i.e., vertex and the graph Fourier domains) to represent graph signals, this thesis shows that the total number of nonzero elements of a graph signal and its representation in the graph Fourier domain is lower bounded by a quantity depending on the underlying graph. The thesis also presents the necessary and sufficient condition for the existence of 2-sparse and 3-sparse eigenvectors of a connected graph. When such eigenvectors exist, the uncertainty bound is very low, tight, and independent of the global structure of the graph.
\r\n\r\nThe thesis also considers the classical spectral concentration problem. In the context of polynomial graph filters, the problem reduces to the polynomial concentration problem studied more generally by Slepian in the 70's. The thesis studies the asymptotic behavior of the optimal solution in the case of narrow bandwidth. Different examples of graphs are also compared in order to show that the maximum energy compaction and the optimal filter depends heavily on the graph spectrum.
\r\n\r\nIn the last part, the thesis considers the estimation of the starting time of a heat diffusion process from its noisy measurements when there is a single point source located on a known vertex of a graph with unknown starting time. In particular, the Cram\u00e9r-Rao lower bound for the estimation problem is derived, and it is shown that for graphs with higher connectivity the problem has a larger lower bound making the estimation problem more difficult.
", "doi": "10.7907/44dx-3g83", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:13965", "collection": "thesis", "collection_id": "13965", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09242020-094028488", "primary_object_url": { "basename": "oguzhan_teke_2020.pdf", "content": "final", "filesize": 14690337, "license": "other", "mime_type": "application/pdf", "url": "/13965/1/oguzhan_teke_2020.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Signals on Networks: Random Asynchronous and Multirate Processing, and Uncertainty Principles", "author": [ { "family_name": "Teke", "given_name": "Oguzhan", "orcid": "0000-0002-1131-5206", "clpid": "Teke-Oguzhan" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The processing of signals defined on graphs has been of interest for many years, and finds applications in a diverse set of fields such as sensor networks, social and economic networks, and biological networks. In graph signal processing applications, signals are not defined as functions on a uniform time-domain grid but they are defined as vectors indexed by the vertices of a graph, where the underlying graph is assumed to model the irregular signal domain. Although analysis of such networked models is not new (it can be traced back to the consensus problem studied more than four decades ago), such models are studied recently from the view-point of signal processing, in which the analysis is based on the \"graph operator\" whose eigenvectors serve as a Fourier basis for the graph of interest. With the help of graph Fourier basis, a number of topics from classical signal processing (such as sampling, reconstruction, filtering, etc.) are extended to the case of graphs.
\r\n\r\nThe main contribution of this thesis is to provide new directions in the field of graph signal processing and provide further extensions of topics in classical signal processing. The first part of this thesis focuses on a random and asynchronous variant of \"graph shift,\" i.e., localized communication between neighboring nodes. Since the dynamical behavior of randomized asynchronous updates is very different from standard graph shift (i.e., state-space models), this part of the thesis focuses on the convergence and stability behavior of such random asynchronous recursions. Although non-random variants of asynchronous state recursions (possibly with non-linear updates) are well-studied problems with early results dating back to the late 60's, this thesis considers the convergence (and stability) in the statistical mean-squared sense and presents the precise conditions for the stability by drawing parallels with switching systems. It is also shown that systems exhibit unexpected behavior under randomized asynchronicity: an unstable system (in the synchronous world) may be stabilized simply by the use of randomized asynchronicity. Moreover, randomized asynchronicity may result in a lower total computational complexity in certain parameter settings. The thesis presents applications of the random asynchronous model in the context of graph signal processing including an autonomous clustering of network of agents, and a node-asynchronous communication protocol that implements a given rational filter on the graph.
\r\n\r\nThe second part of the thesis focuses on extensions of the following topics in classical signal processing to the case of graph: multirate processing and filter banks, discrete uncertainty principles, and energy compaction filters for optimal filter design. The thesis also considers an application to the heat diffusion over networks.
\r\n\r\nMultirate systems and filter banks find many applications in signal processing theory and implementations. Despite the possibility of extending 2-channel filter banks to bipartite graphs, this thesis shows that this relation cannot be generalized to M-channel systems on M-partite graphs. As a result, the extension of classical multirate theory to graphs is nontrivial, and such extensions cannot be obtained without certain mathematical restrictions on the graph. The thesis provides the necessary conditions on the graph such that fundamental building blocks of multirate processing remain valid in the graph domain. In particular, it is shown that when the underlying graph satisfies a condition called M-block cyclic property, classical multirate theory can be extended to the graphs.
\r\n\r\nThe uncertainty principle is an essential mathematical concept in science and engineering, and uncertainty principles generally state that a signal cannot have an arbitrarily \"short\" description in the original basis and in the Fourier basis simultaneously. Based on the fact that graph signal processing proposes two different bases (i.e., vertex and the graph Fourier domains) to represent graph signals, this thesis shows that the total number of nonzero elements of a graph signal and its representation in the graph Fourier domain is lower bounded by a quantity depending on the underlying graph. The thesis also presents the necessary and sufficient condition for the existence of 2-sparse and 3-sparse eigenvectors of a connected graph. When such eigenvectors exist, the uncertainty bound is very low, tight, and independent of the global structure of the graph.
\r\n\r\nThe thesis also considers the classical spectral concentration problem. In the context of polynomial graph filters, the problem reduces to the polynomial concentration problem studied more generally by Slepian in the 70's. The thesis studies the asymptotic behavior of the optimal solution in the case of narrow bandwidth. Different examples of graphs are also compared in order to show that the maximum energy compaction and the optimal filter depends heavily on the graph spectrum.
\r\n\r\nIn the last part, the thesis considers the estimation of the starting time of a heat diffusion process from its noisy measurements when there is a single point source located on a known vertex of a graph with unknown starting time. In particular, the Cram\u00e9r-Rao lower bound for the estimation problem is derived, and it is shown that for graphs with higher connectivity the problem has a larger lower bound making the estimation problem more difficult.
", "doi": "10.7907/44dx-3g83", "publication_date": "2021", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:14150", "collection": "thesis", "collection_id": "14150", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05172021-044724906", "type": "thesis", "title": "Structured Signal Recovery from Nonlinear Measurements with Applications in Phase Retrieval and Linear Classification", "author": [ { "family_name": "Salehi", "given_name": "Fariborz", "orcid": "0000-0002-9679-1016", "clpid": "Salehi-Fariborz" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Kostina", "given_name": "Victoria", "orcid": "0000-0002-2406-7440", "clpid": "Kostina-V" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Nonlinear models are widely used in signal processing, statistics, and machine learning to model real-world applications. A popular class of such models is the single-index model where the response variable is related to a linear combination of dependent variables through a link function. In other words, if x \u2208 Rp denotes the input signal, the posterior mean of the generated output y has the form, E[y|x] = \u03c1(xTw), where \u03c1 :R \u2192 R is a known function (referred to as the link function), and w \u2208 Rp is the vector of unknown parameters. When \u03c1(\u2022) is invertible, this class of models is called generalized linear models (GLMs). GLMs are commonly used in statistics and are often viewed as flexible generalizations of linear regression. Given n measurements (samples) from this model, D = {(xi, yi) | 1 \u2264q i \u2264 n}, the goal is to estimate the parameter vector w. While the model parameters are assumed to be unknown, in many applications these parameters follow certain structures (sparse, low-rank, group-sparse, etc.) The knowledge on this structure can be used to form more accurate estimators.
\r\n\r\nThe main contribution of this thesis is to provide a precise performance analysis for convex optimization programs that are used for parameter estimation in two important classes of single-index models. These classes are: (1) phase retrieval in signal processing, and (2) binary classification in statistical learning.
\r\n\r\nThe first class of models studied in this thesis is the phase retrieval problem, where the goal is to recover a discrete complex-valued signal from amplitudes of its linear combinations. Methods based on convex optimization have recently gained significant attentions in the literature. The conventional convex-optimization-based methods resort to the idea of lifting which makes them computationally inefficient. In addition to providing an analysis of the recovery threshold for the semidefinite-programming-based methods, this thesis studies the performance of a new convex relaxation for the phase retrieval problem, known as phasemax, which is computationally more efficient as it does not lift the signal to higher dimensions. Furthermore, to address the case of structured signals, regularized phasemax is introduced along with a precise characterization of the conditions for its perfect recovery in the asymptotic regime.
\r\n\r\nThe next important application studied in this thesis is the binary classification in statistical learning. While classification models have been studied in the literature since 1950's, the understanding of their performance has been incomplete until very recently. Inspired by the maximum likelihood (ML) estimator in logistic models, we analyze a class of optimization programs that attempts to find the model parameters by minimizing an objective that consists of a loss function (which is often inspired by the ML estimator) and an additive regularization term that enforces our knowledge on the structure. There are two operating regimes for this problem depending on the separability of the training data set D. In the asymptotic regime, where the number of samples and the number of parameters grow to infinity, a phase transition phenomenon is demonstrated that happens at a certain over-parameterization ratio. We compute this phase transition for the setting where the underlying data is drawn from a Gaussian distribution.
\r\n\r\nIn the case where the data is non-separable, the ML estimator is well-defined, and its attributes have been studied in the classical statistics. However, these classical results fail to provide reasonable estimate in the regime where the number of data points is proportional to the number of samples. One contribution of this thesis is to provide an exact analysis on the performance of the regularized logistic regression when the number of training data is proportional to the number of samples. When the data is separable (a.k.a. the interpolating regime), there exist multiple linear classifiers that perfectly fit the training data. In this regime, we introduce and analyze the performance of \"extended margin maximizers\" (EMMs). Inspired by the max-margin classifier, EMM classifiers simultaneously consider maximizing the margin and the structure of the parameter. Lastly, we discuss another generalization to the max-margin classifier, referred to as the robust max-margin classifier, that takes into account the perturbations by an adversary. It is shown that for a broad class of loss functions, gradient descent iterates (with proper step sizes) converge to the robust max-margin classifier.
", "doi": "10.7907/1c69-wq71", "publication_date": "2021-06-11", "thesis_type": "phd", "thesis_year": "2021" }, { "id": "thesis:11754", "collection": "thesis", "collection_id": "11754", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:07252019-145728798", "primary_object_url": { "basename": "Thesis_Hyunjun_Cho.pdf", "content": "final", "filesize": 7396311, "license": "other", "mime_type": "application/pdf", "url": "/11754/1/Thesis_Hyunjun_Cho.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Real-Time Biosensing and Energy Harvesting on Human Body", "author": [ { "family_name": "Cho", "given_name": "Hyunjun", "orcid": "0000-0002-8963-5525", "clpid": "Cho-Hyunjun" } ], "thesis_advisor": [ { "family_name": "Choo", "given_name": "Hyuck", "orcid": "0000-0002-8903-7939", "clpid": "Choo-Hyuck" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Gharib", "given_name": "Morteza", "orcid": "0000-0003-0754-4193", "clpid": "Gharib-M" }, { "family_name": "Scherer", "given_name": "Axel", "orcid": "0000-0002-2160-9064", "clpid": "Scherer-A" }, { "family_name": "Choo", "given_name": "Hyuck", "orcid": "0000-0002-8903-7939", "clpid": "Choo-Hyuck" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis covers two technologies that can be applied to the human body for real-time applicable usages: biosensors and energy harvesters. The first part of the thesis describes optical biosensing techniques based on surface-enhanced Raman spectroscopy (SERS). Our large-scale spatially uniform Raman enhancing substrates allow low-level bio molecule detection due to their strong plasmonic enhancement of the 3D Au-NP clusters. This method also enables low-level insulin sensing as well as insulin concentration analysis in islet secretion. These results can lead to developing simple and easy biosensing methods allowing real-time biosensing applications including convenient monitoring of health, early disease detection, and diabetes-related clinical measurements.
\r\n\r\nThe second part of the thesis suggests an energy harvesting method using vocal vibrations. The vocal folds produce mechanical vibrations that can serve as an energy source with consistent amplitude and frequency. The vibration hotspots exist at various locations on the human upper body. The energy harvesting system consisting of piezoelectric devices and energy harvesting circuits generates 3.99 mW of electrical power. The amount of energy generated from vocal vibrations is sufficient to charge a Li-Po battery which can drive an LCD display or charge Bluetooth headphones. This method demonstrating a relatively high power generation and convenience of practical use can provide a real-time complementary charging technique for wearable electronics like wireless headphones and smart glasses as well as medical implantable devices such as deep brain stimulators, cochlear implants and pacemakers.
", "doi": "10.7907/ZN7F-ZF71", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:13804", "collection": "thesis", "collection_id": "13804", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06092020-005908250", "primary_object_url": { "basename": "PhD_Thesis(4).pdf", "content": "final", "filesize": 2361036, "license": "other", "mime_type": "application/pdf", "url": "/13804/1/PhD_Thesis(4).pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Universality Laws and Performance Analysis of the Generalized Linear Models", "author": [ { "family_name": "Abbasi", "given_name": "Ehsan", "orcid": "0000-0002-0185-7933", "clpid": "Abbasi-Ehsan" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the past couple of decades, non-smooth convex optimization has emerged as a powerful tool for the recovery of structured signals (sparse, low rank, etc.) from noisy linear or non-linear measurements in a variety of applications in genomics, signal processing, wireless communications, machine learning, etc.. Taking advantage of the particular structure of the unknown signal of interest is critical since in most of these applications, the dimension p of the signal to be estimated is comparable, or even larger than the number of observations n. With the advent of Compressive Sensing there has been a very large number of theoretical results that study the estimation performance of non-smooth convex optimization in such a high-dimensional setting.
\r\n\r\nA popular approach for estimating an unknown signal \u03b2\u2080 \u03f5 \u211d\u1d56 in a generalized linear model, with observations y = g(X\u03b2\u2080) \u03f5 \u211d\u207f, is via solving the estimator \u03b2̂ = arg min\u03b2 L(y, X\u03b2 + \u03bbf(\u03b2). Here, L(\u2022,\u2022) is a loss function which is convex with respect to its second argument, and f(\u2022) is a regularizer that enforces the structure of the unknown \u03b2\u2080. We first analyze the generalization error performance of this estimator, for the case where the entries of X are drawn independently from real standard Gaussian distribution. The precise nature of our analysis permits an accurate performance comparison between different instances of these estimators, and allows to optimally tune the hyperparameters based on the model parameters. We apply our result to some of the most popular cases of generalized linear models, such as M-estimators in linear regression, logistic regression and generalized margin maximizers in binary classification problems, and Poisson regression in count data models. The key ingredient of our proof is the Convex Gaussian Min-max Theorem (CGMT), which is a tight version of the Gaussian comparison inequality proved by Gordon in 1988. Unfortunately, having real iid entries in the features matrix X is crucial in this theorem, and it cannot be naturally extended to other cases.
\r\n\r\nBut for some special cases, we prove some universality properties and indirectly extend these results to more general designs of the features matrix X, where the entries are not necessarily real, independent, or identically distributed. This extension, enables us to analyze problems that CGMT was incapable of, such as models with quadratic measurements, phase-lift in phase retrieval, and data recovery in massive MIMO, and help us settle a few long standing open problems in these areas.
", "doi": "10.7907/873c-ej41", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:13622", "collection": "thesis", "collection_id": "13622", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01152020-210801253", "type": "thesis", "title": "Convex Relaxations for Graph and Inverse Eigenvalue Problems", "author": [ { "family_name": "Candogan", "given_name": "Utkan Onur", "orcid": "0000-0002-1416-4909", "clpid": "Candogan-Utkan-Onur" } ], "thesis_advisor": [ { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" }, { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis is concerned with presenting convex optimization based tractable solutions for three fundamental problems:
\r\n\r\n1. Planted subgraph problem: Given two graphs, identifying the subset of vertices of the larger graph corresponding to the smaller one.
\r\n\r\n2. Graph edit distance problem: Given two graphs, calculating the number of edge/vertex additions and deletions required to transform one graph into the other.
\r\n\r\n3. Affine inverse eigenvalue problem: Given a subspace \u03b5 \u2282 𝕊\u207f and a vector of eigenvalues \u03bb \u2208 \u211d\u207f, finding a symmetric matrix with spectrum \u03bb contained in \u03b5.
\r\n\r\nThese combinatorial and algebraic problems frequently arise in various application domains such as social networks, computational biology, chemoinformatics, and control theory. Nevertheless, exactly solving them in practice is only possible for very small instances due to their complexity. For each of these problems, we introduce convex relaxations which succeed in providing exact or approximate solutions in a computationally tractable manner.
\r\n\r\nOur relaxations for the two graph problems are based on convex graph invariants, which are functions of graphs that do not depend on a particular labeling. One of these convex relaxations, coined the Schur-Horn orbitope, corresponds to the convex hull of all matrices with a given spectrum, and plays a prominent role in this thesis. Specifically, we utilize relaxations based on the Schur-Horn orbitope in the context of the planted subgraph problem and the graph edit distance problem. For both of these problems, we identify conditions under which the Schur-Horn orbitope based relaxations exactly solve the corresponding problem with overwhelming probability. Specifically, we demonstrate that these relaxations turn out to be particularly effective when the underlying graph has a spectrum comprised of few distinct eigenvalues with high multiplicities. In addition to relaxations based on the Schur-Horn orbitope, we also consider outer-approximations based on other convex graph invariants such as the stability number and the maximum-cut value for the graph edit distance problem. On the other hand, for the inverse eigenvalue problem, we investigate two relaxations arising from a sum of squares hierarchy. These relaxations have different approximation qualities, and accordingly induce different computational costs. We utilize our framework to generate solutions for, or certify unsolvability of the underlying inverse eigenvalue problem.
\r\n\r\nWe particularly emphasize the computational aspect of our relaxations throughout this thesis. We corroborate the utility of our methods with various numerical experiments.
", "doi": "10.7907/ZV0D-SW58", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:11755", "collection": "thesis", "collection_id": "11755", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:07252019-221240608", "primary_object_url": { "basename": "LimYuXian_FinalPhDthesis.pdf", "content": "final", "filesize": 7262509, "license": "other", "mime_type": "application/pdf", "url": "/11755/1/LimYuXian_FinalPhDthesis.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "L-Band Multi-Polarization Radar Scatterometry over Global Forests: Modelling, Analysis, and Applications", "author": [ { "family_name": "Lim", "given_name": "Yu Xian", "orcid": "0000-0002-3777-7986", "clpid": "Lim-Yu-Xian" } ], "thesis_advisor": [ { "family_name": "van Zyl", "given_name": "Jakob J.", "clpid": "van-Zyl-J-J" } ], "thesis_committee": [ { "family_name": "Elachi", "given_name": "Charles", "clpid": "Elachi-C" }, { "family_name": "Hajimiri", "given_name": "Ali", "clpid": "Hajimiri-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "van Zyl", "given_name": "Jakob J.", "clpid": "van-Zyl-J-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Spaceborne L-band radars have the ability to penetrate vegetation canopies over forested areas, suggesting a potential for regular and frequent global monitoring of both the vegetation state and the subcanopy soil moisture. However, L-band radar\u2019s sensitivity to both vegetation and ground also complicates the relationship between the radar observations and the ecological and geophysical parameters. Accurate yet parsimonious forward models of the radar backscatter are valuable to building an understanding of these relationships. In the first part of this thesis, a model of L-band multi-polarization radar backscatter from forests, intended for use at regional to global spatial scales, is presented. Novel developments in the model include the consideration of multiple scattering within the dense vegetation canopy, and the application of a general model of plant allometry to mitigate the need for much intensive field data for training or over-tuning towards specific sites and tree species.
\r\n\r\nAided by our model, in the remainder and majority of the thesis, a detailed analysis and interpretation of L-band backscatter over global forests is performed, using data from the Aquarius and SMAP missions. Quantitative differences in backscatter predicted by our model due to freeze/thaw states, branch orientation, and flooding are partially verified against the data, and fitted values of aboveground-biomass and microwave vegetation optical depths are comparable to independent estimates in the literature. Polarization information is used to help distinguish vegetation and ground effects on spatial and temporal variations. We show that neither vegetation nor ground effects alone can explain spatial variations within the same land cover class. For temporal variations during unfrozen periods, soil moisture is found to often be an important factor at timescales of a week to several months, although vegetation changes remain a non-negligible factor. We report the observation of significant differences in backscatter depending on beam azimuthal angle, possibly due to plant phototropism.
\r\n\r\nWe also investigated diurnal variations, which have the potential to reveal signals related to plant transpiration. SMAP data from May-July 2015 showed that globally, co-polarized backscatter was generally higher at 6PM compared to 6AM over boreal forests, which is not what one might expect based on previous studies. Based on our modelling, increased canopy extinction at 6AM is a possible cause, but this is unproven and its true underlying physical cause undetermined.
\r\n\r\nFinally, by making simplifying approximations on our forward model, we propose and explore algorithms for soil moisture retrieval under forest canopies using L-band scatterometry, with preliminary evaluations suggesting improved performance over existing algorithms.
", "doi": "10.7907/7Y4D-JD17", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:13758", "collection": "thesis", "collection_id": "13758", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06012020-120425051", "type": "thesis", "title": "Riemannian Optimization for Convex and Non-Convex Signal Processing and Machine Learning Applications", "author": [ { "family_name": "Douik", "given_name": "Ahmed", "orcid": "0000-0001-7791-9443", "clpid": "Douik-Ahmed" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Kostina", "given_name": "Victoria", "clpid": "Kostina-V" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The performance of most algorithms for signal processing and machine learning applications highly depends on the underlying optimization algorithms. Multiple techniques have been proposed for solving convex and non-convex problems such as interior-point methods and semidefinite programming. However, it is well known that these algorithms are not ideally suited for large-scale optimization with a high number of variables and/or constraints. This thesis exploits a novel optimization method, known as Riemannian optimization, for efficiently solving convex and non-convex problems with signal processing and machine learning applications. Unlike most optimization techniques whose complexities increase with the number of constraints, Riemannian methods smartly exploit the structure of the search space, a.k.a., the set of feasible solutions, to reduce the embedded dimension and efficiently solve optimization problems in a reasonable time. However, such efficiency comes at the expense of universality as the geometry of each manifold needs to be investigated individually. This thesis explains the steps of designing first and second-order Riemannian optimization methods for smooth matrix manifolds through the study and design of optimization algorithms for various applications. In particular, the paper is interested in contemporary applications in signal processing and machine learning, such as community detection, graph-based clustering, phase retrieval, and indoor and outdoor location determination. Simulation results are provided to attest to the efficiency of the proposed methods against popular generic and specialized solvers for each of the above applications.", "doi": "10.7907/jt3c-0m30", "publication_date": "2020", "thesis_type": "phd", "thesis_year": "2020" }, { "id": "thesis:11436", "collection": "thesis", "collection_id": "11436", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04032019-102853075", "type": "thesis", "title": "Decoding the Past", "author": [ { "family_name": "Jain", "given_name": "Siddharth", "orcid": "0000-0002-9164-6119", "clpid": "Jain-Siddharth" } ], "thesis_advisor": [ { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Winfree", "given_name": "Erik", "clpid": "Winfree-E" }, { "family_name": "Schwartz", "given_name": "Moshe", "clpid": "Schwartz-Moshe" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The human genome is continuously evolving, hence the sequenced genome is a snapshot in time of this evolving entity. Over time, the genome accumulates mutations that can be associated with different phenotypes - like physical traits, diseases, etc. Underlying mutation accumulation is an evolution channel (the term channel is motivated by the notion of communication channel introduced by Shannon [1] in 1948 and started the area of Information Theory), which is controlled by hereditary, environmental, and stochastic factors. The premise of this thesis is to understand the human genome using information theory framework. In particular, it focuses on: (i) the analysis and characterization of the evolution channel using measures of capacity, expressiveness, evolution distance, and uniqueness of ancestry and uses these insights for (ii) the design of error correcting codes for DNA storage, (iii) inversion symmetry in the genome and (iv) cancer classification.
\r\n\r\nThe mutational events characterizing this evolution channel can be divided into two categories, namely point mutations and duplications. While evolution through point mutations is unconstrained, giving rise to combinatorially many possibilities of what could have happened in the past, evolution through duplications adds constraints limiting the number of those possibilities. Further, more than 50% of the genome has been observed to consist of repeated sequences. We focus on the much constrained form of duplications known as tandem duplications in order to understand the limits of evolution by duplication. Our sequence evolution model consists of a starting sequence called seed and a set of tandem duplication rules. We find limits on the diversity of sequences that can be generated by tandem duplications using measures of capacity and expressiveness. Additionally, we calculate bounds on the duplication distance which is used to measure the timing of generation by these duplications. We also ask questions about the uniqueness of seed for a given sequence and completely characterize the duplication length sets where the seed is unique or non-unique. These insights also led us to design error correcting codes for any number of tandem duplication errors that are useful for DNA-storage based applications. For uniform duplication length and duplication length bounded by 2, our designed codes achieve channel capacity. We also define and measure uncertainty in decoding when the duplication channel is misinformed. Moreover, we add substitutions to our tandem duplication model and calculate sequence generation diversity for a given budget of substitutions.
\r\n\r\nWe also use our duplication model to explain the inversion symmetry observed in the genome of many species. The inversion symmetry is popularly known as the 2nd Chargaff Rule, according to which in a single strand DNA, the frequency of a k-mer is almost the same as the frequency of its reverse complement. The insights gained by these problems led us to investigate the tandem repeat regions in the genome. Tandem repeat regions in the genome can be traced back in time algorithmically to make inference about the effect of the hereditary, environmental and stochastic factors on the mutation rate of the genome. By inferring the evolutionary history of the tandem repeat regions, we show how this knowledge can be used to make predictions about the risk of incurring a mutation based disease, specifically cancer. More precisely, we introduce the concept of mutation profiles that are computed without any comparative analysis, but instead by analyzing the short tandem repeat regions in a single healthy genome and capturing information about the individual's evolution channel. Using gradient boosting on data from more than 5,000 TCGA (The Cancer Genome Atlas) cancer patients, we demonstrate that these mutation profiles can accurately distinguish between patients with various types of cancer. For example, the pairwise validation accuracy of the classifier between PAAD (pancreas) patients and GBM (brain) patients is 93%. Our results show that healthy unaffected cells still contain a cancer-specific signal, which opens the possibility of cancer prediction from a healthy genome.
", "doi": "10.7907/K286-5N63", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:11136", "collection": "thesis", "collection_id": "11136", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:07262018-030251324", "type": "thesis", "title": "Periodically Disturbed Oscillators", "author": [ { "family_name": "Hong", "given_name": "Brian Daffern", "orcid": "0000-0001-8099-0312", "clpid": "Hong-Brian-Daffern" } ], "thesis_advisor": [ { "family_name": "Hajimiri", "given_name": "Ali", "clpid": "Hajimiri-A" } ], "thesis_committee": [ { "family_name": "Hajimiri", "given_name": "Ali", "clpid": "Hajimiri-A" }, { "family_name": "Emami", "given_name": "Azita", "clpid": "Emami-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "By controlling the timing of events and enabling the transmission of data over long distances, oscillators can be considered to generate the \"heartbeat\" of modern electronic systems. Their utility, however, is boosted significantly by their peculiar ability to synchronize to external signals that are themselves periodic in time. Although this fascinating phenomenon has been studied by scientists since the 1600s, models for describing this behavior have seen a disconnect between the rigorous, methodical approaches taken by mathematicians and the design-oriented, physically-based analyses carried out by engineers. While the analytical power of the former is often concealed by an inundation of abstract mathematical machinery, the accuracy and generality of the latter are constrained by the empirical nature of the ensuing derivations. We hope to bridge that gap here.
\r\n\r\nIn this thesis, a general theory of electrical oscillators under the influence of a periodic injection is developed from first principles. Our approach leads to a fundamental yet intuitive understanding of the process by which oscillators lock to a periodic injection, as well as what happens when synchronization fails and the oscillator is instead injection pulled. By considering the autonomous and periodically time-varying nature that underlies all oscillators, we build a time-synchronous model that is valid for oscillators of any topology and periodic disturbances of any shape. A single first-order differential equation is shown to be capable of making accurate, quantitative predictions about a wide array of properties of periodically disturbed oscillators: the range of injection frequencies for which synchronization occurs, the phase difference between the injection and the oscillator under lock, stable vs. unstable modes of locking, the pull-in process toward lock, the dynamics of injection pulling, as well as phase noise in both free-running and injection-locked oscillators. The framework also naturally accommodates superharmonic injection-locked frequency division, subharmonic injection-locked frequency multiplication, and the general case of an arbitrary rational relationship between the injection and oscillation frequencies. A number of novel insights for improving the performance of systems that utilize injection locking are also elucidated. In particular, we explore how both the injection waveform and the oscillator's design can be modified to optimize the lock range. The resultant design techniques are employed in the implementation of a dual-moduli prescaler for frequency synthesis applications which features low power consumption, a wide operating range, and a small chip area.
\r\n\r\nFor the commonly used inductor-capacitor (LC) oscillator, we make a simple modification to our framework that takes the oscillation amplitude into account, greatly enhancing the model's accuracy for large injections. The augmented theory uniquely captures the asymmetry of the lock range as well as the distinct characteristics exhibited by different types of LC oscillators. Existing injection locking and pulling theories in the available literature are subsumed as special cases of our model. It is important to note that even though the veracity of our theoretical predictions degrades as the size of the injection grows due to our framework's linearization with respect to the disturbance, our model's validity across a broad range of practical injection strengths are borne out by simulations and measurements on a diverse collection of integrated LC, ring, and relaxation oscillators. Lastly, we also present a phasor-based analysis of LC and ring oscillators which yields a novel perspective into how the injection current interacts with the oscillator's core nonlinearity to facilitate injection locking.
", "doi": "10.7907/W0A7-4258", "publication_date": "2019", "thesis_type": "phd", "thesis_year": "2019" }, { "id": "thesis:11029", "collection": "thesis", "collection_id": "11029", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06062018-132643508", "primary_object_url": { "basename": "tenneti-srikanth-venkata-thesis-V4.pdf", "content": "final", "filesize": 14012477, "license": "other", "mime_type": "application/pdf", "url": "/11029/14/tenneti-srikanth-venkata-thesis-V4.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "The Nested Periodic Subspaces: Extensions of Ramanujan Sums for Period Estimation", "author": [ { "family_name": "Tenneti", "given_name": "Srikanth Venkata", "orcid": "0000-0002-5415-3681", "clpid": "Tenneti-Srikanth-Venkata" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Kostina", "given_name": "Victoria", "clpid": "Kostina-V" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the year 1918, the Indian mathematician Srinivasa Ramanujan proposed a set of sequences called Ramanujan Sums as bases to expand arithmetic functions in number theory. Today, exactly a 100 years later, we will show that these sequences re-emerge as exciting tools in a completely different context: For the extraction of periodic patterns in data. Combined with the state-of-the-art techniques of DSP, Ramanujan Sums can be used as the starting point for developing powerful algorithms for periodicity applications.
\r\n\r\nThe primary inspiration for this thesis comes from a recent extension of Ramanujan sums to subspaces known as the Ramanujan subspaces. These subspaces were designed to span any sequence with integer periodicity, and have many interesting properties. Starting with Ramanujan subspaces, this thesis first develops an entire family of such subspace representations for periodic sequences. This family, called Nested Periodic Subspaces due to their unique structure, turns out to be the least redundant sets of subspaces that can span periodic sequences.
\r\n\r\nThree classes of new algorithms are proposed using the Nested Periodic Subspaces: dictionaries, filter banks, and eigen-space methods based on the auto-correlation matrix of the signal. It will be shown that these methods are especially advantageous to use when the data-length is short, or when the signal is a mixture of multiple hidden periods. The dictionary techniques were inspired by recent advances in sparsity based compressed sensing. Apart from the l1 norm based convex programs currently used in other applications, our dictionaries can admit l2 norm formulations that have linear and closed form solutions, even when the systems is under-determined. A new filter bank is also proposed using the Ramanujan sums. This, named the Ramanujan Filter Bank, can accurately track the instantaneous period for signals that exhibit time varying periodic nature. The filters in the Ramanujan Filter Bank have simple integer valued coefficients, and directly tile the period vs time plane, unlike classical STFT (Short Time Fourier Transform) and wavelets, which tile the time-frequency plane. The third family of techniques developed here are a generalization of the classic MUSIC (MUltiple SIgnal Classification) algorithm for periodic signals. MUSIC is one of the most popular techniques today for line spectral estimation. However, periodic signals are not just any unstructured line spectral signals. There is a nice harmonic spacing between the lines which is not exploited by plain MUSIC. We will show that one can design much more accurate adaptations of MUSIC using Nested Periodic Subspaces. Compared to prior variants of MUSIC for the periodicity problem, our approach is much faster and yields much more accurate results for signals with integer periods. This work is also the first extension of MUSIC that uses simple integer valued basis vectors instead of using traditional complex-exponentials to span the signal subspace. The advantages of the new methods are demonstrated both on simulations, as well as real world applications such as DNA micro-satellites, protein repeats and absence seizures.
\r\n\r\nApart from practical contributions, the theory of Nested Periodic Subspaces offers answers to a number of fundamental questions that were previously unanswered. For example, what is the minimum contiguous data-length needed to be able to identify the period of a signal unambiguously? Notice that the answer we seek is a fundamental identifiability bound independent of any particular period estimation technique. Surprisingly, this basic question has never been answered before. In this thesis, we will derive precise expressions for the minimum necessary and sufficient datalengths for this question. We also extend these bounds to the context of mixtures of periodic signals. Once again, even though mixtures of periodic signals often occur in many applications, aspects such as the unique identifiability of the component periods were never rigorously analyzed before. We will present such an analysis as well.
\r\n\r\nWhile the above question deals with the minimum contiguous datalength required for period estimation, one may ask a slightly different question: If we are allowed to pick the samples of a signal in a non-contiguous fashion, how should we pick them so that we can estimate the period using the least number of samples? This question will be shown to be quite difficult to answer in general. In this thesis, we analyze a smaller case in this regard, namely, that of resolving between two periods. It will be shown that the analysis is quite involved even in this case, and the optimal sampling pattern takes an interesting form of sparsely located bunches. This result can also be extended to the case of multi-dimensional periodic signals.
\r\n\r\nWe very briefly address multi-dimensional periodicity in this thesis. Most prior DSP literature on multi-dimensional discrete time periodic signals assumes the period to be parallelepipeds. But as shown by the artist M. C. Escher, one can tile the space using a much more diverse variety of shapes. Is it always possible to account for such other periodic shapes using the traditional notion of parallelepiped periods? An interesting analysis in this regard is presented towards the end of the thesis.
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n", "doi": "10.7907/1n4t-5876", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10970", "collection": "thesis", "collection_id": "10970", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302018-095132389", "primary_object_url": { "basename": "Liu_Chun-Lin_2018.pdf", "content": "final", "filesize": 2762411, "license": "other", "mime_type": "application/pdf", "url": "/10970/1/Liu_Chun-Lin_2018.pdf", "version": "v8.0.0" }, "type": "thesis", "title": "Sparse Array Signal Processing: New Array Geometries, Parameter Estimation, and Theoretical Analysis", "author": [ { "family_name": "Liu", "given_name": "Chun-Lin", "orcid": "0000-0003-3135-9684", "clpid": "Liu-Chun-Lin" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Kostina", "given_name": "Victoria", "clpid": "Kostina-V" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Array signal processing focuses on an array of sensors receiving the incoming waveforms in the environment, from which source information, such as directions of arrival (DOA), signal power, amplitude, polarization, and velocity, can be estimated. This topic finds ubiquitous applications in radar, astronomy, tomography, imaging, and communications. In these applications, sparse arrays have recently attracted considerable attention, since they are capable of resolving O(N2) uncorrelated source directions with N physical sensors. This is unlike the uniform linear arrays (ULA), which identify at most N-1 uncorrelated sources with N sensors. These sparse arrays include minimum redundancy arrays (MRA), nested arrays, and coprime arrays. All these arrays have an O(N2)-long central ULA segment in the difference coarray, which is defined as the set of differences between sensor locations. This O(N2) property makes it possible to resolve O(N2) uncorrelated sources, using only N physical sensors.
\r\n\r\nThe main contribution of this thesis is to provide a new direction for array geometry and performance analysis of sparse arrays in the presence of nonidealities. The first part of this thesis focuses on designing novel array geometries that are robust to effects of mutual coupling. It is known that, mutual coupling between sensors has an adverse effect on the estimation of DOA. While there are methods to counteract this through appropriate modeling and calibration, they are usually computationally expensive, and sensitive to model mismatch. On the other hand, sparse arrays, such as MRA, nested arrays, and coprime arrays, have reduced mutual coupling compared to ULA, but all of these have their own disadvantages. This thesis introduces a new array called the super nested array, which has many of the good properties of the nested array, and at the same time achieves reduced mutual coupling. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of super nested arrays in the presence of mutual coupling.
\r\n\r\nTwo-dimensional planar sparse arrays with large difference coarrays have also been known for a long time. These include billboard arrays, open box arrays (OBA), and 2D nested arrays. However, all of them have considerable mutual coupling. This thesis proposes new planar sparse arrays with the same large difference coarrays as the OBA, but with reduced mutual coupling. The new arrays include half open box arrays (HOBA), half open box arrays with two layers (HOBA-2), and hourglass arrays. Among these, simulations show that hourglass arrays have the best estimation performance in presence of mutual coupling.
\r\n\r\nThe second part of this thesis analyzes the performance of sparse arrays from a theoretical perspective. We first study the Cram\u00e9r-Rao bound (CRB) for sparse arrays, which poses a lower bound on the variances of unbiased DOA estimators. While there exist landmark papers on the study of the CRB in the context of array processing, the closed-form expressions available in the literature are not applicable in the context of sparse arrays for which the number of identifiable sources exceeds the number of sensors. This thesis derives a new expression for the CRB to fill this gap. Based on the proposed CRB expression, it is possible to prove the previously known experimental observation that, when there are more sources than sensors, the CRB stagnates to a constant value as the SNR tends to infinity. It is also possible to precisely specify the relation between the number of sensors and the number of uncorrelated sources such that these sources could be resolved.
\r\n\r\nRecently, it has been shown that correlation subspaces, which reveal the structure of the covariance matrix, help to improve some existing DOA estimators. However, the bases, the dimension, and other theoretical properties of correlation subspaces remain to be investigated. This thesis proposes generalized correlation subspaces in one and multiple dimensions. This leads to new insights into correlation subspaces and DOA estimation with prior knowledge. First, it is shown that the bases and the dimension of correlation subspaces are fundamentally related to difference coarrays, which were previously found to be important in the study of sparse arrays. Furthermore, generalized correlation subspaces can handle certain forms of prior knowledge about source directions. These results allow one to derive a broad class of DOA estimators with improved performance.
\r\n\r\nIt is empirically known that the coarray structure is susceptible to sensor failures, and the reliability of sparse arrays remains a significant but challenging topic for investigation. This thesis advances a general theory for quantifying such robustness, by studying the effect of sensor failure on the difference coarray. We first present the (k-)essentialness property, which characterizes the combinations of the faulty sensors that shrink the difference coarray. Based on this, the notion of (k-)fragility is proposed to quantify the reliability of sparse arrays with faulty sensors, along with comprehensive studies of their properties. These novel concepts provide quite a few insights into the interplay between the array geometry and its robustness. For instance, for the same number of sensors, it can be proved that ULA is more robust than the coprime array, and the coprime array is more robust than the nested array. Rigorous development of these ideas leads to expressions for the probability of coarray failure, as a function of the probability of sensor failure.
\r\n\r\nThe thesis concludes with some remarks on future directions and open problems.
", "doi": "10.7907/NSTQ-SD57", "publication_date": "2018", "thesis_type": "phd", "thesis_year": "2018" }, { "id": "thesis:10179", "collection": "thesis", "collection_id": "10179", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05172017-103505376", "primary_object_url": { "basename": "Zhou_Edward Haojiang_2017.pdf", "content": "final", "filesize": 54748561, "license": "other", "mime_type": "application/pdf", "url": "/10179/44/Zhou_Edward Haojiang_2017.pdf", "version": "v13.0.0" }, "type": "thesis", "title": "Optical Focusing and Imaging through Scattering Media", "author": [ { "family_name": "Zhou", "given_name": "Edward Haojiang", "orcid": "0000-0001-7020-9502", "clpid": "Zhou-Edward-Haojiang" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Judkewitz", "given_name": "Benjamin", "clpid": "Judkewitz-Benjamin" }, { "family_name": "Wang", "given_name": "Lihong", "clpid": "Wang-Lihong" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Cai", "given_name": "Long", "clpid": "Cai-Long" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Optical techniques, which have been widely used in various fields including bio-medicine, remote sensing, astronomy, and industrial production, play an important role in modern life. Optical focusing and imaging, which correspond to the basic methods of utilizing light, are key to the implementation of optical techniques. In free space or a nearly transparent medium, optical imaging and focusing can be easily realized by using conventional optical elements, such as lenses and mirrors, due to the ballistic propagation of light in these media. However, in scattering media like biological tissue and fog, refractive index inhomogeneities cause diffusive propagation of light that increases with depth, which restricts the use of optical methods in thick, scattering media. Generally speaking, scattering media poses three challenges to optical focusing and imaging: wavefront aberrations, glare, and decorrelation. Wavefront aberrations can randomize light traveling through a scattering medium, disrupt the formation of focus, and break the conjugate relation in imaging. Glare caused by backscattering will largely impair the visibility of imaging, and decorrelation in dynamic media requires systems that counter the effect of scattering to operate faster than the decorrelation time. In this thesis, we explored solutions to the problem of scattering from different aspects. We presented Time Reversal by Analysis of Changing wavefronts from Kinetic targets (TRACK) technique to realize noninvasive optical focusing through a scattering medium. We showed that by taking the difference between time-varying scattering fields caused by a moving object and applying optical phase conjugation, light can be focused back to the location previously occupied by the object. To tackle the decorrelation of living tissue, we built up a fast digital optical phase conjugation (DOPC) system based on FPGA and DMD, which has a response time of 5.3 ms and was the fastest DOPC system in the world before 2017. We demonstrated that the system is fast enough to focus light through 2.3mm-thick living mouse skin. As for glare, inspired by noise canceling headphones, we invented an optical analogue termed coherence gated negation (CGN) technique. CGN can optically cancel out the glare in an active illumination imaging scenario to realize imaging through scattering media, like fog. In the experiment, we suppressed the glare by an order of magnitude and allowed improved imaging of a weak target. Finally, we demonstrated a method to image a moving target through scattering media noninvasively. Its principle roots are in the speckle-correlation-based imaging (SCI) invented by Ori Katz. We improved the technique and extended its application to bright field imaging of a moving target.
