Combined Feed
https://feeds.library.caltech.edu/people/Liu-Chun-Lin/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:34:42 +0000Design of coprime DFT arrays and filter banks
https://resolver.caltech.edu/CaltechAUTHORS:20150508-123246910
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2014
DOI: 10.1109/ACSSC.2014.7094484
Coprime arrays offer degrees of freedom of O(MN) given O(M +N) sensors, where M and N are coprime integers. The performance of coprime arrays is based on coprime DFT filter banks (coprime DFTFBs), which cascade an M-channel DFTFB and an N-channel DFTFB to achieve MN-channel filter banks. However, practical designs of coprime DFTFBs have not been fully studied. In this paper, a systematic design is related to IFIR filter designs, based on M, N, filter orders, and peak ripples. Our design owns a parameter λ that provides tradeoffs between passbands and stopbands. A design example for different λ is also presented.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/87hj8-z1q27Coprime arrays and samplers for space-time adaptive processing
https://resolver.caltech.edu/CaltechAUTHORS:20160722-143825916
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2015
DOI: 10.1109/ICASSP.2015.7178394
This paper extends the use of coprime arrays and samplers for the case of moving sources. Space-time adaptive processing (STAP) plays an important role in estimating direction-of-arrivals (DOAs) and radial velocities of emitting sources. However, the detection performance is fundamentally limited by the array geometry and the temporal samplers at each sensor. Coprime arrays and coprime samplers offer an enhanced degree of freedom of O(MN) using only O(M + N) physical sensors or samples. In this paper, we propose coprime joint angle-Doppler estimation (coprime JADE), which incorporates both coprime arrays and coprime samplers with the STAP framework. Nonuniform time samples at different sensors can be used to generate a sampled autocorrelation matrix, from which we compute a spatial smoothed matrix. It will be proved that spatial smoothed matrices can be used in the MUSIC algorithm for parameter estimation. With sufficient snapshots, coprime JADE distinguishes O(M_1N_1M_2N_2) independent sources if it corresponds to coprime arrays and coprime samplers with coprime integers (M_1,N_1) and (M_2,N_2), respectively. It is verified through simulations that coprime JADE resolves the angle-Doppler information better compared to other conventional algorithms.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jqrjm-fzx30Coprime DFT filter bank design: Theoretical bounds and guarantees
https://resolver.caltech.edu/CaltechAUTHORS:20160722-155946933
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2015
DOI: 10.1109/ICASSP.2015.7178694
Coprime DFT filter banks (coprime DFTFB) achieve the effect of an MN-DFTFB by using two DFTFBs of size only M and N, where M and N are coprime integers. However, coprime DFTFBs need to be designed properly, to avoid unwanted bumps in stopbands or unsatisfactory total spectrum coverage, quantified by overall amplitude responses. In this paper, a detailed theoretical analysis will be made on the tradeoffs between bumps and overall amplitude responses. It will be shown that the bump level at the center frequency f_b of a bump, is approximately one-fourth of the overall amplitude response at f_b. Then, a novel design will be introduced based on an optimization problem pertaining to overall amplitude responses. The original problem is relaxed to a computationally tractable optimization program, which can be solved with alternating minimization algorithms. It is verified with simulations that the new designs cover the spectrum completely.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/17d5f-z1647Remarks on the Spatial Smoothing Step in Coarray MUSIC
https://resolver.caltech.edu/CaltechAUTHORS:20150317-074438744
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2015
DOI: 10.1109/LSP.2015.2409153
Sparse arrays such as nested and coprime arrays use a technique called spatial smoothing in order to successfully perform MUSIC in the difference-coarray domain. In this paper it is shown that the spatial smoothing step is not necessary in the sense that the effect achieved by that step can be obtained more directly. In particular, with R_(ss) denoting the spatial smoothed matrix with finite snapshots, it is shown here that the noise eigenspace of this matrix can be directly obtained from another matrix R which is much easier to compute from data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/cbdvf-yfj49Tensor MUSIC in Multidimensional Sparse Arrays
https://resolver.caltech.edu/CaltechAUTHORS:20160901-122213310
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2015
DOI: 10.1109/ACSSC.2015.7421458
Tensor-based MUSIC algorithms have been successfully applied to parameter estimation in array processing. In this paper, we apply these for sparse arrays, such as nested arrays and coprime arrays, which are known to boost the degrees of freedom to O(N2) given O(N) sensors. We consider two tensor decomposition methods: CANDECOMP/PARAFAC (CP) and high-order singular value decomposition (HOSVD) to derive novel tensor MUSIC spectra for sparse arrays. It will be demonstrated that the tensor MUSIC spectrum via HOSVD suffers from cross-term issues while the tensor MUSIC spectrum via CP identifies sources unambiguously, even in high- dimensional tensors.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r817k-k7843Super Nested Arrays: Sparse arrays with Less Mutual Coupling than Nested Arrays