", "doi": "10.7907/Z9TX3CD1", "publication_date": "2017", "thesis_type": "phd", "thesis_year": "2017" }, { "id": "thesis:10146", "collection": "thesis", "collection_id": "10146", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04262017-114441886", "type": "thesis", "title": "Compact Microscope System for Biomedical Applications", "author": [ { "family_name": "Kim", "given_name": "Jinho", "clpid": "Kim-Jinho" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Tai", "given_name": "Yu-Chong", "clpid": "Tai-Yu-Chong" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Lester", "given_name": "Henry A.", "clpid": "Lester-H-A" }, { "family_name": "Elowitz", "given_name": "Michael B.", "clpid": "Elowitz-M-B" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Demands for an imaging system which has high space-bandwidth product (SBP) are increasing in modern biomedical research as the amount of information to be dealt with is increasing. However, conventional microscopy has a limited SBP of about 10 mega pixels, and as such if a user wants an image in high resolution, the field of view (FOV) of the image is reduced, or if a wide FOV is necessary, the user needs to give up the resolution of image. A common way of overcoming this SBP limit in the conventional microscopy is to use mechanical moving stages and scan through wide sample area, however, it is time consuming to image large area using a high numerical aperture (NA) objective lens. This thesis presents compact imaging systems based on Fourier ptychographic microscopy for biomedical applications which are able to increase SBP without having any mechanical moving parts: one imaging system for an incubator embedded imaging system to be used in in-vitro cell culture monitoring, and the other for a high throughput 96 well plate imaging system for fast drug screening.
", "doi": "10.7907/Z9H9937R", "publication_date": "2017", "thesis_type": "phd", "thesis_year": "2017" }, { "id": "thesis:9549", "collection": "thesis", "collection_id": "9549", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:01262016-194420781", "primary_object_url": { "basename": "Pengthesis.pdf", "content": "final", "filesize": 2095107, "license": "other", "mime_type": "application/pdf", "url": "/9549/1/Pengthesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Distributed Control and Optimization for Communication and Power Systems", "author": [ { "family_name": "Peng", "given_name": "Qiuyu", "clpid": "Peng-Qiuyu" } ], "thesis_advisor": [ { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" } ], "thesis_committee": [ { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" }, { "family_name": "Chandy", "given_name": "K. Mani", "clpid": "Chandy-K-M" }, { "family_name": "Doyle", "given_name": "John Comstock", "clpid": "Doyle-J-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.
\r\n\r\nThis thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.
\r\n\r\nOur second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.
\r\n\r\nSecond, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.
", "doi": "10.7907/Z99C6VBW", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9231", "collection": "thesis", "collection_id": "9231", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10202015-173005082", "primary_object_url": { "basename": "thesis_final_10-20-15.pdf", "content": "final", "filesize": 38189479, "license": "other", "mime_type": "application/pdf", "url": "/9231/1/thesis_final_10-20-15.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Computational Microscopy: Turning Megapixels into Gigapixels", "author": [ { "family_name": "Horstmeyer", "given_name": "Roarke William", "orcid": "0000-0002-2480-9141", "clpid": "Horstmeyer-Roarke-William" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Zheng", "given_name": "Guoan", "clpid": "Zheng-Guoan" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The layout of a typical optical microscope has remained effectively unchanged over the past century. Besides the widespread adoption of digital focal plane arrays, relatively few innovations have helped improve standard imaging with bright-field microscopes. This thesis presents a new microscope imaging method, termed Fourier ptychography, which uses an LED to provide variable sample illumination and post-processing algorithms to recover useful sample information. Examples include increasing the resolution of megapixel-scale images to one gigapixel, measuring quantitative phase, achieving oil-immersion quality resolution without an immersion medium, and recovering complex\r\nthree dimensional sample structure.", "doi": "10.7907/Z95Q4T1W", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9836", "collection": "thesis", "collection_id": "9836", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06032016-144604076", "type": "thesis", "title": "Recovering Structured Signals in High Dimensions via Non-Smooth Convex Optimization: Precise Performance Analysis", "author": [ { "family_name": "Thrampoulidis", "given_name": "Christos", "orcid": "0000-0001-9053-9365", "clpid": "Thrampoulidis-Christos" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The typical scenario that arises in modern large-scale inference problems is one where the ambient dimension of the unknown signal is very large (e.g., high-resolution images, recommendation systems), yet its desired properties lie in some low-dimensional structure such as, sparsity or low-rankness. In the past couple of decades, non-smooth convex optimization methods have emerged as a powerful tool to extract those structures, since they are often computationally efficient, and also they offer enough flexibility while simultaneously being amenable to performance analysis. Especially, since the advent of Compressed Sensing (CS) there has been significant progress towards this direction. One of the key ideas is that random linear measurements offer an efficient way to acquire structured signals. When the measurement matrix has entries iid from a wide class of distributions (including Gaussians), a series of recent works have established a complete and transparent theory that precisely captures the performance in the noiseless setting. In the more practical scenario of noisy measurements the performance analysis task becomes significantly more challenging and corresponding precise and unifying results have hitherto remained scarce. The available class of optimization methods, often referred to as regularized M-estimators, is now richer; additional factors (e.g., the noise distribution, the loss function, and the regularizer parameter) and several different measures of performance (e.g., squared-error, probability of support recovery) need to be taken into account.
\r\n\r\nThis thesis develops a novel analytical framework that overcomes these challenges, and establishes {precise asymptotic performance guarantees for regularized M-estimators under Gaussian measurement matrices. In particular, the framework allows for a unifying analysis among different instances (such as the Generalized LASSO, and the LAD, to name a few) and accounts for a wide class of performance measures. Among others, we show results on the mean-squared-error of the Generalized-LASSO method and make insightful connections to the classical theory of ordinary least squares and to noiseless CS. Empirical evidence is presented that suggests the Gaussian assumption is not necessary. Beyond iid measurement matrices, motivated by practical considerations, we study certain classes of random matrices with orthogonal rows and establish their superior performance when compared to Gaussians.
\r\n\r\nA prominent application of this generic theory is on the analysis of the bit-error rate (BER) of the popular convex-relaxation of the Maximum Likelihood decoder for recovering BPSK signals in a massive Multiple Input Multiple Output setting. Our precise BER analysis allows comparison of these schemes to the unattainable Matched-filter bound, and further suggests means to provably boost their performance.
\r\n\r\nThe last challenge is to evaluate the performance under non-linear measurements. For the Generalized LASSO, it is shown that this is (asymptotically) equivalent to the one under noisy linear measurements with appropriately scaled variance. This encompasses state-of-the art theoretical results of one-bit CS , and is also used to prove that the optimal quantizer of the measurements that minimizes the estimation error of the Generalized LASSO is the celebrated Lloyd-Max quantizer.
\r\n\r\nThe framework is based on Gaussian process methods; in particular, on a new strong and tight version of a classical comparison inequality (due to Gordon, 1988) in the presence of additional convexity assumptions. We call this the Convex Gaussian Min-max Theorem (CGMT).
", "doi": "10.7907/Z998850V", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9814", "collection": "thesis", "collection_id": "9814", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05312016-051759406", "primary_object_url": { "basename": "Kishore_Jaganathan_2016_Thesis.pdf", "content": "final", "filesize": 3539409, "license": "other", "mime_type": "application/pdf", "url": "/9814/1/Kishore_Jaganathan_2016_Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Convex Programming-Based Phase Retrieval: Theory and Applications", "author": [ { "family_name": "Jaganathan", "given_name": "Kishore", "clpid": "Jaganathan-Kishore" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Phase retrieval is the problem of recovering a signal from its Fourier magnitude. This inverse problem arises in many areas of engineering and applied physics, and has been studied for nearly a century. Due to the absence of Fourier phase, the available information is incomplete in general. Classic identifiability results state that phase retrieval of one-dimensional signals is impossible, and that phase retrieval of higher-dimensional signals is almost surely possible under mild conditions. However, there are no efficient recovery algorithms with theoretical guarantees. Classic algorithms are based on the method of alternating projections. These algorithms do not have theoretical guarantees, and have limited recovery abilities due to the issue of convergence to local optima.
\r\n\r\nRecently, there has been a renewed interest in phase retrieval due to technological advances in measurement systems and theoretical developments in structured signal recovery. In particular, it is now possible to obtain specific kinds of additional magnitude-only information about the signal, depending on the application. The premise is that, by carefully redesigning the measurement process, one could potentially overcome the issues of phase retrieval. To this end, another approach could be to impose certain kinds of prior on the signal, depending on the application. On the algorithmic side, convex programming based approaches have played a key role in modern phase retrieval, inspired by their success in provably solving several quadratic constrained problems.
\r\n\r\nIn this work, we study several variants of phase retrieval using modern tools, with focus on applications like X-ray crystallography, diffraction imaging, optics, astronomy and radar. In the one-dimensional setup, we first develop conditions, which when satisfied, allow unique reconstruction. Then, we develop efficient recovery algorithms based on convex programming, and provide theoretical guarantees. The theory and algorithms we develop are independent of the dimension of the signal, and hence can be used in all the aforementioned applications. We also perform a comparative numerical study of the convex programming and the alternating projection based algorithms. Numerical simulations clearly demonstrate the superior ability of the convex programming based methods, both in terms of successful recovery in the noiseless setting and stable reconstruction in the noisy setting.
", "doi": "10.7907/Z9C82775", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9771", "collection": "thesis", "collection_id": "9771", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05262016-142345346", "primary_object_url": { "basename": "Mooseok_Jang_2016_Thesis.pdf", "content": "final", "filesize": 53211730, "license": "other", "mime_type": "application/pdf", "url": "/9771/1/Mooseok_Jang_2016_Thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Optical Phase Conjugation and Its Applications in Biology", "author": [ { "family_name": "Jang", "given_name": "Mooseok", "orcid": "0000-0003-1977-9539", "clpid": "Jang-Mooseok" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Yariv", "given_name": "Amnon", "clpid": "Yariv-A" }, { "family_name": "Vellekoop", "given_name": "Ivo", "clpid": "Vellekoop-I" }, { "family_name": "Gradinaru", "given_name": "Viviana", "clpid": "Gradinaru-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Optical phase conjugation is a process where an incoming electromagnetic wave is reflected with a reversed phase. The propagation direction of an incoming beam (equivalently, local phase gradient) can thereby be precisely reversed by the phase conjugate beam. This intriguing effect, so called \"time-reversal of electromagnetic waves,\" allows cancellation of spatial distortion introduced into the incoming beam. Recently, this concept has provided a new avenue to overcome or utilize random scattering in the field of biophotonics.
\r\n\r\nThis thesis discusses a number of interrelated topics regarding optical phase conjugation and its applications in biology. First, two examples of exploiting optical phase conjugation for light focusing are presented. The first example shows that the axial resolution can be improved based on the counter-propagating property of the phase-conjugate beam, and the second example demonstrates how the random scattering media can be used to enhance the flexibility in focusing range. We then discuss a new class of techniques that involves the use of guidestars in the phase conjugation process for deep tissue (> 1mm) light focusing and imaging. In the context of in vivo application, we model and estimate the penetration depth limit of one prominent example of this approach, time-reversed ultrasonically encoded (TRUE) optical focusing. Based on the analysis, we show that the iteration of phase conjugation operation can improve the contrast and resolution of the focal spot created inside deep tissue. We also present a new kind of guidestar-assisted method, time-reversed ultrasound microbubble encoded (TRUME) light focusing, which can focus light with sub-ultrasound wavelength resolution. At last, the effect of dynamic scatterers on time-reversal fidelity is studied to explore the possibility of applying the optical phase conjugation techniques in living tissue.
", "doi": "10.7907/Z99G5JSN", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9765", "collection": "thesis", "collection_id": "9765", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05262016-112813537", "primary_object_url": { "basename": "thesis.pdf", "content": "", "filesize": 1308192, "license": "other", "mime_type": "application/pdf", "url": "/9765/1/thesis.pdf", "version": "v1.0.0" }, "type": "thesis", "title": "Electricity Markets for the Smart Grid: Networks, Timescales, and Integration with Control", "author": [ { "family_name": "Cai", "given_name": "Wuhan Desmond", "orcid": "0000-0001-9207-1890", "clpid": "Cai-Wuhan-Desmond" } ], "thesis_advisor": [ { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" }, { "family_name": "Chandy", "given_name": "K. Mani", "clpid": "Chandy-K-M" }, { "family_name": "Ledyard", "given_name": "John O.", "clpid": "Ledyard-J-O" } ], "thesis_committee": [ { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" }, { "family_name": "Chandy", "given_name": "K. Mani", "clpid": "Chandy-K-M" }, { "family_name": "Ledyard", "given_name": "John O.", "clpid": "Ledyard-J-O" }, { "family_name": "Doyle", "given_name": "John Comstock", "clpid": "Doyle-J-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "We are at the dawn of a significant transformation in the electric industry. Renewable generation and customer participation in grid operations and markets have been growing at tremendous rates in recent years and these trends are expected to continue. These trends are likely to be accompanied by both engineering and market integration challenges. Therefore, to incorporate these resources efficiently into the grid, it is important to deal with the inefficiencies in existing markets. The goal of this thesis is to contribute new insights towards improving the design of electricity markets.
\r\n\r\nThis thesis makes three main contributions. First, we provide insights into how the economic dispatch mechanism could be designed to account for price-anticipating participants. We study this problem in the context of a networked Cournot competition with a market maker and we give an algorithm to find improved market clearing designs. Our findings illustrate the potential inefficiencies in existing markets and provides a framework for improving the design of the markets. Second, we provide insights into the strategic interactions between generation flexibility and forward markets. Our key insight is an observation that spot market capacity constraints can significantly impact the efficiency and existence of equilibrium in forward markets, as they give producers incentives to strategically withhold offers from the markets. Third, we provide insights into how optimization decomposition theory can guide optimal design of the architecture of power systems control. In particular, we illustrate a context where decomposition theory enables us to jointly design market and control mechanisms to allocate resources efficiently across both the economic dispatch and frequency regulation timescales.\r\n
", "doi": "10.7907/Z9BG2KZG", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9688", "collection": "thesis", "collection_id": "9688", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04282016-051723211", "primary_object_url": { "basename": "Xiaoze_Thesis_Caltech_04282016.pdf", "content": "final", "filesize": 13112405, "license": "other", "mime_type": "application/pdf", "url": "/9688/1/Xiaoze_Thesis_Caltech_04282016.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Computational Microscopy: Breaking the Limit of Conventional Optics", "author": [ { "family_name": "Ou", "given_name": "Xiaoze", "orcid": "0000-0001-9918-0221", "clpid": "Ou-Xiaoze" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Tai", "given_name": "Yu-Chong", "clpid": "Tai-Yu-Chong" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Shapiro", "given_name": "Mikhail G.", "clpid": "Shapiro-M-G" }, { "family_name": "Cai", "given_name": "Long", "clpid": "Cai-Long" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Computational imaging is flourishing thanks to the recent advancement in array photodetectors and image processing algorithms. This thesis presents Fourier ptychography, which is a computational imaging technique implemented in microscopy to break the limit of conventional optics. With the implementation of Fourier ptychography, the resolution of the imaging system can surpass the diffraction limit of the objective lens's numerical aperture; the quantitative phase information of a sample can be reconstructed from intensity-only measurements; and the aberration of a microscope system can be characterized and computationally corrected. This computational microscopy technique enhances the performance of conventional optical systems and expands the scope of their applications.", "doi": "10.7907/Z9M32SRZ", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9597", "collection": "thesis", "collection_id": "9597", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:03022016-094235703", "type": "thesis", "title": "Advanced Monte Carlo Simulation and Machine Learning for Frequency Domain Optical Coherence Tomography", "author": [ { "family_name": "Zhao", "given_name": "Sinan", "clpid": "Zhao-Sinan" } ], "thesis_advisor": [ { "family_name": "Yariv", "given_name": "Amnon", "clpid": "Yariv-A" } ], "thesis_committee": [ { "family_name": "Yariv", "given_name": "Amnon", "clpid": "Yariv-A" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Crosignani", "given_name": "Bruno", "clpid": "Crosignani-B" }, { "family_name": "Ng", "given_name": "Willie", "clpid": "Ng-Willie" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Optical Coherence Tomography(OCT) is a popular, rapidly growing imaging technique with an increasing number of bio-medical applications due to its noninvasive nature. However, there are three major challenges in understanding and improving an OCT system: (1) Obtaining an OCT image is not easy. It either takes a real medical experiment or requires days of computer simulation. Without much data, it is difficult to study the physical processes underlying OCT imaging of different objects simply because there aren't many imaged objects. (2) Interpretation of an OCT image is also hard. This challenge is more profound than it appears. For instance, it would require a trained expert to tell from an OCT image of human skin whether there is a lesion or not. This is expensive in its own right, but even the expert cannot be sure about the exact size of the lesion or the width of the various skin layers. The take-away message is that analyzing an OCT image even from a high level would usually require a trained expert, and pixel-level interpretation is simply unrealistic. The reason is simple: we have OCT images but not their underlying ground-truth structure, so there is nothing to learn from. (3) The imaging depth of OCT is very limited (millimeter or sub-millimeter on human tissues). While OCT utilizes infrared light for illumination to stay noninvasive, the downside of this is that photons at such long wavelengths can only penetrate a limited depth into the tissue before getting back-scattered. To image a particular region of a tissue, photons first need to reach that region. As a result, OCT signals from deeper regions of the tissue are both weak (since few photons reached there) and distorted (due to multiple scatterings of the contributing photons). This fact alone makes OCT images very hard to interpret.
\r\n\r\nThis thesis addresses the above challenges by successfully developing an advanced Monte Carlo simulation platform which is 10000 times faster than the state-of-the-art simulator in the literature, bringing down the simulation time from 360 hours to a single minute. This powerful simulation tool not only enables us to efficiently generate as many OCT images of objects with arbitrary structure and shape as we want on a common desktop computer, but it also provides us the underlying ground-truth of the simulated images at the same time because we dictate them at the beginning of the simulation. This is one of the key contributions of this thesis. What allows us to build such a powerful simulation tool includes a thorough understanding of the signal formation process, clever implementation of the importance sampling/photon splitting procedure, efficient use of a voxel-based mesh system in determining photon-mesh interception, and a parallel computation of different A-scans that consist a full OCT image, among other programming and mathematical tricks, which will be explained in detail later in the thesis.
\r\n\r\nNext we aim at the inverse problem: given an OCT image, predict/reconstruct its ground-truth structure on a pixel level. By solving this problem we would be able to interpret an OCT image completely and precisely without the help from a trained expert. It turns out that we can do much better. For simple structures we are able to reconstruct the ground-truth of an OCT image more than 98% correctly, and for more complicated structures (e.g., a multi-layered brain structure) we are looking at 93%. We achieved this through extensive uses of Machine Learning. The success of the Monte Carlo simulation already puts us in a great position by providing us with a great deal of data (effectively unlimited), in the form of (image, truth) pairs. Through a transformation of the high-dimensional response variable, we convert the learning task into a multi-output multi-class classification problem and a multi-output regression problem. We then build a hierarchy architecture of machine learning models (committee of experts) and train different parts of the architecture with specifically designed data sets. In prediction, an unseen OCT image first goes through a classification model to determine its structure (e.g., the number and the types of layers present in the image); then the image is handed to a regression model that is trained specifically for that particular structure to predict the length of the different layers and by doing so reconstruct the ground-truth of the image. We also demonstrate that ideas from Deep Learning can be useful to further improve the performance.
\r\n\r\nIt is worth pointing out that solving the inverse problem automatically improves the imaging depth, since previously the lower half of an OCT image (i.e., greater depth) can be hardly seen but now becomes fully resolved. Interestingly, although OCT signals consisting the lower half of the image are weak, messy, and uninterpretable to human eyes, they still carry enough information which when fed into a well-trained machine learning model spits out precisely the true structure of the object being imaged. This is just another case where Artificial Intelligence (AI) outperforms human. To the best knowledge of the author, this thesis is not only a success but also the first attempt to reconstruct an OCT image at a pixel level. To even give a try on this kind of task, it would require fully annotated OCT images and a lot of them (hundreds or even thousands). This is clearly impossible without a powerful simulation tool like the one developed in this thesis.
", "doi": "10.7907/Z9X63JVM", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:9141", "collection": "thesis", "collection_id": "9141", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09042015-171723764", "primary_object_url": { "basename": "MatthewThill2016_thesis.pdf", "content": "final", "filesize": 1775919, "license": "other", "mime_type": "application/pdf", "url": "/9141/1/MatthewThill2016_thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Algebraic Techniques in Coding Theory: Entropy Vectors, Frames, and Constrained Coding", "author": [ { "family_name": "Thill", "given_name": "Matthew David", "orcid": "0000-0003-0885-6260", "clpid": "Thill-Matthew-David" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Divsalar", "given_name": "Dariush", "clpid": "Divsalar-D" }, { "family_name": "Kostina", "given_name": "Victoria", "clpid": "Kostina-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The study of codes, classically motivated by the need to communicate information reliably in the presence of error, has found new life in fields as diverse as network communication, distributed storage of data, and even has connections to the design of linear measurements used in compressive sensing. But in all contexts, a code typically involves exploiting the algebraic or geometric structure underlying an application. In this thesis, we examine several problems in coding theory, and try to gain some insight into the algebraic structure behind them.
\r\n\r\nThe first is the study of the entropy region - the space of all possible vectors of joint entropies which can arise from a set of discrete random variables. Understanding this region is essentially the key to optimizing network codes for a given network. To this end, we employ a group-theoretic method of constructing random variables producing so-called \"group-characterizable\" entropy vectors, which are capable of approximating any point in the entropy region. We show how small groups can be used to produce entropy vectors which violate the Ingleton inequality, a fundamental bound on entropy vectors arising from the random variables involved in linear network codes. We discuss the suitability of these groups to design codes for networks which could potentially outperform linear coding.
\r\n\r\nThe second topic we discuss is the design of frames with low coherence, closely related to finding spherical codes in which the codewords are unit vectors spaced out around the unit sphere so as to minimize the magnitudes of their mutual inner products. We show how to build frames by selecting a cleverly chosen set of representations of a finite group to produce a \"group code\" as described by Slepian decades ago. We go on to reinterpret our method as selecting a subset of rows of a group Fourier matrix, allowing us to study and bound our frames' coherences using character theory. We discuss the usefulness of our frames in sparse signal recovery using linear measurements.
\r\n\r\nThe final problem we investigate is that of coding with constraints, most recently motivated by the demand for ways to encode large amounts of data using error-correcting codes so that any small loss can be recovered from a small set of surviving data. Most often, this involves using a systematic linear error-correcting code in which each parity symbol is constrained to be a function of some subset of the message symbols. We derive bounds on the minimum distance of such a code based on its constraints, and characterize when these bounds can be achieved using subcodes of Reed-Solomon codes.
", "doi": "10.7907/Z9F18WNW", "publication_date": "2016", "thesis_type": "phd", "thesis_year": "2016" }, { "id": "thesis:8834", "collection": "thesis", "collection_id": "8834", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04272015-133555770", "primary_object_url": { "basename": "Wei_Mao_Thesis_2015.pdf", "content": "final", "filesize": 1159546, "license": "other", "mime_type": "application/pdf", "url": "/8834/1/Wei_Mao_Thesis_2015.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Information-Theoretic Studies and Capacity Bounds: Group Network Codes and Energy Harvesting Communication Systems", "author": [ { "family_name": "Mao", "given_name": "Wei", "clpid": "Mao-Wei" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Kostina", "given_name": "Victoria", "clpid": "Kostina-V" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wierman", "given_name": "Adam C.", "clpid": "Wierman-A-C" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Network information theory and channels with memory are two important but difficult frontiers of information theory. In this two-parted dissertation, we study these two areas, each comprising one part. For the first area we study the so-called entropy vectors via finite group theory, and the network codes constructed from finite groups. In particular, we identify the smallest finite group that violates the Ingleton inequality, an inequality respected by all linear network codes, but not satisfied by all entropy vectors. Based on the analysis of this group we generalize it to several families of Ingleton-violating groups, which may be used to design good network codes. Regarding that aspect, we study the network codes constructed with finite groups, and especially show that linear network codes are embedded in the group network codes constructed with these Ingleton-violating families. Furthermore, such codes are strictly more powerful than linear network codes, as they are able to violate the Ingleton inequality while linear network codes cannot. For the second area, we study the impact of memory to the channel capacity through a novel communication system: the energy harvesting channel. Different from traditional communication systems, the transmitter of an energy harvesting channel is powered by an exogenous energy harvesting device and a finite-sized battery. As a consequence, each time the system can only transmit a symbol whose energy consumption is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is random, instantaneous, and has memory. Furthermore, naturally, the energy harvesting process is observed causally at the transmitter, but no such information is provided to the receiver. Both of these features pose great challenges for the analysis of the channel capacity. In this work we use techniques from channels with side information, and finite state channels, to obtain lower and upper bounds of the energy harvesting channel. In particular, we study the stationarity and ergodicity conditions of a surrogate channel to compute and optimize the achievable rates for the original channel. In addition, for practical code design of the system we study the pairwise error probabilities of the input sequences.", "doi": "10.7907/Z9ZS2TFB", "publication_date": "2015", "thesis_type": "phd", "thesis_year": "2015" }, { "id": "thesis:8888", "collection": "thesis", "collection_id": "8888", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05262015-094933189", "primary_object_url": { "basename": "CarlosGonzalez2015_thesis.pdf", "content": "final", "filesize": 1591603, "license": "other", "mime_type": "application/pdf", "url": "/8888/73/CarlosGonzalez2015_thesis.pdf", "version": "v9.0.0" }, "type": "thesis", "title": "Optimal Data Distributions in Machine Learning", "author": [ { "family_name": "Gonz\u00e1lez Palacios", "given_name": "Carlos Roberto", "clpid": "Gonz\u00e1lez-Palacios-Carlos-Roberto" } ], "thesis_advisor": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Perona", "given_name": "Pietro", "clpid": "Perona-P" } ], "thesis_committee": [ { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Perona", "given_name": "Pietro", "clpid": "Perona-P" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Yue", "given_name": "Yisong", "clpid": "Yue-Yisong" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the first part of the thesis we explore three fundamental questions that arise naturally when we conceive a machine learning scenario where the training and test distributions can differ. Contrary to conventional wisdom, we show that in fact mismatched training and test distribution can yield better out-of-sample performance. This optimal performance can be obtained by training with the dual distribution. This optimal training distribution depends on the test distribution set by the problem, but not on the target function that we want to learn. We show how to obtain this distribution in both discrete and continuous input spaces, as well as how to approximate it in a practical scenario. Benefits of using this distribution are exemplified in both synthetic and real data sets.
\r\n\r\nIn order to apply the dual distribution in the supervised learning scenario where the training data set is fixed, it is necessary to use weights to make the sample appear as if it came from the dual distribution. We explore the negative effect that weighting a sample can have. The theoretical decomposition of the use of weights regarding its effect on the out-of-sample error is easy to understand but not actionable in practice, as the quantities involved cannot be computed. Hence, we propose the Targeted Weighting algorithm that determines if, for a given set of weights, the out-of-sample performance will improve or not in a practical setting. This is necessary as the setting assumes there are no labeled points distributed according to the test distribution, only unlabeled samples.
\r\n\r\nFinally, we propose a new class of matching algorithms that can be used to match the training set to a desired distribution, such as the dual distribution (or the test distribution). These algorithms can be applied to very large datasets, and we show how they lead to improved performance in a large real dataset such as the Netflix dataset. Their computational complexity is the main reason for their advantage over previous algorithms proposed in the covariate shift literature.
\r\n\r\nIn the second part of the thesis we apply Machine Learning to the problem of behavior recognition. We develop a specific behavior classifier to study fly aggression, and we develop a system that allows analyzing behavior in videos of animals, with minimal supervision. The system, which we call CUBA (Caltech Unsupervised Behavior Analysis), allows detecting movemes, actions, and stories from time series describing the position of animals in videos. The method summarizes the data, as well as it provides biologists with a mathematical tool to test new hypotheses. Other benefits of CUBA include finding classifiers for specific behaviors without the need for annotation, as well as providing means to discriminate groups of animals, for example, according to their genetic line.
", "doi": "10.7907/Z9DR2SD5", "publication_date": "2015", "thesis_type": "phd", "thesis_year": "2015" }, { "id": "thesis:8635", "collection": "thesis", "collection_id": "8635", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:08182014-091546460", "primary_object_url": { "basename": "SametOymak2015.pdf", "content": "final", "filesize": 2756128, "license": "other", "mime_type": "application/pdf", "url": "/8635/1/SametOymak2015.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations", "author": [ { "family_name": "Oymak", "given_name": "Samet", "clpid": "Oymak-Samet" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" }, { "family_name": "Chandrasekaran", "given_name": "Venkat", "clpid": "Chandrasekaran-V" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Fazel", "given_name": "Maryam", "clpid": "Fazel-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.
\r\n\r\nIn sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be \"relaxed\" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:
\r\nMore specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.
", "doi": "10.7907/Z9S46PWX", "publication_date": "2015", "thesis_type": "phd", "thesis_year": "2015" }, { "id": "thesis:8814", "collection": "thesis", "collection_id": "8814", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:04082015-142940694", "type": "thesis", "title": "Rewriting Schemes for Flash Memory", "author": [ { "family_name": "En Gad", "given_name": "Eyal", "clpid": "En-Gad-Eyal" } ], "thesis_advisor": [ { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" } ], "thesis_committee": [ { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Effros", "given_name": "Michelle", "clpid": "Effros-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Langberg", "given_name": "Michael", "clpid": "Langberg-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Flash memory is a leading storage media with excellent features such as random access and\r\nhigh storage density. However, it also faces significant reliability and endurance challenges.\r\nIn flash memory, the charge level in the cells can be easily increased, but removing charge\r\nrequires an expensive erasure operation. In this thesis we study rewriting schemes that\r\nenable the data stored in a set of cells to be rewritten by only increasing the charge level\r\nin the cells. We consider two types of modulation scheme; a convectional modulation based\r\non the absolute levels of the cells, and a recently-proposed scheme based on the relative cell\r\nlevels, called rank modulation. The contributions of this thesis to the study of rewriting\r\nschemes for rank modulation include the following: we
\r\n\r\n•propose a new method of rewriting in rank modulation, beyond the previously proposed\r\nmethod of \u201cpush-to-the-top\u201d;
\r\n•study the limits of rewriting with the newly proposed method, and derive a tight upper\r\nbound of 1 bit per cell;
\r\n•extend the rank-modulation scheme to support rankings with repetitions, in order to\r\nimprove the storage density;
\r\n•derive a tight upper bound of 2 bits per cell for rewriting in rank modulation with\r\nrepetitions;
\r\n•construct an efficient rewriting scheme that asymptotically approaches the upper bound\r\nof 2 bit per cell.
\r\n\r\nThe next part of this thesis studies rewriting schemes for a conventional absolute-levels\r\nmodulation. The considered model is called \u201cwrite-once memory\u201d (WOM). We focus on\r\nWOM schemes that achieve the capacity of the model. In recent years several capacity-achieving\r\nWOM schemes were proposed, based on polar codes and randomness extractors.\r\nThe contributions of this thesis to the study of WOM scheme include the following: we
\r\n\r\n•propose a new capacity-achievingWOM scheme based on sparse-graph codes, and show\r\nits attractive properties for practical implementation;
\r\n•improve the design of polarWOMschemes to remove the reliance on shared randomness\r\nand include an error-correction capability.
\r\n\r\nThe last part of the thesis studies the local rank-modulation (LRM) scheme, in which a\r\nsliding window going over a sequence of real-valued variables induces a sequence of permutations.\r\nThe LRM scheme is used to simulate a single conventional multi-level flash cell.\r\nThe simulated cell is realized by a Gray code traversing all the relative-value states where,\r\nphysically, the transition between two adjacent states in the Gray code is achieved by using\r\na single \u201cpush-to-the-top\u201d operation. The main results of the last part of the thesis are two\r\nconstructions of Gray codes with asymptotically-optimal rate.
", "doi": "10.7907/Z9R49NQ3", "publication_date": "2015", "thesis_type": "phd", "thesis_year": "2015" }, { "id": "thesis:8491", "collection": "thesis", "collection_id": "8491", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06052014-214022941", "type": "thesis", "title": "Microfabricated Tools and Engineering Methods for Sensing Bioanalytes", "author": [ { "family_name": "Rajagopal", "given_name": "Aditya", "clpid": "Rajagopal-Aditya" } ], "thesis_advisor": [ { "family_name": "Scherer", "given_name": "Axel", "clpid": "Scherer-A" } ], "thesis_committee": [ { "family_name": "Tombrello", "given_name": "Thomas A.", "clpid": "Tombrello-T-A" }, { "family_name": "Fraser", "given_name": "Scott E.", "clpid": "Fraser-S-E" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Baltimore", "given_name": "David L.", "clpid": "Baltimore-D-L" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "There is a convergence between the needs of the medical community and the capabilities of the engineering community. For example, the scale of biomedical devices and sensors allow for finer, more cost-effective quantification of biological and chemical targets. By using micro-fabrication techniques, we design and demonstrate a variety of microfluidic sensors and actuators that allow us to interact with a biochemical environment. We demonstrate the performance of microfluidic blood-filtrations chips, immune-diagnostic assays, and evaporative coolers. Furthermore, we show how micro-fabricated platinum filaments can be used for highly localized heating and temperature measurement. We demonstrate that these filaments can be used as miniature IR spectroscopic sources. Finally, we describe and demonstrate novel combinatorial coding methods for increasing the information extracted from biochemical reactions. We show proof-principle of these techniques in the context of Taqman PCR as well as persistence length PCR.", "doi": "10.7907/Z9W9575D", "publication_date": "2014", "thesis_type": "phd", "thesis_year": "2014" }, { "id": "thesis:8095", "collection": "thesis", "collection_id": "8095", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:02212014-174719213", "primary_object_url": { "basename": "Thesis_final_SALee.pdf", "content": "final", "filesize": 3968641, "license": "other", "mime_type": "application/pdf", "url": "/8095/1/Thesis_final_SALee.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Bright-Field and Fluorescence Chip-Scale Microscopy for Biological Imaging", "author": [ { "family_name": "Lee", "given_name": "Seung Ah", "clpid": "Lee-Seung-Ah" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Tai", "given_name": "Yu-Chong", "clpid": "Tai-Yu-Chong" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Ismagilov", "given_name": "Rustem F.", "clpid": "Ismagilov-R-F" }, { "family_name": "Choo", "given_name": "Hyuck", "clpid": "Choo-Hyuck" } ], "local_group": [ { "literal": "Kavli Nanoscience Institute" }, { "literal": "div_eng" } ], "abstract": "Optical microscopy is an essential tool in biological science and one of the gold standards for medical examinations. Miniaturization of microscopes can be a crucial stepping stone towards realizing compact, cost-effective and portable platforms for biomedical research and healthcare. This thesis reports on implementations of bright-field and fluorescence chip-scale microscopes for a variety of biological imaging applications. The term \u201cchip-scale microscopy\u201d refers to lensless imaging techniques realized in the form of mass-producible semiconductor devices, which transforms the fundamental design of optical microscopes.
\r\n\r\nOur strategy for chip-scale microscopy involves utilization of low-cost Complementary metal Oxide Semiconductor (CMOS) image sensors, computational image processing and micro-fabricated structural components. First, the sub-pixel resolving optofluidic microscope (SROFM), will be presented, which combines microfluidics and pixel super-resolution image reconstruction to perform high-throughput imaging of fluidic samples, such as blood cells. We discuss design parameters and construction of the device, as well as the resulting images and the resolution of the device, which was 0.66 \u00b5m at the highest acuity. The potential applications of SROFM for clinical diagnosis of malaria in the resource-limited settings is discussed.
\r\n\r\nNext, the implementations of ePetri, a self-imaging Petri dish platform with microscopy resolution, are presented. Here, we simply place the sample of interest on the surface of the image sensor and capture the direct shadow images under the illumination. By taking advantage of the inherent motion of the microorganisms, we achieve high resolution (~1 \u00b5m) imaging and long term culture of motile microorganisms over ultra large field-of-view (5.7 mm \u00d7 4.4 mm) in a specialized ePetri platform. We apply the pixel super-resolution reconstruction to a set of low-resolution shadow images of the microorganisms as they move across the sensing area of an image sensor chip and render an improved resolution image. We perform longitudinal study of Euglena gracilis cultured in an ePetri platform and image based analysis on the motion and morphology of the cells. The ePetri device for imaging non-motile cells are also demonstrated, by using the sweeping illumination of a light emitting diode (LED) matrix for pixel super-resolution reconstruction of sub-pixel shifted shadow images. Using this prototype device, we demonstrate the detection of waterborne parasites for the effective diagnosis of enteric parasite infection in resource-limited settings.
\r\n\r\nThen, we demonstrate the adaptation of a smartphone\u2019s camera to function as a compact lensless microscope, which uses ambient illumination as its light source and does not require the incorporation of a dedicated light source. The method is also based on the image reconstruction with sweeping illumination technique, where the sequence of images are captured while the user is manually tilting the device around any ambient light source, such as the sun or a lamp. Image acquisition and reconstruction is performed on the device using a custom-built android application, constructing a stand-alone imaging device for field applications. We discuss the construction of the device using a commercial smartphone and demonstrate the imaging capabilities of our system.
\r\n\r\nFinally, we report on the implementation of fluorescence chip-scale microscope, based on a silo-filter structure fabricated on the pixel array of a CMOS image sensor. The extruded pixel design with metal walls between neighboring pixels successfully guides fluorescence emission through the thick absorptive filter to the photodiode layer of a pixel. Our silo-filter CMOS image sensor prototype achieves 13-\u00b5m resolution for fluorescence imaging over a wide field-of-view (4.8 mm \u00d7 4.4 mm). Here, we demonstrate bright-field and fluorescence longitudinal imaging of living cells in a compact, low-cost configuration.
\r\n", "doi": "10.7907/HNWJ-J182", "publication_date": "2014", "thesis_type": "phd", "thesis_year": "2014" }, { "id": "thesis:7217", "collection": "thesis", "collection_id": "7217", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09292012-041022964", "type": "thesis", "title": "On Delay and Security in Network Coding", "author": [ { "family_name": "Dikaliotis", "given_name": "Theodoros K.", "clpid": "Dikaliotis-Theodoros-K" } ], "thesis_advisor": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" } ], "thesis_committee": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Effros", "given_name": "Michelle", "orcid": "0000-0003-3757-0675", "clpid": "Effros-M" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Low", "given_name": "Steven H.", "orcid": "0000-0001-6476-3048", "clpid": "Low-S-H" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, delay and security issues in network coding are considered. First, we study the delay incurred in the transmission of a fixed number of packets through acyclic networks comprised of erasure links. The two transmission schemes studied are routing with hop-by-hop retransmissions, where every node in the network simply stores and forwards its received packets, and linear coding, where nodes mix their packets by forwarding linear combinations of all their previously received packets. We show that even though the achievable rates of coding and routing are the same, network coding can have an increasingly better performance than routing as the number of packets increases.
\r\n\r\nSecondly, we investigate the security benefits of network coding. We investigate the achievable secrecy rate region in a general network of noisy wiretap channels with general communication demands. The eavesdropper has access to an unknown set of links, and on the wiretapped links observes a degraded version of the intended receiver's observation. While characterizing the capacity in general is an open problem, in the noise-free case there exist inner and outer bounds. In the noisy case, we show how one can change any of the wiretap channels to a noiseless degraded broadcast channel, so that the derived network's rate region bounds, and under certain conditions is equivalent, to that of the initial network. Specifically, we showed that in case the eavesdropper can choose only a single link to wiretap at each time, then one can change all the links in the network with corresponding noiseless ones, creating an equivalent noiseless secrecy problem. In the case where the eavesdropper can wiretap multiple links simultaneously, we derive upper and lower bounding noiseless network problems.
\r\n\r\nFinally, we consider design practical code design for the detection of adversarial errors in a distributed storage system. We build on work of functions that can fool linear polynomials to create and communicate hash functions of the data in order to detect with high probability the maliciously attacked nodes in the system.
", "doi": "10.7907/1KE1-DW91", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7217", "collection": "thesis", "collection_id": "7217", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:09292012-041022964", "type": "thesis", "title": "On Delay and Security in Network Coding", "author": [ { "family_name": "Dikaliotis", "given_name": "Theodoros K.", "clpid": "Dikaliotis-Theodoros-K" } ], "thesis_advisor": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" } ], "thesis_committee": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Effros", "given_name": "Michelle", "orcid": "0000-0003-3757-0675", "clpid": "Effros-M" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Low", "given_name": "Steven H.", "orcid": "0000-0001-6476-3048", "clpid": "Low-S-H" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, delay and security issues in network coding are considered. First, we study the delay incurred in the transmission of a fixed number of packets through acyclic networks comprised of erasure links. The two transmission schemes studied are routing with hop-by-hop retransmissions, where every node in the network simply stores and forwards its received packets, and linear coding, where nodes mix their packets by forwarding linear combinations of all their previously received packets. We show that even though the achievable rates of coding and routing are the same, network coding can have an increasingly better performance than routing as the number of packets increases.
\r\n\r\nSecondly, we investigate the security benefits of network coding. We investigate the achievable secrecy rate region in a general network of noisy wiretap channels with general communication demands. The eavesdropper has access to an unknown set of links, and on the wiretapped links observes a degraded version of the intended receiver's observation. While characterizing the capacity in general is an open problem, in the noise-free case there exist inner and outer bounds. In the noisy case, we show how one can change any of the wiretap channels to a noiseless degraded broadcast channel, so that the derived network's rate region bounds, and under certain conditions is equivalent, to that of the initial network. Specifically, we showed that in case the eavesdropper can choose only a single link to wiretap at each time, then one can change all the links in the network with corresponding noiseless ones, creating an equivalent noiseless secrecy problem. In the case where the eavesdropper can wiretap multiple links simultaneously, we derive upper and lower bounding noiseless network problems.
\r\n\r\nFinally, we consider design practical code design for the detection of adversarial errors in a distributed storage system. We build on work of functions that can fool linear polynomials to create and communicate hash functions of the data in order to detect with high probability the maliciously attacked nodes in the system.
", "doi": "10.7907/1KE1-DW91", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7758", "collection": "thesis", "collection_id": "7758", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05282013-115316389", "type": "thesis", "title": "Transceiver Designs and Analysis for LTI, LTV and Broadcast Channels - New Matrix Decompositions and Majorization Theory", "author": [ { "family_name": "Liu", "given_name": "Chih-Hao", "clpid": "Liu-Chih-Hao" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Quirk", "given_name": "Kevin J.", "clpid": "Quirk-K-J" }, { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.
\r\n\r\nIn this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.
\r\n\r\nThe first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.
\r\n\r\nIn the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. \r\nUnder the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.
\r\n\r\nThe third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.
\r\n\r\nFinally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.
\r\n", "doi": "10.7907/2VFF-SZ70", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7870", "collection": "thesis", "collection_id": "7870", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06072013-153438961", "type": "thesis", "title": "New Directions In Sparse Sampling and Estimation For Underdetermined Systems", "author": [ { "family_name": "Pal", "given_name": "Piya", "clpid": "Pal-Piya" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "van Zyl", "given_name": "Jakob J.", "clpid": "van-Zyl-J-J" }, { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A central objective in signal processing is to infer meaningful information from a set of measurements or data. While most signal models have an overdetermined structure (the number of unknowns less than the number of equations), traditionally very few statistical estimation problems have considered a data model which is underdetermined (number of unknowns more than the number of equations). However, in recent times, an explosion of theoretical and computational methods have been developed primarily to study underdetermined systems by imposing sparsity on the unknown variables. This is motivated by the observation that inspite of the huge volume of data that arises in sensor networks, genomics, imaging, particle physics, web search etc., their information content is often much smaller compared to the number of raw measurements. This has given rise to the possibility of reducing the number of measurements by down sampling the data, which automatically gives rise to underdetermined systems.
\r\n\r\nIn this thesis, we provide new directions for estimation in an underdetermined system, both for a class of parameter estimation problems and also for the problem of sparse recovery in compressive sensing. There are two main contributions of the thesis: design of new sampling and statistical estimation algorithms for array processing, and development of improved guarantees for sparse reconstruction by introducing a statistical framework to the recovery problem.
\r\n\r\nWe consider underdetermined observation models in array processing where the number of unknown sources simultaneously received by the array can be considerably larger than the number of physical sensors. We study new sparse spatial sampling schemes (array geometries) as well as propose new recovery algorithms that can exploit priors on the unknown signals and unambiguously identify all the sources. The proposed sampling structure is generic enough to be extended to multiple dimensions as well as to exploit different kinds of priors in the model such as correlation, higher order moments, etc.
\r\n\r\nRecognizing the role of correlation priors and suitable sampling schemes for underdetermined estimation in array processing, we introduce a correlation aware framework for recovering sparse support in compressive sensing. We show that it is possible to strictly increase the size of the recoverable sparse support using this framework provided the measurement matrix is suitably designed. The proposed nested and coprime arrays are shown to be appropriate candidates in this regard. We also provide new guarantees for convex and greedy formulations of the support recovery problem and demonstrate that it is possible to strictly improve upon existing guarantees.
\r\n\r\nThis new paradigm of underdetermined estimation that explicitly establishes the fundamental interplay between sampling, statistical priors and the underlying sparsity, leads to exciting future research directions in a variety of application areas, and also gives rise to new questions that can lead to stand-alone theoretical results in their own right.
\r\n\r\n", "doi": "10.7907/P0E1-5G05", "publication_date": "2013", "thesis_type": "phd", "thesis_year": "2013" }, { "id": "thesis:7100", "collection": "thesis", "collection_id": "7100", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302012-155108063", "type": "thesis", "title": "Distributed Control and Computing: Optimal Estimation, Error Correcting Codes, and Interactive Protocols", "author": [ { "family_name": "Sukhavasi", "given_name": "Ravi Teja", "clpid": "Sukhavasi-Ravi-Teja" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Doyle", "given_name": "John Comstock", "orcid": "0000-0002-1828-2486", "clpid": "Doyle-J-C" }, { "family_name": "Murray", "given_name": "Richard M.", "clpid": "Murray-R-M" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Emerging applications of networked control and distributed computing are characterized by decentralization of information and the need to exchange it over potentially unreliable communication networks. This results in novel interactive communication scenarios that are incompatible with conventional information and coding theoretic approaches. To address this gap, through the early and late 1990's, a new information theoretic notion called anytime reliability and a new coding paradigm called tree codes were proposed. Although the central role of tree codes in several interactive communication problems such as distributed control and computing has been well understood, there have been no practical constructions till date. For the first time, we have an explicit ensemble of linear tree codes with efficient encoding and decoding for the class of erasure channels. In the process, we have developed novel non-asymptotic sufficient conditions on the kind of communication reliability required to stabilize control systems over noisy channels. We also study the application of tree codes to interactive protocols over erasure networks and illustrate their benefits through the example of average consensus.", "doi": "10.7907/7431-FH32", "publication_date": "2012", "thesis_type": "phd", "thesis_year": "2012" }, { "id": "thesis:7074", "collection": "thesis", "collection_id": "7074", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05242012-174045229", "primary_object_url": { "basename": "Thesis_HsiChunLiu.pdf", "content": "final", "filesize": 2427683, "license": "other", "mime_type": "application/pdf", "url": "/7074/1/Thesis_HsiChunLiu.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Theory and Experiment of Slow-Light Coupled-Resonator Structures", "author": [ { "family_name": "Liu", "given_name": "Hsi-Chun", "clpid": "Liu-Hsi-Chun" } ], "thesis_advisor": [ { "family_name": "Yariv", "given_name": "Amnon", "clpid": "Yariv-A" } ], "thesis_committee": [ { "family_name": "Yariv", "given_name": "Amnon", "clpid": "Yariv-A" }, { "family_name": "Crosignani", "given_name": "Bruno", "clpid": "Crosignani-B" }, { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Vahala", "given_name": "Kerry J.", "clpid": "Vahala-K-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Slow light has been an inter-disciplinary topic and a rapidly growing area, especially over the last decade with the improvement of fabrication technology. The ability to slow down and control the group velocity of light may find applications such as optical buffers, optical delay lines, and enhanced light-matter interaction in optical modulator, amplifier, detectors, lasers, and nonlinear optics. The spirit of slow light is to replace a bulky device with a much shorter, compact structure.
\r\n\r\nThis thesis explores the design and experiment of coupled-resonator optical waveguides (CROWs), which consist of arrays of optical resonators in which light propagates through the coupling between resonators. The group velocity of light is dictated by the inter-resonator coupling strength. Light can be significantly slowed down if the inter-resonator coupling is weak. CROWs can be realized with various types of resonators. This thesis focuses on grating resonators in silicon waveguides, including grating-defect resonators and bandgap-modulated resonators. With the strong gratings, the grating resonators are only a few microns long. We control the inter-resonator coupling via the number of holes between adjacent resonators.
\r\n\r\nThe major limitations in the realization of CROWs have been various kinds of transmission losses, including the resonator losses, the discontinuity between CROWs and the coupling waveguides, and the fabrication disorder. These transmission losses limit the achievable group velocity and the maximum number of resonators. We address these transmission losses throughout this thesis. The resonator losses are overcome with the design and optimized fabrication of tapered grating-defect resonators and bandgap-modulated resonators. The discontinuity between CROWs and waveguides is reduced by tailoring the coupling along the CROW for adiabatic conversion. The optimization of the CROW response leads to the study of filter design based on CROW. Filter design formalism based on coupled-mode theory is presented. The effect of fabrication disorder on CROWs is analyzed, and the Butterworth filters are shown to be more robust against fabrication disorder. The fabrication and measurement of grating CROWs are presented, featuring high-Q (Q=105) grating resonators, coupling of up to 50 resonators, control of group velocity between c/13 and c/49, and Butterworth filters.
\r\n\r\nFinally, an optical analog of electromagnetically induced transparency is presented. The structure consists of two co-spatial gratings imposed on a three-mode waveguide. One of the supermodes, the Dark mode, possesses a group velocity which depends on the ratio of the grating strengths. The group velocity can be nearly zero if the two grating strengths are nearly identical.
\r\n", "doi": "10.7907/GVBF-4T29", "publication_date": "2012", "thesis_type": "phd", "thesis_year": "2012" }, { "id": "thesis:7142", "collection": "thesis", "collection_id": "7142", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06072012-001523622", "primary_object_url": { "basename": "Thesis_Feb1.pdf", "content": "final", "filesize": 4981655, "license": "other", "mime_type": "application/pdf", "url": "/7142/1/Thesis_Feb1.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Combinatorial Regression and Improved Basis Pursuit for Sparse Estimation", "author": [ { "family_name": "Khajehnejad", "given_name": "M. Amin", "clpid": "Khajehnejad-M-Amin" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tropp", "given_name": "Joel A.", "orcid": "0000-0003-1024-1791", "clpid": "Tropp-J-A" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Dimakis", "given_name": "Alexandros G.", "orcid": "0000-0002-4244-7033", "clpid": "Dimakis-A-G" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Sparse representations accurately model many real-world data sets. Some form of sparsity is conceivable in almost every practical application, from image and video processing, to spectral sensing in radar detection, to bio-computation and genomic signal processing. Modern statistics and estimation theory have come up with ways for efficiently accounting for sparsity in enhanced information retrieval systems. In particular, \\emph{compressed sensing} and \\emph{matrix rank minimization} are two newly born branches of dimensionality reduction techniques, with very promising horizons. Compressed sensing addresses the reconstruction of sparse signals from ill-conditioned linear measurements, a mathematical problem that arises in practical applications in one of the following forms: model fitting (regression), analog data compression, sub-Nyquist sampling, and data privacy. Low-rank matrix estimation addresses the reconstruction of multi-dimensional data (matrices) with strong coherence properties (low rank) under restricted sensing. This model is motivated by modern problems in machine learning, dynamic systems, and quantum computing.
\r\n\r\nThis thesis provides an in-depth study of recent developments in the fields of compressed sensing and matrix rank minimization, and sets forth new directions for improved sparse recovery techniques. The contributions are threefold: the design of combinatorial structures for sparse encoding, the development of improved recovery algorithms, and extension of sparse vector recovery techniques to other problems.
\r\n\r\nWe propose combinatorial structures for the measurement matrix that facilitate compressing sparse analog signal representations with better guarantees than any of the currently existing architectures. Our constructions are mostly deterministic and are based on ideas from expander graphs, LDPC error-correcting codes and combinatorial separators.
\r\n\r\nWe propose novel reconstruction algorithms that are amenable to the combinatorial structures we study, and have various advantages over the conventional convex optimization techniques for sparse recovery. In addition, we separately study the convex optimization Basis Pursuit method for compressed sensing, and propose regularization schemes that expand the success domain for such algorithms. Our studies contain rigorous analysis, numerical simulations, and examples from practical applications.
\r\n\r\nLastly, we extend some of our proposed techniques to low-rank matrix estimation and channel coding. These generalizations lead to the development of a novel and fast reconstruction algorithm for matrix rank minimization, and a modified regularized linear-programming-based decoding algorithm for detecting codewords of a linear LDPC code during an erroneous communication.
\r\n", "doi": "10.7907/04J6-Y832", "publication_date": "2012", "thesis_type": "phd", "thesis_year": "2012" }, { "id": "thesis:7100", "collection": "thesis", "collection_id": "7100", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:05302012-155108063", "type": "thesis", "title": "Distributed Control and Computing: Optimal Estimation, Error Correcting Codes, and Interactive Protocols", "author": [ { "family_name": "Sukhavasi", "given_name": "Ravi Teja", "clpid": "Sukhavasi-Ravi-Teja" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Doyle", "given_name": "John Comstock", "orcid": "0000-0002-1828-2486", "clpid": "Doyle-J-C" }, { "family_name": "Murray", "given_name": "Richard M.", "clpid": "Murray-R-M" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Emerging applications of networked control and distributed computing are characterized by decentralization of information and the need to exchange it over potentially unreliable communication networks. This results in novel interactive communication scenarios that are incompatible with conventional information and coding theoretic approaches. To address this gap, through the early and late 1990's, a new information theoretic notion called anytime reliability and a new coding paradigm called tree codes were proposed. Although the central role of tree codes in several interactive communication problems such as distributed control and computing has been well understood, there have been no practical constructions till date. For the first time, we have an explicit ensemble of linear tree codes with efficient encoding and decoding for the class of erasure channels. In the process, we have developed novel non-asymptotic sufficient conditions on the kind of communication reliability required to stabilize control systems over noisy channels. We also study the application of tree codes to interactive protocols over erasure networks and illustrate their benefits through the example of average consensus.", "doi": "10.7907/7431-FH32", "publication_date": "2012", "thesis_type": "phd", "thesis_year": "2012" }, { "id": "thesis:6495", "collection": "thesis", "collection_id": "6495", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06022011-214438378", "type": "thesis", "title": "Random Matrix Recursions in Estimation, Control, and Adaptive Filtering", "author": [ { "family_name": "Vakili", "given_name": "Ali", "clpid": "Vakili-Ali" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" }, { "family_name": "Murray", "given_name": "Richard M.", "clpid": "Murray-R-M" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This dissertation is devoted to the study of estimation and control over systems that can be described by linear time-varying state-space models. Examples of such systems are encountered frequently in systems theory, e.g., wireless sensor networks, adaptive filtering, distributed control, etc. Recent developments in distributed catastrophe surveillance, smart transportation, and power grid control systems further motivate such a study.
\r\n\r\nWhile linear time-invariant systems are well-understood, there is no general theory that captures various aspects of time-varying counterparts. With little exception, tackling these problems normally boils down to studying time-varying linear or non-linear recursive matrix equations, known as Lyapunov and Riccati recursions that are notoriously hard to analyze. We employ the theory of random matrices to elucidate different facets of these recursions and answer several important questions about the performance, stability, and convergence of estimation and control over such systems.
\r\n\r\nWe make two general assumptions. First, we assume that the coefficient matrices are drawn from jointly stationary matrix-valued random processes. The stationarity assumption hardly restricts the analysis since almost all cases of practical interest fall into this category. We further assume that the state vector size, n, is relatively large. The law of large numbers however guarantees fast convergence to the asymptotic results for n being as small as 10. Under these assumptions, we develop a framework capable of characterizing steady-state and transient behavior of adaptive filters and control and estimation over communication networks. This framework proves promising by successfully tackling several problems for the first time in the literature.
\r\n\r\nWe first study random Lyapunov recursions and characterize their transient and steady-state behavior. Lyapunov recursions appear in several classes of adaptive filters and also as lower bounds of random Riccati recursions in distributed Kalman filtering. We then look at random Riccati recursions whose nonlinearity makes them much more complicated to study. We investigate standard recursive-least-squares (RLS) filtering and extend our analysis beyond the standard case to filtering with multiple measurements, as well as the case of intermittent measurements. Finally, we study Kalman filtering with intermittent observations, which is frequently used to model wireless sensor networks. In all of these cases we obtain interesting universal laws that depend on the structure of the problem, rather than specific model parameters. We verify the accuracy of our results through various simulations for systems with as few as 10 states.
\r\n", "doi": "10.7907/HCKN-7W53", "publication_date": "2011", "thesis_type": "phd", "thesis_year": "2011" }, { "id": "thesis:6514", "collection": "thesis", "collection_id": "6514", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06092011-140731576", "type": "thesis", "title": "Entropy Region and Network Information Theory", "author": [ { "family_name": "Shadbakht", "given_name": "Sormeh", "clpid": "Shadbakht-Sormeh" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wierman", "given_name": "Adam C.", "orcid": "0000-0002-5923-0199", "clpid": "Wierman-A-C" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This dissertation takes a step toward a general framework for solving network information theory problems by studying the capacity region of networks through the entropy region.
\r\n\r\nWe first show that the capacity of a large class of acyclic memoryless multiuser information theory problems can be formulated as convex optimization over the region of entropy vectors of the network random variables. This capacity characterization is universal, and is advantageous over previous formulations in that it is single letter. Besides, it is significant as it reveals the fundamental role of the entropy region in determining the capacity of network information theory problems.
\r\n\r\nWith this viewpoint, the rest of the thesis is dedicated to the study of the entropy region, and its consequences for networks. A full characterization of the entropy region has proven to be a very challenging problem, and thus, we mostly consider inner bound constructions. For discrete random variables, our approaches include characterization of entropy vectors with a lattice-derived probability distribution, the entropy region of binary random variables, and the linear representable region. Through these characterizations, and using matroid representability results, we study linear coding capacity of networks in different scenarios (e.g., binary operations in a network, or networks with two sources).
\r\n\r\nWe also consider continuous random variables by studying the entropy region of jointly Gaussian random variables. In particular, we determine the sufficiency of Gaussian random variables for characterizing the entropy region of 3 random variables in general. For more than 3 random variables, we point out the set of minimal necessary and sufficient conditions for a vector to be an entropy vector of jointly Gaussian random variables.
\r\n\r\nFinally, in the absence of a full analytical characterization of the entropy region, it is desirable to be able to perform numerical optimization over this space. In this regard, we propose a certain Monte Carlo method that enables one to numerically optimize entropy functions of discrete random variables, and also the achievable rates in wired networks. This method can be further adjusted for decentralized operation of networks. The promise of this technique is shown through various simulations of several interesting network problems.
\r\n", "doi": "10.7907/P8ZB-4D40", "publication_date": "2011", "thesis_type": "phd", "thesis_year": "2011" }, { "id": "thesis:6496", "collection": "thesis", "collection_id": "6496", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06032011-113200456", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 2489805, "license": "other", "mime_type": "application/pdf", "url": "/6496/1/thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "The Roles of Majorization and Generalized Triangular Decomposition in Communication and Signal Processing", "author": [ { "family_name": "Weng", "given_name": "Ching-Chih", "clpid": "Weng-Ching-Chih" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Quirk", "given_name": "Kevin J.", "clpid": "Quirk-K-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Signal processing is an art that deals with the representation, transformation, and manipulation of the signals and the information they contain based on their specific features. The field of signal processing has always benefited from the interaction between theory, applications, and technologies for implementing the systems. The development of signal processing theory, in particular, relies heavily on mathematical tools including analysis, probability theory, matrix theory, and many others.
\r\n\r\nRecently, the theory of majorization, which is an extremely useful tool for deriving inequalities, was introduced to the signal processing society in the context of MIMO communication system design. This also led many researchers to develop a fundamental matrix decomposition called generalized triangular decomposition (GTD), which was general enough to include many existing matrix orthogonal decompositions as special cases.
\r\n\r\nThe main contribution of this thesis is toward the use of majorization and GTD to the theory and many applications of signal processing. In particular, the focus is on developing new signal processing methods based on these mathematical tools for digital communication, data compression, and filter bank design. We revisit some classical problems and show that the theories of majorization and GTD provide a general framework for solving these problems. For many important new problems not solved earlier, they also provide elegant solutions.
\r\n\r\nThe first part of the thesis focuses on transceiver design for multiple-input multiple-output (MIMO) communications. The first problem considered is the joint optimization of transceivers with linear precoders, decision feedback equalizers (DFEs), and bit allocation schemes for frequency flat MIMO channels. We show that the generalized triangular decomposition offers an optimal family of solutions to this problem. This general framework incorporates many existing designs, such as the optimal linear transceiver, the ZF-VBLAST system, and the geometric mean decomposition (GMD) transceiver, as special cases. It also predicts many novel optimal solutions that have not been observed before. We also discuss the use of each of these theoretical solutions under practical considerations. In addition to total power constraints, we also consider the transceiver optimization under individual power constraints and other linear constraints on the transmitting covariance matrix, which includes a more realistic individual power constraint on each antenna. We show the use of semi-definite programming (SDP), and the theory of majorization again provides a general framework for optimizing the linear transceivers as well as the DFE transceivers. The transceiver design for frequency selective MIMO channels is then considered. Block diagonal GMD (BD-GMD), which is a special instance of GTD with block diagonal structure in one of the semi-unitary matrices, is used to design transceivers that have many desirable properties in both performance and computation.
\r\n\r\nThe second part of the thesis focuses on signal processing algorithms for data compressions and filter bank designs. We revisit the classical transform coding problem (for optimizing the theoretical coding gain in the high bit rate regime) from the view point of GTD and majorization theory. A general family of optimal transform coders is introduced based on GTD. This family includes the Karhunen-Lo\\'{e}ve transform (KLT), and the prediction-based lower triangular transform (PLT) as special cases. The coding gain of the entire family, with optimal bit allocation, is maximized and equal to those of the KLT and the PLT. Other special cases of the GTD-TC are the GMD (geometric mean decomposition) and the BID (bidiagonal transform). The GMD in particular has the property that the optimum bit allocation is a uniform allocation. We also propose using dither quantization in the GMD transform coder. Under the uniform bit loading scheme, it is shown that the proposed dithered GMD transform coders perform significantly better than the original GMD coder in the low rate regime.
\r\n\r\nAnother important signal processing problem, namely the filter bank optimization based on the knowledge of input signal statistics, is then considered. GTD and the theory of majorization are again used to give a new look to this classical problem. We propose GTD filter banks as subband coders for optimizing the theoretical coding gain. The orthonormal GTD filter bank and the biorthogonal GTD filter bank are discussed in detail. We show that in both cases there are two fundamental properties in the optimal solutions, namely, {\\it total decorrelation} and {\\it spectrum equalization}. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband coders have superior performance than optimal traditional subband coders. In addition, the uniform bit loading scheme can be used in the optimal biorthogonal GTD coders with no loss of optimality. This solves the granularity problem in the conventional optimum bit loading formula. The use of the GTD filter banks in frequency selective MIMO communication systems is also discussed. Finally, the connection between the GTD filter bank and the traditional filter bank is clearly indicated.
\r\n", "doi": "10.7907/2R1B-QE65", "publication_date": "2011", "thesis_type": "phd", "thesis_year": "2011" }, { "id": "thesis:6514", "collection": "thesis", "collection_id": "6514", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:06092011-140731576", "type": "thesis", "title": "Entropy Region and Network Information Theory", "author": [ { "family_name": "Shadbakht", "given_name": "Sormeh", "clpid": "Shadbakht-Sormeh" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wierman", "given_name": "Adam C.", "orcid": "0000-0002-5923-0199", "clpid": "Wierman-A-C" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This dissertation takes a step toward a general framework for solving network information theory problems by studying the capacity region of networks through the entropy region.
\r\n\r\nWe first show that the capacity of a large class of acyclic memoryless multiuser information theory problems can be formulated as convex optimization over the region of entropy vectors of the network random variables. This capacity characterization is universal, and is advantageous over previous formulations in that it is single letter. Besides, it is significant as it reveals the fundamental role of the entropy region in determining the capacity of network information theory problems.
\r\n\r\nWith this viewpoint, the rest of the thesis is dedicated to the study of the entropy region, and its consequences for networks. A full characterization of the entropy region has proven to be a very challenging problem, and thus, we mostly consider inner bound constructions. For discrete random variables, our approaches include characterization of entropy vectors with a lattice-derived probability distribution, the entropy region of binary random variables, and the linear representable region. Through these characterizations, and using matroid representability results, we study linear coding capacity of networks in different scenarios (e.g., binary operations in a network, or networks with two sources).
\r\n\r\nWe also consider continuous random variables by studying the entropy region of jointly Gaussian random variables. In particular, we determine the sufficiency of Gaussian random variables for characterizing the entropy region of 3 random variables in general. For more than 3 random variables, we point out the set of minimal necessary and sufficient conditions for a vector to be an entropy vector of jointly Gaussian random variables.
\r\n\r\nFinally, in the absence of a full analytical characterization of the entropy region, it is desirable to be able to perform numerical optimization over this space. In this regard, we propose a certain Monte Carlo method that enables one to numerically optimize entropy functions of discrete random variables, and also the achievable rates in wired networks. This method can be further adjusted for decentralized operation of networks. The promise of this technique is shown through various simulations of several interesting network problems.
\r\n", "doi": "10.7907/P8ZB-4D40", "publication_date": "2011", "thesis_type": "phd", "thesis_year": "2011" }, { "id": "thesis:5295", "collection": "thesis", "collection_id": "5295", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10122009-094525715", "type": "thesis", "title": "Instrumentation for Wide Bandwidth Radio Astronomy", "author": [ { "family_name": "Jones", "given_name": "Glenn Evans", "clpid": "Jones-Glenn-Evans" } ], "thesis_advisor": [ { "family_name": "Weinreb", "given_name": "Sander", "orcid": "0000-0002-9353-6204", "clpid": "Weinreb-S" } ], "thesis_committee": [ { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Weinreb", "given_name": "Sander", "orcid": "0000-0002-9353-6204", "clpid": "Weinreb-S" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Readhead", "given_name": "Anthony C. S.", "orcid": "0000-0001-9152-961X", "clpid": "Readhead-A-C-S" }, { "family_name": "Kuiper", "given_name": "Thomas B. H.", "clpid": "Kuiper-T-B-H" }, { "family_name": "Jarnot", "given_name": "Robert F.", "clpid": "Jarnot-R-F" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Centimeter wavelength radio astronomy spans approximately two decades in frequency, from roughly 500 MHz to 50 GHz. In contrast, radio astronomy instruments have traditionally been limited to at most octave bandwidths, necessitating multiple instruments on a given telescope to cover a large fraction of the spectrum. This paradigm is infeasible for the next generation of telescopes, which will likely consist of hundreds to thousands of small dishes combined together in an array, because each receiver must be replicated for each element in the array. Therefore, wide bandwidth instrumentation must be developed for radio astronomy.
\r\n\r\nThis thesis presents a novel radio telescope with excellent system noise temperature and reasonable efficiency across an instantaneous fractional bandwidth greater than 4:1; amongst the widest ever demonstrated. This instrument illustrates that extremely wide bandwidth instruments are feasible, even in the presence of terrestrial interference. To make use of the enormous instantaneous bandwidth, a flexible, high performance, and cost effective digital signal processing system is also presented. Theory, design, and measurements of special purpose digital spectrometers built to minimize the effects of terrestrial interference are included.
\r\n\r\nAside from the practical advantages offered by wide bandwidth instrumentation, new scientific applications are also made possible. A special purpose system for performing detailed studies of giant radio pulses from rotating neutron stars (pulsars) is presented, along with demonstrations including some of the largest fractional bandwidth observations of these pulses made to date. This system includes a sensitive trigger which corrects for the dispersive effects of the interstellar medium in real time and a deep capture buffer optimized for observing repetitive transient phenomena. Measurements made using the trigger system at Arecibo Observatory are also presented to demonstrate the portability of the instrument.
", "doi": "10.7907/BMZR-P813", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5329", "collection": "thesis", "collection_id": "5329", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10262009-081233260", "primary_object_url": { "basename": "Thesis.pdf", "content": "final", "filesize": 1662489, "license": "other", "mime_type": "application/pdf", "url": "/5329/1/Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Compressive Sensing for Sparse Approximations: Constructions, Algorithms, and Analysis", "author": [ { "family_name": "Xu", "given_name": "Weiyu", "clpid": "Xu-Weiyu" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Candes", "given_name": "Emmanuel J.", "clpid": "Candes-E-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Tropp", "given_name": "Joel A.", "clpid": "Tropp-J-A" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Compressive sensing is an emerging research field that has applications in signal processing, error correction, medical imaging, seismology, and many more other areas. It promises to efficiently recover a sparse signal vector via a much smaller number of linear measurements than its dimension. Naturally, how to design these linear measurements, how to construct the original high-dimensional signals efficiently and accurately, and how to analyze the sparse signal recovery algorithms are important issues in the developments of compressive sensing. This thesis is devoted to addressing these fundamental issues in the field of compressive sensing.
\r\n\r\nIn compressive sensing, random measurement matrices are generally used and \u2113\u2081 minimization algorithms often use linear programming or other optimization methods to recover the sparse signal vectors. But explicitly constructible measurement matrices providing performance guarantees were elusive and \u2113\u2081 minimization algorithms are often very demanding in computational complexity for applications involving very large problem dimensions. In chapter 2, we propose and discuss a compressive sensing scheme with deterministic performance guarantees using deterministic explicitly constructible expander graph-based measurement matrices and show that the sparse signal recovery can be achieved with linear complexity. This is the first of such a kind of compressive sensing scheme with linear decoding complexity, deterministic performance guarantees of linear sparsity recovery, and deterministic explicitly constructible measurement matrices.
\r\n\r\nThe popular and powerful \u2113\u2081 minimization algorithms generally give better sparsity recovery performances than known greedy decoding algorithms. In chapter 3, starting from a necessary and sufficient null-space condition for achieving a certain signal recovery accuracy, using high-dimensional geometry, we give a unified null-space Grassmann angle-based analytical framework for compressive sensing. This new framework gives sharp quantitative trade-offs between the signal sparsity and the recovery accuracy of the \u2113\u2081 optimization for approximately sparse signal. Our results concern the fundamental \"balancedness\" properties of linear subspaces and so may be of independent mathematical interest.
\r\n\r\nThe conventional approach to compressed sensing assumes no prior information on the unknown signal other than the fact that it is sufficiently sparse over a particular basis. In many applications, however, additional prior information is available. In chapter 4, we will consider a particular model for the sparse signal that assigns a probability of being zero or nonzero to each entry of the unknown vector. The standard compressed sensing model is therefore a special case where these probabilities are all equal. Following the introduction of the null-space Grassmann angle-based analytical framework in this thesis, we are able to characterize the optimal recoverable sparsity thresholds using weighted \u2113\u2081 minimization algorithms with the prior information.
\r\n\r\nThe roles of \u2113\u2081 minimization algorithm in recovering sparse signals from incomplete measurements are now well understood, and sharp recoverable sparsity thresholds for \u2113\u2081 minimization have been obtained. The iterative reweighted \u2113\u2081 minimization algorithms or related algorithms have been empirically observed to boost the recoverable sparsity thresholds for certain types of signals, but no rigorous theoretical results have been established to prove this fact. In chapter 5, we try to provide a theoretical foundation for analyzing the iterative reweighted \u2113\u2081 algorithms. In particular, we show that for a nontrivial class of signals, the iterative reweighted \u2113\u2081 minimization can indeed deliver recoverable sparsity thresholds larger than the \u2113\u2081 minimization. Again, our results are based on the null-space Grassmann angle-based analytical framework.
\r\n\r\nEvolving from compressive sensing problems, where we are interested in recovering sparse vector signals from compressed linear measurements, we will turn our attention to recovering matrices of low rank from compressed linear measurements in chapter 6, which is a challenging problem that arises in many applications in machine learning, control theory, and discrete geometry. This class of optimization problems is NP-HARD, and for most practical problems there are no efficient algorithms that yield exact solutions. A popular heuristic replaces the rank function with the nuclear norm of the decision variable and has been shown to provide the optimal low rank solution in a variety of scenarios. We analytically assess the practical performance of this heuristic for finding the minimum rank matrix subject to linear constraints. We start from the characterization of a necessary and sufficient condition that determines when this heuristic finds the minimum rank solution. We then obtain probabilistic bounds on the matrix dimensions and rank and the number of constraints, such that our conditions for success are satisfied for almost all linear constraint sets as the matrix dimensions tend to infinity. Empirical evidence shows that these probabilistic bounds provide accurate predictions of the heuristic's performance in non-asymptotic scenarios.
", "doi": "10.7907/F63K-GT12", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5279", "collection": "thesis", "collection_id": "5279", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09062009-213639", "primary_object_url": { "basename": "Thesis.pdf", "content": "final", "filesize": 1213699, "license": "other", "mime_type": "application/pdf", "url": "/5279/1/Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Coding for Wireless Broadcast and Network Secrecy", "author": [ { "family_name": "Cui", "given_name": "Tao", "clpid": "Cui-Tao" } ], "thesis_advisor": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" } ], "thesis_committee": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Effros", "given_name": "Michelle", "orcid": "0000-0003-3757-0675", "clpid": "Effros-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Low", "given_name": "Steven H.", "orcid": "0000-0001-6476-3048", "clpid": "Low-S-H" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the first part of this thesis, we exploit wireless broadcast across different layers in wireless networks. The wireless channel is distinguished by its broadcast nature. Wireless broadcast provides a fertile ground to improve the efficiency of existing wireless networks and design new ones.
\r\n\r\nSpecifically, we first consider relaying strategies for memoryless two-way relay channels at the physical layer. We generalize networking layer network coding operating on a finite field to physical layer network coding, which is a mapping from the relay's received signal to its transmitted signal. We analyze the symbol-error performance of several relay strategies, and optimize the relay function via functional analysis. Our results indicate that the interference caused by wireless broadcast can be exploited to improve the spectrum efficiency.
\r\n\r\nWe then develop a cross-layer framework with wireless broadcast, which integrates rate control, network coding and scheduling in transport, network and link layers. Under the primary interference model, we show that the link scheduling problem is the maximum weighted hypergraph matching problem, which is NP-complete. We propose several distributed approximation algorithms and bound their worst case performance.
\r\n\r\nNext, we describe a new class of medium access control (MAC) protocol, which uses successive interference cancelation to resolve packet collision due to wireless broadcast. Each user is allowed to transmit at different data rates chosen randomly from an appropriately determined set of rates. We characterize the throughput of the proposed protocol compared to that with a centralized controller. A game-theoretic framework along with the dynamic algorithms is proposed to achieve the desired throughput optimal equilibrium, which provides a valuable perspective to understand existing MAC protocols and a general framework to design new ones to improve the system performance.
\r\n\r\nIn the second part of this thesis, we consider the problem of secure transmission in the presence of a wiretapper. Due to wireless broadcast, wireless signals are particularly easy to jam and intercept. We derive the secrecy capacity region for the case when the location of the wiretapped links is known and propose several achievable strategies for the case when such information is unknown. We give an example to show that the secrecy capacities of the two cases are generally unequal and show that in both cases computing the secrecy capacity is NP-complete.
\r\n", "doi": "10.7907/JYV2-DM74", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5279", "collection": "thesis", "collection_id": "5279", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09062009-213639", "primary_object_url": { "basename": "Thesis.pdf", "content": "final", "filesize": 1213699, "license": "other", "mime_type": "application/pdf", "url": "/5279/1/Thesis.pdf", "version": "v4.0.0" }, "type": "thesis", "title": "Coding for Wireless Broadcast and Network Secrecy", "author": [ { "family_name": "Cui", "given_name": "Tao", "clpid": "Cui-Tao" } ], "thesis_advisor": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" } ], "thesis_committee": [ { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Effros", "given_name": "Michelle", "orcid": "0000-0003-3757-0675", "clpid": "Effros-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Low", "given_name": "Steven H.", "orcid": "0000-0001-6476-3048", "clpid": "Low-S-H" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the first part of this thesis, we exploit wireless broadcast across different layers in wireless networks. The wireless channel is distinguished by its broadcast nature. Wireless broadcast provides a fertile ground to improve the efficiency of existing wireless networks and design new ones.
\r\n\r\nSpecifically, we first consider relaying strategies for memoryless two-way relay channels at the physical layer. We generalize networking layer network coding operating on a finite field to physical layer network coding, which is a mapping from the relay's received signal to its transmitted signal. We analyze the symbol-error performance of several relay strategies, and optimize the relay function via functional analysis. Our results indicate that the interference caused by wireless broadcast can be exploited to improve the spectrum efficiency.
\r\n\r\nWe then develop a cross-layer framework with wireless broadcast, which integrates rate control, network coding and scheduling in transport, network and link layers. Under the primary interference model, we show that the link scheduling problem is the maximum weighted hypergraph matching problem, which is NP-complete. We propose several distributed approximation algorithms and bound their worst case performance.
\r\n\r\nNext, we describe a new class of medium access control (MAC) protocol, which uses successive interference cancelation to resolve packet collision due to wireless broadcast. Each user is allowed to transmit at different data rates chosen randomly from an appropriately determined set of rates. We characterize the throughput of the proposed protocol compared to that with a centralized controller. A game-theoretic framework along with the dynamic algorithms is proposed to achieve the desired throughput optimal equilibrium, which provides a valuable perspective to understand existing MAC protocols and a general framework to design new ones to improve the system performance.
\r\n\r\nIn the second part of this thesis, we consider the problem of secure transmission in the presence of a wiretapper. Due to wireless broadcast, wireless signals are particularly easy to jam and intercept. We derive the secrecy capacity region for the case when the location of the wiretapped links is known and propose several achievable strategies for the case when such information is unknown. We give an example to show that the secrecy capacities of the two cases are generally unequal and show that in both cases computing the secrecy capacity is NP-complete.
\r\n", "doi": "10.7907/JYV2-DM74", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5295", "collection": "thesis", "collection_id": "5295", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10122009-094525715", "type": "thesis", "title": "Instrumentation for Wide Bandwidth Radio Astronomy", "author": [ { "family_name": "Jones", "given_name": "Glenn Evans", "clpid": "Jones-Glenn-Evans" } ], "thesis_advisor": [ { "family_name": "Weinreb", "given_name": "Sander", "orcid": "0000-0002-9353-6204", "clpid": "Weinreb-S" } ], "thesis_committee": [ { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Weinreb", "given_name": "Sander", "orcid": "0000-0002-9353-6204", "clpid": "Weinreb-S" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Readhead", "given_name": "Anthony C. S.", "orcid": "0000-0001-9152-961X", "clpid": "Readhead-A-C-S" }, { "family_name": "Kuiper", "given_name": "Thomas B. H.", "clpid": "Kuiper-T-B-H" }, { "family_name": "Jarnot", "given_name": "Robert F.", "clpid": "Jarnot-R-F" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Centimeter wavelength radio astronomy spans approximately two decades in frequency, from roughly 500 MHz to 50 GHz. In contrast, radio astronomy instruments have traditionally been limited to at most octave bandwidths, necessitating multiple instruments on a given telescope to cover a large fraction of the spectrum. This paradigm is infeasible for the next generation of telescopes, which will likely consist of hundreds to thousands of small dishes combined together in an array, because each receiver must be replicated for each element in the array. Therefore, wide bandwidth instrumentation must be developed for radio astronomy.
\r\n\r\nThis thesis presents a novel radio telescope with excellent system noise temperature and reasonable efficiency across an instantaneous fractional bandwidth greater than 4:1; amongst the widest ever demonstrated. This instrument illustrates that extremely wide bandwidth instruments are feasible, even in the presence of terrestrial interference. To make use of the enormous instantaneous bandwidth, a flexible, high performance, and cost effective digital signal processing system is also presented. Theory, design, and measurements of special purpose digital spectrometers built to minimize the effects of terrestrial interference are included.
\r\n\r\nAside from the practical advantages offered by wide bandwidth instrumentation, new scientific applications are also made possible. A special purpose system for performing detailed studies of giant radio pulses from rotating neutron stars (pulsars) is presented, along with demonstrations including some of the largest fractional bandwidth observations of these pulses made to date. This system includes a sensitive trigger which corrects for the dispersive effects of the interstellar medium in real time and a deep capture buffer optimized for observing repetitive transient phenomena. Measurements made using the trigger system at Arecibo Observatory are also presented to demonstrate the portability of the instrument.
", "doi": "10.7907/BMZR-P813", "publication_date": "2010", "thesis_type": "phd", "thesis_year": "2010" }, { "id": "thesis:5179", "collection": "thesis", "collection_id": "5179", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03292009-070752", "primary_object_url": { "basename": "Thesis-yujiu-final-20090331.pdf", "content": "final", "filesize": 3325286, "license": "other", "mime_type": "application/pdf", "url": "/5179/1/Thesis-yujiu-final-20090331.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Circuits and Systems for Wireless Concurrent Communication", "author": [ { "family_name": "Wang", "given_name": "Yu-Jiu", "orcid": "0000-0002-2534-1069", "clpid": "Wang-Yu-Jiu" } ], "thesis_advisor": [ { "family_name": "Hajimiri", "given_name": "Ali", "clpid": "Hajimiri-A" } ], "thesis_committee": [ { "family_name": "Hajimiri", "given_name": "Ali", "clpid": "Hajimiri-A" }, { "family_name": "Emami", "given_name": "Azita", "clpid": "Emami-A" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Weinreb", "given_name": "Sander", "clpid": "Weinreb-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Concurrency is a special kind of analog circuit parallelism that uses a single circuit with necessary bandwidth to process multiple signals at the same time. Concurrent radios offer a higher data rate and improved system diversity. Our comprehensive treatment comprises proposals for potential transceiver architectures, invention of circuit blocks, and provisions of innovative analysis methods.
\r\n\r\nThe analysis of concurrent circuits are often complex. To simplify noise analysis, a R^(N^2 )-vector space is first proposed to re-formulate the N-port network noise modeling problem. Any internal physical source inside the noisy network contributes a small vector in the defined R^(N^2)-vector space, and the aggregate statistical behavior of this noisy network can be viewed as the vector sum of these vectors. Applying this concept to FET noise modeling leads to several modified FET noise models, in which three uncorrelated noise sources are sufficient to describe the statistical behavior of an intrinsic FET. The use of these new FET models can simplify the analysis, simulation, and optimization of low noise systems without sacrificing accuracy.