https://resolver.caltech.edu/CaltechAUTHORS:20160322-153051833
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2016
DOI: 10.1109/ICASSP.2016.7472223
In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With N denoting the number of sensors, these sparse arrays offer O(N^2) freedoms for source estimation because
their difference coarrays have O(N^2)-long ULA segments. These arrays have different shortcomings: coprime arrays have holes in the coarray, MRAs have no closed-form expressions, and nested arrays have relatively large mutual coupling. This paper introduces a new array called the super nested array, which has all the good properties
of the nested array, and at the same time reduces mutual coupling significantly. For fixed N, the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with separation λ/2 is significantly
reduced. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ez1be-e4350Coprime coarray interpolation for DOA estimation via nuclear norm minimization
https://resolver.caltech.edu/CaltechAUTHORS:20160823-094540045
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}, {'id': 'Pal-P', 'name': {'family': 'Pal', 'given': 'Piya'}}]}
Year: 2016
DOI: 10.1109/ISCAS.2016.7539135
Coprime arrays, consisting of two uniform linear arrays whose inter-element separations are coprime, can resolve O(MN) sources using only O(M + N) sensors. However, holes in the coarray prevent us from using the full coarray in the MUSIC algorithm for DOA estimation. Through interpolation, it may be possible to use the remaining elements of the coarray to increase the degrees of freedom beyond what is captured in the contiguous ULA section in the coarray. Techniques like positive definite Toeplitz completion, array interpolation, and sparse recovery, manage to include all the information in the coarray, but they demand extra fine-tuned parameters and have individual drawbacks. In this paper, a simple and tractable convex framework via nuclear norm minimization is presented. This approach has no extra tuning parameters and overcomes several undesired issues of other techniques. Numerical examples indicate that, in many instances, the proposed method not only increases the estimation accuracy but also distinguishes more sources than other methods.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yzyxm-7nz73Discrete Laguerre Gaussian Transforms and Their Applications
https://resolver.caltech.edu/CaltechAUTHORS:20160603-091929213
Authors: {'items': [{'id': 'Pei-Soo-Chang', 'name': {'family': 'Pei', 'given': 'Soo-Chang'}}, {'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Lai-Yun-Chiu', 'name': {'family': 'Lai', 'given': 'Yun-Chiu'}}]}
Year: 2016
DOI: 10.1109/TSP.2016.2537275
Laguerre Gaussian functions serve as a complete and orthonormal basis for a variety of physical problems, such as 2D isotropic quantum harmonic oscillators and circularly symmetric laser modes. In this paper, we propose "discrete Laguerre Gaussian functions," which are defined such that some elegant physical properties are preserved and a fast computation algorithm of complexity O(N logN) is available. Discrete Laguerre Gaussian transforms, as introduced in this paper, inherit nice properties from discrete Laguerre Gaussian functions and admit signal analysis over circularly symmetric patterns. It is demonstrated through examples that discrete Laguerre Gaussian transforms find applications in circular pattern keypoints selection, object detection, image compression, rotational invariance feature for pattern recognition, and rotational angle estimation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/rgehe-b1872New Cramér-Rao bound expressions for coprime and other sparse arrays
https://resolver.caltech.edu/CaltechAUTHORS:20160921-132608343
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2016
DOI: 10.1109/SAM.2016.7569620
The Cramér-Rao bound (CRB) offers a lower bound on the variances of unbiased estimates of parameters, e.g., directions of arrival (DOA) in array processing. 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 easy to use in the context of sparse arrays (such as minimum redundancy arrays (MRAs), nested arrays, or coprime arrays) for which the number of identifiable sources D exceeds the number of sensors N. Under such situations, the existing literature does not spell out the conditions under which the Fisher information matrix is nonsingular, or the condition under which specific closed-form expressions for the CRB remain valid. This paper derives a new expression for the CRB to fill this gap. The conditions for validity of this expression are expressed as the rank condition of a matrix defined based on the difference coarray. The rank condition and the closed-form expression lead to a number of new insights. For example, 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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yk9wh-b7r59High Order Super Nested Arrays
https://resolver.caltech.edu/CaltechAUTHORS:20160919-103121476
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2016
DOI: 10.1109/SAM.2016.7569621