\r\n\r\nBroadband low-noise amplifier is a critical block in concurrent receiver systems. We propose a novel low-noise weighted distributed amplifier (WDA) topology, which uses the internal finite-impulse-response filtering inside a conventional distributed amplifier to partially suppress internal thermal noise. A distinct advantage of this topology is its tolerance to input parasitic capacitance which can be used to provide good electro-static discharge (ESD) protection without sacrificing its noise performance and power consumption. A compact 3.1\u250010.6 GHz WDA IC is built on a 130 nm CMOS process. Experimental results show 2.3\u25004.5 dB NF at 23 mW power consumption.
\r\n\r\nUsing concurrency in wireless link can boost communication data rate. As a proof-of concept, we propose dynamically scalable concurrent communication by dividing the 7.5 GHz bandwidth of the unlicensed 3.1\u250010.6 GHz spectrum into seven concurrent channels. A CMOS octa-core RF receiver is implemented to validate the idea. Based on the receiver measurement results, a wireless link can be built to achieve a 16 Gbps channel limit at five meter TX-RX distance at 400 mW power consumption.
\r\n\r\nTunable concurrency can improve the receiver diversity. A prototype 6\u250018 GHz concurrent tunable dual-band phased array receiver element IC is proposed and built on a 130 nm CMOS process. Experimental results demonstrate successful dual-band RF reception within a low band (6\u250010.4 GHz) and high band (10.4\u250018 GHz) with 300 MHz baseband bandwidth. A final four-element phased array receiver built from the prototyped ICs shows an array pattern with worst-case 21 dB peak-to-null ratio across all frequencies.
\r\n\r\nConcurrency can also be used to achieve multi-beam reception by providing multiple phase-shifts for each RF signals and combining them separately at baseband outputs. A 10.4\u250018 GHz concurrent dual-beam phased array receiver is proposed based on this concept, and is implemented on a 130 nm CMOS process. A final four-element phased array system shows successful concurrent dual-beam reception at the same RF frequency.
Yu-Jiu Wang (209\r\n", "doi": "10.7907/FZ1R-MJ30", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:4949", "collection": "thesis", "collection_id": "4949", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12112008-102138", "primary_object_url": { "basename": "JigangWuThesis.pdf", "content": "final", "filesize": 1620248, "license": "other", "mime_type": "application/pdf", "url": "/4949/1/JigangWuThesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Coherence Domain Optical Imaging Techniques", "author": [ { "family_name": "Wu", "given_name": "Jigang", "clpid": "Wu-Jigang" } ], "thesis_advisor": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" } ], "thesis_committee": [ { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Yariv", "given_name": "Amnon", "clpid": "Yariv-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Fraser", "given_name": "Scott E.", "clpid": "Fraser-S-E" }, { "family_name": "Tai", "given_name": "Yu-Chong", "clpid": "Tai-Yu-Chong" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Coherence domain optical imaging techniques have been developing quickly in the past few decades after the invention of laser. In this thesis, I will report the imaging methods that constitute my research projects during these years of graduate studies, including paired-angle-rotation scanning (PARS) forward-imaging probe for optical coherence tomography (OCT), full-field phase imaging technique based on harmonically matched diffraction grating (G1G2 grating), and Fresnel zone plate (FZP) based optifluidic microscopy (OFM). Compared with conventional optical microscopy, the coherence domain optical imaging has many advantages and greatly extends the application of imaging techniques.
\r\n\r\nOCT, based on low-coherence interferometry, is a high-resolution imaging technique that has been successfully applied to many biomedical applications. The development of various probes for OCT further made this technique applicable to endoscopic imaging. In the project of PARS-OCT probe, I have developed a forward-imaging probe based on two rotating angle-cut GRIN lenses. The diameter of the first prototype PARS-OCT probe that I made is 1.65 mm. My colleagues further built a probe with diameter of 0.82 mm. To our knowledge, this is the smallest forward-imaging probe that has been reported. The first prototype probe was characterized and successfully used to acquire OCT images of a Xenopus laevis tadpole.
\r\n\r\nFull-field phase imaging techniques are important for metrology and can also obtain high-resolution images for biological samples, especially transparent samples such as living cells. We have developed a novel full-field phase imaging technique based on the G1G2 grating. The G1G2 interferometry uses the G1G2 grating as a beam splitter/combiner and can confer nontrivial phase shift between output interference signals. Thus the phase and intensity information of the sample can be obtained by processing the two direct CCD images acquired at the output ports of the G1G2 grating. The details of this technique are explained in this thesis, and the phase imaging results for standard phase objects and biological samples are also shown.
\r\n\r\nOFM is a novel high-resolution and low-cost chip-level microscope developed by our group several years ago. Combining the unique imaging concept and microfluidic techniques, OFM system can be potentially useful to many biomedical applications, such as cytometry, blood parasite diagnosis, and water quality inspection. In the project of FZP-OFM, I applied the FZP to project the OFM aperture array onto an imaging sensor for OFM imaging. In this way, the sensor and the aperture array can be separated and will be useful for some situations. To demonstrate its capability, the FZP-OFM system was used to acquire OFM images of the protist Euglena gracilis.
\r\n\r\nThe studies in my research show the possibility of the application of various coherence domain optical imaging techniques in biomedical area, which is the primary objective of this thesis.
", "doi": "10.7907/6H07-PA44", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:2521", "collection": "thesis", "collection_id": "2521", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06082009-131045", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1717594, "license": "other", "mime_type": "application/pdf", "url": "/2521/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Signal Processing Algorithms for MIMO Radar", "author": [ { "family_name": "Chen", "given_name": "Scott Chun-Yang", "clpid": "Chen-Scott-Chun-Yang" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Radar is a system that uses electromagnetic waves to detect, locate and measure the speed of reflecting objects such as aircraft, ships, spacecraft, vehicles, people, weather formations, and terrain. It transmits the electromagnetic waves into space and receives the echo signal reflected from objects. By applying signal processing algorithms on the reflected waveform, the reflecting objects can be detected. Furthermore, the location and the speed of the objects can also be estimated. Radar was originally an acronym for \"RAdio Detection And Ranging\". Today radar has become a standard English noun. Early radar development was mostly driven by military and military is still the dominant user and developer of radar technology. Military applications include surveillance, navigation, and weapon guidance. However, radar now has a broader range of applications including meteorological detection of precipitation, measuring ocean surface waves, air traffic control, police detection of speeding traffic, sports radar speed guns, and preventing car or ship collisions.
\r\n\r\nRecently, the concept of MIMO radar has been proposed. The MIMO radar is a multiple antenna radar system which is capable of transmitting arbitrary waveform from each antenna element. In the traditional phased array radar, the transmitting antennas are limited to transmit scaled versions of the same waveform. However the MIMO radar allows the multiple antennas to transmit arbitrary waveforms. Like MIMO communications, MIMO radar offers a new paradigm for signal processing research. MIMO radar possesses significant potentials for fading mitigation, resolution enhancement, and interference and jamming suppression. Fully exploiting these potentials can result in significantly improved target detection, parameter estimation, target tracking and recognition performance. The MIMO radar technology has rapidly drawn considerable attention from many researchers. Several advantages of MIMO radar have been discovered by many different researchers such as increased diversity of the target information, excellent interference rejection capability, improved parameter identifiability, and enhanced flexibility for transmit beampattern design. The degrees of freedom introduced by MIMO radar improves the performance of the radar systems in many different aspects. However, it also generates some issues. It increases the number of dimensions of the received signals. Consequently, this increases the complexity of the receiver. Furthermore, the MIMO radar transmits an incoherent waveform on each of the transmitting antennas. This in general reduces the processing gain compared to the phased array radar. The multiple arbitrary waveforms also affects the range and Doppler resolution of the radar system.
\r\n\r\nThe main contribution of this thesis is to study the signal processing issues in MIMO radar and propose novel algorithms for improving the MIMO radar system. In the first part of this thesis, we focus on the MIMO radar receiver algorithms. We first study the robustness of the beamformer used in MIMO radar receiver. It is known that the adaptive beamformer is very sensitive to the DOA (direction-of-arrival) mismatch. In MIMO radar, the aperture of the virtual array can be much larger than the physical receiving array in the SIMO radar. This makes the performance of the beamformer more sensitive to the DOA errors in the MIMO radar case. In this thesis, we propose an adaptive beamformer that is robust against the DOA mismatch. This method imposes constraints such that the magnitude responses of two angles exceed unity. Then a diagonal loading method is used to force the magnitude responses at the arrival angles between these two angles to exceed unity. Therefore the proposed method can always force the gains at a desired interval of angles to exceed a constant level while suppressing the interferences and noise. A closed form solution to the proposed minimization problem is introduced, and the diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has an excellent SINR (signal to noise-plus-interference ratio) performance and a complexity comparable to the standard adaptive beamformer. We also study the space-time adaptive processing (STAP) for MIMO radar systems. With a slight modification, STAP methods developed originally for the single-input multiple-output (SIMO) radar (phased array radar) can also be used in MIMO radar. However, in the MIMO radar, the rank of the jammer-and-clutter subspace becomes very large, especially the jammer subspace. It affects both the complexity and the convergence of the STAP algorithm. In this thesis, we explore the clutter space and its rank in the MIMO radar. By using the geometry of the problem rather than data, the clutter subspace can be represented using prolate spheroidal wave functions (PSWF). Using this representation, a new STAP algorithm is developed. It computes the clutter space using the PSWF and utilizes the block diagonal property of the jammer covariance matrix. Because of fully utilizing the geometry and the structure of the covariance matrix, the method has very good SINR performance and low computational complexity.
\r\n\r\nThe second half of the thesis focuses on the transmitted waveform design for MIMO radar systems. We first study the ambiguity function of the MIMO radar and the corresponding waveform design methods. In traditional (SIMO) radars, the ambiguity function of the transmitted pulse characterizes the compromise between range and Doppler resolutions. It is a major tool for studying and analyzing radar signals. The idea of ambiguity function has recently been extended to the case of MIMO radar. In this thesis, we derive several mathematical properties of the MIMO radar ambiguity function. These properties provide some insights into the MIMO radar waveform design. We also propose a new algorithm for designing the orthogonal frequency-hopping waveforms. This algorithm reduces the sidelobes in the corresponding MIMO radar ambiguity function and makes the energy of the ambiguity function spread evenly in the range and angular dimensions. Therefore the resolution of the MIMO radar system can be improved. In addition to designing the waveform for increasing the system resolution, we also consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. An extended target can be viewed as a collection of infinite number of point targets. The reflected waveform from a point target is just a delayed and scaled version of the transmitted waveform. However, the reflected waveform from an extended target is a convolved version of the transmitted waveform with a target spreading function. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. The numerical results show that the proposed iterative algorithms converge faster and also have significant better SINR performances than previously reported algorithms.
\r\n", "doi": "10.7907/TPT1-9V58", "publication_date": "2009", "thesis_type": "phd", "thesis_year": "2009" }, { "id": "thesis:913", "collection": "thesis", "collection_id": "913", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03102008-010821", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 1803026, "license": "other", "mime_type": "application/pdf", "url": "/913/1/thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Blind Channel Estimation Using Redundant Precoding: New Algorithms, Analysis, and Theory", "author": [ { "family_name": "Su", "given_name": "Borching", "orcid": "0000-0001-8617-2601", "clpid": "Su-Borching" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-A" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Digital signal processing (DSP) techniques have played an important role in channel equalization and estimation in communication systems. While channel equalization and estimation are usually done by pilot-assisted methods in most systems, algorithms for blind channel estimation have also been largely studied due to high bandwidth efficiency. However, up to date, most blind methods possess disadvantages such as slow convergence speed, high complexity, poor performance, etc., compared to pilot-assisted methods. These drawbacks have made many consider blind methods as inapplicable in modern communication systems which feature fast-varying channels.
\r\n\r\nIn this thesis, we consider the blind channel estimation problem in block transmission systems with linear redundant precoding (LRP) which have been widely adopted in modern communication systems in recent years. The main contribution of this thesis is to considerably reduce the amount of received data required for blind estimation and suggest blind methods which are applicable even in fast-varying environments (e.g., in wireless channels). New algorithms are proposed, performance analysis derived, and theoretical issues studied.
\r\n\r\nThe first part of the thesis focuses on new algorithms for blind channel estimation and blind block synchronization in LRP systems. Two major types of linear redundant precoding, namely zero-padding (ZP) and cyclic prefixing (CP), are considered in this thesis. We first propose a generalized, subspace-based algorithm for blind channel estimation in ZP systems of which two previously reported algorithms are special cases. The generalization uses an integer parameter called {it repetition index} which represents the number of repeated uses of each received block. The number of received blocks required for subspace-based blind estimation is roughly inversely proportional to the repetition index. By choosing a larger repetition index, the amount of received data can be significantly reduced.
\r\n\r\nThe concept of repetition index is also applied in blind channel estimation in CP systems, which are more widely used than ZP systems in many current communication standards such as orthogonal frequency division multiplexing (OFDM) systems. The use of repetition index in CP systems is much less obvious and conceptually more complicated than in ZP systems. By choosing a repetition index larger than unity, the number of received blocks needed for blind estimation is significantly reduced compared to all previously reported methods. Theoretically, the proposed method can perform blind estimation using only three received blocks in absence of noise. In practice, the number of received blocks needed to yield a satisfactory bit error rate performance is usually on the order of half the block size. The proposed algorithm can be directly applied in OFDM systems without any modification of transmitter structure. A semiblind algorithm for channel estimation in OFDM systems is also proposed based on the extension of the blind algorithm.
\r\n\r\nAnother important problem, namely the blind block synchronization, is also studied. Most existing blind estimation methods in LRP systems assume the block boundaries of the received streams are perfectly known to the receiver, but this assumption is usually not true in practice since no extra known samples are transmitted. Two algorithms for blind block synchronization are proposed for ZP and CP systems, respectively. In particular, the block synchronization problem in CP systems is a broader version of the timing synchronization problem in the OFDM systems. The proposed algorithms exploit the concept of repetition index and both theoretical and simulation results suggest their advantages over all previously reported algorithms, especially when the amount of received data is limited.
\r\n\r\nThe second part of the thesis deals with theoretical issues related to blind channel estimation. Performance analysis of the generalized blind channel estimation algorithm in ZP systems is first given and shows that the system performance in terms of channel estimation mean square error (MSE) is very close to the Cramer-Rao bound (CRB), even when only two received blocks are available. Another important theoretical problem, namely the signal richness preservation problem, is also studied. Signal richness is an essential property for input signals in subspace-based blind channel estimation algorithms studied in this thesis. This property, however, may be altered by a linear precoder. Necessary and sufficient conditions for a linear precoder to preserve signal richness are explored. Several relevant interesting mathematical problems are also studied.
\r\n", "doi": "10.7907/R7MS-KQ06", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:1881", "collection": "thesis", "collection_id": "1881", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05192008-161405", "primary_object_url": { "basename": "Sebastien_Leprince_PhD_Thesis_2008.pdf", "content": "final", "filesize": 37994806, "license": "other", "mime_type": "application/pdf", "url": "/1881/1/Sebastien_Leprince_PhD_Thesis_2008.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Monitoring Earth Surface Dynamics with Optical Imagery", "author": [ { "family_name": "Leprince", "given_name": "Sebastien", "orcid": "0000-0003-4555-8975", "clpid": "Leprince-Sebastien" } ], "thesis_advisor": [ { "family_name": "Avouac", "given_name": "Jean-Philippe", "clpid": "Avouac-J-P" } ], "thesis_committee": [ { "family_name": "Avouac", "given_name": "Jean-Philippe", "clpid": "Avouac-J-P" }, { "family_name": "Elachi", "given_name": "Charles", "clpid": "Elachi-C" }, { "family_name": "Simons", "given_name": "Mark", "clpid": "Simons-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Perona", "given_name": "Pietro", "clpid": "Perona-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Despite the increasing availability of high-quality optical satellite images, continuous monitoring of Earth's surface changes is still of limited use due to technical limitations. To overcome these limitations, this thesis presents a processing chain to accurately orthorectify and co-register sets of satellite and aerial images, which, associated with a precise correlation technique, allow for the measurement of horizontal ground deformations with accuracy better than 1/10 of the pixel size. The irregular resampling problem is addressed to avoid introducing aliasing in the orthorectified images. Image registration and correlation is achieved with an iterative, unbiased processor that estimates the phase plane in the Fourier domain for sub-pixel shift detection. Errors due to the imaging system are calibrated and modeled, topography artifacts are characterized and solutions are proposed to compensate or to filter them.
\r\n\r\nA software package implementing these procedures, Co-registration of Optically Sensed Images and Correlation (COSI-Corr), is available from the Caltech Tectonics Observatory website. The procedure is validated in several different contexts, and applied to seismo-tectonics and glaciology studies.
\r\n\r\nAccurate measurements of horizontal co-seismic displacements in the near fault zone allow unambiguous imaging of surface ruptures. It is shown that measurements of surface ruptures from optical aerial and satellite images compare well with field measurements, and that in addition they have the potential of densely measuring the fault perpendicular component, and the off-fault distributed slip. When combined with seismic waveform modeling, fault geometry and surface offsets add crucial constraints to describe in details the seismic faulting process.
\r\n\r\nDense maps of glacier velocity are reported for several glaciers in Europe and in the Himalayas. Optical image correlation proves robust even in challenging mountainous areas, allowing accurate measurements of glacier flow velocity. Seasonal variations of glacier flow velocity are well identified, suggesting that such measurements can be used to better study the effects of climate change, and to refine the tuning of numerical glacier models.
", "doi": "10.7907/ZMTV-GV90", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:4747", "collection": "thesis", "collection_id": "4747", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12032007-113628", "primary_object_url": { "basename": "thesisETD.pdf", "content": "final", "filesize": 1011757, "license": "other", "mime_type": "application/pdf", "url": "/4747/1/thesisETD.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Optimization Algorithms in Wireless and Quantum Communications", "author": [ { "family_name": "Stojnic", "given_name": "Mihailo", "clpid": "Stojnic-Mihailo" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Since the first communication systems were developed, the scientific community has been witnessing attempts to increase the amount of information that can be transmitted. In the last 10--15 years there has been a tremendous amount of research towards developing multi-antenna systems which would hopefully provide high-data-rate transmissions. However, increasing the overall amount of transmitted information increases the complexity of the necessary signal processing. A large portion of this thesis deals with several important issues in signal processing of multi-antenna systems. In almost every particular case the goal is to develop a technique/algorithm so that the overall complexity of the signal processing is significantly decreased.
\r\n\r\nIn the first part of the thesis a very important problem of signal detection in MIMO (multiple-input multiple-output) systems is considered. The problem is analyzed in two different scenarios: when the transmission medium (channel) 1) is known and 2) is unknown at the receiver. The former case is often called coherent and the later non-coherent MIMO detection. Both cases usually amount to solving highly complex NP-hard combinatorial optimization problems. For the coherent case we develop a significant improvement of the traditional sphere decoder algorithm commonly used for this type of detection. An interesting connection between the new improved algorithm and the H-infinity estimation theory is established, and the performance improvement over the standard sphere decoder is demonstrated. For the non-coherent case we develop a counterpart to the standard sphere decoder, the so-called out-sphere decoder. The complexity of the algorithm is viewed as a random variable; its expected value is analyzed and shown to be significantly smaller than the one of the overall exhaustive search. In the non-coherent case, in addition to the complexity analysis of the exact out-sphere decoder, we analyze the performance loss of a suboptimal technique. We show that only a moderate loss of a few dbs in power required at the transmitter will occur if a polynomial algorithm based on the semi-definite relaxation is used in place of any exact technique (which of course is not known to be polynomial).
\r\n\r\nIn the second part of the thesis we consider a few problems that arise in wireless broadcast channels. Namely, we consider the problem of the information symbol vector design at the transmitter. A polynomial linear precoding technique is constructed. It enables achieving data rates very close to the ones achieved with DPC (dirty paper coding) technique. Additionally, for another suboptimal polynomial scheme (the so-called nulling and cancelling), we show that it asymptotically achieves the same data rate as the optimal, exponentially complex, DPC.
\r\n\r\nIn the last part of the thesis we consider a quantum counterpart of the signal detection from classical communication. In quantum systems the signals are quantum states and the quantum detection problem amounts to designing measurement operators which have to satisfy certain quantum mechanics laws. A specific type of quantum detection called unambiguous detection, which has numerous applications including quantum filtering, has recently attracted a lot of attention in the research community. We develop a general framework for numerically solving this problem using the tools from the convex optimization theory. Furthermore, in the special case where the two quantum states are of rank 2, we construct an explicit analytical solution for the measurement operators.
\r\n\r\nAt the end we would like to emphasize that the contribution of this thesis goes beyond the specific problems mentioned here. Most algorithmic optimization techniques developed in this paper are generally applicable. While it is a fact that our results were originally motivated by wireless and quantum communications applications, we believe that the developed techniques will find applications in many different areas where similar optimization problems appear.
\r\n", "doi": "10.7907/D6RN-ZD88", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:1879", "collection": "thesis", "collection_id": "1879", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05192008-132422", "primary_object_url": { "basename": "Thesis.pdf", "content": "final", "filesize": 9566604, "license": "other", "mime_type": "application/pdf", "url": "/1879/1/Thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Microfabricated High-Performance Liquid Chromatography (HPLC) System with Closed-Loop Flow Control", "author": [ { "family_name": "Shih", "given_name": "Jason J.", "clpid": "Shih-Jason-J" } ], "thesis_advisor": [ { "family_name": "Tai", "given_name": "Yu-Chong", "clpid": "Tai-Yu-Chong" } ], "thesis_committee": [ { "family_name": "Tai", "given_name": "Yu-Chong", "clpid": "Tai-Yu-Chong" }, { "family_name": "Emami", "given_name": "Azita", "clpid": "Emami-A" }, { "family_name": "Yang", "given_name": "Changhuei", "clpid": "Yang-Changhuei" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Lee", "given_name": "Terry D.", "clpid": "Lee-T-D" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis presents the development of a microfabricated high-performance liquid chromatography (HPLC) system. The design, fabrication, and characterization of individual HPLC components such as high-pressure pumps, mixers, flow sensors, composition sensors, separation columns, filters, and detectors is presented. These individual components were then integrated to create robust, feedback-driven separation systems capable of performing gradient, reverse-phase, nanoscale HPLC. Two separate separation systems were created. The first integrated system was a microfluidic device for HPLC tandem mass spectrometry (HPLC-MS/MS) designed for proteomic applications. The second system was a portable HPLC conductivity detection (HPLC-CD) system designed for point-of-care applications such as biodetection. Both systems demonstrated good performance and repeatability. The performance of these systems is largely attributable to the development of HPLC-compatible sensors that could provide precise control over the elution profiles. These microfluidic closed-loop flow control systems represent an important advancement in the microfluidics field, where open-loop flow control is universally used, and risks becoming inadequate with the increasing complexity of microfluidic systems.", "doi": "10.7907/8A6W-2X34", "publication_date": "2008", "thesis_type": "phd", "thesis_year": "2008" }, { "id": "thesis:1499", "collection": "thesis", "collection_id": "1499", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-04252007-122857", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 610479, "license": "other", "mime_type": "application/pdf", "url": "/1499/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Asymptotic Analysis of Wireless Systems with Rayleigh Fading", "author": [ { "family_name": "Rao", "given_name": "Chaitanya Kumar", "clpid": "Rao-Chaitanya-Kumar" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Perona", "given_name": "Pietro", "orcid": "0000-0002-7583-5809", "clpid": "Perona-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis looks at ways to improve either the reliability or the rate at which we can successfully transmit information over Rayleigh-fading wireless communication channels.
\r\n\r\nWe study four wireless schemes, the first in the low signal-to-noise ratio (SNR) regime, the remaining three at high SNR. The analysis provides insights that apply to more general SNRs.
\r\n\r\nFirstly we investigate a point-to-point multiple antenna link at low SNR. At low SNR channel estimates can be unreliable, and therefore we assume the channel is unknown to both transmitter and receiver. Adopting a block-fading model we find the mutual information between transmitter and receiver up to second order in the SNR. The expression is valid for input distributions with regular behavior of fourth- and sixth-order moments, in particular most practical schemes. Subject to input-signal constraints, we determine the optimal signaling to maximize this mutual information.
\r\n\r\nWe undertake high SNR analysis by finding the diversity-multiplexing gain trade-off of three further wireless systems with fading. Using techniques from existing works we find the optimal diversity-multiplexing gain trade-off for an M by N multiple antenna system with R single antenna relays. This uses a two-stage protocol in which the source first transmits to relays, then the relays multiply their received signal by a unitary matrix, before forwarding the result to the receiver. The trade-off is found to be equal to that of a multiple-input multiple-output (MIMO) link with R transmit and min{M,N} receive antennas.
\r\n\r\nNext we consider a network with two source-destination pairs (an interference channel) and establish relationships between the rate and diversity achievable by certain schemes. We show through two more schemes how cooperation amongst the nodes achieves a higher diversity, but with a reduced rate of the system. These schemes can easily be generalized from two to m source-destination pairs.
\r\n\r\nA final scheme is considered where n relay nodes are added to the m source-destination pairs, which act to cancel interference in an aim to increase diversity. The outage behavior of this scheme is analyzed and it is shown that for sufficiently many relay nodes, a diversity linear in n can be obtained.
", "doi": "10.7907/YYD6-VP11", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:3157", "collection": "thesis", "collection_id": "3157", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-08172006-130145", "primary_object_url": { "basename": "main.pdf", "content": "final", "filesize": 2051167, "license": "other", "mime_type": "application/pdf", "url": "/3157/1/main.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Distributed Estimation and Control in Networked Systems", "author": [ { "family_name": "Gupta", "given_name": "Vijay", "clpid": "Gupta-Vijay" } ], "thesis_advisor": [ { "family_name": "Murray", "given_name": "Richard M.", "clpid": "Murray-R-M" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Murray", "given_name": "Richard M.", "clpid": "Murray-R-M" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Schulman", "given_name": "Leonard J.", "clpid": "Schulman-L-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Rapid advances in information processing, communication and sensing technologies have enabled more and more devices to be provided with embedded processors, networking capabilities and sensors. For the field of estimation and control, it is now possible to consider an architecture in which many simple components communicate and cooperate to achieve a joint team goal. This distributed (or networked) architecture promises much in terms of performance, reliability and simplicity of design; however, at the same time, it requires extending the traditional theories of control, communication and computation and, in fact, looking at a unified picture of the three fields. A systematic theory of how to design distributed systems is currently lacking.
\r\n\r\nThis dissertation takes the first steps towards understanding the effects of imperfect information flow in distributed systems from an estimation and control perspective and coming up with new design principles to counter these effects. Designing networked systems is difficult because such systems challenge two basic assumptions of traditional control theory - presence of a central node with access to all the information about the system and perfect transmission of information among components. We formulate and solve many problems that deal with the removal of one, or both, of these assumptions. The chief idea explored in this dissertation is the joint design of information flow and the control law. While traditional control design has concentrated on calculating the optimal control input by assuming a particular information flow between the components, our approach seeks to synthesize the optimal information flow along with the optimal control law that satisfies the constraints of the information flow. Thus besides the question of 'What should an agent do?', the questions of 'Whom should an agent talk to?', 'What should an agent communicate?', 'When should an agent communicate?' and so on also have to be answered. The design of the information flow represents an important degree of freedom available to the system designer that has hitherto largely been ignored. As we demonstrate in the dissertation, the joint design of information flow and the optimal control input satisfying the constraints of that information flow yields large improvements in performance over simply trying to fit traditional design theories on distributed systems.
\r\n\r\nWe begin by formulating a distributed control problem in which many agents in a formation need to cooperate to minimize a joint cost function. We provide numerical algorithms to synthesize the optimal constrained control law that involve solving linear equations only and hence are free from numerical issues plaguing the other approaches proposed in the literature. We then provide and analyze a model to understand the issue of designing the topology according to which the agents interact. The results are very surprising since there are cases when allowing communication to happen between two agents may, in fact, be detrimental to the performance.
\r\n\r\nWe then move on to consider the effects of communication channels on control performance. To counter such effects, we propose the idea of encoding information for the purpose of estimation and control prior to transmission. Although information theoretic techniques are not possible in our problem, we are able to solve for a recursive yet optimal encoder / decoder structure in many cases. This information flow design oriented approach has unique advantages such as being optimal for any packet drop pattern, being able to include the effect of known but random delays easily, letting us escape the limits set by reliability for transmission of data across a network by using intermediate nodes as 'repeaters' similar to a digital communication network and so on.
\r\n\r\nWe finally take a look at combining the effects of multiple sources of information and communication channels on estimation and control. We look at a distributed estimation problem in which, at every time step, only a subset out of many sensors can transmit information to the estimator. This is also a representative resource allocation problem. We propose the idea of stochastic communication patterns that allows us to include the effects of communication channels explicitly during system design. Thus, instead of tree-search based algorithms proposed in the literature, we provide stochastic scheduling algorithms that can take into account the random packet drop effect of the channels. We also consider a distributed control problem with switching topologies and solve for the optimal controller. The tools that we develop are applicable to many other scenarios and we demonstrate some of them in the dissertation.
\r\n\r\nAlong the way, we look at many other related problems in the dissertation. As an example, we provide initial results about the issue of robustness of a distributed system design to a malfunctioning agent. This notion is currently lacking in the control and estimation community, but has to be a part of any effective theory for designing networked or distributed systems.
", "doi": "10.7907/KWN2-X741", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:1561", "collection": "thesis", "collection_id": "1561", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05012007-133654", "primary_object_url": { "basename": "Cedric_Anen_PhD_Thesis.pdf", "content": "final", "filesize": 5260880, "license": "other", "mime_type": "application/pdf", "url": "/1561/1/Cedric_Anen_PhD_Thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Neural Correlates of Economic and Moral Decision-Making", "author": [ { "family_name": "Anen", "given_name": "C\u00e9dric Robert", "clpid": "Anen-C\u00e9dric-Robert" } ], "thesis_advisor": [ { "family_name": "Quartz", "given_name": "Steven R.", "clpid": "Quartz-S-R" } ], "thesis_committee": [ { "family_name": "Quartz", "given_name": "Steven R.", "clpid": "Quartz-S-R" }, { "family_name": "Camerer", "given_name": "Colin F.", "clpid": "Camerer-C-F" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Our daily lives are shaped by a series of decision processes, ranging from very unimportant choices to life-changing judgments. The complexity of the decision processes increases tremendously when the decision-making takes place in a social context, i.e., when other human beings are directly involved in the decision. In such conditions the decision-maker not only tries to maximize his own utility, but also needs to take into account the interdependent nature of the situation. Information about others' preferences, characteristics, and actions play an important role, and need to be thoroughly evaluated and predicted before making a decision. In this thesis we explore the neural correlates of two different types of social decision-making.
\r\n\r\nIn the first experiment we investigate economic decision-making in the context of a two-player social exchange game. In order to maximize their overall and personal earnings, players need to cooperate and build up a trust relationship with their partner. Synchronized neural data is recorded from the two interacting brains using functional magnetic resonance imaging. In this thesis we present four main findings: (i) the neural correlates of strategic uncertainty and how it can be used to predict a player's future strategic choice; (ii) the dynamic interaction of the brains of two interacting players; (iii) the neural correlates of trust and its development over the course of the game; and (iv) how the brain distinguishes between one's own actions and those of another person.
\r\n\r\nThe second experiment investigates the neural basis of moral decision-making and other- regarding preferences. Subjects have to make a morally difficult decision between helping two groups of children while trading off between efficiency and equity. By parametrically varying these variables, we show how two brain structures, the insula and the caudate, are actively involved in the decision-making process.
\r\n\r\nTaken together the results presented in this thesis shed some light on how our brain evaluates social situations, and how it uses social measures such as trust, agency, strategic interaction, and fairness to make decisions.
\r\n", "doi": "10.7907/W3VS-MW78", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:4413", "collection": "thesis", "collection_id": "4413", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-11052006-173021", "primary_object_url": { "basename": "thesis_final.pdf", "content": "final", "filesize": 1820220, "license": "other", "mime_type": "application/pdf", "url": "/4413/1/thesis_final.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Performance Limits and Design Issues in Wireless Networks", "author": [ { "family_name": "Farajidana", "given_name": "Amir", "clpid": "Farajidana-Amir" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The increasing utilization of networks, especially wireless networks, for different applications and in different aspects of modern life, has directed a great deal of attention towards the analysis and optimal design of networks. Distinguishing features of the wireless environment and the distributed nature of the network setup have raised many important challenges in finding the performance limits of different tasks such as communication, control, and computation over networks. There are also many design issues concerning the complexity and the robustness of wireless systems that should be addressed for a thorough understanding and an efficient operation of wireless networked systems. This thesis deals with a few of the challenges associated with the fundamental performance limits and optimal design of wireless networks.
\r\n\r\nIn the first part, we analyze performance limits of two applications for a special class of wireless networks called wireless erasure networks. These networks incorporate some of the essential features of the wireless environment. We look at the performance limits of two applications over these networks. The first application is data transmission with two different traffic patterns, namely multicast and broadcast. The capacity region and the optimal coding scheme for the multicast scenario are found, and outer and inner bounds on the capacity region for the broadcast scenario are provided. The second application considered in this thesis is estimation and control of a dynamical process at a remote location connected through a wireless erasure network to a sensor observing the process. In this case, we characterize the minimum steady-state error and its dependency on the parameters of the network. The final problem considered in the first part of the thesis concerns power consumption (as a performance measure) in wireless networks. We propose and analyze a simple scheme based on the idea of distributed beamforming that saves us in terms of power consumption for dense sensor and ad-hoc networks. We quantify this gain compared to the case when nodes have isolated communications without participating in the network.
\r\n\r\nThe second part of the thesis deals with two design issues in the downlink of cellular wireless networks. The first issue is related to quality of service provisioning in the downlink scenario. We investigate the problem of differentiated rate scheduling in which different users demand different sets of rates. We obtain explicit and practical scheduling schemes to achieve the rate constraints and at the same time maximize the throughput. These schemes are based on the idea of opportunistic beamforming, are simple, and require little amount of feedback to the transmitter. We further show that the throughput loss due to imposing the rate constraints is negligible for large systems.
\r\n\r\nThe next issue considered in this thesis is the robustness of the capacity region of multiple antenna Gaussian broadcast channels to the channel estimation error at the transmitter and the users. These channels are mathematical models for the downlink of cellular systems. We provide an inner bound on the capacity region of these channels and show that this inner bound is equivalent to the capacity region of a dual multiple access channel with a noise covariance that depends on the transmit powers. This duality is explored to show the effect of the estimation error on the sum-rate for a large number of users and in the large power regime. Finally, a training-based scheme for the block fading multiple antenna broadcast channels is proposed.
", "doi": "10.7907/PRMQ-0644", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:5182", "collection": "thesis", "collection_id": "5182", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-04092007-162353", "primary_object_url": { "basename": "Yoon_Thesis.pdf", "content": "final", "filesize": 3195815, "license": "other", "mime_type": "application/pdf", "url": "/5182/1/Yoon_Thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Signal Processing Methods for Genomic Sequence Analysis", "author": [ { "family_name": "Yoon", "given_name": "Byung-Jun", "clpid": "Yoon-Byung-Jun" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Smolke", "given_name": "Christina D.", "clpid": "Smolke-C-D" }, { "family_name": "Ho", "given_name": "Tracey C.", "clpid": "Ho-Tracey" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Signal processing is the art of representing, transforming, analyzing, and manipulating signals. It deals with a wide range of signals, from speech and audio signals to images and video signals, and many others. Signal processing techniques have been found very useful in diverse applications. Traditional applications include signal enhancement, denoising, speech recognition, audio and image compression, radar signal processing, and digital communications, just to name a few. In recent years, signal processing techniques have been also applied to the analysis of biological data with considerable success. For example, they have been used for predicting protein-coding genes, analyzing ECG signals and MRI data, enhancing and normalizing DNA microarray images, modeling gene regulatory networks, and so forth.
\r\n\r\nIn this thesis, we consider the application of signal processing methods to the analysis of biological sequences, especially, DNA and RNA molecules. We demonstrate how conventional signal processing techniques--such as digital filters and filter banks--can contribute to this end, and also show how we can extend the traditional models--such as the hidden Markov models (HMMs)--to better serve this purpose.
\r\n\r\nThe first part of the thesis focuses on signal processing methods that can be utilized for analyzing RNA sequences. The primary purposes of this part are to develop a statistical model that is suitable for representing RNA sequence profiles and to propose an effective framework that can be used for finding new homologues (i.e., similar RNAs that are biologically related) of known RNAs. Many functional RNAs have secondary structures that are well conserved among different species. The RNA secondary structure gives rise to long-range correlations between distant bases, which cannot be represented using traditional HMMs. In order to overcome this problem, we propose a new statistical model called the context-sensitive HMM (csHMM). The csHMM is an extension of the traditional HMM, where certain states have variable emission and transition probabilities that depend on the context. The context-sensitive property increases the descriptive power of the model significantly, making csHMMs capable of representing long-range correlations between distant symbols. Based on the proposed model, we present efficient algorithms that can be used for finding the optimal state sequence and computing the probability of an observed symbol string. We also present a training algorithm that can be used for optimizing the parameters of a csHMM. We give several examples that illustrate how csHMMs can be used for modeling various RNA secondary structures and recognizing them.
\r\n\r\nBased on the concept of csHMM, we introduce profile-csHMMs, which are specifically constructed csHMMs that have linear repetitive structures (i.e., state-transition diagrams). Profile-csHMMs are especially useful for building probabilistic representations of RNA sequence families, including pseudoknots. We also propose a dynamic programming algorithm called the sequential component adjoining (SCA) algorithm that can systematically find the optimal state sequence of an observed symbol string based on a profile-csHMM. In order to demonstrate the effectiveness of profile-csHMMs, we build a structural alignment tool for RNA sequences and show that the profile-csHMM approach can yield highly accurate predictions at a relatively low computational cost. At the end, we describe how the profile-csHMM can be used for finding homologous RNAs, and we propose a practical scheme for making the search significantly faster without affecting the prediction accuracy.
\r\n\r\nIn the second part of the thesis, we focus on the application of digital filters and filter banks in DNA sequence analysis. Firstly, we demonstrate how we can use digital filters for predicting protein-coding genes. Many coding regions in DNA molecules are known to display a period-3 behavior, which can be effectively detected using digital filters. Efficient schemes are proposed that can be used for designing such filters. Experimental results will show that the digital filtering approach can clearly identify the coding regions at a very low computational cost. Secondly, we propose a method based on a bank of IIR lowpass filters that can be used for predicting CpG islands, which are specific regions in DNA molecules that are abundant in the dinucleotide CpG. This filter bank is used to process the sequence of log-likelihood ratios obtained from two Markov chains, where the respective Markov chains model the base transition probabilities inside and outside the CpG islands. The locations of the CpG islands are predicted by analyzing the output signals of the filter bank. It will be shown that the filter bank approach can yield reliable prediction results without sacrificing the resolution of the predicted start/end positions of the CpG islands.
\r\n", "doi": "10.7907/48J3-G286", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:4016", "collection": "thesis", "collection_id": "4016", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-10102006-120159", "primary_object_url": { "basename": "mythesisElk.pdf", "content": "final", "filesize": 4398499, "license": "other", "mime_type": "application/pdf", "url": "/4016/1/mythesisElk.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "New Approaches to the Analysis and Design of Reed-Solomon Related Codes", "author": [ { "family_name": "El-Khamy", "given_name": "Mostafa Said", "clpid": "El-Khamy-Mostafa-Said" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Divsalar", "given_name": "Dariush", "clpid": "Divsalar-D" }, { "family_name": "Fossorier", "given_name": "Marc", "clpid": "Fossorier-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The research that led to this thesis was inspired by Sudan's breakthrough that demonstrated that Reed-Solomon codes can correct more errors than previously thought. This breakthrough can render the current state-of-the-art Reed-Solomon decoders obsolete. Much of the importance of Reed-Solomon codes stems from their ubiquity and utility. This thesis takes a few steps toward a deeper understanding of Reed-Solomon codes as well as toward the design of efficient algorithms for decoding them.
\r\n\r\nAfter studying the binary images of Reed-Solomon codes, we proceeded to analyze their performance under optimum decoding. Moreover, we investigated the performance of Reed-Solomon codes in network scenarios when the code is shared by many users or applications. We proved that Reed-Solomon codes have many more desirable properties. Algebraic soft decoding of Reed-Solomon codes is a class of algorithms that was stirred by Sudan's breakthrough. We developed a mathematical model for algebraic soft decoding. By designing Reed-Solomon decoding algorithms, we showed that algebraic soft decoding can indeed approach the ultimate performance limits of Reed-Solomon codes. We then shifted our attention to products of Reed-Solomon codes. We analyzed the performance of linear product codes in general and Reed-Solomon product codes in particular. Motivated by these results we designed a number of algorithms, based on Sudan's breakthrough, for decoding Reed-Solomon product codes. Lastly, we tackled the problem of analyzing the performance of sphere decoding of lattice codes and linear codes, e.g., Reed-Solomon codes, with an eye on the tradeoff between performance and complexity.
", "doi": "10.7907/TQRJ-GM19", "publication_date": "2007", "thesis_type": "phd", "thesis_year": "2007" }, { "id": "thesis:3264", "collection": "thesis", "collection_id": "3264", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-08292005-100440", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 2307728, "license": "other", "mime_type": "application/pdf", "url": "/3264/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Broadband Wireless Broadcast Channels: Throughput, Performance, and PAPR Reduction", "author": [ { "family_name": "Sharif", "given_name": "Masoud", "clpid": "Sharif-Masoud" } ], "thesis_advisor": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" } ], "thesis_committee": [ { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Divsalar", "given_name": "Dariush", "clpid": "Divsalar-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The ever-growing demand for higher rates and better quality of service in cellular systems has attracted many researchers to study techniques to boost the capacity and improve the performance of cellular systems. The main candidates to increase the capacity are to use multiple antennas or to increase the bandwidth. This thesis attempts to solve a few challenges regarding scheduling schemes in the downlink of cellular networks, and the implementation of modulation schemes suited for wideband channels.
\r\n\r\nDownlink scheduling in cellular systems is known to be a bottleneck for future broadband wireless communications. Information theoretic results on broadcast channels provide the limits for the maximum achievable rates for each receiver and transmission schemes to achieve them. It turns out that the sum-rate capacity (sum-rate (or throughput) refers to the sum of the transmission rates to all users) of a multi-antenna broadcast channel heavily depends on the availability of channel state information (CSI) at the transmitter. Unfortunately, the dirty paper coding (DPC) scheme which achieves the capacity region is extremely computationally intensive especially in multiuser context. Furthermore, relying on the assumption that full CSI is available from all the n users may not be feasible in practice.
\r\n\r\nIn the first part of the thesis, we obtain the scaling law of the sum-rate capacity for large n and for a homogeneous fading MIMO (multiple input multiple output) broadcast channel, and then propose a simple scheme that only requires little (partial) CSI and yet achieves the same scaling law. Another important issue in downlink scheduling is to maintain fairness among users with different distances to the transmitter. Interestingly, we prove that our scheduling scheme becomes fair provided that the number of transmit antennas is large enough. We further analyze the impact of using a throughput optimal scheduling on the delay in sending information to the users. Finally, we look into the problem of differentiated rate scheduling in which different users demand for different sets of rates. We obtain explicit scheduling schemes to achieve the rate constraints.
\r\n\r\nIn the second part of the thesis, we focus on orthogonal frequency division multiplexing (OFDM), which is the most promising technique for broadband wireless channels (mainly due to its simplicity of channel equalization even in a severe multipath fading environment). The main disadvantage of this modulation, however, is its high peak to mean envelope power ratio (PMEPR). This is due to the fact that the OFDM signal consists of many (say n) harmonically related subcarriers which may, in the worst-case, add up constructively and lead to large peaks (of order n) in the signal.
\r\n\r\nDespite this worst-case performance, we show that when each subcarrier is chosen from some given constellation, the PMEPR behaves like log{n} almost surely, for large n. This implies that there exist almost full-rate codes with a PMEPR of log{n} for large n. We further prove that there exist codes with rate not vanishing to zero such that the PMEPR is less than a constant (independent of n). We also construct high rate codes with a guaranteed PMEPR of log{n}. Simulation results show that in a system with 128 subcarriers and using 16QAM, the PMEPR of a multicarrier signal can be reduced from 13.5 to 3.4 which is within 1.6dB of the PMEPR of a single carrier system.
", "doi": "10.7907/25JK-Z952", "publication_date": "2006", "thesis_type": "phd", "thesis_year": "2006" }, { "id": "thesis:3369", "collection": "thesis", "collection_id": "3369", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09072004-204814", "primary_object_url": { "basename": "yindithesis_onesided.pdf", "content": "final", "filesize": 1723665, "license": "other", "mime_type": "application/pdf", "url": "/3369/1/yindithesis_onesided.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Space-Time Code Design and Its Applications in Wireless Networks", "author": [ { "family_name": "Jing", "given_name": "Yindi", "clpid": "Jing-Yindi" } ], "thesis_advisor": [ { "family_name": "Doyle", "given_name": "John Comstock", "clpid": "Doyle-J-C" } ], "thesis_committee": [ { "family_name": "Doyle", "given_name": "John Comstock", "clpid": "Doyle-J-C" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Low", "given_name": "Steven H.", "clpid": "Low-S-H" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis has two main contributions: the designs of differential/non-differential unitary space-time codes for multiple-antenna systems and the analysis of the diversity gain when using space-time coding among nodes in wireless networks.
\r\n\r\nCapacity has long been a bottleneck in wireless communications. Recently, multiple-antenna techniques have been used in wireless communications to combat the fading effect, which improves both the channel capacity and performance greatly. A recently proposed method for communicating with multiple antennas over block-fading channels is unitary space-time modulation, which can achieve the channel capacity at high SNR. However, it is not clear how to generate well performing unitary space-time codes that lend themselves to efficient encoding and decoding. In this thesis, the design of unitary space-time codes using Cayley transform is proposed. The codes are designed based on an information-theoretic criterion and have a polynomial-time near-maximum-likelihood decoding algorithm. Simulations suggest that the resulting codes allow for effective high-rate data transmissions in multiple-antenna communication systems without knowing the channel. Another well-known transmission scheme for multiple-antenna systems with unknown channel information at both the transmitter and the receiver is differential unitary space-time modulation. It can be regarded as a generalization of DPSK and is suitable for continuous fading. In differential unitary space-time modulation, fully diverse constellations, i.e., sets of unitary matrices whose pairwise differences are non-singular, are wanted for their good pairwise error properties. In this thesis, Lie groups and their representations are used in solving the design problem. Fully diverse differential unitary space-time codes for systems with four and three transmit antennas are constructed based on the Lie groups Sp(2) and SU(3). The designed codes have high diversity products, lend themselves to a fast maximum-likelihood decoding algorithm, and simulation results show that they outperform other existing codes, especially at high SNR.
\r\n\r\nThen the idea of space-time coding devised for multiple-antenna systems is applied to communications over wireless networks. In wireless relay networks, the relay nodes encode the signals they receive from the transmit node into a distributed space-time code and transmit the encoded signals to the receive node. It is shown in this thesis that at very high SNR, the diversity gain achieved by this scheme is almost the same as that of a multiple-antenna system whose number of transmit antennas is the same as the number of relay nodes in the network, which means that the relay nodes work as if they can cooperate fully and have full knowledge of the message. However, at moderate SNR, the diversity gain of the wireless network is inferior to that of the multiple-antenna system. It is further shown that for a fixed total power consumed in the network, the optimal power allocation is that the transmitter uses half the power and the relays share the other half fairly. This result addresses the question of what performance a relay network can achieve. Both it and its extensions have many applications to wireless ad hoc and sensory network communications.
", "doi": "10.7907/QYN9-0Z55", "publication_date": "2005", "thesis_type": "phd", "thesis_year": "2005" }, { "id": "thesis:2332", "collection": "thesis", "collection_id": "2332", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05312005-225644", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 2726540, "license": "other", "mime_type": "application/pdf", "url": "/2332/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Linearized and High Frequency Electrooptic Modulators", "author": [ { "family_name": "Cummings", "given_name": "Uri Vaughan", "clpid": "Cummings-Uri-Vaughan" } ], "thesis_advisor": [ { "family_name": "Bridges", "given_name": "William B.", "clpid": "Bridges-W-B" } ], "thesis_committee": [ { "family_name": "Bridges", "given_name": "William B.", "clpid": "Bridges-W-B" }, { "family_name": "Hajimiri", "given_name": "Ali", "clpid": "Hajimiri-A" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Schaffner", "given_name": "James H.", "clpid": "Schaffner-J-H" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "An analysis is performed of many standard and linearized electrooptic modulators known in the industry. The transfer functions of these modulators are evaluated under a consistent set of performance figures of merit, which are gain and spur-free dynamic range, using a canonical set of optical link parameters. The tolerance of the needed precision of the parameters of the linearization mechanisms of all of these modulators is compared over the entire interesting range of noise bandwidth.
\r\n\r\nA computer program was written to analyze the frequency dependence of any modulator transfer function under any set of functional inputs. The program is used to illustrate and compare the frequency dependence of the figures of merit of all of the modulators for which a d-c analysis was performed. Further analysis looks at the effect of greater noise-bandwidth and recovering the frequency-dependent degradation of gain and dynamic range through re-phasing techniques. The gain of directional couplers is analyzed in-depth.
\r\n\r\nTwo novel modulator schemes are produced. The first uses reflective wave techniques to retime the electrical and optical waves half way through the modulator. The second uses fabrication geometry and properties of the linearization technique to make a more robust modulator (applicable to three of the modulators analyzed).
\r\n\r\nA 94 GHz antenna-coupled directional coupler modulator was initially demonstrated using an old modulator chip from Finbar Sheehy. A peculiar bug with the chip was uncovered. And a new modulator experiment was constructed and many aspects of the experimental apparatus were optimized. Though the revised experiment ultimately did not yield modulation side bands, it did couple a 94 GHz microwave signal into the optical waveguide, and many interesting challenges of high frequency electrooptic modulator fabrication were evaluated and improved upon.
", "doi": "10.7907/GTD7-V873", "publication_date": "2005", "thesis_type": "phd", "thesis_year": "2005" }, { "id": "thesis:2381", "collection": "thesis", "collection_id": "2381", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06022004-013457", "primary_object_url": { "basename": "Diego_Dugatkin_Thesis.pdf", "content": "final", "filesize": 1007427, "license": "other", "mime_type": "application/pdf", "url": "/2381/1/Diego_Dugatkin_Thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Optimization of Multi-Resolution Source Codes", "author": [ { "family_name": "Dugatkin", "given_name": "Diego G.", "clpid": "Dugatkin-Diego-G" } ], "thesis_advisor": [ { "family_name": "Effros", "given_name": "Michelle", "clpid": "Effros-M" } ], "thesis_committee": [ { "family_name": "Effros", "given_name": "Michelle", "clpid": "Effros-M" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Chan", "given_name": "Tony F-C", "clpid": "Chan-T-F" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis studies the optimization of multi-resolution source codes. A multi-resolution source code is a data compression algorithm that generates a bit-stream that can be truncated at any point to reconstruct low-resolution representations of the original data. By progressively refining the description, these codes allow the receiver to get representations of progressively increasing quality from a single file.
\r\n\r\nThe optimization methods presented here are based on the minimization of a Lagrangian performance measure, which is a weighted sum of rates and distortions at the different resolutions of the multi-resolution code. The Lagrangian coefficients are the weights that parameterize the priorities assigned to the resolutions. The relative value of these parameters can be set according to the user's preferences regarding which rates are more important, the probability of decoding the file at each possible rate, or any other prioritization rationale. We present a method for converting design constraints into the corresponding Lagrangian parameters.
\r\n\r\nWe also use a Lagrangian analysis to investigate optimality properties of multi-resolution codes. Specifically, we explore the characterization of the theoretically optimal output density functions of a two-resolution source code for any arbitrary set of priorities over the resolutions.
\r\n\r\nOnce the priority function has been identified, the goal is to design the multi-resolution code that yields the best rate-distortion trade-off for those priorities. The minimization of the multi-resolution Lagrangian is somewhat specific to the framework and type of multi-resolution code. We pursue this goal in several coding frameworks.
\r\n\r\nThe first framework is the multi-resolution vector quantizer (MRVQ) framework. Prior work on the topic described optimal MRVQ design for both fixed- and variable-rate systems but implemented only fixed-rate codes. The earliest portion of this thesis began with the implementation of the earlier described algorithm for variable-rate MRVQ for use as a testbed for understanding the important question of how to choose the Lagrangian parameters for multi-resolution codes to meet a collection of desired constraints.
\r\n\r\nArmed with a new understanding of parameter choice in the MRVQ framework, we moved next to the more sophisticated coding framework of wavelet-based embedded bit-plane coders. New results in this framework include improvements on the Set Partitioning in Hierarchical Trees (SPIHT) and the Group Testing for Wavelets (GTW) algorithms that apply the lessons learned from MRVQ theory in these more sophisticated wavelet coding frameworks. Experimental results demonstrate the performance benefits associated with this approach.
", "doi": "10.7907/RZ2Y-1Z78", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:1913", "collection": "thesis", "collection_id": "1913", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05212004-153855", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 584160, "license": "other", "mime_type": "application/pdf", "url": "/1913/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Iterative Decoding for Wireless Networks", "author": [ { "family_name": "Palanki", "given_name": "Ravi", "clpid": "Palanki-Ravi" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Yedidia", "given_name": "Jonathan S.", "clpid": "Yedidia-J-S" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Dolinar", "given_name": "Samuel J.", "clpid": "Dolinar-S-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The invention of turbo codes and low density parity check (LDPC) codes has made it possible for us for design error correcting codes with low decoding complexity and rates close to channel capacity. However, such codes have been studied in detail only for the most basic communication system, in which a single transmitter sends data to a single receiver over a channel whose statistics are known to both the transmitter and the receiver. Such a simplistic model is not valid in the case of a wireless network, where multiple transmitters might want to communicate with multiple receivers at the same time over a channel which can vary rapidly.
\r\n \r\nWhile the design of efficient error correction codes for a general wireless network is an extremely hard problem, it should be possible to design such codes for several important special cases. This thesis takes a few steps in that direction. We analyze the performance of low density parity check codes under iterative decoding in certain simple networks and prove Shannon-theoretic results for more complex networks.
\r\n \r\nMore specifically, we analyze the iterative decoding algorithm in two very important special cases: (a) when the transmitter and receiver have no prior knowledge of the channel and (b) when the channel is a multiple access channel. We also apply iterative decoding to some non-LDPC codes on the binary symmetric channel and the additive white Gaussian noise channel. Finally, we derive capacity results for a class of wireless multicast networks and a class of fading channels.
", "doi": "10.7907/05AN-ME34", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:1800", "collection": "thesis", "collection_id": "1800", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05142004-214312", "primary_object_url": { "basename": "tkacenko_phd_thesis.pdf", "content": "final", "filesize": 1272977, "license": "other", "mime_type": "application/pdf", "url": "/1800/1/tkacenko_phd_thesis.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Optimization Algorithms for Realizable Signal-Adapted Filter Banks", "author": [ { "family_name": "Tkacenko", "given_name": "Andre", "clpid": "Tkacenko-Andre" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Vrcelj", "given_name": "Bojan", "clpid": "Vrcelj-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Multirate filter banks are fundamental systems commonly used in digital signal processing (DSP). Typically, they are used to decompose a discrete-time signal into a set of frequency selective components called subband signals. Filter banks have been found to be useful for lossy data compression schemes such as MP3 and JPEG 2000, denoising, and signal estimation. In the last decade, transmultiplexers, the dual structures of multirate filter banks, have been shown to be useful in digital communications systems such as discrete multitone (DMT) systems for channel equalization and inter/intra-symbol interference cancellation in the presence of noise.
\r\n\r\nRecently, a special type of filter bank adapted to its input known as the principal component filter bank (PCFB) has been shown to be simultaneously optimal for a wide variety of objectives. Such filter banks are not only optimal for relevant data compression type objectives such as coding gain and multiresolution, but also for digital communications type objectives such as power minimization, when the filter bank is implemented in its transmultiplexer form. The only problem is that PCFBs, which are defined over classes of paraunitary (PU) filter banks, are only known to exist for certain classes. In particular, PCFBs are in general known to exist only in the extremal cases where the analysis/synthesis polyphase matrix has zero memory and doubly infinite memory, respectively. Furthermore, for many practical cases of inputs, the filters corresponding to the infinite-order PCFB have ideal bandpass response and are as such unrealizable. When the polyphase matrix has finite memory or a finite impulse response (FIR), it is believed that PCFBs do not exist, although this has not yet been formally proven in the literature.
\r\n\r\nThe main contribution of this thesis is to bridge the gap between the zero memory PCFB and the infinite-order one. To that end, a variety of methods for the design of realizable signal-adapted FIR filter banks is presented. It is shown that a popular conventional method for designing signal-adapted FIR PU filter banks, which only requires the design of an optimal FIR compaction filter, is in fact not well suited for designing good filter banks due to the exponential complexity caused by the nonuniqueness of the FIR compaction filter. To avoid this dilemma, we propose a method by which all of the filters are obtained together. In particular, the method consists of finding an FIR PU least-squares approximant to the infinite-order PCFB polyphase matrix. Using an elegant complete parameterization of FIR PU systems in terms of canonical building blocks, an iterative greedy algorithm for solving the least-squares problem is presented. Simulation results provided here show that as the order or memory of the signal-adapted FIR PU filter bank increases, the filter bank behaves more and more like the infinite-order PCFB in terms of a variety of objectives including coding gain, multiresolution, and power minimization. This serves to bridge the gap between the zero memory and infinite memory PCFBs, which previously has not been done in the literature.
\r\n\r\nIn addition to being useful for the design of PCFB-like FIR filter banks, the proposed iterative algorithm can also be used for a variety of other design problems including the FIR PU interpolation problem. Unlike the traditional FIR interpolation problem, whose solution is known in closed form, the FIR PU interpolation problem is far more difficult and is in fact still open. Despite this, the proposed algorithm can be used to find an approximant to an interpolant and sometimes even find an interpolant, as we show here through simulations.
\r\n\r\nIn the second part of the thesis, we focus on the design of realizable signal-adapted quantized filter banks in which the filters are FIR but otherwise unconstrained. The filters are chosen to minimize the mean-squared error of the output, which is shown to be equivalent to maximizing the coding gain of the system. By alternately optimizing the analysis and synthesis filters, an iterative greedy algorithm, different from that mentioned above, is proposed for the design of such filter banks. Simulation results provided show that the filter banks designed exhibit performance close to the information theoretic rate-distortion bound.
\r\n\r\nFinally, we show how some of the techniques used in the above iterative algorithms can be used for the design of a channel shortening equalizer. Channel shortening equalizers, which arise in the context of digital communications, have been found to be necessary for DMT systems such as the digital subscriber loop (DSL) in which the channel impulse response must be shortened to the length of the cyclic prefix. In particular, we show how the eigenfilter technique which is used in the above-mentioned FIR PU iterative greedy algorithm, can be used for the design of a noise optimized channel shortening equalizer. As opposed to other techniques, which require a Cholesky decomposition of a certain matrix for every delay parameter considered, the proposed method is lower in complexity in that it only requires a single such decomposition for all delay values. Despite this significant decrease in complexity, it is shown through simulations that the equalizers designed using this technique perform nearly optimally in terms of observed bit rate.
", "doi": "10.7907/QZYN-ND12", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:2719", "collection": "thesis", "collection_id": "2719", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06252003-115639", "primary_object_url": { "basename": "mythesis.pdf", "content": "final", "filesize": 3861858, "license": "other", "mime_type": "application/pdf", "url": "/2719/1/mythesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Multirate Signal Processing Concepts in Digital Communications", "author": [ { "family_name": "Vrcelj", "given_name": "Bojan", "clpid": "Vrcelj-Bojan" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Hassibi", "given_name": "Babak", "clpid": "Hassibi-B" }, { "family_name": "Candes", "given_name": "Emmanuel J.", "clpid": "Candes-E-J" }, { "family_name": "Mese", "given_name": "Murat", "clpid": "Mese-M" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Multirate systems are building blocks commonly used in digital signal processing (DSP). Their function is to alter the rate of the discrete-time signals, by adding or deleting a portion of the signal samples. They are essential in various standard signal processing techniques such as signal analysis, denoising, compression and so forth. During the last decade, however, they have increasingly found applications in new and emerging areas of signal processing, as well as in several neighboring disciplines such as digital communications.
\r\n\r\nThe main contribution of this thesis is aimed towards a better understanding of multirate systems and their use in modern communication systems. To this end, we first study a property of linear systems appearing in certain multirate structures. This property is called biorthogonal partnership and represents a terminology introduced recently to address a need for a descriptive term for such class of filters. In the thesis we especially focus on the extensions of this simple idea to the case of vector signals (MIMO biorthogonal partners) and to accommodate for nonintegral decimation ratios (fractional biorthogonal partners).
\r\n\r\nThe main results developed here study the properties of biorthogonal partners, e.g., the conditions for the existence of stable and of finite impulse response (FIR) partners. In this context we develop the parameterization of FIR solutions, which makes the search for the best partner in a given application analytically tractable. This proves very useful in their central application, namely, channel equalization in digital communications with signal oversampling at the receiver. A good channel equalizer in this context is one that helps neutralize the distortion on the signal introduced by the channel propagation but not at the expense of amplifying the channel noise.
\r\n\r\nIn the second part of the thesis, we focus on another class of multirate systems, used at the transmitter side in order to introduce redundancy in the data stream. This redundancy generally serves to facilitate the equalization process by forcing certain structure on the transmitted signal. We first consider the transmission systems that introduce the redundancy in the form of a cyclic prefix. The examples of such systems include the discrete multitone (DMT) and the orthogonal frequency division multiplexing (OFDM) systems. We study the signal precoding in such systems, aimed at improving the performance by minimizing the noise power at the receiver.
\r\n\r\nWe also consider a different class of communication systems with signal redundancy, namely, the multiuser systems based on code division multiple access (CDMA). We specifically focus on the special class of CDMA systems called 'a mutually orthogonal usercode receiver' (AMOUR). We show how to find the best equalizer from the class of zero-forcing solutions in such systems, and then increase the size of this class by employing alternative sampling strategies at the receiver.
", "doi": "10.7907/ABS2-4505", "publication_date": "2004", "thesis_type": "phd", "thesis_year": "2004" }, { "id": "thesis:2652", "collection": "thesis", "collection_id": "2652", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06202002-170522", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 571645, "license": "other", "mime_type": "application/pdf", "url": "/2652/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Graph-Based Codes and Iterative Decoding", "author": [ { "family_name": "Khandekar", "given_name": "Aamod Dinkar", "clpid": "Khandekar-Aamod-Dinkar" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The field of error correcting codes was revolutionized by the introduction of turbo codes in 1993. These codes demonstrated dramatic performance improvements over any previously known codes, with significantly lower complexity. Since then, much progress has been made towards understanding the performance of these codes, as well as in using this understanding to design even better codes.
\r\n\r\nThis thesis takes a few more steps in both these directions. We develop a new technique, called the typical set bound, for analyzing the asymptotic performance of code ensembles based on their weight enumerators. This technique yields very tight bounds on the maximum-likelihood decoding threshold of code ensembles, and is powerful enough to reproduce Shannon's noisy coding theorem for the class of binary-input symmetric channels.
\r\n\r\nWe also introduce a new class of codes called irregular repeat-accumulate (IRA) codes, which are adapted from the previously known class of repeat-accumulate (RA) codes. These codes are competitive in terms of decoding performance with the class of irregular low-density parity-check (LDPC) codes, which are arguably the best class of codes known today, at least for long block lengths. In addition, IRA codes have a significant advantage over irregular LDPC codes in terms of encoding complexity.
\r\n\r\nWe also derive an analytical bound regarding iterative decoding thresholds of code ensembles on general binary-input symmetric channels, an area in which theoretical results are currently lacking.
", "doi": "10.7907/Q06G-MW38", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:2652", "collection": "thesis", "collection_id": "2652", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06202002-170522", "primary_object_url": { "basename": "thesis.pdf", "content": "final", "filesize": 571645, "license": "other", "mime_type": "application/pdf", "url": "/2652/1/thesis.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Graph-Based Codes and Iterative Decoding", "author": [ { "family_name": "Khandekar", "given_name": "Aamod Dinkar", "clpid": "Khandekar-Aamod-Dinkar" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Preskill", "given_name": "John P.", "orcid": "0000-0002-2421-4762", "clpid": "Preskill-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The field of error correcting codes was revolutionized by the introduction of turbo codes in 1993. These codes demonstrated dramatic performance improvements over any previously known codes, with significantly lower complexity. Since then, much progress has been made towards understanding the performance of these codes, as well as in using this understanding to design even better codes.
\r\n\r\nThis thesis takes a few more steps in both these directions. We develop a new technique, called the typical set bound, for analyzing the asymptotic performance of code ensembles based on their weight enumerators. This technique yields very tight bounds on the maximum-likelihood decoding threshold of code ensembles, and is powerful enough to reproduce Shannon's noisy coding theorem for the class of binary-input symmetric channels.
\r\n\r\nWe also introduce a new class of codes called irregular repeat-accumulate (IRA) codes, which are adapted from the previously known class of repeat-accumulate (RA) codes. These codes are competitive in terms of decoding performance with the class of irregular low-density parity-check (LDPC) codes, which are arguably the best class of codes known today, at least for long block lengths. In addition, IRA codes have a significant advantage over irregular LDPC codes in terms of encoding complexity.
\r\n\r\nWe also derive an analytical bound regarding iterative decoding thresholds of code ensembles on general binary-input symmetric channels, an area in which theoretical results are currently lacking.
", "doi": "10.7907/Q06G-MW38", "publication_date": "2003", "thesis_type": "phd", "thesis_year": "2003" }, { "id": "thesis:6190", "collection": "thesis", "collection_id": "6190", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:11302010-111553894", "primary_object_url": { "basename": "Mehta_nb_2001.pdf", "content": "final", "filesize": 15354693, "license": "other", "mime_type": "application/pdf", "url": "/6190/1/Mehta_nb_2001.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Impact of User Mobility on Resource Allocation Schemes in Cellular Radio Systems", "author": [ { "family_name": "Mehta", "given_name": "Neelesh B.", "orcid": "0000-0002-3614-049X", "clpid": "Mehta-Neelesh-B" } ], "thesis_advisor": [ { "family_name": "Goldsmith", "given_name": "Andrea Jo", "orcid": "0000-0001-5686-800X", "clpid": "Goldsmith-A-J" } ], "thesis_committee": [ { "family_name": "Goldsmith", "given_name": "Andrea Jo", "orcid": "0000-0001-5686-800X", "clpid": "Goldsmith-A-J" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Divsalar", "given_name": "Dariush", "orcid": "0000-0001-9176-3078", "clpid": "Divsalar-D" }, { "family_name": "Kiely", "given_name": "Aaron B.", "clpid": "Kiely-A-B" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Next generation wireless cellular radio systems are being designed to provide anytime, anywhere communication capabilities to serve a range of applications. The ability to support mobility is a key reason for the increasing demand for such systems. To accommodate this demand, efficient resource allocation schemes that can operate over the harsh wireless channel environment need to be devised. User mobility has a significant influence on the design and performance of these schemes. The focus of this dissertation is the analysis of the impact of mobility on such resource allocation schemes.\r\nWhat impact mobility has depends on the scheme under consideration. We first analyze the impact of user mobility on the performance of a link adaptation scheme that employs\r\nthe recently proposed no-transmission mode. In this scheme, users adapt their modulation and coding for transmitting data packets based on their estimates of the link condition\r\nand suspend transmissions when link quality is very poor. Based on a simplified system model, we derive expressions for the system performance as a function of the basic, system-defining parameters. We show that for a stable system, the channel correlation, a function of user speed and feed-back delay of estimates, is an important factor that determines the optimal link adaptation thresholds. We then study a packet based multiple access scheme called Packet Reservation Multiple Access (PRMA), which can simultaneously handle the different traffic requirements of periodic, delay intolerant (voice) and bursty, delay tolerant (data) users. An approximate technique is developed to analyze the impact of user mobility\r\nas well as channel fading and interference-induced packet errors on PRMA. Both these effects lead to a premature loss of reservation and, consequently, more dropped packets\r\nfor voice users. Finally, we look at dedicated channel assignment schemes that assign an entire channel to a user for the duration of his conversation. We investigate heuristic prediction based techniques that take into account mobility traffic statistics to modify the\r\nnew call access criteria. This is done so as to introduce prioritization for hand-off requests in hitherto unprioritized channel assignment schemes.", "doi": "10.7907/9fje-n644", "publication_date": "2001", "thesis_type": "phd", "thesis_year": "2001" }, { "id": "thesis:6190", "collection": "thesis", "collection_id": "6190", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:11302010-111553894", "primary_object_url": { "basename": "Mehta_nb_2001.pdf", "content": "final", "filesize": 15354693, "license": "other", "mime_type": "application/pdf", "url": "/6190/1/Mehta_nb_2001.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Impact of User Mobility on Resource Allocation Schemes in Cellular Radio Systems", "author": [ { "family_name": "Mehta", "given_name": "Neelesh B.", "orcid": "0000-0002-3614-049X", "clpid": "Mehta-Neelesh-B" } ], "thesis_advisor": [ { "family_name": "Goldsmith", "given_name": "Andrea Jo", "orcid": "0000-0001-5686-800X", "clpid": "Goldsmith-A-J" } ], "thesis_committee": [ { "family_name": "Goldsmith", "given_name": "Andrea Jo", "orcid": "0000-0001-5686-800X", "clpid": "Goldsmith-A-J" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Divsalar", "given_name": "Dariush", "orcid": "0000-0001-9176-3078", "clpid": "Divsalar-D" }, { "family_name": "Kiely", "given_name": "Aaron B.", "clpid": "Kiely-A-B" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Next generation wireless cellular radio systems are being designed to provide anytime, anywhere communication capabilities to serve a range of applications. The ability to support mobility is a key reason for the increasing demand for such systems. To accommodate this demand, efficient resource allocation schemes that can operate over the harsh wireless channel environment need to be devised. User mobility has a significant influence on the design and performance of these schemes. The focus of this dissertation is the analysis of the impact of mobility on such resource allocation schemes.\r\nWhat impact mobility has depends on the scheme under consideration. We first analyze the impact of user mobility on the performance of a link adaptation scheme that employs\r\nthe recently proposed no-transmission mode. In this scheme, users adapt their modulation and coding for transmitting data packets based on their estimates of the link condition\r\nand suspend transmissions when link quality is very poor. Based on a simplified system model, we derive expressions for the system performance as a function of the basic, system-defining parameters. We show that for a stable system, the channel correlation, a function of user speed and feed-back delay of estimates, is an important factor that determines the optimal link adaptation thresholds. We then study a packet based multiple access scheme called Packet Reservation Multiple Access (PRMA), which can simultaneously handle the different traffic requirements of periodic, delay intolerant (voice) and bursty, delay tolerant (data) users. An approximate technique is developed to analyze the impact of user mobility\r\nas well as channel fading and interference-induced packet errors on PRMA. Both these effects lead to a premature loss of reservation and, consequently, more dropped packets\r\nfor voice users. Finally, we look at dedicated channel assignment schemes that assign an entire channel to a user for the duration of his conversation. We investigate heuristic prediction based techniques that take into account mobility traffic statistics to modify the\r\nnew call access criteria. This is done so as to introduce prioritization for hand-off requests in hitherto unprioritized channel assignment schemes.", "doi": "10.7907/9fje-n644", "publication_date": "2001", "thesis_type": "phd", "thesis_year": "2001" }, { "id": "thesis:6116", "collection": "thesis", "collection_id": "6116", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10072010-095516188", "type": "thesis", "title": "Filter Bank Optimization with Applications in Noise Suppression and Communications", "author": [ { "family_name": "Akkarakaran", "given_name": "Sony John", "clpid": "Akkarakaran-Sony-John" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Divsalar", "given_name": "Dariush", "orcid": "0000-0001-9176-3078", "clpid": "Divsalar-D" }, { "family_name": "Hassibi", "given_name": "Babak", "orcid": "0000-0002-1375-5838", "clpid": "Hassibi-B" }, { "family_name": "Djokovic", "given_name": "Igor", "clpid": "Djokovic-I" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A filter bank (FB) is used to analyze or decompose a signal into several frequency bands, which are processed separately and then combined. This allows us to allocate processing resources in a manner tailored to the distribution of the relevant signal features among the bands. A judicious allocation leads to improved system performance over direct processing of the input signal (without using an FB). FBs have found applications in almost every area of modern digital signal processing, including audio, image and video compression and communications.
\r\n\r\nThe main thrust of this thesis is towards the optimization of FBs based on the statistical properties of their input. We establish the optimality of a type of FB called the principal component filter bank (PCFB) for numerous signal processing problems. The PCFB depends on the input power spectrum and on the class of M channel orthonormal FBs over which we seek to optimize the FB. PCFB optimality for compression and progressive transmission has been observed to varying degrees in the past. Our work provides a unified framework for orthonormal FB optimization, that includes these earlier results as special cases. It also covers many other problems not observed earlier, notably in noise suppression and communications.
\r\n\r\nA central result that we establish is that the PCFB is the optimum orthonormal FB whenever the minimization objective is a concave function of the vector of subband variances of the FB. Many signal processing problems result in such objectives. The earlier results on PCFB optimality for compression can be explained by this framework. Another example not noticed earlier is FBbased white noise reduction using zeroth order Wiener filters or hard thresholds in the subbands. Yet another case involves the discrete multitone modulation (DMT) communication system, used in ADSL (asymmetric digital subscriber line) and wireless OFDM (orthogonal frequency division multiplexing) technologies. These systems use the transmultiplexer configuration of an FB, which is usually chosen as a DFT or cosine-modulated FB for efficiency of implementation. We show that at increased implementation cost, we can minimize the transmission power requirement (for a given bitrate and error probability) by using the PCFB associated with a certain normalized noise spectrum. We present simulation examples with realistic channel and noise models for the ADSL system to compare the performance of the PCFB against other types of FBs, such as the DFT.
\r\n\r\nWe study various extensions of the basic PCFB optimality result. The noise suppression problem becomes more involved when the noise is colored, because the objective then depends on both signal and noise subband variances. For a specific FB class, namely the orthogonal transform coder class, we show that a simultaneous PCFB for the signal and noise is optimal (if it exists). For the class of unconstrained FBs, this does not hold in general; we develop an algorithm that computes the best FB for piecewise constant spectra. In some cases, PCFB optimality extends to classes of biorthogonal FBs too, although there are many open problems in this area, as we point out. We study the effect of nonexistence of a PCFB on the FB optimizations and show how they usually become analytically intractable. We show that PCFBs do not exist for the classes of DFT and cosine-modulated FBs. We also study nonuniform FB optimization: We establish the definition of nonuniform PCFBs and study their existence and optimality, which are shown to be much more restricted when compared with uniform PCFBs.
\r\n\r\nLastly, we study a related open problem on the parameterization of nonuniform perfect reconstruction (PR) FBs of various classes, such as the rational and FIR classes. Not all nonuniform PRFBs can be built by the common method of using tree structures of uniform PRFBs. Given a set of decimators, is there a rational PRFB using them? If so, what are all the PRFBs possible? When are they necessarily derivable from a tree structure? Very little is known about the answers to many such questions. For example, for existence of rational PRFBs with a given set of decimators, certain conditions on the decimators are known to be necessary, while certain others are sufficient. However, conditions that are both necessary and sufficient are unknown. One of our contributions is to strengthen considerably the known conditions. This is an important step towards a complete PR theory for nonuniform filter banks.
", "doi": "10.7907/4712-9414", "publication_date": "2001", "thesis_type": "phd", "thesis_year": "2001" }, { "id": "thesis:6098", "collection": "thesis", "collection_id": "6098", "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10052010-135012445", "primary_object_url": { "basename": "Daniell_ce_2000.pdf", "content": "final", "filesize": 44278078, "license": "other", "mime_type": "application/pdf", "url": "/6098/1/Daniell_ce_2000.pdf", "version": "v5.0.0" }, "type": "thesis", "title": "Object Recognition in Compressed Imagery.", "author": [ { "family_name": "Daniell", "given_name": "Cynthia Evors", "clpid": "Daniell-Cynthia-Evors" } ], "thesis_advisor": [ { "family_name": "Goodman", "given_name": "Rodney M.", "clpid": "Goodman-R-M" } ], "thesis_committee": [ { "family_name": "Koch", "given_name": "Christof", "orcid": "0000-0001-6482-8067", "clpid": "Koch-C" }, { "family_name": "Psaltis", "given_name": "Demetri", "orcid": "0000-0003-4684-8800", "clpid": "Psaltis-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Goodman", "given_name": "Rodney M.", "clpid": "Goodman-R-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "It is often necessary to search for objects in large databases of compressed imagery. In the past, object recognition and image compression have generally been treated as separate problems, resulting in inefficient suboptimal performance. Moreover, computational and storage issues make it fundamentally prohibitive to uncompress large images prior to object recognition. We provide two complementary solutions to the problem of object recognition in compressed imagery, each of which integrates subband and correlation filtering in a unique manner.
\r\n\r\nOne key benefit of correlation filters is that, as linear systems, they are highly compatible with the subband filtering process. This enables us to provide a seamless operation in which object recognition and data compression are viewed as continuations of the same process. The public MSTAR data set illustrates our results on a three class problem of 79 Synthetic Aperture Radar images at one foot resolution.
\r\n\r\nOur general framework, the Pattern Recognition Subband Coder (PRSC), provides simultaneous synthesis and recognition at full resolution in a computationally efficient architecture. Its parallelism enables a result 1.6 times faster, in the limit, than correlation on uncompressed imagery. Furthermore, by jointly optimizing the synthesis and recognition filters, the PRSC achieves 100% recognition accuracy on our compressed data set, improving performance over that produced from the original (uncompressed) data set, by 3.7%. We maintain this success for compression ratios up to 6:1.
\r\n\r\nAddressing the issue of reduced resolution recognition, our Subband Domain Correlation Filters operate directly on the subband coefficients at multiple resolution levels. For compression ratios of at least 20:1, we achieve recognition performance of at least 90%, 85%, and 75%, respectively, on two, four, and eight foot resolution data.
\r\n\r\nThus, through our solutions with compressed imagery, we outperform correlation results on the equivalent original imagery in terms of both speed and accuracy, as well as provide success at reduced resolutions of the data.
", "doi": "10.7907/6z3z-ar86", "publication_date": "2000", "thesis_type": "phd", "thesis_year": "2000" }, { "id": "thesis:531", "collection": "thesis", "collection_id": "531", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02062008-130016", "primary_object_url": { "basename": "Horn_gb_1999.pdf", "content": "final", "filesize": 4819303, "license": "other", "mime_type": "application/pdf", "url": "/531/1/Horn_gb_1999.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Iterative decoding and pseudo-codewords", "author": [ { "family_name": "Horn", "given_name": "Gavin B.", "clpid": "Horn-G-B" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Divsalar", "given_name": "Dariush", "clpid": "Divsalar-D" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the last six years, we have witnessed an explosion of interest in the coding theory community, in iterative decoding and graphical models, due primarily to the invention of turbo codes. While the structural properties of turbo codes and low density parity check codes have now been put on a firm theoretical footing, what is still lacking is a satisfactory theoretical explanation as to why iterative decoding algorithms perform as well as they do. In this thesis we make a first step by discussing the behavior of various iterative decoders for the graphs of tail-biting codes and cycle codes. By increasing our understanding of the behavior of the iterative min-sum (MSA) and sum-product (SPA) algorithms on graphs with cycles, we can design codes which achieve better performance.\n\nMuch of this thesis is devoted to the analysis of the performance of the MSA and SPA on the graphs for tail-biting codes and cycle codes. We give sufficient conditions for the MSA to converge to the maximum likelihood codeword after a finite number of iterations. We also use the familiar union bound argument to characterize the performance of the MSA after many iterations. For a cycle code, we show that the performance of the MSA decoder is asymptotically as good as maximum likelihood. For tail-biting codes this will depend on our choice of trellis.\n", "doi": "10.7907/RS6G-C640", "publication_date": "1999", "thesis_type": "phd", "thesis_year": "1999" }, { "id": "thesis:771", "collection": "thesis", "collection_id": "771", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02262008-093428", "primary_object_url": { "basename": "Xu_m_1999.pdf", "content": "final", "filesize": 3766240, "license": "other", "mime_type": "application/pdf", "url": "/771/1/Xu_m_1999.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Iterative decoding and graphical code representations", "author": [ { "family_name": "Xu", "given_name": "Meina", "clpid": "Xu-Meina" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Divsalar", "given_name": "Dariush", "clpid": "Divsalar-D" }, { "family_name": "Kaleh", "given_name": "Ghassan Kawas", "clpid": "Kaleh-G-K" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Tanner", "given_name": "Michael", "clpid": "Tanner-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Since the invention of turbo codes, there has been an explosion of interest in iterative decoding and graphical representation of codes. This thesis examines the iterative decoding of codes defined on graphs with cycles, which appears to be an efficient means of achieving the Shannon limit. Much of this analysis is on the iterative min-sum decoding of tail-biting codes and cycle codes. We have identified the pseudocodeword as the cause of the suboptimal performance of the iterative decoder, and we have obtained a union bound for the performance of the iterative decoder on both AWGN and BSC channels. Using the union bound argument, for cycle codes, we have shown that the performance of the iterative decoder is asymptotically as good as that of the ML decoder. As for tail-biting codes, the same thing is true if the lowest weight pseudocodeword is at least the minimum weight of the code. Unfortunately, the analysis of tail-biting codes and cycle codes does not extend to turbo codes and low density parity check codes in general. Our next approach is to determine the average behavior of message passing algorithms by studying the evolution of their \"message\" densities. For the class of \"repeat and accumulate\" serially concatenated turbo-like codes, we have devised an algorithm for determining their \"threshold\" values. When the signal-to-noise ratio is larger than the threshold value, the error probabilities of message passing algorithms approach zero, whereas if the signal-to-noise ratio is less than the threshold value, the error probability stays bounded away from zero. Some message passing algorithms and graphical representation of codes are efficient means of devising ML or MAP decoding algorithms. We have proposed a junction tree representation for linear block codes, and we have shown that the minimum junction tree can be less complex than the minimal trellis.", "doi": "10.7907/q731-9q50", "publication_date": "1999", "thesis_type": "phd", "thesis_year": "1999" }, { "id": "thesis:1834", "collection": "thesis", "collection_id": "1834", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05162005-084223", "primary_object_url": { "basename": "00_cover.pdf", "content": "final", "filesize": 7260, "license": "other", "mime_type": "application/pdf", "url": "/1834/1/00_cover.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Highly available distributed storage systems", "author": [ { "family_name": "Xu", "given_name": "Lihao", "clpid": "Xu-Lihao" } ], "thesis_advisor": [ { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" } ], "thesis_committee": [ { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "van Tilborg", "given_name": "Henk C.A.", "clpid": "van-Tilborg-H-C-A" }, { "family_name": "Chandy", "given_name": "K. Mani", "clpid": "Chandy-K-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "As the need for data explodes with the passage of time and the increase of computing power, data storage becomes more and more important. Distributed storage, as distributed computing before it, is coming of age as a good solution to make systems highly available, i.e., highly scalable, reliable and efficient. The focus of this thesis is how to achieve data reliability and efficiency in distributed storage systems. This thesis consists of two parts. The first part deals with the reliability of distributed storage systems. Reliability is achieved by computationally efficient MDS array codes that eliminate single points of failure in the systems, thus providing more reliability and flexibility to the systems. Such codes can be used as general MDS error-correcting codes. They are particularly suitable for use in distributed storage systems. The second part deals with the efficiency of distributed storage systems. Methods are proposed to improve the performance of data server and storage systems significantly through the proper use of data redundancy. These methods are based on error-correcting codes, particularly the MDS array codes developed in the first part.\r\n\r\nTwo new classes of MDS array codes are presented: the X-Code and the B-Code. The encoding operations of both codes are optimal, i.e., their update complexity achieves the theoretical lower bound. They distribute parity bits over all columns rather than concentrating them on some parity columns. As with other array codes, the error model for both codes is that errors or erasures are columns of the array, i.e., if at least one bit of a column is an error or erasure, then the whole column is considered to be an error or erasure. Both codes are of distance 3, i.e., they can either: correct two erasures, detect two errors or correct one error. In addition to encoding algorithms, efficient decoding algorithms are proposed, both for erasure-correcting and for error-correcting. In fact, the erasure-correcting algorithms are also optimal in terms of computation complexity.\r\n\r\nThe X-Code has a very simple geometrical structure: the parity bits are constructed along two groups of parallel parity lines of slopes 1 and -1. This is the origin of the name X-Code. This simple geometrical structure allows simple erasure-decoding and error-decoding algorithms, using only XORs and vector cyclic-shift operations.\r\n\r\nThe significance of the B-code not only includes all its optimality properties: MDS, optimal encoding and optimal decoding, but also its relation with a 3-decade old graph theory problem. It is proven in this thesis that constructing a B-Code of odd length is exactly equivalent to constructing a perfect one-factorization (or P1F) of a complete graph. Constructing a P1F of an arbitrary complete graph has remained a conjecture since the early 1960's. Though the P1F conjecture remains unsolved, the B-code as the first real application of the P1F problem will hopefully spur more research on it. It is also conjectured in this thesis that constructing a B-Code of any length, even or odd, is equivalent to constructing a P1F of a complete graph. An efficient error-correcting algorithm for the B-Code is also presented, which is based on the relations between the B-Code and its dual. The algorithm might give a hint of how to develop efficient decoding algorithms for other codes.\r\n\r\nWhile it is intuitive that redundancy can bring reliability to a system, this thesis gives another direction: using redundancy actively to improve performance (efficiency) of distributed data systems. The results in this direction are both theoretical and experimental. System models are extracted from experiments in real practical systems; analytical results are derived using these and are then fed back to experiments for verification.\r\n\r\nIn this thesis, a novel deterministic voting scheme that uses error-correcting codes is proposed. The voting scheme generalizes all known simple deterministic voting algorithms. It can be tuned to various application environments with different error rates to drastically reduce average communication complexity, i.e., the amount of information that must be transmitted in order to get correct voting results.\r\n\r\nTwo problems are identified to improve the performance of general data server systems, namely the data distribution problem and the data acquisition problem. Solutions to these are proposed, as are general analytical results on performance of (n, k) systems. A simple service time model of a practical disk-based distributed server system is given. This model, which is based on experimental results, is a starting point for data distribution and data acquisition schemes. These results, both experimental and analytical, can be further used for more sophisticated scheduling schemes to optimize or improve the performance of data server systems that serve multiple clients simultaneously.\r\n\r\nFinally, some research problems related to storage systems are proposed as future directions.", "doi": "10.7907/EQK9-8C84", "publication_date": "1999", "thesis_type": "phd", "thesis_year": "1999" }, { "id": "thesis:5051", "collection": "thesis", "collection_id": "5051", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12182007-111636", "primary_object_url": { "basename": "Owen_rl_1999.pdf", "content": "final", "filesize": 3303518, "license": "other", "mime_type": "application/pdf", "url": "/5051/1/Owen_rl_1999.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Detection and Analysis of Musical Events Using Model-Based Signal Processing", "author": [ { "family_name": "Owen", "given_name": "Randall Lee", "clpid": "Owen-Randall-Lee" } ], "thesis_advisor": [ { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "thesis_committee": [ { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Murray", "given_name": "Richard M.", "orcid": "0000-0002-5785-7481", "clpid": "Murray-R-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The present work is directed to the detection and analysis of notes, chords and other musical events produced by a stringed musical instrument, specifically the guitar. The chords generated by a guitar are polyphonic, meaning that they comprise multiple notes sounded simultaneously. Each note is also spectrally complex, in that it comprises a\r\nfundamental tone and several harmonics. Despite this complexity, the statistics of the signal containing the notes and chords are expected to be similar to those of human speech. This similarity will allow the signal to be characterized as a parametric random process so that established mathematical and speech recognition techniques can be used\r\nto extract the events from the signal. The analysis of musical signals is an important application since it is a logical extension to the problem of speech recognition. Moreover, a robust computer-based solution to this problem could have both research and commercial applications.
\r\n\r\n\r\nA system for automated detection and analysis of musical events, such as notes and chords, has been designed. The system is comprised of two main elements: the event library and a set of match measures. The event library contains a hierarchy of event models each corresponding to a distinct musical note or chord. Each event model is structured as a hidden Markov model (HMM), \u03bb = (A, B, \u03c0), having the four distinct states labeled attack, sustain, decay or silence, that correspond to the specific physical states of the musical event. Associated with each model state Q={q1, \u2022\u2022\u2022 , q4} are a set of M observation symbols V={ v1,v2, \u2022\u2022\u2022 , vM} and a set of three probability distributions: a transition probability distribution A={aij} , an observable probability distribution B={bj(k)} and an initial probability distribution \u03c0=\u03c0{i}. Three match measures are developed for solving the recognition problem: one for estimating the HMM parameters, one for determining the optimal state sequence of the HMM and one for evaluating the probability that a given observation sequence was produced by a specific HMM. The observation sequence is derived from the input signal by sampling, converting to a spectral representation, and digitally coding using standard speech recognition\r\ntechniques. The three match measures correspond, respectively, to training the model, refining the model and matching an event to a model, each of which is performed using conventional speech processing algorithms.
", "doi": "10.7907/GPBA-SM95", "publication_date": "1999", "thesis_type": "engd", "thesis_year": "1999" }, { "id": "thesis:687", "collection": "thesis", "collection_id": "687", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02202008-104935", "primary_object_url": { "basename": "Kirac_a_1999.pdf", "content": "final", "filesize": 6313690, "license": "other", "mime_type": "application/pdf", "url": "/687/1/Kirac_a_1999.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Optimal orthonormal subband coding and lattice quantization with vector dithering", "author": [ { "family_name": "Kirac", "given_name": "Ahmet", "clpid": "Kirac-A" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Fadavi", "given_name": "Jalil", "clpid": "Fadavi-J" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the digital era that we live in, efficient coding of signals is an unquestionable need. This thesis is about one of the most useful and popular technique of digital coding: subband coding. Subband coding and its cousin wavelet-based coding are now the preferred methods for not only speech, but also audio, image, and video signals. Subband coding involves a linear part which is a filter bank, and a nonlinear part which is usually a uniform scalar quantization of each of the subbands. Subband coders are classified according to the type of filter bank used for its transform. This thesis is mainly about orthonormal subband coding. The ability of an orthonormal filter bank to decompose the signal into components that have a diverse set of signal energies is an indicator of its efficiency for subband coding. Such a diversity in the set of the subband energies is fully utilized by a process called bit allocation. The traditional results on the optimality of a filter bank for given input statistics assume that the quantizers operate at high bit rates.\n\nThis thesis presents optimality results under more general quantizer models without assuming high bit rates. This is accomplished by revealing the relationship between the problems of optimal orthonormal subband coding and principal component representation of signals. The latter is done using what is called a principal component filter bank (PCFB). A PCFB is one that compacts most of the energy of a signal into smaller subsets of subbands. To date, there has not been significant theoretical developments in the field of optimal nonuniform subband coding, although the successful techniques of wavelet-based coding are among the state of the art in practice. Such techniques utilize a form of a nonuniform filter bank with a certain structure which makes it efficient for its implementation. In this thesis, we provide optimality results for the nonuniform orthonormal subband coding as well. As in the uniform case, the principal component representation of signals continues to play the key role. We introduce nonuniform PCFB's and link them to the optimal subband coding problem. A PCFB, in particular, contains a filter that compacts most of the signal energy into one single channel: energy compaction filter. The thesis goes into details of designing such filters optimally. In particular, we propose an analytical method in the two-channel case and a very efficient window method in the arbitrary M\u2014channel case. Multistage design of compaction filters has also been worked out.\n\nFinally we extend the analysis of uniform scalar quantization to multiple dimensions. We provide an exact statistical relationship between a lattice quantizer noise and its input vector. We then extend the idea of dithering to the vector case. Dithering is a means of statistically rendering the quantization noise independent of the input. We address the optimal choice of a lattice for a given dimension and also optimal pre- and post-filtering of a dithered lattice quantizer.\n", "doi": "10.7907/ec82-t391", "publication_date": "1999", "thesis_type": "phd", "thesis_year": "1999" }, { "id": "thesis:5051", "collection": "thesis", "collection_id": "5051", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12182007-111636", "primary_object_url": { "basename": "Owen_rl_1999.pdf", "content": "final", "filesize": 3303518, "license": "other", "mime_type": "application/pdf", "url": "/5051/1/Owen_rl_1999.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Detection and Analysis of Musical Events Using Model-Based Signal Processing", "author": [ { "family_name": "Owen", "given_name": "Randall Lee", "clpid": "Owen-Randall-Lee" } ], "thesis_advisor": [ { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" } ], "thesis_committee": [ { "family_name": "Culick", "given_name": "Fred E. C.", "clpid": "Culick-F-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Murray", "given_name": "Richard M.", "orcid": "0000-0002-5785-7481", "clpid": "Murray-R-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The present work is directed to the detection and analysis of notes, chords and other musical events produced by a stringed musical instrument, specifically the guitar. The chords generated by a guitar are polyphonic, meaning that they comprise multiple notes sounded simultaneously. Each note is also spectrally complex, in that it comprises a\r\nfundamental tone and several harmonics. Despite this complexity, the statistics of the signal containing the notes and chords are expected to be similar to those of human speech. This similarity will allow the signal to be characterized as a parametric random process so that established mathematical and speech recognition techniques can be used\r\nto extract the events from the signal. The analysis of musical signals is an important application since it is a logical extension to the problem of speech recognition. Moreover, a robust computer-based solution to this problem could have both research and commercial applications.
\r\n\r\n\r\nA system for automated detection and analysis of musical events, such as notes and chords, has been designed. The system is comprised of two main elements: the event library and a set of match measures. The event library contains a hierarchy of event models each corresponding to a distinct musical note or chord. Each event model is structured as a hidden Markov model (HMM), \u03bb = (A, B, \u03c0), having the four distinct states labeled attack, sustain, decay or silence, that correspond to the specific physical states of the musical event. Associated with each model state Q={q1, \u2022\u2022\u2022 , q4} are a set of M observation symbols V={ v1,v2, \u2022\u2022\u2022 , vM} and a set of three probability distributions: a transition probability distribution A={aij} , an observable probability distribution B={bj(k)} and an initial probability distribution \u03c0=\u03c0{i}. Three match measures are developed for solving the recognition problem: one for estimating the HMM parameters, one for determining the optimal state sequence of the HMM and one for evaluating the probability that a given observation sequence was produced by a specific HMM. The observation sequence is derived from the input signal by sampling, converting to a spectral representation, and digitally coding using standard speech recognition\r\ntechniques. The three match measures correspond, respectively, to training the model, refining the model and matching an event to a model, each of which is performed using conventional speech processing algorithms.
", "doi": "10.7907/GPBA-SM95", "publication_date": "1999", "thesis_type": "engd", "thesis_year": "1999" }, { "id": "thesis:492", "collection": "thesis", "collection_id": "492", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02042008-081232", "primary_object_url": { "basename": "Tuqan_j_1998.pdf", "content": "final", "filesize": 5795987, "license": "other", "mime_type": "application/pdf", "url": "/492/1/Tuqan_j_1998.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Statistical optimization of multirate systems and orthonormal filter banks", "author": [ { "family_name": "Tuqan", "given_name": "Jamal", "clpid": "Tuqan-J" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "Effros", "given_name": "Michelle", "clpid": "Effros-M" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The design of multirate systems and/or filter banks adapted to the input signal statistics is a generic problem that arises naturally in variety of communications and signal processing applications. The two main applications we have in mind are the statistical optimization of subband coders for signal compression and the multirate modeling of WSS random processes. These two applications lead naturally to the important concepts of energy compaction filters and principal component filter banks. In this thesis, we study three problems that are directly related to the above mentioned applications. The first problem is motivated by the observation that in the presence of subband quantizers, it is a loss of generality to assume that the synthesis section in a filter bank is the inverse of the analysis section. We therefore consider the statistical optimization of linear time invariant (LTI) pre- and postfilters surrounding a quantization system. Unlike in previous work, the postfilter is not restricted to be the inverse of the prefilter. Closed form expressions for the optimum filters as well as the resulting minimum mean square error (m.m.s.e.) are derived. The importance of the m.m.s.e. expression is that it clearly quantifies the additional gain obtained by relaxing the perfect reconstruction assumption. In the second problem, we study the quantization of a certain class of non bandlimited signals, modeled as the output of L < M interpolation filters where M is the interpolation factor. Using the fact that these signals are oversampled, we show how to decrease substantially the quantization noise variance using appropriate multirate reconstruction schemes. We also optimize a variety of noise shapers, indicating the corresponding additional reduction in the average mean square error for each case. The results of this chapter extend, using multirate signal processing theory, some well known techniques of efficient A/D converters (e.g. sigma-delta modulators) that usually apply only to bandlimited signals. In the last problem, a novel procedure to design globally optimal FIR energy compaction filters is presented. Energy compaction filters are important due to their close connection to orthonormal filter banks adapted to the input signal statistics. In fact, for the two channel case, the problems are equivalent. A special case of compaction filters arise also in applications such as echo cancelation, time varying systems identification, standard subband filter design and optimal transmitter and receiver design in digital communications. The new proposed approach guarantees theoretical optimality which previous methods could not achieve. Furthermore, the new algorithm is:\ni) extremely general in the sense that it can be tailored to cover any of the above applications.\nii) numerically robust.\niii) can be solved efficiently using interior point methods.\nThe design of a special class of two channel IIR compaction filters is also considered. We show that, in general, this class of optimum IIR compaction filters, parameterized by a single coefficient, are competitive with very high order optimum FIR filters.\n", "doi": "10.7907/vx5t-w383", "publication_date": "1998", "thesis_type": "phd", "thesis_year": "1998" }, { "id": "thesis:1013", "collection": "thesis", "collection_id": "1013", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03192008-090303", "primary_object_url": { "basename": "Yu_z_1997.pdf", "content": "final", "filesize": 4659562, "license": "other", "mime_type": "application/pdf", "url": "/1013/1/Yu_z_1997.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Design Issues in Communications Networks: Reliability and Traffic Analysis", "author": [ { "family_name": "Yu", "given_name": "Zhong", "clpid": "Yu-Zhong" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Goldsmith", "given_name": "Andrea Jo", "orcid": "0000-0001-5686-800X", "clpid": "Goldsmith-A-J" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis aims to investigate two rather separate issues: network reliability and traffic analysis. The first concerns the reliability for unreliable systems, including communications networks with possible link failures, and more general fault-tolerant systems. The second concerns the traffic characteristics specifically in ATM networks with respect to the performance of statistical multiplexers.\r\n\r\nOne way in which we studied the reliability issue is via mean time to failure (MTTF) which considers systems that have component failures and repairs with exponential distributions. Such systems can be modeled by continuous-time discrete- state Markov chains. We investigated the MTTF from a more general framework of fault-tolerant systems (FTS), and developed two systematic approaches, the allpath-weight approach and the signal-flow-graph approach, to compute the MTTF. We also derived a simple asymptotic formula for estimating the MTTF, and obtained asymptotically the optimal networks in terms of the MTTF.\r\n\r\nThe other way in which we studied the reliability issue is via reliability polynomials for a system with component failures with certain fixed probability that is independent of time, but a function of the size of the system. No repair is allowed. We modeled such systems by random graphs, and analyzed reliability polynomials in a framework of random graph theory. We specifically focused on certain regular random graphs and analyzed the evolution of the regular random graphs, by showing a transition phenomenon when such a regular random graph evolves from edge probability zero to probability one because of the expansion of graph size, and identified its threshold function. Our work extends the study of the evolution of random graphs to regular random graphs which do not appear in the literature of random graphs, and our results are generalizations of some famous previously known results in random graph theory.\r\n\r\nAs for the second issue of traffic analysis in ATM networks, we first studied, via the approach of generating functions, Markov on-off traffic and the performance behavior of a statistical multiplexer with such traffic. We developed a heuristic procedure which allowed us to compute the expected buffer occupancy of a statistical multiplexer with Markov on-off traffic, and obtained closed form formulas showing that the expected buffer occupancy under such traffic not only depends on the incoming traffic intensity, but also largely on the burstiness of incoming traffic. The expected buffer occupancy becomes unbounded with large enough traffic burstiness, even though the traffic intensity is small. These results showed that burstiness control of traffic was very critical in designing ATM networks.\r\n\r\nWe then introduced a class of burst-constrained traffic sources, the periodic interchangeable (PI) traffic, and applied generalized Ballot theorems to analyze the buffer occupancy in a statistical multiplexer with PI traffic. We derived closed form formulas for survivor functions, expected buffer occupancy, and simple asymptotic formula that can be used as a rule of thumb for dimensioning buffer size in designing a statistical multiplexer. The results obtained could shed light on the study of worst case performance of statistical multiplexers for burst-constrained traffic sources in ATM networks.", "doi": "10.7907/pa8m-ay72", "publication_date": "1997", "thesis_type": "phd", "thesis_year": "1997" }, { "id": "thesis:1013", "collection": "thesis", "collection_id": "1013", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03192008-090303", "primary_object_url": { "basename": "Yu_z_1997.pdf", "content": "final", "filesize": 4659562, "license": "other", "mime_type": "application/pdf", "url": "/1013/1/Yu_z_1997.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Design Issues in Communications Networks: Reliability and Traffic Analysis", "author": [ { "family_name": "Yu", "given_name": "Zhong", "clpid": "Yu-Zhong" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Goldsmith", "given_name": "Andrea Jo", "orcid": "0000-0001-5686-800X", "clpid": "Goldsmith-A-J" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Bruck", "given_name": "Jehoshua", "orcid": "0000-0001-8474-0812", "clpid": "Bruck-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis aims to investigate two rather separate issues: network reliability and traffic analysis. The first concerns the reliability for unreliable systems, including communications networks with possible link failures, and more general fault-tolerant systems. The second concerns the traffic characteristics specifically in ATM networks with respect to the performance of statistical multiplexers.\r\n\r\nOne way in which we studied the reliability issue is via mean time to failure (MTTF) which considers systems that have component failures and repairs with exponential distributions. Such systems can be modeled by continuous-time discrete- state Markov chains. We investigated the MTTF from a more general framework of fault-tolerant systems (FTS), and developed two systematic approaches, the allpath-weight approach and the signal-flow-graph approach, to compute the MTTF. We also derived a simple asymptotic formula for estimating the MTTF, and obtained asymptotically the optimal networks in terms of the MTTF.\r\n\r\nThe other way in which we studied the reliability issue is via reliability polynomials for a system with component failures with certain fixed probability that is independent of time, but a function of the size of the system. No repair is allowed. We modeled such systems by random graphs, and analyzed reliability polynomials in a framework of random graph theory. We specifically focused on certain regular random graphs and analyzed the evolution of the regular random graphs, by showing a transition phenomenon when such a regular random graph evolves from edge probability zero to probability one because of the expansion of graph size, and identified its threshold function. Our work extends the study of the evolution of random graphs to regular random graphs which do not appear in the literature of random graphs, and our results are generalizations of some famous previously known results in random graph theory.\r\n\r\nAs for the second issue of traffic analysis in ATM networks, we first studied, via the approach of generating functions, Markov on-off traffic and the performance behavior of a statistical multiplexer with such traffic. We developed a heuristic procedure which allowed us to compute the expected buffer occupancy of a statistical multiplexer with Markov on-off traffic, and obtained closed form formulas showing that the expected buffer occupancy under such traffic not only depends on the incoming traffic intensity, but also largely on the burstiness of incoming traffic. The expected buffer occupancy becomes unbounded with large enough traffic burstiness, even though the traffic intensity is small. These results showed that burstiness control of traffic was very critical in designing ATM networks.\r\n\r\nWe then introduced a class of burst-constrained traffic sources, the periodic interchangeable (PI) traffic, and applied generalized Ballot theorems to analyze the buffer occupancy in a statistical multiplexer with PI traffic. We derived closed form formulas for survivor functions, expected buffer occupancy, and simple asymptotic formula that can be used as a rule of thumb for dimensioning buffer size in designing a statistical multiplexer. The results obtained could shed light on the study of worst case performance of statistical multiplexers for burst-constrained traffic sources in ATM networks.", "doi": "10.7907/pa8m-ay72", "publication_date": "1997", "thesis_type": "phd", "thesis_year": "1997" }, { "id": "thesis:90", "collection": "thesis", "collection_id": "90", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-01092008-082210", "primary_object_url": { "basename": "Cheng_jf_1997.pdf", "content": "final", "filesize": 3705135, "license": "other", "mime_type": "application/pdf", "url": "/90/1/Cheng_jf_1997.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Iterative decoding", "author": [ { "family_name": "Cheng", "given_name": "Jung-Fu", "clpid": "Cheng-Jung-Fu" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Goldsmith", "given_name": "Andrea Jo", "clpid": "Goldsmith-A-J" }, { "family_name": "Divsalar", "given_name": "Dariush", "clpid": "Divsalar-D" }, { "family_name": "Chandy", "given_name": "K. Mani", "clpid": "Chandy-K-M" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Though coding theory suggests long error correcting codes chosen at random perform close to the optimum, the problem of designing good codes has traditionally been attacked by developing codes with a lot of structure, which lends itself to feasible decoders. The challenge to find practical decoders for long random codes has not been seriously considered until the recent introduction of turbo codes in 1993. This methodology of multi-stage iterative decoding with exchange of soft information, applied to codes with pseudo-random structure, has provided a whole new approach to construct good codes and to decode them with low complexity. This thesis examines the theoretical ground as well as the design and implementation details of these iterative decoding techniques. The methodology is first applied to parallel concatenated unit-memory convolutional codes and generalized concatenated convolutional codes to demonstrate its power and the general design principle. We then show that, by representing these coding systems with appropriate Bayesian belief networks, all the ad hoc algorithms can be derived from a general statistical inference belief propagation algorithm A class of new binary codes based on low-density generator matrices is proposed to eliminate the arbitrariness and unnecessary constraints in turbo coding we have recognized from this Bayesian network viewpoint. Contrary to the turbo decoding paradigm where sequential processing is accomplished by very powerful central units, the decoding algorithm for the new code is highly parallel and distributive. We also apply these codes to M-ary modulations using multilevel coding techniques to achieve higher spectral efficiency. In all cases, we have constructed systems with flexible error protection capability and performance within 1 dB of the channel capacity.\r\n", "doi": "10.7907/ydj9-zq05", "publication_date": "1997", "thesis_type": "phd", "thesis_year": "1997" }, { "id": "thesis:116", "collection": "thesis", "collection_id": "116", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-01102008-145701", "primary_object_url": { "basename": "Lin_yp_1997.pdf", "content": "final", "filesize": 9156612, "license": "other", "mime_type": "application/pdf", "url": "/116/1/Lin_yp_1997.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "One- and Two-Dimensional Cosine Modulated Filter Banks", "author": [ { "family_name": "Lin", "given_name": "Yuan-Pei", "clpid": "Lin-Yuan-Pei" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Subband coding as a lossy data compression technique was first introduced for speech coding. It has been demonstrated to be a very competitive coding method for general audio signals as well as images. Subband coding has been incorporated in various popular coding standards. Essential to the implementation of subband coding is an M-channel filter bank that partitions the input signal into M subbands. In the context of 1D (one-dimensional) filter bank design, the CMFB (cosine modulated filter bank) is well-known for design and implementation efficiency. All the filters in the filter bank are cosine modulated versions of a prototype filter. As a result the cost of design as well as complexity is reduced dramatically by a factor of M. In this thesis we study the design of CMFB in 1D case and 2D (two-dimensional) case.
\r\n\r\nIn previous works on 1D CMFB, the filters in the filter bank do not have linear phase, which is considered an important feature in image coding applications. The design of cosine modulated filter banks with linear-phase filters is the first topic to be presented in this thesis. Design examples will be given to show that filter banks with filters having good frequency selectivity can be obtained in spite of the linear phase constraint.
\r\n\r\nFor the design of 2D cosine modulated filter banks, the simplest approach is to cascade 1D filter banks in the form of a tree. This type of 2D filter banks are referred to as separable. The frequency support of the filters in a separable filter bank are restricted to rectangular shapes. Nonseparable filter banks allow more flexible partitions of the frequency plane and achieve better performance. Almost all the existing design techniques for 2D nonseparable filter banks are developed exclusively for the two-channel case. We will consider two types of 2D M-channel nonseparable filter banks, the two-parallelogram type and the four-parallelogram type. These are respectively the classes of filter banks in which the passbands of the filters consist of two and four parallelograms. In these designs additional cosine modulated constraints will be incorporated for design and implementation economy.
", "doi": "10.7907/n255-7g92", "publication_date": "1997", "thesis_type": "phd", "thesis_year": "1997" }, { "id": "thesis:171", "collection": "thesis", "collection_id": "171", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-01142008-075936", "primary_object_url": { "basename": "Lin_w_1997.pdf", "content": "final", "filesize": 5213603, "license": "other", "mime_type": "application/pdf", "url": "/171/1/Lin_w_1997.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "The trellis complexity of block and convolutional codes", "author": [ { "family_name": "Lin", "given_name": "Wei", "clpid": "Lin-Wei" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Kiely", "given_name": "Aaron B.", "clpid": "Kiely-A-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wilson", "given_name": "Richard M.", "clpid": "Wilson-R-M" }, { "family_name": "Dolinar", "given_name": "Samuel J.", "clpid": "Dolinar-S-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.\r\n\r\nThis thesis concerns the computational complexity of high performance decoding algorithms. The primary objective is to design the most efficient maximum-likelihood (ML) decoders for both block codes and convolutional codes. By efficient, we mean an implementation of ML decoding algorithms on trellises that minimize the computational complexity (the total number of additions and comparisons). Trellises are graph representations of codes. Since decoding complexity is completely determined by the particular trellis employed, the problem is equivalent to constructing the minimal trellis (one that has the minimum number of edges, vertices and bifurcations) for a given code.\r\n\r\nThere are four parts to this research. The first problem we attacked was to construct the minimal trellises for block codes over the coordinate permutations. The related problem of finding a coordinate permutation that minimizes the number of vertices at a given depth in the minimal trellis for a binary linear block code [36] has been proven to be NP-complete. Our approach was based on the concept of span of the generator matrices, which connects the code parameters and the trellis complexity. New bounds on measures of trellis complexity such as [E] (the total number of edges) and [V] (the total number of vertices) were obtained from the analysis of the span distribution. Aiming to minimize the total span in a generator matrix, an efficient, effective \"divide-and-conquer\" algorithm and variants were proposed to search for the optimal or a good trellis structure for any block code. For example, it took about 12 minutes on a Sun Sparc Station 20 to find one optimal permutation for the [48,24,12] QR code from 48! candidates.\r\n\r\nBy introducing the concept of trellis-canonical generator matrices and a simple algorithm to compute one, we developed a general theory of minimal trellises for convolutional codes. In this theory, punctured convolutional codes no longer have to be treated as special cases. By then, the minimal trellises for block and convolutional codes were both well-defined. This allowed one to make a direct performance-complexity comparison between block codes and convolutional codes.\r\n\r\nThe ratio of performance (measured by the asymptotic coding gain-ACG) and complexity (measured by the logarithm trellis edge complexity-LTC) defines the coding efficiency. By means of the span analysis, we also proved a universal lower bound on the complexity to performance ratio. It implies that [...] can never be smaller than 1 for any code, block or convolutional. In some cases, the bound is optimal or asymptotically optimal. The study suggests that optimal codes in terms of minimum distance or free distance do not necessarily offer the best coding efficiency.\r\n\r\nThe last problem addressed in this dissertation is the implementation of maximum-likelihood decoding and the computational complexity for convolutional codes. By combining the optimal sectionalization technique [45] with minimal trellis theory, a low complexity hybrid decoding algorithm was developed. For some partial unit memory convolutional codes, its decoding complexity is significantly superior to other known algorithms. There are two components of the computational complexity. One is the edge metric computation cost [...]. We proved a lower bound on [...] which is independent of the computation mechanism (sequential or parallel). This bound is optimal in some cases. The other is the cost of the state metric updating which is inferable from the trellis structure. This sets a lower bound on the computational complexity for any implementation.\r\n\r\nFinally we give a general review of research activities on this subject and present a list of open problems.\r\n", "doi": "10.7907/5130-4858", "publication_date": "1997", "thesis_type": "phd", "thesis_year": "1997" }, { "id": "thesis:4977", "collection": "thesis", "collection_id": "4977", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12122007-145855", "primary_object_url": { "basename": "Erimli_b_1996.pdf", "content": "final", "filesize": 5690083, "license": "other", "mime_type": "application/pdf", "url": "/4977/1/Erimli_b_1996.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Switching Algorithms and Buffer Management in Asynchronous Transfer Mode Networks", "author": [ { "family_name": "Erimli", "given_name": "Bahadir", "clpid": "Erimli-Bahadir" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, two different but related concepts in Asynchronous Transfer Mode (ATM) are discussed. Due to its multirate nature, ATM creates new problems in terms of switching and buffering. In the first part, the switching problems are investigated. The situation is rooted upon the multirate connections in a 'circuit-switching-like' environment. The multirate nature of ATM results in the loss of strictly nonblocking three stage space-division switches unless a 'speed-up factor' is provided between the outside ports and the internal links of the switch. To keep this factor to a minimum, call routing algorithms are considered as a possible solution. Several call routing algorithms are compared in terms of their blocking probability under various circumstances. A simple algorithm, named fixed priority routing algorithm, stands out among these, both in terms of simplicity and low blocking rate. Afterwards a bin packing model is used to investigate the reasons behind this.
\r\n\r\nIn the second part, buffer management in ATM nodes is considered. In the traditional sense, the burstier the traffic is, the higher, it was believed, the cell loss will be at a buffer into which a number of these sources are transmitting. It is shown that this is not always the case and under the circumstances defined - the worst-case model - other types of sources that output traffic that is less bursty might create higher cell loss than burstier sources. All sources considered are leaky-bucket controlled and stay within their contract limits with the network at all times. Initially greedy on-off source and the three-state source types are compared. After establishing that the comparison between these two in terms of cell loss rate is highly dependent on the size of the buffer being transmitted onto, other source types that might create even higher cell loss rates are searched for. One such characteristic group of sources is found and is presented.
", "doi": "10.7907/agbk-bn50", "publication_date": "1996", "thesis_type": "engd", "thesis_year": "1996" }, { "id": "thesis:5126", "collection": "thesis", "collection_id": "5126", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12222007-114654", "primary_object_url": { "basename": "Phoong_sm_1996.pdf", "content": "final", "filesize": 10055459, "license": "other", "mime_type": "application/pdf", "url": "/5126/1/Phoong_sm_1996.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Time-varying and finite field filter banks", "author": [ { "family_name": "Phoong", "given_name": "See-May", "clpid": "Phoong-See-May" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Bruck", "given_name": "Jehoshua", "clpid": "Bruck-J" }, { "family_name": "Effros", "given_name": "Michelle", "clpid": "Effros-M" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Xia", "given_name": "Xiang-Gen", "clpid": "Xia-Xiang-Gen" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Filter banks find many applications in signal processing. This thesis deals with four different problems in filter banks.\r\n\r\nFirst we find a new application of filter banks: Filter bank convolver. We prove two filter bank convolution theorems which tell us how to do the convolution in the subbands. Applying the multirate technique to the problem of convolution, we obtain a significant improvement in the accuracy of the convolutional result when the computation is done with finite precision. The derivation also leads to a low sensitivity robust structure for FIR filters.\r\n\r\nIn the second part, a new class of two-channel biorthogonal filter banks is proposed. We successfully design IIR filter banks which achieve the following desired properties simultaneously: (i) Perfect reconstruction (PR); (ii) causality and stability; (iii) near linear-phase; (iv) frequency selectivity. Two classes of causal stable maximally flat IIR wavelets are derived and closed form formulas are given. We also provide a novel mapping of the proposed 1D framework into 2D. The mapping preserves: (i) PR; (ii) stability in the IIR case and linear phase in the FIR case; (iii) frequency selectivity; (iv) low complexity.\r\n\r\nIn the third part, the theory of paraunitary (PU) filter banks is extended to the case of GF(q) with prime q. We show that finite field PU filter banks are very different from real or complex PU filter banks. Despite all the differences, we are able to prove a number of factorization theorems. All unitary matrices in GF(q) are factorizable in terms of Householder-like matrices. The class of first-order PU matrices, the lapped orthogonal transform in finite fields, can always be expressed as a product of degree-one or degree-two building blocks.\r\n\r\nFinally the theory of conventional LTI filter banks is extended to the time-varying case. We develop a polyphase representation method for time-varying filter bank (TVFB). Using the proposed polyphase approach, we are able to show some unusual properties which are not exhibited by the conventional LTI filter banks. For example, we can show that for a PR TVFB, the losslessness of analysis bank does not always imply that of the synthesis bank, and a PR TVFB in general will only generate a discrete-time frame, rather than a basis, for the class of finite energy signals. The class of lossless TVFB is studied in detail. We show that all lossless linear time-varying systems are invertible and provide explicit construction of the inverse. The interplay between invertibility, uniqueness and losslessness of the inverse is investigated. The factorizability of lossless TVFB is addressed and we show that there are factorizable and unfactorizable examples.", "doi": "10.7907/1bzz-ba31", "publication_date": "1996", "thesis_type": "phd", "thesis_year": "1996" }, { "id": "thesis:4977", "collection": "thesis", "collection_id": "4977", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12122007-145855", "primary_object_url": { "basename": "Erimli_b_1996.pdf", "content": "final", "filesize": 5690083, "license": "other", "mime_type": "application/pdf", "url": "/4977/1/Erimli_b_1996.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Switching Algorithms and Buffer Management in Asynchronous Transfer Mode Networks", "author": [ { "family_name": "Erimli", "given_name": "Bahadir", "clpid": "Erimli-Bahadir" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, two different but related concepts in Asynchronous Transfer Mode (ATM) are discussed. Due to its multirate nature, ATM creates new problems in terms of switching and buffering. In the first part, the switching problems are investigated. The situation is rooted upon the multirate connections in a 'circuit-switching-like' environment. The multirate nature of ATM results in the loss of strictly nonblocking three stage space-division switches unless a 'speed-up factor' is provided between the outside ports and the internal links of the switch. To keep this factor to a minimum, call routing algorithms are considered as a possible solution. Several call routing algorithms are compared in terms of their blocking probability under various circumstances. A simple algorithm, named fixed priority routing algorithm, stands out among these, both in terms of simplicity and low blocking rate. Afterwards a bin packing model is used to investigate the reasons behind this.
\r\n\r\nIn the second part, buffer management in ATM nodes is considered. In the traditional sense, the burstier the traffic is, the higher, it was believed, the cell loss will be at a buffer into which a number of these sources are transmitting. It is shown that this is not always the case and under the circumstances defined - the worst-case model - other types of sources that output traffic that is less bursty might create higher cell loss than burstier sources. All sources considered are leaky-bucket controlled and stay within their contract limits with the network at all times. Initially greedy on-off source and the three-state source types are compared. After establishing that the comparison between these two in terms of cell loss rate is highly dependent on the size of the buffer being transmitted onto, other source types that might create even higher cell loss rates are searched for. One such characteristic group of sources is found and is presented.
", "doi": "10.7907/agbk-bn50", "publication_date": "1996", "thesis_type": "engd", "thesis_year": "1996" }, { "id": "thesis:3587", "collection": "thesis", "collection_id": "3587", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09172007-153727", "primary_object_url": { "basename": "Deora_sk_1995.pdf", "content": "final", "filesize": 3646275, "license": "other", "mime_type": "application/pdf", "url": "/3587/1/Deora_sk_1995.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Channel assignment algorithms in cellular radio networks", "author": [ { "family_name": "Deora", "given_name": "Sanjeev K.", "clpid": "Deora-S-K" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Goldsmith", "given_name": "Andrea Jo", "clpid": "Goldsmith-A-J" }, { "family_name": "Blanchard", "given_name": "John", "clpid": "Blanchard-J" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, we study and compare the performance of several distributed channel assignment algorithms (CAAs) in a cellular system. The CAA which is used to assign a channel to a new call greatly influences the amount of traffic the system can support. We are interested in the design and analysis of algorithms which perform well, but at the same time are relatively easy to implement. In this thesis, we have analyzed the performance of a very simple CAA which we call the Timid Algorithm, in the limiting case of a large number of channels. We have been able to show that, under a plausible mathematical hypothesis, the algorithm is asymptotically optimal, where \"asymptotically\" refers to a system with a large number of channels. This is very surprising as there are algorithms of much higher complexity which provably do not have this property.\n\nThe Timid Algorithm is asymptotically optimal, but it requires a large number of channels for a satisfactory performance. We looked at some algorithms which retain the simplicity of the Timid algorithm but which can be expected to give a good performance even with a smaller number of channels. We called one such algorithm the Modified DCAA. We present some simulation results which show that this algorithm gives a reasonably good performance even when the number of channels is small. One of the ways to increase the capacity of a cellular system is through the use of micro-cells. The Modified DCAA, because of its distributed nature and low complexity, is particularly suitable for such microcellular systems.\n\nWe also present a method for computing the upper bound on the performance of any CAA in a cellular system with adjacent channel constraints. The method, although computationally intensive, may be useful for determining how close an algorithm's performance is to the optimal performance.\n\nFinally, we discuss ways of obtaining the set of \"allowable\" states for a system. We also present some \"measurement-based\" algorithms and compare their performance with \"prediction-based\" algorithms.\n", "doi": "10.7907/1nxh-ak43", "publication_date": "1995", "thesis_type": "phd", "thesis_year": "1995" }, { "id": "thesis:3869", "collection": "thesis", "collection_id": "3869", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-10022007-131456", "primary_object_url": { "basename": "Flanagan_mj_1995.pdf", "content": "final", "filesize": 5056787, "license": "other", "mime_type": "application/pdf", "url": "/3869/1/Flanagan_mj_1995.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Reduced-complexity digital sinusoid generators and oversampled data converters", "author": [ { "family_name": "Flanagan", "given_name": "Michael J.", "clpid": "Flanagan-M-J" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Zimmerman", "given_name": "G. A.", "clpid": "Zimmerman-G-A" } ], "thesis_committee": [ { "family_name": "Zimmerman", "given_name": "G. A.", "clpid": "Zimmerman-G-A" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Satorius", "given_name": "Edgar H.", "clpid": "Satorius-E-H" }, { "family_name": "Galton", "given_name": "I.", "clpid": "Galton-I" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis separately addresses two important issues in signal processing: digital sinusoid generators and oversampled data converters. The first part of the thesis addresses noise additive, or dithering, techniques that exponentially reduce the complexity of digital sinusoid generators for a given level of spur performance. With the appropriate dither signals the quantization noise can be rendered nearly white and free of large spurs, or periodic error components, without recourse to large look-up tables. New analysis shows that when the phase dither signal is the sum of M uniform white variates, the phase spurs are at a level of -6(M + 1) dBc per look-up phase bit instead of the usual -6 dBc per phase bit in a non-dithered system. This exponentially reduces the complexity of the digital sinusoid generator for a given spur requirement at the expense of linearly increasing the nearly-white quantization noise.
\r\n\r\nThe second part of the thesis presents two metric-based approaches to the design of over-sampled data converters (ODCs). The first approach leads to an architecture which is derived based on the minimization of a causal, constrained-memory, power-spectral-distortion metric. This architecture is compared to standard ΔΣ modulators and shown to have superior noise performance under some conditions.
\r\n\r\nAnother metric-based approach to the design of ODCs uses a more general distortion metric and incorporates elements of vector quantization, eigensystems and analysis of the discrete prolate spheroidal wave functions. This enables the application of vector quantization theory to oversampled data converters. A vector-quantizer-based ODC architecture called the eigenmodulator is motivated and analyzed. Rate-distortion results are presented for the important case of a band-limited Gaussian input. When both the complexity of the eigenmodulator and the oversampling ratio become large, it is shown that the distribution of the output vectors in an important transform space becomes joint Gaussian. This is shown to be important in light of the centroid condition for an optimal vector quantizer. The implication of this result on the choice of output scaling for the single-bit data converter is addressed.
\r\n", "doi": "10.7907/SP61-8895", "publication_date": "1995", "thesis_type": "phd", "thesis_year": "1995" }, { "id": "thesis:3586", "collection": "thesis", "collection_id": "3586", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09172007-152709", "primary_object_url": { "basename": "Djokovic_i_1995.pdf", "content": "final", "filesize": 6227068, "license": "other", "mime_type": "application/pdf", "url": "/3586/1/Djokovic_i_1995.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Optimization issues in wavelets and filter banks", "author": [ { "family_name": "Djokovic", "given_name": "Igor", "clpid": "Djokovic-I" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Mead", "given_name": "Carver", "orcid": "0000-0003-4051-0462", "clpid": "Mead-C-A" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Cuk", "given_name": "Slobodan", "clpid": "Cuk-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In the last decade or so, we have witnessed a rapid development of the wavelet and filter bank theory. Wavelets find applications in signal compression, computer vision, geophysics, pattern recognition, numerical analysis, and function theory, just to name a few. Filter banks, on the other hand, offer very efficient implementation of different algorithms in connection with wavelets. The thesis deals with three problems in filter banks and wavelets.\r\n\r\nIn the first part, we show that perfect reconstruction is equivalent to biorthogonality of the filters. Using this, we examine existence issues in nonuniform filter banks. We show that whenever there exists a rational biorthogonal filter bank, then there is a rational orthonormal filter bank as well. We also derive a number of necessary conditions for the existence of perfect reconstruction nonuniform filter banks. We show how the tools developed in the first part can be used for decorrelation of subband signals.\r\n\r\nThe second problem deals with optimality issues in wavelet and filter bank theory. We tune scaling function for the analysis of WSS random processes, so that the energy is concentrated in as few transform coefficients as possible. The corresponding problem in the filter bank theory is that of adapting filter responses to a given (discrete time) WSS random process so as to achieve a better energy compaction.\r\n\r\nFinally, the last part is devoted to developing sampling theory for multiresolution subspaces. More precisely, we extend existing uniform sampling theory to periodically nonuniform sampling. This extension offers one very important advantage over the existing sampling theory. By allowing for periodically nonuniform sampling grid, it is possible to have compactly supported synthesis functions, which was not the case before. Several variations on the basic theme are considered. Also, an application of the developed techniques to efficient computation of inner products in multiresolution subspaces is presented.", "doi": "10.7907/pyy4-dt15", "publication_date": "1995", "thesis_type": "phd", "thesis_year": "1995" }, { "id": "thesis:4782", "collection": "thesis", "collection_id": "4782", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12042007-132203", "primary_object_url": { "basename": "Lee_mc_1994.pdf", "content": "final", "filesize": 18210332, "license": "other", "mime_type": "application/pdf", "url": "/4782/1/Lee_mc_1994.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Still and Moving Image Compression Systems Using Multiscale Techniques", "author": [ { "family_name": "Lee", "given_name": "Ming-Chieh", "clpid": "Lee-Ming-Chieh" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Mead", "given_name": "Carver", "orcid": "0000-0003-4051-0462", "clpid": "Mead-C-A" }, { "family_name": "Cheung", "given_name": "Kar-Ming", "clpid": "Cheung-Kar-Ming" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Multi-scale techniques have been popular methods for image and video compression. The basic idea behind these techniques is to decompose the original signals into several components of different scales, however the scale is defined, of different sizes. One then applies appropriate encoding strategies to different components to achieve compression by taking advantage of various properties. In this thesis, we review and present several new schemes of multi-scale techniques using linear and nonlinear systems. Linear techniques, which use linear filters for decomposition, have been thoroughly investigated and widely applied because of their simplicity in implementation and analysis. Herein we describe how to appropriately combine these techniques in order to process the signals more efficiently and advantageously; moreover, the picture quality of the quantized images can be improved. The sub-band coding technique is used as the basis for these combinations. As for the nonlinear technique, we would like to take advantage of the nonlinear features of images (such as edges) in compression to achieve compressing and enhancing of the images. Herein we design several nonlinear multi-resolution systems, using various nonlinear filters, to decompose the signals in a proper form. We show that, in terms of rate-distortion performance, where mean squared error is used as the distortion criterion, these schemes are close to, or even better than, JPEG standard, whereas the encoding and, especially, decoding complexity is lower than that of JPEG. We can obtain much better image quality (in the perceptual sense), however, by applying suitable simple and fast lossless compression schemes to sub-images. Simulation results are demonstrated to show the advantages and feasibility of the proposed scheme. In summary, we mention the current status and future trends of compression technologies.", "doi": "10.7907/02w7-rg28", "publication_date": "1994", "thesis_type": "phd", "thesis_year": "1994" }, { "id": "thesis:4975", "collection": "thesis", "collection_id": "4975", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12122007-135636", "primary_object_url": { "basename": "Antsos_d_1994.pdf", "content": "final", "filesize": 10519161, "license": "other", "mime_type": "application/pdf", "url": "/4975/1/Antsos_d_1994.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Computer-aided modeling and analysis of passive microwave and millimeter-wave high-temperature superconductor circuits and components", "author": [ { "family_name": "Antsos", "given_name": "Dimitrios", "clpid": "Antsos-D" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "As their critical temperatures continue to rise, high-temperature superconductors (HTS) promise applications in microwave, and to some extent in millimeter-wave circuits, because they should exhibit lower loss, in these frequencies, than their normal metal counterparts. However, in the case of passive circuits, fundamental performance limits (finite insertion loss) still exist and apply, as explored in this thesis.\n\nCommercial computer-aided design (CAD) and analysis software tools exist, that permit design and analysis of normal metal microwave and millimeter-wave circuits. These tools minimize design and manufacturing errors and the need for costly re-work and design iterations. In the case of HTS circuits these tools are insufficient because of three effects present in HTS circuits that do not exist in normal metal circuits. First, because of manufacturing practices, the HTS layers on substrates are usually very thin; of the order of the magnetic field penetration depth. Second, there is an additional internal inductance, the kinetic inductance, which is due to the inertia of the superelectrons. Third, high input power induces high magnetic fields and current densities which drive the superconductor into its normal state, in which it is an insulator.\n\nThis thesis is a study of these phenomena and their effects on quasi-TEM transmission line circuit performance. Methods for accounting for these effects and introducing them into currently available CAD tools are presented. These methods are applied to three example circuits for which modeled and measured performance is compared.\n\nThe viability and advantages of HTS waveguides are also studied and analyzed. A finite difference analysis program is presented.", "doi": "10.7907/fb3q-7f74", "publication_date": "1994", "thesis_type": "phd", "thesis_year": "1994" }, { "id": "thesis:4944", "collection": "thesis", "collection_id": "4944", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12112007-082807", "primary_object_url": { "basename": "Raphaeli_d_1994.pdf", "content": "final", "filesize": 9455630, "license": "other", "mime_type": "application/pdf", "url": "/4944/1/Raphaeli_d_1994.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Noncoherent Coded Modulation", "author": [ { "family_name": "Raphaeli", "given_name": "Dan", "clpid": "Raphaeli-Dan" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, we are concerned with the transmission of data over noncoherent channels (the carrier phase is random). We consider a receiving system which does not attempt to estimate the carrier phase from the received data. Instead, the transmitter and receiver will be designed so that the data transmission is robust with respect to the unknown phase variations of the channel. For the transmitter, we propose new combined coding and modulation, specifically designed to match the noncoherent channel. For the receiver, efficient decoders to noncoherently decode the coded modulation are developed. As a result, we are able to show, both analytically and by computer simulations, that Noncoherent Coded Modulation (NCM) approaches the performance of coded coherent modulation. NCM achieves almost the same power efficiency without bandwidth expansion or an extensive increase in complexity.
\r\n\r\nWe consider the problem of the Uniform Error Property (UEP) for a broad class of transmitters and receivers. A sufficient condition for a general linear code to satisfy the UEP is presented and a structure of a trellis-coded modulation that satisfies this condition is offered. We call these codes \"linear noncoherent trellis-coded modulation\" since they apply to noncoherent detection. The problem of noncoherently catastrophic codes, which can result in noncoherent detection of trellis codes, is discussed and a general solution which does not rely on differential encoding of the code output is offered.
\r\n\r\nHigh performance noncoherent detection is achieved using multiple symbol observations. Unlike previous approaches, a sliding window is used for the observations, with each observation covering several branches of the trellis, so that the observations are time-overlapped. We define a new type of noncoherent maximum likelihood sequence estimator, and analyze its performance over the Additive White Gaussian Noise (AWGN) channel by numerical calculation of the union bound. We perform a computerized search and present new high performance coded M-ary Phase Shift Keying (PSK) modulations for noncoherent detection and their performance. The new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection. We evaluate the performance of NCM in the presence of phase jitter in the channel. The method can also be used for multiple symbol demodulation of M-ary Differential PSK (MDPSK) and of Continuous Phase Modulation (CPM). We provide results for both, full and partial response CPM schemes as well as convolutionally coded CPM. The complexity and power efficiency of this new method is superior to all past schemes known to the author for noncoherent detection.
\r\n\r\nThe optimal implementation of the decoder, using the Viterbi Algorithm (VA), is given. For L-symbols observation, it requires a number of states that grows exponentially with L. Three novel sub-optimal algorithms are presented, whose number of states is the same as the original code so their complexity has a relatively weak dependence on L. For practical values of L, these algorithms are substantially less complex than the optimal algorithm.
\r\n\r\nThe first suboptimal algorithm to be described is called the Basic Decision Feedback Algorithm (BDFA). In this algorithm, the symbols from the decisions are fed back to be used in the subsequent decisions. This algorithm suffers from increased error event probability and from error propagation. However, by a small modification of the BDFA, we obtain another improved algorithm, which will be called Modified Decision Feedback Algorithm (MDFA).
\r\n\r\nTo obtain close to optimal performance, the third algorithm, the Estimated Future Decision Feedback Algorithm (EFDFA) is offered. This sophisticated algorithm, which uses the BDFA as a basic building block, is based on a novel concept called \"estimated future.\" Performance analysis and simulation results are given.
", "doi": "10.7907/fexw-ex94", "publication_date": "1994", "thesis_type": "phd", "thesis_year": "1994" }, { "id": "thesis:4782", "collection": "thesis", "collection_id": "4782", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-12042007-132203", "primary_object_url": { "basename": "Lee_mc_1994.pdf", "content": "final", "filesize": 18210332, "license": "other", "mime_type": "application/pdf", "url": "/4782/1/Lee_mc_1994.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Still and Moving Image Compression Systems Using Multiscale Techniques", "author": [ { "family_name": "Lee", "given_name": "Ming-Chieh", "clpid": "Lee-Ming-Chieh" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Mead", "given_name": "Carver", "orcid": "0000-0003-4051-0462", "clpid": "Mead-C-A" }, { "family_name": "Cheung", "given_name": "Kar-Ming", "clpid": "Cheung-Kar-Ming" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Multi-scale techniques have been popular methods for image and video compression. The basic idea behind these techniques is to decompose the original signals into several components of different scales, however the scale is defined, of different sizes. One then applies appropriate encoding strategies to different components to achieve compression by taking advantage of various properties. In this thesis, we review and present several new schemes of multi-scale techniques using linear and nonlinear systems. Linear techniques, which use linear filters for decomposition, have been thoroughly investigated and widely applied because of their simplicity in implementation and analysis. Herein we describe how to appropriately combine these techniques in order to process the signals more efficiently and advantageously; moreover, the picture quality of the quantized images can be improved. The sub-band coding technique is used as the basis for these combinations. As for the nonlinear technique, we would like to take advantage of the nonlinear features of images (such as edges) in compression to achieve compressing and enhancing of the images. Herein we design several nonlinear multi-resolution systems, using various nonlinear filters, to decompose the signals in a proper form. We show that, in terms of rate-distortion performance, where mean squared error is used as the distortion criterion, these schemes are close to, or even better than, JPEG standard, whereas the encoding and, especially, decoding complexity is lower than that of JPEG. We can obtain much better image quality (in the perceptual sense), however, by applying suitable simple and fast lossless compression schemes to sub-images. Simulation results are demonstrated to show the advantages and feasibility of the proposed scheme. In summary, we mention the current status and future trends of compression technologies.", "doi": "10.7907/02w7-rg28", "publication_date": "1994", "thesis_type": "phd", "thesis_year": "1994" }, { "id": "thesis:454", "collection": "thesis", "collection_id": "454", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02022005-162907", "primary_object_url": { "basename": "Mouchtaris_pn_1993.pdf", "content": "final", "filesize": 2914850, "license": "other", "mime_type": "application/pdf", "url": "/454/1/Mouchtaris_pn_1993.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Analysis of an interactive video architecture", "author": [ { "family_name": "Mouchtaris", "given_name": "Petros N.", "clpid": "Mouchtaris-P-N" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Chandy", "given_name": "K. Mani", "clpid": "Chandy-K-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A new residential application for interactive video is proposed. There is a service provider that prepares and distributes daily news programs customized to subscriber interest. The provider assembles the programs from short news clips and uses a profile data base of subscribers for selecting the appropriate clips. The time of viewing the program can be selected by the customers in near-real-time. We model this service and propose a network architecture that can support it. There is a main node that contains most of the storage and sourcing facilities, and an intermediate node to which all customers are connected. Multicasting is used as much as possible for reducing the traffic load on the network. In addition to that, popular material is stored in the intermediate node which is closer to the customers, which further decreases the traffic load.\n\nOur main concern is the time that a customer has to wait until he starts getting his program. This time is a function of the capacity of the link that connects the main node to the intermediate node, the so-called main link. The case that the main link can only transport a single video connection is considered first. We propose a recurrent algorithm that calculates the probabilities of the states and uses them for evaluating the expected wait, and prove that there is a very simple relationship between the expected wait and the probabilities of the states. A simplified analysis that directly computes the expected wait is proposed next. This approach is computationally more efficient but does not give us any information about the probabilities of the states.\n\t\nFor the general case that the main link can transport more than one video connection, we generalize the recurrent algorithm that calculates the probabilities of the states and the simple relationship between the expected wait and the probabilities of the states. For the cases that the complexity of our algorithm is too large, we propose and evaluate three approximate techniques for estimating the expected wait. In the first technique we use the results for the case that a main link can only transport a single connection for estimating the results for the general case. In the second technique we use the idea of rescaling time. In the third, motivated by the fluid-flow theory, we solve a deterministic problem and use the results of that problem for estimating the expected wait for the problem we are interested in. We show that these approximate techniques compare well with simulations. Thus, we can now decide what the capacity of the main link should be so that our system has the desired performance, and we can do that even if the number of customers is very large.\n", "doi": "10.7907/A9Z4-N267", "publication_date": "1993", "thesis_type": "phd", "thesis_year": "1993" }, { "id": "thesis:3207", "collection": "thesis", "collection_id": "3207", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-08232007-095226", "primary_object_url": { "basename": "Chen_t_1993.pdf", "content": "final", "filesize": 5842550, "license": "other", "mime_type": "application/pdf", "url": "/3207/1/Chen_t_1993.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Multidimensional multirate filters and filter banks : theory, design, and implementation", "author": [ { "family_name": "Chen", "given_name": "Tsuhan", "clpid": "Chen-Tsuhan" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Simon", "given_name": "Marvin K.", "clpid": "Simon-M-K" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Multidimensional (MD) multirate systems, which find applications in the coding and compression of image and video data, and in high definition television (HDTV) systems, have recently attracted much attention. Central to these systems is the idea of sampling lattices. The basic building blocks in an MD multirate system are the decimation matrix M, the expansion matrix L, and MD digital filters. When M and L are diagonal, most of the one-dimensional (1D) multirate results can be extended automatically, using separable approaches (i.e., separate operations in each dimension). Separable approaches are commonly used in practice due to their low complexity in implementation. However, nonseparable operations, with respect to nondiagonal decimation and expansion matrices, often provide more flexibility and better performance. Several applications, such as the conversion between progressive and interlaced video signals, actually require the use of nonseparable operations. For the nonseparable case, extensions of 1D results to the MD case are nontrivial. In this thesis, we will introduce some developments in these extensions. The three main results are: the design of nonseparable MD filters and filter banks derived from 1D filters, the commutativity of MD decimators and expanders and its applications to the efficient polyphase implementation of MD rational decimation systems, and the vector space framework for unifying MD filter bank and wavelet theory. In particular, properties of integer matrices like matrix fraction descriptions, coprimeness, the Bezout identity, etc., of which the polynomial versions are known in system theory, are used for the first time in the area of multirate signal processing.\r\n", "doi": "10.7907/XHE8-RB96", "publication_date": "1993", "thesis_type": "phd", "thesis_year": "1993" }, { "id": "thesis:3052", "collection": "thesis", "collection_id": "3052", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-08082007-081649", "primary_object_url": { "basename": "Ramesh_r_1992.pdf", "content": "final", "filesize": 3839996, "license": "other", "mime_type": "application/pdf", "url": "/3052/1/Ramesh_r_1992.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Efficient multichannel methods for high-rate data transmission with application to ISDN (or) pouring water to get more out of copper", "author": [ { "family_name": "Ramesh", "given_name": "Rajaram", "clpid": "Ramesh-R" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, we are concerned with the transmission of data over channels with intersymbol interference. We consider input signals which are multiplexed versions of several parallel input signals, with the aim of splitting the input signal spectrum into disparate frequency bands and shaping the input spectrum by adjusting the power on each of the frequency bands. We introduce a multirate signal processing framework for the representation of the channel under these conditions and derive simple equivalents for the channel and the associated processors.\n\nUsing the equivalent circuits, we derive simple equalization schemes for the channel by drawing from the theory of polynomial matrices. We show that vector equalization can be reduced to a combination of prefiltering, postfiltering and scalar equalization of a few of the parallel input signals. We also discuss several interesting properties of this decomposition.\n\nIn the case when the channel is corrupted by colored noise, we derive expressions for the optimum prefilters and postfilters with decision feedback equalization that minimize the mean-squared error between the input and the output, given a constraint on the input power. For uncorrelated inputs, the scheme leads to a set of parallel independent scalar channels with the optimum postfilter whitening the noise, which permits the optimal use of trellis codes for data transmission.\n\nWe apply the scheme to a special channel, viz., the ISDN digital subscriber loop. The main impairments on this channel are intersymbol interference and crosstalk due to adjacent loops in the same binder group. Crosstalk is an especially interesting case of noise since it depends on the signal being transmitted; we assume that all loops in a binder group transmit using the same scheme. We consider two cases of crosstalk noise: when transmission between different loops in a binder group is synchronized, the crosstalk noise is wide-sense cyclostationary, and with a lack of synchronization between loops, the crosstalk noise is wide-sense stationary. We present methods to determine the optimum filters for data transmission and the optimum input power distributions for both these cases. We demonstrate the possibility of data transmission at the T1 rate, i.e., 1.544 Mb/s over most loops in the local loop plant. We also find that synchronizing transmission between different loops in a binder group does not get us much; the difference in the throughputs for the cases of cyclostationary crosstalk and wide-sense stationary crosstalk does not seem to justify the effort involved in synchronization.", "doi": "10.7907/s4r5-wm48", "publication_date": "1992", "thesis_type": "phd", "thesis_year": "1992" }, { "id": "thesis:2958", "collection": "thesis", "collection_id": "2958", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-07202007-150751", "primary_object_url": { "basename": "Galton_i_1992.pdf", "content": "final", "filesize": 4181602, "license": "other", "mime_type": "application/pdf", "url": "/2958/1/Galton_i_1992.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "An analysis of quantization noise in delta sigma modulation and its application to parallel delta sigma modulation", "author": [ { "family_name": "Galton", "given_name": "Ian", "clpid": "Galton-I" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.\r\n\r\nThe trend toward digital signal processing in communication systems has resulted in a large demand for fast, accurate analog-to-digital (A/D) converters, and advances in VLSI technology have made [...] modulator based A/D converters attractive solutions. However, because they are non-linear systems, they have proven difficult to analyze. Rigorous analyses have been previously performed only for a small number of artificial input sequences and then only for the simplest of [...] modulator architectures. This thesis consists of three self-contained papers addressing these and related problems. The first two papers extend the repertoire of tractable input sequences for most of the known DE modulator architectures. The third paper applies the results from the first two papers to develop a scalable architecture for parallel [...] Modulation.\r\n\r\nThe first paper concentrates on the first-order [...] modulator and develops rigorous results for a large class of input sequences. Under the assumptions that some circuit noise is present and that the input sequence does not cause overload, a simple autocorrelation expression is developed that is only locally dependent upon the input sequence. Ergodic properties are derived and various examples are presented.\r\n\r\nIn the second paper, a rigorous analysis of the granular quantization noise in a general class of DE modulators is developed. Again under the assumption that some circuit noise is present, the joint statistics of the granular quantization noise sequences are determined and the sequences are shown to be correlation ergodic. The exact results developed for the granular quantization noise are shown to approximately hold for the overall quantization noise if the quantizers in the [...] modulator overload occasionally.\r\n\r\nThe third paper develops a scalable A/D converter architecture consisting of multiple [...] modulators. By combining [...] modulator based A/D converters, each with an oversampling ratio of N, an effective oversampling ratio of approximately NM is achieved with only an M-fold increase in the quantization noise power. In particular, the special case of N = 1 allows for full-rate analog to digital conversion. Unlike most other approaches to trading modulator complexity for accuracy, the system retains the robustness of the individual [...] modulators to circuit imperfections.\r\n", "doi": "10.7907/BF7F-6D40", "publication_date": "1992", "thesis_type": "phd", "thesis_year": "1992" }, { "id": "thesis:2858", "collection": "thesis", "collection_id": "2858", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-07122007-085228", "primary_object_url": { "basename": "Rose_k_1991.pdf", "content": "final", "filesize": 2854013, "license": "other", "mime_type": "application/pdf", "url": "/2858/1/Rose_k_1991.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Deterministic annealing, clustering, and optimization", "author": [ { "family_name": "Rose", "given_name": "Kenneth", "clpid": "Rose-K" } ], "thesis_advisor": [ { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "Fox", "given_name": "Geoffrey C.", "clpid": "Fox-G-C" }, { "family_name": "Kechris", "given_name": "Alexander S.", "clpid": "Kechris-A-S" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This work introduces the concept of deterministic annealing (DA) as a useful approach to clustering and other related optimization problems. It is strongly motivated by analogies to statistical physics, but is formally derived within information theory and probability theory. This approach enables escaping local optima that plague traditional techniques, without the extremely slow schedules typically required by stochastic methods. The clustering solutions obtained by DA are totally independent of the choice of initial configuration.\n\nA probabilistic framework is constructed, which is based on the principle of maximum entropy. The association probabilities at a given average distortion are Gibbs distributions parametrized by the corresponding Lagrange multiplier [beta], which is inversely proportional to the temperature in the physical analogy. By computing marginal probabilities within the framework, an effective cost is obtained, which is minimized to find the most probable set of cluster representatives at a given temperature. This effective cost is the free energy in statistical mechanics, which is indeed optimized at isothermal, stochastic equilibrium.\n\nWithin the probabilistic framework, annealing is introduced by controlling the Lagrange multiplier [beta]. This annealing is interpreted as gradually reducing the \"fuzziness\" of the associations. Phase transitions are identified in the process, which are, in fact, cluster splits. A sequence of phase transitions produces a hierarchy of fuzzy-clustering solutions. Critical [beta] are computed exactly for the first phase transition and approximately for the following ones.\n\nSpecific algorithms are derivable from the general approach, to address different aspects of clustering in the large variety of application fields. Here, algorithms are derived, and simulation results are presented for the three major classes, namely, hard clustering, fuzzy clustering, and hierarchical clustering. From the experimental results it appears that DA is substantially superior to traditional techniques.\n\nThe last part of the work extends the approach to deal with a larger family of optimization problems that can be reformulated as constrained clustering. A probabilistic framework for constrained clustering is derived based on the principle of maximum entropy. It is shown that for our annealing purpose, the constraint can be directly applied to the free energy. Three examples of constrained clustering are discussed. Mass-constrained clustering is formulated and yields an improvement of the clustering procedure. The process is now independent of the number of representatives and their multiplicity in the clusters. Secondly, the travelling salesman problem (TSP) is reformulated as constrained clustering, yielding the elastic net approach. A second Lagrange multiplier is identified, which is used to obtain a more powerful annealing method. Finally, self-organization of neural networks is shown to be closely related to TSP, and a similar annealing method is suggested. A fuzzy solution is sought to obtain the optimal net for a given training data set.\n", "doi": "10.7907/8N1R-3G60", "publication_date": "1991", "thesis_type": "phd", "thesis_year": "1991" }, { "id": "thesis:2860", "collection": "thesis", "collection_id": "2860", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-07122007-103754", "primary_object_url": { "basename": "Sathe_vp_1991.pdf", "content": "final", "filesize": 7345223, "license": "other", "mime_type": "application/pdf", "url": "/2860/1/Sathe_vp_1991.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Multirate adaptive filtering algorithms : analysis and applications", "author": [ { "family_name": "Sathe", "given_name": "Vinay Padmakar", "clpid": "Sathe-V-P" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "In this thesis, we discuss the application of multirate signal processing concepts to adaptive filtering to achieve low computational complexity and speed. To be able to analyze systems involving multirate building blocks, we have studied effects of multirate filters on the statistics of random inputs. As an example of the multirate adaptive filtering concepts, we study the problem of adaptive identification of an unknown bandlimited channel. We show that the bandlimited property can be very efficiently exploited to reduce both the speed and number of computations. The new method embeds an adaptive filter into multirate filters to reduce complexity and speed of computation.\n\nWe have applied the theoretical results obtained for the effects of multirate building blocks on stationary inputs to the adaptive identification scheme above and shown that the optimal filter is a matrix filter. We have shown through simulations that for a practical setup, a scalar adaptive filter performs almost as well if the fixed filters in the scheme are designed to have good stopband attenuation.\n\nIn a practical implementation of adaptive algorithms, computational noise is of concern. Most of the current analysis focuses on deriving the worst case upper bound on the roundoff errors. We analyze some basic signal processing steps by introducing a statistical flavor to it. This analysis answers questions such as \"what is a typical value of the roundoff error?\" In particular, for the case of dot product computation, we obtain expressions for the roundoff noise variance for the floating point case, and compare the results with the fixed point noise roundoff noise analysis. We also perform error variance analysis of Givens rotation and Householder transformation. These two algorithms are used in the upper triangularization of matrices. We have compared the results obtained for these cases and shown that error variance for the Householder case is lower, meaning that the Householder transformation adds lower roundoff error \"on an average\".\n\nWe also address the problem of bandlimited extrapolation of discrete-time signals. We have explained why the term \"best solution\" does not have a unique answer. Several new techniques for bandlimited extrapolation of discrete-time segments are explored. These methods apply to a wide range of situations (including multiple-burst interpolation of multiband signals). A closed form expression for the optimal solution (for a given value of the energy of extrapolated sequence) has been obtained and evaluated for various values of the final energy. The various methods are compared on the basis of out-of-band energy of the extrapolated signal, total energy of the extrapolated signal (in relation to that of the given segment), and numerical robustness.", "doi": "10.7907/ec5w-7460", "publication_date": "1991", "thesis_type": "phd", "thesis_year": "1991" }, { "id": "thesis:3581", "collection": "thesis", "collection_id": "3581", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09172003-101254", "primary_object_url": { "basename": "Wedge_sw_1991.pdf", "content": "final", "filesize": 3121197, "license": "other", "mime_type": "application/pdf", "url": "/3581/1/Wedge_sw_1991.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Computer-aided design of low noise microwave circuits", "author": [ { "family_name": "Wedge", "given_name": "Scott William", "clpid": "Wedge-S-W" } ], "thesis_advisor": [ { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" } ], "thesis_committee": [ { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Elachi", "given_name": "Charles", "clpid": "Elachi-C" }, { "family_name": "Zmuidzinas", "given_name": "Jonas", "clpid": "Zmuidzinas-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Devoid of most natural and manmade noise, microwave frequencies have detection sensitivities limited by internally generated receiver noise. Low-noise amplifiers are therefore critical components in radio astronomical antennas, communications links, radar systems, and even home satellite dishes. A general technique to accurately predict the noise performance of microwave circuits has been lacking. Current noise analysis methods have been limited to specific circuit topologies or neglect correlation, a strong effect in microwave devices. Presented here are generalized methods, developed for computer-aided design implementation, for the analysis of linear noisy microwave circuits comprised of arbitrarily interconnected components. Included are descriptions of efficient algorithms for the simultaneous analysis of noisy and deterministic circuit parameters based on a wave variable approach. The methods are therefore particularly suited to microwave and millimeter-wave circuits. Noise contributions from lossy passive components and active components with electronic noise are considered. Also presented is a new technique for the measurement of device noise characteristics that offers several advantages over current measurement methods.", "doi": "10.7907/ZRTG-GX48", "publication_date": "1991", "thesis_type": "phd", "thesis_year": "1991" }, { "id": "thesis:2741", "collection": "thesis", "collection_id": "2741", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-06272007-082624", "primary_object_url": { "basename": "Koilpillai_rd_1991.pdf", "content": "final", "filesize": 6230810, "license": "other", "mime_type": "application/pdf", "url": "/2741/1/Koilpillai_rd_1991.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Design issues in multirate digital filter banks, including transmultiplexers", "author": [ { "family_name": "Koilpillai", "given_name": "Ravinder David", "clpid": "Koilpillai-R-D" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.\r\n\r\nSeveral aspects of the theory and design of FIR digital filter banks for analysis/synthesis systems are studied in this thesis. In particular, we focus on filter banks satisfying the perfect reconstruction (PR) property. We present a new approach to design PR filter banks wherein the filter bank is obtained by cosine-modulation of a linear-phase prototype filter of length N = 2mM, m [...] 1 (where M is the number of channels). The PR property is satisfied because the polyphase component matrix of the modulated filter bank is lossless. This is achieved by satisfying the necessary and sufficient condition - a pairwise power complementary property between the 2M polyphase components of the prototype. In this approach, regardless of the number of channels, we still design only the prototype. The design procedure involves the two-channel lossless lattice. This approach compares favorably (in terms of the number of parameters to be optimized and the ease of design) with other design techniques. Design examples and detailed comparisons are presented.\r\n\r\nThe existing approaches for designing PR filter banks include the lattice based methods, which structurally force the polyphase component matrix to be lossless. New initialization procedures, which can be used to initialize the values of all the lattice parameters (prior to optimization), are presented. The main advantage is that we can get 'good' initializations by using conventional Quadrature Mirror Filter (QMF) banks and pseudo-QMF banks (which can be readily designed, but do not satisfy PR). It is shown that these filter banks have polyphase component matrices that are 'approximately' lossless. The initialization also enables the design of a family of PR filter banks.\r\n\r\nIn conventional approaches to pseudo-QMF design, the prototype filter is obtained by optimization, wherein lies the main computational effort. We present a new approach in which the prototype of a M-channel filter bank is obtained by spectral factorization (of a 2Mth band filter), thereby eliminating the need for optimization. The overall transfer function T(z) has linear-phase and an approximate 'flat' magnitude response in the region [epsilon][...][omega][...] ([pi] - [epsilon] where [epsilon] depends on the transition bandwidth of the prototype [...]. A new spectral factorization algorithm (non-iterative) which is based on the Inverse Linear Predictive Coding (LPC) technique is presented. Design examples for the above method are obtained by using this algorithm.\r\n\r\nFinally, we consider a dual of the QMF circuit - the transmultiplexer (TMUX). Traditional TMUX designs suppress the undesirable crosstalk. The crosstalk-free transmultiplexer (CF-TMUX) focuses on crosstalk cancellation, rather that suppression. It is shown that the filters of a CF-TMUX are the same as the filters of a 1-skewed AF-QMF bank. In addition, if the QMF bank satisfies PR, then the TMUX also achieves PR.", "doi": "10.7907/C6MF-3A43", "publication_date": "1991", "thesis_type": "phd", "thesis_year": "1991" }, { "id": "thesis:1707", "collection": "thesis", "collection_id": "1707", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-05092007-130540", "primary_object_url": { "basename": "Liu_vct_1990.pdf", "content": "final", "filesize": 4977200, "license": "other", "mime_type": "application/pdf", "url": "/1707/1/Liu_vct_1990.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "One and two-dimensional digital mutirate systems with applications in sub-sampling and bandlimited signal reconstruction", "author": [ { "family_name": "Liu", "given_name": "Vincent Cheng-Teh", "clpid": "Liu-V-C" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Psaltis", "given_name": "Demetri", "clpid": "Psaltis-D" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis deals with the two-dimensional (2D) multirate quadrature mirror filter (QMF) bank and new applications of 1D and 2D multirate filter bank concepts to the periodic nonuniform sampling and reconstruction of bandlimited signals. The potential use of multirate filter banks in the statistically optimal estimation of signals in the presence of wide-sense cyclostationary noise is also examined. The two-dimensional QMF bank is free from aliasing if and only if a certain polyphase matrix product related to the filter bank possesses the 2D pseudo-circulant property. A 2D FIR filter bank can be designed with the perfect reconstruction property if the polyphase matrix of its analysis filter bank is constrained to be a 2D lossless matrix. A design example is included. The losslessness constraint is satisfied by imposing a cascaded structure of first-degree lossless sections on the polyphase matrix. A limited factroization theorem is derived for 2D FIR lossless systems where the order in one of the two dimensions is limited to unity. In the area of nonuniform sampling of multiband bandlimited signals, the filter bank approach is utilized to derive a computationally efficient method for reconstructing bandlimited signals. The above scheme can also be viewed as a mean of compressing and reconstructing an oversampled bandlimited signal. It is shown that such a scheme has lower computational complexity than traditional methods of sampling rate alteration. The results can be extended to nonuniform sampling in two-dimensions using integer lattices. A further application of the multirate filter bank is in signal estimation in the presence of cyclostationary noise. The necessary and sufficient condition for the filter bank to preserve the wide-sense stationarity of the input is derived. Several applications where cyclostationary noise is present are indicated, and through the use of simulations the performance of the optimal filter bank can be compared with the conventional scalar optimal filter. The roundoff noise in orthogonal matrix building blocks is analyzed, since these building blocks are commonly present in filter bank implementations.", "doi": "10.7907/cvbb-m844", "publication_date": "1990", "thesis_type": "phd", "thesis_year": "1990" }, { "id": "thesis:924", "collection": "thesis", "collection_id": "924", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03112007-120230", "primary_object_url": { "basename": "Onyszchuk_im_1990.pdf", "content": "final", "filesize": 8033617, "license": "other", "mime_type": "application/pdf", "url": "/924/1/Onyszchuk_im_1990.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "On the Performance of Convolutional Codes", "author": [ { "family_name": "Onyszchuk", "given_name": "Ivan M.", "clpid": "Onyszchuk-Ivan-M" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis contains error bounds, algorithms, and techniques for evaluating the performance of convolutional codes on the Additive White Gaussian Noise (AWGN) channel. Convolutional encoders are analyzed using simple binary operations in order to determine the longest possible \"zero-run\" output and if \"catastrophic error propagation\" may occur. Methods and algorithms are presented for computing the weight enumerator and other generating functions, associated with convolutional codes, which are used to upper-bound maximum-likelihood (i.e., Viterbi) decoder error rates on memoryless channels. In particular, the complete path enumerator T(D, L, I) is obtained for the memory 6, rate 1/2, NASA standard code. A new, direct technique yields the corresponding bit-error generating function. These procedures may be used to count paths between nodes in a finite directed graph or to calculate transfer functions in circuits and networks modelled by signal flow graphs. A modified Viterbi decoding algorithm is used to obtain numbers for error bound computations.
\r\n\r\nNew bounds and approximations for maximum-likelihood convolutional decoder first-event, bit, and symbol error rates are derived, the latter one for concatenated coding system analysis. Berlekamp's tangential union bound for maximum-likelihood, block decoder word error probability on the AWGN channel is adapted for convolutional codes. Approximations to bit and symbol error rates are obtained that remain within 0.2 dB of simulation results at low signal-to-noise ratios, where many convolutional codes operate but the standard bounds are useless. An upper bound on the loss caused by truncating survivors in a Viterbi decoder leads to estimates of minimum practical truncation lengths. Lastly, the power loss due to quantizing received (demodulated) symbols from the AWGN channel is studied. Effective schemes are described for uniform channel symbol quantization, branch metric calculations, and path metric renormalization in Viterbi decoders.
", "doi": "10.7907/7nb5-gy54", "publication_date": "1990", "thesis_type": "phd", "thesis_year": "1990" }, { "id": "thesis:711", "collection": "thesis", "collection_id": "711", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02222007-083438", "type": "thesis", "title": "General Structural Representations for Multi-Input Multi-Output Discrete-Time FIR and IIR Lossless Systems", "author": [ { "family_name": "Do\u011fanata", "given_name": "Zinnur", "clpid": "Do\u011fanata-Zinnur" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Knowles", "given_name": "James K.", "clpid": "Knowles-J-K" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Discrete-time lossless systems have been found to be of great importance in many signal processing applications. However, a representation for lossless transfer matrices that spans all such matrices with the smallest possible number of parameters has not been proposed earlier. Existing representations are usually for special cases and therefore not general enough. In this study, two general and minimal representations are presented for multi-input, multi-output FIR and IIR lossless systems. The first representation is in terms of planar rotations and it leads to multi-input, multi-output lattice structures. The second representation is in terms of unit-norm vectors and it enables shorter convergence times in optimization applications. A simple modification of this representation leads to structures that remain lossless under quantization. The structures that follow from these representations share some properties such as the orthogonality of the implementations, and minimality of the number of parameters and scalar delays they are. Since all lossless transfer matrices can be spanned by appropriately adjusting their parameters, these structures can be particularly useful in applications that involve optimization under the constraint of losslessness. Some examples of such applications are included.
", "doi": "10.7907/h011-7b66", "publication_date": "1990", "thesis_type": "phd", "thesis_year": "1990" }, { "id": "thesis:626", "collection": "thesis", "collection_id": "626", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02132007-105916", "type": "thesis", "title": "Synthesis of PWM and Quasi-Resonant DC-to-DC Power Converters", "author": [ { "family_name": "Maksimovi\u0107", "given_name": "Dragan", "orcid": "0000-0002-8867-0230", "clpid": "Maksimovi\u0107-Dragan" } ], "thesis_advisor": [ { "family_name": "Cuk", "given_name": "Slobodan", "clpid": "Cuk-S" }, { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" } ], "thesis_committee": [ { "family_name": "Cuk", "given_name": "Slobodan", "clpid": "Cuk-S" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" }, { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" }, { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wiggins", "given_name": "Stephen R.", "clpid": "Wiggins-S-R" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Synthesis of DC-to-DC converter topologies in the two largest families - PWM and Quasi-Resonant (QR) - is completed in this thesis.
\r\n\r\nIn a PWM converter, two linear time-invariant networks, consisting of only capacitors and inductors, source and load, are switched at constant frequency with duty ratio D. From defining assumptions, several general properties of PWM converter networks are derived. The established general properties interrelate the number of elements, attainable DC conversion ratio M(D), and features such as continuous terminal currents or possible coupling of inductors.
\r\n\r\nBased on matrix representation of the converter topology, the systematic synthesis procedure for generation of PWM converters with a given number of reactive elements is constructed. A prescribed set of requirements is the input for the procedure. The requirements may include desired DC conversion ratio, continuous terminal currents, possible coupling of inductors and a given number of switches. In particular, the number of switches implemented as transistors can be specified. Outputs of the procedure are complete classes of PWM converters that satisfy the input requirements. A number of useful PWM topologies, which have not been identified before, are uncovered. A comparison of members of the classes is included.
\r\n\r\nSeveral extensions of PWM converters are considered, including insertion of the isolation transformer and two discontinuous operating modes for which unified DC analyses are completed.
\r\n\r\nQuasi-Resonant converters are defined as two-switch PWM converter networks to which resonant elements are added. Synthesis of QR, converters is based on the recognition that there are only a finite number of topologically distinct positions for resonant elements within a two-switch PWM parent converter. If a single resonant inductor and a single resonant capacitor are added to a two-switch PWM topology, examination of all possible positions yields a total of six QR classes, which come in dual pairs. Two pairs are identified as known QR classes, namely, Zero-Current/Zero-Voltage (ZV/ZC) and Zero-Current/Zero-Voltage Quasi-Square-Wave (ZC-QSW/ZV-QSW). The remaining two classes, named Off-Resonant and On-Resonant Quasi-PWM (Qf-PWM/Qn-PWM), have not been recognized so far. The names originate from the fact that Q-PWM converters can be regarded as PWM converters operating in both discontinuous modes simultaneously. The synthesis procedure can be generalized to encompass additional resonant elements. As an example, classes of Zero-Current and Zero-Voltage Multi-Resonant (ZC-MR/ZV-MR) converters are formally defined.
\r\n\r\nIn contrast to square-wave switch waveforms in PWM converters, all QR topologies exhibit smooth quasi-sinusoidal waveforms and therefore reduced switching losses. Of particular interest are operating modes in which all switching transitions are at zero current or at zero voltage.
\r\n\r\nA study of operating modes and a DC analysis unified with respect to all PWM parents and all topological variations are carried out for four selected classes of QR Converters - Qn-PWM, ZV, ZV-QSW, and ZV-MR. It is emphasized that for a QR converter, topology alone is not sufficient to derive DC conversion properties. Subject to different switch implementations and control timing, the emerging operating modes can result in vastly different behavior of the same converter topology.
\r\n\r\nTwo switch implementations are considered - conventional, with one controllable switch and one diode, and the one that resembles the technique of synchronous rectification - with two controllable switches. In the first case, with the exception of converters in two Q-PWM classes, only variable-frequency control is applicable. However, if both switches are controllable, constant-frequency control is restored in all QR classes, and several novel operating modes of practical interest are uncovered.
\r\n\r\nVarious QR classes and operating modes are compared with respect to sets of switching transitions, sensitivity to parasitic elements, available operating region, frequency range and stresses on switching devices. The role of free parameters in various design trade-offs is exposed, thus allowing a designer to select and realize the topology best suited for a particular application.
", "doi": "10.7907/B8XA-2R90", "publication_date": "1989", "thesis_type": "phd", "thesis_year": "1989" }, { "id": "thesis:425", "collection": "thesis", "collection_id": "425", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02012005-084251", "type": "thesis", "title": "Robust Analysis of Feedback Systems with Parametric and Dynamic Structured Uncertainty", "author": [ { "family_name": "S\u00e1nchez Pe\u00f1a", "given_name": "Ricardo Salvador", "clpid": "S\u00e1nchez-Pe\u00f1a-Ricardo-Salvador" } ], "thesis_advisor": [ { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" } ], "thesis_committee": [ { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Doyle", "given_name": "John Comstock", "orcid": "0000-0002-1828-2486", "clpid": "Doyle-J-C" }, { "family_name": "Lorentz", "given_name": "G. G.", "clpid": "Lorentz-G-G" }, { "family_name": "Lorenz", "given_name": "Jens", "clpid": "Lorenz-Jens" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" }, { "family_name": "Morari", "given_name": "Manfred", "clpid": "Morari-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis presents the first general program implementation of the algorithm by deGaston and its generalization by Sideris and deGaston to compute the Multivariable stability margin or Structured singular value of a feedback system under real (independent or related) parametric uncertainty. An improved implementation of the algorithm mentioned above is also considered, which simplifies significantly the code and increases the computational speed. The latter also allows a simple and fast analysis by just checking the extreme values of the set of parameters, with a high probability of achieving the actual stability margin; this being supported by an intense statistical analysis performed at the end of this thesis.
\r\n\r\nA great deal of work has recently been done related to this class of uncertain systems initiated by the well known theorem of Kharitonov. A connection is made in Chapter 4 between these procedures and the above ones in terms of generality of the class of uncertain polynomials considered. A theorem characterizing the set of polynomials whose robust stability can be determined by a finite number of tests is addressed. Sufficient conditions to determine when the latter conditions apply are also given, which in some cases can considerably simplify the analysis. In particular cases, polynomials with related uncertain parameters can be treated in the same way as independent parameters as shown in two examples.
\r\n\r\nThe main part of this thesis is concerned with the analysis of more general type of uncertainties. In particular, the analysis of robust stability for the case when unstructured dynamic uncertainty is combined with real parametric uncertainty is treated in Chapter 5. This can also be applied in the analysis of robust performance for plants with parametric uncertainty. Chapter 6 generalizes the latter to the most general case in which structured dynamic and real parametric uncertainty appear simultaneously in the plant. A computational scheme is given in both cases which uses the algorithm mentioned in the first part and is applied to several examples.
\r\n\r\nAt the end, an example of the robust analysis of an experimental aircraft demonstrates how a practical situation can be handled by this procedure.
", "doi": "10.7907/MM2J-E556", "publication_date": "1989", "thesis_type": "phd", "thesis_year": "1989" }, { "id": "thesis:4488", "collection": "thesis", "collection_id": "4488", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-11102005-091115", "primary_object_url": { "basename": "Nguyen_tq_1989.pdf", "content": "final", "filesize": 7424354, "license": "other", "mime_type": "application/pdf", "url": "/4488/1/Nguyen_tq_1989.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Design and Implementation of Linear-Phase and/or Pairwise-Symmetric Perfect-Reconstruction FIR Multirate Filter Banks", "author": [ { "family_name": "Nguyen", "given_name": "Truong Quang", "clpid": "Nguyen-Truong-Quang" } ], "thesis_advisor": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "thesis_committee": [ { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Swanson", "given_name": "Larry W.", "clpid": "Swanson-L-W" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis studies the structures, design procedures and implementations of FIR perfect-reconstruction digital filter banks. The first part of the thesis deals with the structures and the design procedures of the perfect-reconstruction filter banks where the polyphase transfer matrices are lossless. These structures are parameterized by a set of rotation angles [37]. The usual procedure is to blindly optimize these angles to minimize an objective function where the objective function consists of all the stopband energies of the filters which we would like to design. This procedure is very time-consuming because of the nonlinear objective function and the large number of parameters to be optimized. The pairwise-symmetry property is imposed on these perfect reconstruction systems as a means of decreasing the number of parameters (rotation angles). The pairwise-symmetric property together with a method to initialize these rotation angles gives a very efficient design procedure. Design examples and complexity of the pairwise-symmetric, perfect-reconstruction FIR filter banks have compared well with the approximate perfect-reconstruction systems.
\r\n\r\nThe second part of the thesis studies the structures and the design procedures of perfect-reconstruction filter banks which yield linear-phase filters. By confining the problem to a class, we are able to count exactly the number of linear-phase, perfect-reconstruction filter banks in this class. For the two-channel filter banks, we have obtained structures and design procedures for all nontrivial systems. Comparison with the approximated perfect-reconstruction systems in terms of complexity and performance is made. In our subclass of linear-phase, perfect-reconstruction, there are three structures for the case of three-channel filter banks. By limiting the problem to one of these systems, we obtain structures which yield linear-phase, perfect-reconstruct ion filters. The implementation complexity is studied. Design examples for all new methods presented here are included, along with tabulation of lattice and filter coefficients.
\r\n\r\n[37] Z. Doganata, P. P. Vaidyanathan, and T. Q. Nguyen, \"General Synthesis procedures for FIR lossless transfer matrices for perfect-reconstruction multirate filter bank applications,\" IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. ASSP-36, 1561-1574, Oct. 1988.
", "doi": "10.7907/8z2n-y592", "publication_date": "1989", "thesis_type": "phd", "thesis_year": "1989" }, { "id": "thesis:626", "collection": "thesis", "collection_id": "626", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02132007-105916", "type": "thesis", "title": "Synthesis of PWM and Quasi-Resonant DC-to-DC Power Converters", "author": [ { "family_name": "Maksimovi\u0107", "given_name": "Dragan", "orcid": "0000-0002-8867-0230", "clpid": "Maksimovi\u0107-Dragan" } ], "thesis_advisor": [ { "family_name": "Cuk", "given_name": "Slobodan", "clpid": "Cuk-S" }, { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" } ], "thesis_committee": [ { "family_name": "Cuk", "given_name": "Slobodan", "clpid": "Cuk-S" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" }, { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" }, { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Wiggins", "given_name": "Stephen R.", "clpid": "Wiggins-S-R" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Synthesis of DC-to-DC converter topologies in the two largest families - PWM and Quasi-Resonant (QR) - is completed in this thesis.
\r\n\r\nIn a PWM converter, two linear time-invariant networks, consisting of only capacitors and inductors, source and load, are switched at constant frequency with duty ratio D. From defining assumptions, several general properties of PWM converter networks are derived. The established general properties interrelate the number of elements, attainable DC conversion ratio M(D), and features such as continuous terminal currents or possible coupling of inductors.
\r\n\r\nBased on matrix representation of the converter topology, the systematic synthesis procedure for generation of PWM converters with a given number of reactive elements is constructed. A prescribed set of requirements is the input for the procedure. The requirements may include desired DC conversion ratio, continuous terminal currents, possible coupling of inductors and a given number of switches. In particular, the number of switches implemented as transistors can be specified. Outputs of the procedure are complete classes of PWM converters that satisfy the input requirements. A number of useful PWM topologies, which have not been identified before, are uncovered. A comparison of members of the classes is included.
\r\n\r\nSeveral extensions of PWM converters are considered, including insertion of the isolation transformer and two discontinuous operating modes for which unified DC analyses are completed.
\r\n\r\nQuasi-Resonant converters are defined as two-switch PWM converter networks to which resonant elements are added. Synthesis of QR, converters is based on the recognition that there are only a finite number of topologically distinct positions for resonant elements within a two-switch PWM parent converter. If a single resonant inductor and a single resonant capacitor are added to a two-switch PWM topology, examination of all possible positions yields a total of six QR classes, which come in dual pairs. Two pairs are identified as known QR classes, namely, Zero-Current/Zero-Voltage (ZV/ZC) and Zero-Current/Zero-Voltage Quasi-Square-Wave (ZC-QSW/ZV-QSW). The remaining two classes, named Off-Resonant and On-Resonant Quasi-PWM (Qf-PWM/Qn-PWM), have not been recognized so far. The names originate from the fact that Q-PWM converters can be regarded as PWM converters operating in both discontinuous modes simultaneously. The synthesis procedure can be generalized to encompass additional resonant elements. As an example, classes of Zero-Current and Zero-Voltage Multi-Resonant (ZC-MR/ZV-MR) converters are formally defined.
\r\n\r\nIn contrast to square-wave switch waveforms in PWM converters, all QR topologies exhibit smooth quasi-sinusoidal waveforms and therefore reduced switching losses. Of particular interest are operating modes in which all switching transitions are at zero current or at zero voltage.
\r\n\r\nA study of operating modes and a DC analysis unified with respect to all PWM parents and all topological variations are carried out for four selected classes of QR Converters - Qn-PWM, ZV, ZV-QSW, and ZV-MR. It is emphasized that for a QR converter, topology alone is not sufficient to derive DC conversion properties. Subject to different switch implementations and control timing, the emerging operating modes can result in vastly different behavior of the same converter topology.
\r\n\r\nTwo switch implementations are considered - conventional, with one controllable switch and one diode, and the one that resembles the technique of synchronous rectification - with two controllable switches. In the first case, with the exception of converters in two Q-PWM classes, only variable-frequency control is applicable. However, if both switches are controllable, constant-frequency control is restored in all QR classes, and several novel operating modes of practical interest are uncovered.
\r\n\r\nVarious QR classes and operating modes are compared with respect to sets of switching transitions, sensitivity to parasitic elements, available operating region, frequency range and stresses on switching devices. The role of free parameters in various design trade-offs is exposed, thus allowing a designer to select and realize the topology best suited for a particular application.
", "doi": "10.7907/B8XA-2R90", "publication_date": "1989", "thesis_type": "phd", "thesis_year": "1989" }, { "id": "thesis:425", "collection": "thesis", "collection_id": "425", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02012005-084251", "type": "thesis", "title": "Robust Analysis of Feedback Systems with Parametric and Dynamic Structured Uncertainty", "author": [ { "family_name": "S\u00e1nchez Pe\u00f1a", "given_name": "Ricardo Salvador", "clpid": "S\u00e1nchez-Pe\u00f1a-Ricardo-Salvador" } ], "thesis_advisor": [ { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" } ], "thesis_committee": [ { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Doyle", "given_name": "John Comstock", "orcid": "0000-0002-1828-2486", "clpid": "Doyle-J-C" }, { "family_name": "Lorentz", "given_name": "G. G.", "clpid": "Lorentz-G-G" }, { "family_name": "Lorenz", "given_name": "Jens", "clpid": "Lorenz-Jens" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" }, { "family_name": "Morari", "given_name": "Manfred", "clpid": "Morari-M" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis presents the first general program implementation of the algorithm by deGaston and its generalization by Sideris and deGaston to compute the Multivariable stability margin or Structured singular value of a feedback system under real (independent or related) parametric uncertainty. An improved implementation of the algorithm mentioned above is also considered, which simplifies significantly the code and increases the computational speed. The latter also allows a simple and fast analysis by just checking the extreme values of the set of parameters, with a high probability of achieving the actual stability margin; this being supported by an intense statistical analysis performed at the end of this thesis.
\r\n\r\nA great deal of work has recently been done related to this class of uncertain systems initiated by the well known theorem of Kharitonov. A connection is made in Chapter 4 between these procedures and the above ones in terms of generality of the class of uncertain polynomials considered. A theorem characterizing the set of polynomials whose robust stability can be determined by a finite number of tests is addressed. Sufficient conditions to determine when the latter conditions apply are also given, which in some cases can considerably simplify the analysis. In particular cases, polynomials with related uncertain parameters can be treated in the same way as independent parameters as shown in two examples.
\r\n\r\nThe main part of this thesis is concerned with the analysis of more general type of uncertainties. In particular, the analysis of robust stability for the case when unstructured dynamic uncertainty is combined with real parametric uncertainty is treated in Chapter 5. This can also be applied in the analysis of robust performance for plants with parametric uncertainty. Chapter 6 generalizes the latter to the most general case in which structured dynamic and real parametric uncertainty appear simultaneously in the plant. A computational scheme is given in both cases which uses the algorithm mentioned in the first part and is applied to several examples.
\r\n\r\nAt the end, an example of the robust analysis of an experimental aircraft demonstrates how a practical situation can be handled by this procedure.
", "doi": "10.7907/MM2J-E556", "publication_date": "1989", "thesis_type": "phd", "thesis_year": "1989" }, { "id": "thesis:4461", "collection": "thesis", "collection_id": "4461", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-11082007-085237", "type": "thesis", "title": "A Model for the Study of Very Noisy Channels, and Applications", "author": [ { "family_name": "Majani", "given_name": "Eric Etienne", "clpid": "Majani-Eric-Etienne" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Abu-Mostafa", "given_name": "Yaser S.", "clpid": "Abu-Mostafa-Y-S" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Goodman", "given_name": "Rodney M.", "clpid": "Goodman-R-M" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Very Noisy channels (such as the wideband gaussian channel well-known in deep space communications) have the interesting property that although the maximum number of bits transmitted per symbol is close to zero, the maximum number of bits transmitted per second is not! Furthermore, recent results on the ultimate limits of information density indicate that some channels perform better when pushed to their very noisy limit.
\r\n\r\nWe present a general mathematical model of Very Noisy channels which provides an insight in their behavior, and in some interesting cases, tells us about the limiting behavior of the larger class of noisy channels.
\r\n\r\nTwo classes of Very Noisy Channels are identified and efficient algorithms that compute their capacity are presented. We show that for some Very Noisy broadcast channels, the time-shared coding strategy performs as well as the optimal strategy known as broadcast coding in the limit. Finally, with the help of our model, we derive a tight lower bound on the amount of information lost in a Channel Reduction or Data Compression.
\r\n", "doi": "10.7907/9AF1-K251", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:3696", "collection": "thesis", "collection_id": "3696", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09222006-130413", "type": "thesis", "title": "I. A Unified Analysis of Converters with Resonant Switches. II. Input-Current Shaping for Single-Phase Ac-Dc Power Converters", "author": [ { "family_name": "Freeland", "given_name": "Stephen D.", "clpid": "Freeland-Stephen-D" } ], "thesis_advisor": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" } ], "thesis_committee": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Part I:
\r\n\r\nQuasi-resonant converters are a family of single-switch resonant dc-dc converters featuring zero-current or zero-voltage switching. Recognition of the topological structure uniting these resonant converters--and the rectangular-wave (PWM) converters on which they are based--leads to general models of their dc and low-frequency ac behavior.
\r\n\r\nAn expression is derived that yields the dc conversion ratio of a quasi-resonant converter in terms of the well-known conversion ratio of the underlying PWM topology. A small-signal, low-frequency dynamic model is developed whose parameters also incorporate the PWM conversion ratio. The dc and ac models reveal that any quasi-resonant converter with a full-wave resonant switch has dc and low-frequency behavior identical to that of its PWM parent, with switching-frequency control replacing duty-ratio control. Converters with half-wave resonant switches behave more like PWM converters in discontinuous conduction mode or with current programming, exhibiting lossless damping in the small-signal model and output resistance at dc.
\r\n\r\nAlthough quasi-resonant converters come in an astounding variety of topologies, the dc (and to a large extent ac) behavior of these converters depends only on the underlying PWM topology and the class of resonant switch, and is unchanged by movement of the resonant reactances to various alternative positions.
\r\n\r\nPart 2:
\r\n\r\nThe distorted input-current waveforms of nonlinear electronic loads cause interference and lead to poor utilization of the utility power line, a situation that is rapidly becoming intolerable with the increased application of electronic loads. Input-current shaping, also known as power-factor improvement, addresses the problem of improving current waveforms drawn from the power line. This study is restricted to single-phase ac-dc power conversion systems.
\r\n\r\nCurrent-shaping circuits are shown to fall into just a few categories with common features and limitations. In addition to the more common buck- and boost-based current-shaping converters, a class of circuits with \"automatic\" current shaping is presented and analyzed. A set of rules is derived for determining whether a particular dc-dc converter topology is suitable for use as a current-shaping ac-dc converter, and the rules are used to judge the suitability of several resonant converter topologies for this application. A new, low-cost converter is suggested that combines input-current shaping, isolation, and fast output-voltage regulation.
\r\n\r\nInput-current shaping requires that a converter store significant energy, leading to unfortunate size and weight restrictions. Additional implications of stored energy are examined, along with several methods of reducing the energy storage. It is shown that the ability of a current-shaping converter to regulate its output voltage is severely restricted as a result of the energy requirement. The methods and implications of introducing isolation to a shaping ac-dc converter are also studied.
", "doi": "10.7907/PVNN-X318", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:4445", "collection": "thesis", "collection_id": "4445", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-11072007-090157", "type": "thesis", "title": "Queues of Queues in Communication Networks", "author": [ { "family_name": "Hern\u00e1ndez Valencia", "given_name": "Enrique Jos\u00e9", "clpid": "Hern\u00e1ndez-Valencia-Enrique-Jos\u00e9" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The concept of a camp-on queueing system is related to the idea of having systems of multiple hierarchical queues. Customers requesting service at a service center are queued at one of different queueing stages based on the location of the customer's intended server within the service hierarchy. In many instances, customers in a camp-on model exhibit a dual function customer-server, giving rise to a system with queues of queues. For this model, we assume Poisson distributed arrivals with different classes of customers for each queueing level. The service completion process is regarded as exponentially distributed, a standard assumption for many communication systems.
\r\n\r\nHere we discuss a stationary model for such a Markovian camp-on system. Closed-form solutions are derived for various state occupancy distributions of interest (e.g., joint probability distribution of queue lengths, marginal distributions for subsystems, accumulated workload, etc.), in systems with finite and infinite storage capacity and two queueing levels. Most of these results are also extended to multilevel queueing systems. It is found that this camp-on model is stable whenever all the distinct queues, in isolation, behave as stable systems. The form of the joint probability distribution of queue lengths is not a product of the independent contributions from each subsystem, since it must also account for the relative position of the queues with respect to the initial service center, the root of the service hierarchy.
\r\n\r\nTwo particular applications are discussed in detail: 1) PBX-like communication services, and 2) broadcast delivery services. Performance statistics such as waiting time distributions, blocking probabilities and mean response time are derived. These results show that we do not pay too large a penalty for introducing two or more levels of queueing, and under very extreme conditions (heavy traffic) the delay in response increases only linearly with the number of queueing stages. Broadcast service strategies provide even better performance than conventional point-to-point service, though a broadcast medium is required.
\r\n", "doi": "10.7907/wygw-0f83", "publication_date": "1988", "thesis_type": "phd", "thesis_year": "1988" }, { "id": "thesis:828", "collection": "thesis", "collection_id": "828", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03012008-134552", "primary_object_url": { "basename": "Lau_byb_1987.pdf", "content": "final", "filesize": 4530865, "license": "other", "mime_type": "application/pdf", "url": "/828/1/Lau_byb_1987.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Small-Signal Frequency Response Theory for Ideal Dc-to-Dc Converter Systems", "author": [ { "family_name": "Lau", "given_name": "Billy Ying Bui", "clpid": "Lau-Billy-Ying-Bui" } ], "thesis_advisor": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" } ], "thesis_committee": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" }, { "family_name": "Caughey", "given_name": "Thomas Kirk", "clpid": "Caughey-T-K" }, { "family_name": "Martel", "given_name": "Hardy Cross", "clpid": "Martel-H-C" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "The frequency response problem of switching dc-to-dc converter systems is the problem of computing the small-signal frequency response of the system with respect to its inputs. It arises in the study of the small-signal behavior and in the design of a feedback controller for the dc-to-dc converter system. There are two approaches in tackling the problem: the numerical approach and the analytical approach. This thesis is limited to the analytical approach. There are previous efforts in developing approximate analytical methods for solving the problem; however, these methods are unsatisfactory in one way or another because they are applicable only to few special cases, and valid only in limited range of frequency \u2014 less than half the switching frequency in many cases.
\r\n\r\nThe Small-Signal Frequency Response Theory presented in this thesis is developed to overcome the problems encountered in the application of the approximate analytical methods. Instead of finding an approximate model for a dc-to-dc converter system and postulating that the response of the model is the same as that of the converter system, as in the approximate analytical methods, the new theory computes the frequency response of the perturbed output with respect to perturbations at the control-inputs by the direct application of Fourier Analysis. Hence, the theory is exact in the small-signal limit. Unlike the approximate analytical methods, the results given by the theory are valid at all frequencies provided that the system model used in the calculation of frequency response is valid at all frequencies. In short, the Small-Signal Frequency Response Theory is a mathematical theory for the linearization of an ideal dc-to-dc converter system in the vicinity of its periodic steady state solution.
\r\n\r\nIn the derivation of the results of the Small-Signal Frequency Response Theory, two steps are taken: First, find a difference equation that describes the small-signal motion of the system in the vicinity of the given steady state solution. Second, find the equivalent hold that relates the samples of the perturbed state of the system, given by the difference equation, to the analog output signal. The z-transform of the difference equation with z = esT. is used to relate the spectrum of the sampled perturbed control-input to the spectrum of the sampled perturbed output. The frequency response of the converter system given by the theory resembles the frequency response of a classical single-rate sampled-data system.
\r\n\r\nThe prediction given by the theory and the experimental results for three converter circuits are compared. These three converter circuit have the same basic circuit topology, but different control strategies. The control strategies in these three examples are: constant-switching-frequency PWM, constant-switching-frequency programmed, and bang-bang controlled. It is found that the theory consistently gives good predictions, even up to many times of the switching frequency, while, in many cases, the approximate analytical methods break down.
\r\n\r\nThe theory has the best of both the time domain approach and the frequency domain approach for the analysis of switching dc-to-dc converter systems. It has the exactness of the time domain approach, which uses a difference equation to describe the system, and the measurability of the of frequency domain approach. The exactness and the uniformity of the theory, which has not been achieved before, results in significant impact in the fields of computer-aided design and modelling and analysis in power electronics.
", "doi": "10.7907/mqpe-vz16", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:869", "collection": "thesis", "collection_id": "869", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03042008-093526", "primary_object_url": { "basename": "Dailey_rl_1987.pdf", "content": "final", "filesize": 7485525, "license": "other", "mime_type": "application/pdf", "url": "/869/1/Dailey_rl_1987.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Conic Sector Analysis for Digital Control Systems with Structured Uncertainty", "author": [ { "family_name": "Dailey", "given_name": "Russell Lane", "clpid": "Dailey-Russell-Lane" } ], "thesis_advisor": [ { "family_name": "Doyle", "given_name": "John Comstock", "clpid": "Doyle-J-C" } ], "thesis_committee": [ { "family_name": "Doyle", "given_name": "John Comstock", "clpid": "Doyle-J-C" }, { "family_name": "Sideris", "given_name": "Athanasios", "clpid": "Sideris-A" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Cuk", "given_name": "Slobodan", "clpid": "Cuk-S" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis presents a method which greatly reduces the conservativeness of conic sector analysis for sampled data feedback systems. The new method evaluates the stability and closed-loop performance of systems with structured uncertainty in the plant transfer function, including MIMO systems and those with multiple sampling rates. In contrast to most multirate analysis techniques, the sampling rates need not be related by rational numbers; this allows analysis when samplers are not strobed to a common clock.
\r\n\r\nThe method is based on a theorem from P. M. Thompson which shows how to construct a conic sector containing a hybrid operator. Combining this theorem with the Structured Singular Value approach of J. C. Doyle, with its heavy use of diagonal scaling, provides an analysis framework for systems with multiple structured plant perturbations. Chapter 3 presents a theorem for the optimal conic sector radius in the SISO case; a MIMO extension of the the theorem completes the development of the new method. Chapter 5 gives three examples.
\r\n\r\nChapter 6 presents a new method, based on the complex cepstrum, for synthesis of SISO rational functions to match given \"target\" transfer functions. The method offers complete control over stability and right half plane zeros. It solves directly for poles and zeros, avoiding the numerical sensitivity of methods which solve for polynomial coefficients. It can synthesize minimum phase functions to match a given magnitude or phase curve. In an example, it is used to synthesize a low- order digital replacement for an analog compensator which gives no degradation of stability margin or step response.
\r\n\r\nThis thesis also presents a method for Kranc vector switch decomposition in state space; this is for stability analysis and input-output simulation of perturbed multirate systems. Moving the 30-year-old Kranc technique from the frequency domain to the state-space domain simplifies the analysis tremendously. Because the number of states is preserved, the dimensionality problems long associated with the Kranc method disappear. The new method is also useful for simulating intersample ripple behavior.
", "doi": "10.7907/gz0q-x789", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:813", "collection": "thesis", "collection_id": "813", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-02282008-133009", "primary_object_url": { "basename": "Cheung_km_1987.pdf", "content": "final", "filesize": 3060620, "license": "other", "mime_type": "application/pdf", "url": "/813/1/Cheung_km_1987.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Error-Correction Coding in Data Storage Systems", "author": [ { "family_name": "Cheung", "given_name": "Kar-Ming", "clpid": "Cheung-Kar-Ming" } ], "thesis_advisor": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Swanson", "given_name": "Larry W.", "clpid": "Swanson-L-W" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "This thesis is divided into two parts. The first part is a study of the decoder error probability of linear maximum distance separable (MDS) codes. An exact formula for the decoder error probability of linear MDS codes is derived. The random characteristic of this class of codes is analyzed, and a lower bound for the decoder error probability is given. The second part is a study of error-correction coding in data storage systems, particularly in tape machines. The helical interleaving scheme is generalized from single channel to n parallel channels. A new code, which is specially designed for tape machines, is introduced. This code corrects more error patterns than the AXP code, and it possesses a simple hardware structure. Lastly, a class of error-correcting DC free trellis code, and a class of error-correcting RLL code are introduced.
\r\n", "doi": "10.7907/emtw-yh64", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:823", "collection": "thesis", "collection_id": "823", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03012008-131442", "primary_object_url": { "basename": "Doganata_yn_1987.pdf", "content": "final", "filesize": 4560178, "license": "other", "mime_type": "application/pdf", "url": "/823/1/Doganata_yn_1987.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Analysis of Traffic Problems of Integrated Networks", "author": [ { "family_name": "Do\u011fanata", "given_name": "Yurdaer Nezihi", "clpid": "Do\u011fanata-Yurdaer-Nezihi" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Lorden", "given_name": "Gary A.", "clpid": "Lorden-G-A" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A new approach to the analysis of Markovian queueing networks is developed and applied to traffic problems of voice-data integration networks and trunked mobile radio networks. This approach is shown to be computationally much less complex for large systems compared to previous work.
\r\n\r\nIn the integrated networks we consider, two classes of users share the system facilities. If all the servers are busy, the first class of users are queued, but the second class of users are blocked and cleared from the system. The performance objective of such an integrated network is to trade the time delay performance of the first class of users against the blockage performance of the second class of users to keep the grade of service as high as possible for both classes of traffic.
\r\n\r\nThe key-state approach introduced in this thesis is what makes the analysis of the corresponding Markovian queueing network model of these integrated networks computationally less complex than that of previous work. The performance of integrated networks is investigated under several control strategies and new exact closed-form expressions are obtained for the equilibrium probabilities of the corresponding Markovian models. The results are extended to a more general Markovian process where a bulk of arrivals and departures are allowed.
\r\n\r\nThe key-state approach is expected to become a standard tool for analyzing large queueing networks such as will arise when Integrated Services Digital Networks (ISDN) become widely deployed in the next five years.
", "doi": "10.7907/d844-3g40", "publication_date": "1987", "thesis_type": "phd", "thesis_year": "1987" }, { "id": "thesis:2929", "collection": "thesis", "collection_id": "2929", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-07192006-155419", "primary_object_url": { "basename": "Swaminathan_k_1986.pdf", "content": "final", "filesize": 9865721, "license": "other", "mime_type": "application/pdf", "url": "/2929/1/Swaminathan_k_1986.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Analysis and Demonstration of the Quantile Vocoder", "author": [ { "family_name": "Swaminathan", "given_name": "Kumar", "clpid": "Swaminathan-Kumar" } ], "thesis_advisor": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" } ], "thesis_committee": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Konishi", "given_name": "Masakazu", "clpid": "Konishi-M" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Townes", "given_name": "S.", "clpid": "Townes-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A new scheme for speech compression is proposed, implemented and evaluated in this thesis. In this new scheme, the spectral envelope of the power spectral density of a speech frame is encoded using quartiles or order statistics. The perceptually important features of the spectral envelope are its peaks which correspond to the formant frequencies. The shape of the spectral envelope near the formants can be encoded by a careful choice of the quantiles and quantile orders. Algorithms to choose such a set of quantiles and quantile orders are described. It turns out that this can be done using very few quantiles. Data compression is achieved chiefly this way.
\r\n\r\nThe quantile decoding algorithm estimates the spectral envelope from the quartiles and quantile orders. The first step is to set up a flat spectral density approximation. In this approximation, the spectral envelope is assumed to be constant every interquantile range. This constant value is simply the average power (i.e., ratio of the difference in quantile orders to the difference in quantiles) in that interquantile range. It is shown that the flat spectral density approximation is the maximum entropy solution to the decoding problem. The flat spectral density approximation is then smoothed by fitting an all-pole or autoregressive model. Algorithms to determine the parameters of the autoregressive model are described. These algorithms involve the solution of a system of linear equations, which has a \"Toeplitz plus Hankel\" structure, followed by a standard spectral factorization. The algorithms can easily be extended to pole-zero models as well.
\r\n\r\nThe information about the spectral fine structure is sent through the parameters of the excitation model. A multi-pulse excitation model in cascade with a pitch predictor model has been chosen for this purpose. The theory of the multi-pulse model is reviewed, and algorithms to estimate the parameters of the multi-pulse model as well as the pitch predictor model are presented.
\r\n\r\nQuantization and encoding schemes of various transmission parameters are described. For high and medium bit rate applications, the parameters that need to be transmitted every frame are the quantiles, quantile orders, locations and amplitudes of the excitation pulses, parameters of the pitch predictor model and a gain term. For low bit rate applications, the quantile orders are fixed and so need not be transmitted. The quantization schemes for the quantile orders and for the gain term are shown to be optimal in the sense of minimizing the maximum spectral deviation due to quantization.
\r\n\r\nThe quantile vocoder has been implemented in software at 4.8, 9.6, 16 and 24 Kbits/s. In order to test the vocoder, a speech data base of ten sentences spoken by one male and one female speaker has been used. The so-called segmental signal-to-noise ratio has been used as an objective performance measure to evaluate the vocoder at all bit rates. A subjective method for assessing the quality of the vocoder at various bit rates is also proposed and carried out. The results of the nonreal time quantile vocoder simulations at 4.8, 9.6, 16 and 24 Kbits/s have been recorded and will be played at the end of the talk. The quantile vocoder does indeed seem equivalent to or better than other vocoders at the same bit rates, according to informal listening tests.
", "doi": "10.7907/2XFF-5X20", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:2929", "collection": "thesis", "collection_id": "2929", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-07192006-155419", "primary_object_url": { "basename": "Swaminathan_k_1986.pdf", "content": "final", "filesize": 9865721, "license": "other", "mime_type": "application/pdf", "url": "/2929/1/Swaminathan_k_1986.pdf", "version": "v2.0.0" }, "type": "thesis", "title": "Analysis and Demonstration of the Quantile Vocoder", "author": [ { "family_name": "Swaminathan", "given_name": "Kumar", "clpid": "Swaminathan-Kumar" } ], "thesis_advisor": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" } ], "thesis_committee": [ { "family_name": "Middlebrook", "given_name": "Robert David", "clpid": "Middlebrook-R-D" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Konishi", "given_name": "Masakazu", "clpid": "Konishi-M" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" }, { "family_name": "Townes", "given_name": "S.", "clpid": "Townes-S" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A new scheme for speech compression is proposed, implemented and evaluated in this thesis. In this new scheme, the spectral envelope of the power spectral density of a speech frame is encoded using quartiles or order statistics. The perceptually important features of the spectral envelope are its peaks which correspond to the formant frequencies. The shape of the spectral envelope near the formants can be encoded by a careful choice of the quantiles and quantile orders. Algorithms to choose such a set of quantiles and quantile orders are described. It turns out that this can be done using very few quantiles. Data compression is achieved chiefly this way.
\r\n\r\nThe quantile decoding algorithm estimates the spectral envelope from the quartiles and quantile orders. The first step is to set up a flat spectral density approximation. In this approximation, the spectral envelope is assumed to be constant every interquantile range. This constant value is simply the average power (i.e., ratio of the difference in quantile orders to the difference in quantiles) in that interquantile range. It is shown that the flat spectral density approximation is the maximum entropy solution to the decoding problem. The flat spectral density approximation is then smoothed by fitting an all-pole or autoregressive model. Algorithms to determine the parameters of the autoregressive model are described. These algorithms involve the solution of a system of linear equations, which has a \"Toeplitz plus Hankel\" structure, followed by a standard spectral factorization. The algorithms can easily be extended to pole-zero models as well.
\r\n\r\nThe information about the spectral fine structure is sent through the parameters of the excitation model. A multi-pulse excitation model in cascade with a pitch predictor model has been chosen for this purpose. The theory of the multi-pulse model is reviewed, and algorithms to estimate the parameters of the multi-pulse model as well as the pitch predictor model are presented.
\r\n\r\nQuantization and encoding schemes of various transmission parameters are described. For high and medium bit rate applications, the parameters that need to be transmitted every frame are the quantiles, quantile orders, locations and amplitudes of the excitation pulses, parameters of the pitch predictor model and a gain term. For low bit rate applications, the quantile orders are fixed and so need not be transmitted. The quantization schemes for the quantile orders and for the gain term are shown to be optimal in the sense of minimizing the maximum spectral deviation due to quantization.
\r\n\r\nThe quantile vocoder has been implemented in software at 4.8, 9.6, 16 and 24 Kbits/s. In order to test the vocoder, a speech data base of ten sentences spoken by one male and one female speaker has been used. The so-called segmental signal-to-noise ratio has been used as an objective performance measure to evaluate the vocoder at all bit rates. A subjective method for assessing the quality of the vocoder at various bit rates is also proposed and carried out. The results of the nonreal time quantile vocoder simulations at 4.8, 9.6, 16 and 24 Kbits/s have been recorded and will be played at the end of the talk. The quantile vocoder does indeed seem equivalent to or better than other vocoders at the same bit rates, according to informal listening tests.
", "doi": "10.7907/2XFF-5X20", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:1020", "collection": "thesis", "collection_id": "1020", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03192008-121641", "primary_object_url": { "basename": "Haney_mw_1986.pdf", "content": "final", "filesize": 15585280, "license": "other", "mime_type": "application/pdf", "url": "/1020/1/Haney_mw_1986.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Acousto-Optical Time-and-Space Integrating Processors for Real-Time Synthetic Aperture Radar Imaging", "author": [ { "family_name": "Haney", "given_name": "Michael William", "orcid": "0009-0001-8071-5561", "clpid": "Haney-Michael-William" } ], "thesis_advisor": [ { "family_name": "Psaltis", "given_name": "Demetri", "orcid": "0000-0003-4684-8800", "clpid": "Psaltis-D" } ], "thesis_committee": [ { "family_name": "Psaltis", "given_name": "Demetri", "orcid": "0000-0003-4684-8800", "clpid": "Psaltis-D" }, { "family_name": "Elachi", "given_name": "Charles", "orcid": "009-0002-2156-967X", "clpid": "Elachi-C" }, { "family_name": "Masson", "given_name": "Colin R.", "clpid": "Masson-Colin-R" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Acousto-optical processors for Synthetic Aperture Radar (SAR) imaging are presented. The new processors produce images at real-time rates by combining the operations of data collection, storage, and processing into a compact time-and-space integrating (TSI) architecture. In the TSI approach the 2-D SAR imaging problem is decomposed into a cascade of 2 distinct operations: a 1-D spatial integration of light for range compression, and a 1-D temporal integration of light for azimuth compression. These two operations are coupled via a common path interferometric scheme that is insensitive to mechanical vibrations.
\r\n\r\nThe results of an experimental characterization of the TSI approach, with simulated point scatterer radar echoes, are reported. The performance issues of interferometric bias removal, dynamic range, and resolution are addressed. The architecture is generalized to correct for range migration and the results of a range walk compensation experiment are presented. A programmable version of the TSI architecture, in which the fixed azimuth reference mask is replaced by an acousto-optic light modulator, is described. The application of the programmable architecture to both strip-map and spot-light mode SAR is analyzed and experimentally verified.
", "doi": "10.7907/64T4-7N83", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:1022", "collection": "thesis", "collection_id": "1022", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03192008-140041", "primary_object_url": { "basename": "Guerin_r_1986.pdf", "content": "final", "filesize": 7591623, "license": "other", "mime_type": "application/pdf", "url": "/1022/1/Guerin_r_1986.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Queueing and Traffic in Cellular Radio", "author": [ { "family_name": "Gu\u00e9rin", "given_name": "Roch", "orcid": "0000-0002-8928-9984", "clpid": "Gu\u00e9rin-Roch" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A Cellular Radio system is analyzed from the communications traffic point of view. A cell within a given system is modeled by a multi-server service facility with or without the possibility of queueing some type of customers. Two types of arrivals are distinguished, corresponding to handoff calls (calls already in progress that enter the cell) and originating calls (calls initiated inside the cell). The queueing system used assumes Poisson distributed arrivals with different rates for the two types of customers. We initially assume, as is usually done for telephone communications, an exponential distribution for the service times of the customers. Due to mobility of the subscribers that can travel through several cells in the system, the channel occupancy time is in general different from the total call duration. Using both a simulation of a cellular system and an analytic model we offer evidence that a memory-less distribution may not be too unrealistic for the channel occupancy time.
\r\n\r\nWe derive some traffic policies that give a higher level of protection to handoff calls, and their influence on the other class of customers as well as on the overall traffic is analyzed. The first policies proposed have the advantage of simplicity and provide an efficient way of reducing the blocking probability of handoff calls while only slightly increasing the blocking probability of originating calls. The price paid is, however, a small decrease in the total carried traffic.
\r\n\r\nSome more evolved traffic policies are then introduced that still decrease the blocking probability of handoff calls without much penalizing originating calls whose access to the system will only be slightly delayed. These more evolved policies provide the additional advantage of increasing the total carried traffic, while still providing a higher level of protection to handoff calls.
\r\n", "doi": "10.7907/WY9Y-FB87", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:1022", "collection": "thesis", "collection_id": "1022", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03192008-140041", "primary_object_url": { "basename": "Guerin_r_1986.pdf", "content": "final", "filesize": 7591623, "license": "other", "mime_type": "application/pdf", "url": "/1022/1/Guerin_r_1986.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Queueing and Traffic in Cellular Radio", "author": [ { "family_name": "Gu\u00e9rin", "given_name": "Roch", "orcid": "0000-0002-8928-9984", "clpid": "Gu\u00e9rin-Roch" } ], "thesis_advisor": [ { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" } ], "thesis_committee": [ { "family_name": "McEliece", "given_name": "Robert J.", "clpid": "McEliece-R-J" }, { "family_name": "Beck", "given_name": "James L.", "clpid": "Beck-J-L" }, { "family_name": "Franklin", "given_name": "Joel N.", "clpid": "Franklin-J-N" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "A Cellular Radio system is analyzed from the communications traffic point of view. A cell within a given system is modeled by a multi-server service facility with or without the possibility of queueing some type of customers. Two types of arrivals are distinguished, corresponding to handoff calls (calls already in progress that enter the cell) and originating calls (calls initiated inside the cell). The queueing system used assumes Poisson distributed arrivals with different rates for the two types of customers. We initially assume, as is usually done for telephone communications, an exponential distribution for the service times of the customers. Due to mobility of the subscribers that can travel through several cells in the system, the channel occupancy time is in general different from the total call duration. Using both a simulation of a cellular system and an analytic model we offer evidence that a memory-less distribution may not be too unrealistic for the channel occupancy time.
\r\n\r\nWe derive some traffic policies that give a higher level of protection to handoff calls, and their influence on the other class of customers as well as on the overall traffic is analyzed. The first policies proposed have the advantage of simplicity and provide an efficient way of reducing the blocking probability of handoff calls while only slightly increasing the blocking probability of originating calls. The price paid is, however, a small decrease in the total carried traffic.
\r\n\r\nSome more evolved traffic policies are then introduced that still decrease the blocking probability of handoff calls without much penalizing originating calls whose access to the system will only be slightly delayed. These more evolved policies provide the additional advantage of increasing the total carried traffic, while still providing a higher level of protection to handoff calls.
\r\n", "doi": "10.7907/WY9Y-FB87", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" }, { "id": "thesis:1020", "collection": "thesis", "collection_id": "1020", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-03192008-121641", "primary_object_url": { "basename": "Haney_mw_1986.pdf", "content": "final", "filesize": 15585280, "license": "other", "mime_type": "application/pdf", "url": "/1020/1/Haney_mw_1986.pdf", "version": "v3.0.0" }, "type": "thesis", "title": "Acousto-Optical Time-and-Space Integrating Processors for Real-Time Synthetic Aperture Radar Imaging", "author": [ { "family_name": "Haney", "given_name": "Michael William", "orcid": "0009-0001-8071-5561", "clpid": "Haney-Michael-William" } ], "thesis_advisor": [ { "family_name": "Psaltis", "given_name": "Demetri", "orcid": "0000-0003-4684-8800", "clpid": "Psaltis-D" } ], "thesis_committee": [ { "family_name": "Psaltis", "given_name": "Demetri", "orcid": "0000-0003-4684-8800", "clpid": "Psaltis-D" }, { "family_name": "Elachi", "given_name": "Charles", "orcid": "009-0002-2156-967X", "clpid": "Elachi-C" }, { "family_name": "Masson", "given_name": "Colin R.", "clpid": "Masson-Colin-R" }, { "family_name": "Posner", "given_name": "Edward C.", "clpid": "Posner-E-C" }, { "family_name": "Rutledge", "given_name": "David B.", "clpid": "Rutledge-D-B" }, { "family_name": "Vaidyanathan", "given_name": "P. P.", "orcid": "0000-0003-3003-7042", "clpid": "Vaidyanathan-P-P" } ], "local_group": [ { "literal": "div_eng" } ], "abstract": "Acousto-optical processors for Synthetic Aperture Radar (SAR) imaging are presented. The new processors produce images at real-time rates by combining the operations of data collection, storage, and processing into a compact time-and-space integrating (TSI) architecture. In the TSI approach the 2-D SAR imaging problem is decomposed into a cascade of 2 distinct operations: a 1-D spatial integration of light for range compression, and a 1-D temporal integration of light for azimuth compression. These two operations are coupled via a common path interferometric scheme that is insensitive to mechanical vibrations.
\r\n\r\nThe results of an experimental characterization of the TSI approach, with simulated point scatterer radar echoes, are reported. The performance issues of interferometric bias removal, dynamic range, and resolution are addressed. The architecture is generalized to correct for range migration and the results of a range walk compensation experiment are presented. A programmable version of the TSI architecture, in which the fixed azimuth reference mask is replaced by an acousto-optic light modulator, is described. The application of the programmable architecture to both strip-map and spot-light mode SAR is analyzed and experimentally verified.
", "doi": "10.7907/64T4-7N83", "publication_date": "1986", "thesis_type": "phd", "thesis_year": "1986" } ]