Mutual coupling between sensors has a negative impact on the estimation of directions of arrival (DOAs). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs) have less mutual coupling than uniform linear arrays (ULAs). These sparse arrays also have a difference coarray of size O(N^2), where N is the number of sensors, and can therefore resolve O(N^2) uncorrelated source directions. The various sparse arrays proposed in the literature have their pros and cons. The nested array is practical and easy to use but has a dense ULA part which suffers from mutual coupling effects like the traditional ULA. The recently introduced super nested arrays reduce this mutual coupling problem, while maintaining the desirable hole-free O(N^2) difference coarray of the nested array. In this paper, a generalization of super nested arrays is introduced, called the Qth-order super nested array. This has all the properties of the second-order super nested array with the additional advantage that mutual coupling effects are further reduced for Q > 2. A numerical example is included to demonstrate the superior performance of these arrays.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q424c-55j93Super Nested Arrays: Linear Sparse Arrays with Reduced Mutual Coupling - Part I: Fundamentals
https://resolver.caltech.edu/CaltechAUTHORS:20160502-153525515
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2016
DOI: 10.1109/TSP.2016.2558159
In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., 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 nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With N denoting the number of sensors, these sparse arrays offer O(N^2) freedoms for source estimation because their difference coarrays have O(N^2)-long ULA segments. But these well-known sparse arrays have disadvantages: MRAs do not have simple closedform expressions for the array geometry; coprime arrays have holes in the coarray; and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs. This paper introduces a new array called the super nested array, which has all the good properties of the nested array, and at the same time achieves reduced mutual coupling. There is a systematic procedure to determine sensor locations. For fixed N, the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with small separations (λ/2,2 x λ/2, etc.) is significantly reduced. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays. In the companion paper, a further extension called the Qth-order super nested array is developed, which further reduces mutual coupling.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xjsdg-7mj49Super Nested Arrays: Linear Sparse Arrays with Reduced Mutual Coupling - Part II: High-Order Extensions
https://resolver.caltech.edu/CaltechAUTHORS:20160502-154806504
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2016
DOI: 10.1109/TSP.2016.2558167
In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays such as nested arrays, coprime arrays, and minimum redundancy arrays (MRA) have reduced mutual coupling compared to uniform linear arrays (ULAs). These arrays also have a difference coarray with O(N^2) virtual elements, where N is the number of physical sensors, and can therefore resolve O(N^2) uncorrelated source directions. But these well-known sparse arrays have disadvantages: MRAs do not have simple closed-form expressions for the array geometry; coprime arrays have holes in the coarray; and nested arrays contain a dense ULA in the physical array, resulting in significantly higher mutual coupling than coprime arrays and MRAs. In a companion paper, a sparse array configuration called the (secondorder) super nested array was introduced, which has many of the advantages of these sparse arrays, while removing most of the disadvantages. Namely, the sensor locations are readily computed for any N (unlike MRAs), and the difference coarray is exactly that of a nested array, and therefore hole-free. At the same time, the mutual coupling is reduced significantly (unlike nested arrays). In this paper, a generalization of super nested arrays is introduced, called the Qth-order super nested array. This has all the properties of the second-order super nested array with the additional advantage that mutual coupling effects are further reduced for Q > 2. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8y2a4-16y07Two-Dimensional Sparse Arrays with Hole-Free Coarray and Reduced Mutual Coupling
https://resolver.caltech.edu/CaltechAUTHORS:20161109-150012043
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2016
DOI: 10.1109/ACSSC.2016.7869629
Two-dimensional sparse arrays with hole-free difference coarrays, like billboard arrays and open box arrays, can identify O(N^2) uncorrelated source directions (DOA) using N sensors. These arrays contain some dense ULA segments, leading to many sensor pairs separated by λ/2. The DOA estimation performance often suffers degradation due to mutual coupling between such closely-spaced sensor pairs. This paper introduces a new 2D array called the half open box array. For a given N, this array has the same hole-free coarray as an open box array. At the same time, the number of sensor pairs with small separation is significantly reduced.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/es2bq-0qt56Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors
https://resolver.caltech.edu/CaltechAUTHORS:20170216-084233440
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2017
DOI: 10.1016/j.dsp.2016.04.011
The Cramér–Rao bound (CRB) offers a lower bound on the variances of unbiased estimates of parameters, e.g., directions of arrival (DOA) in array processing. 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 easy to use in the context of sparse arrays (such as minimum redundancy arrays (MRAs), nested arrays, or coprime arrays) for which the number of identifiable sources D exceeds the number of sensors N . Under such situations, the existing literature does not spell out the conditions under which the Fisher information matrix is nonsingular, or the condition under which specific closed-form expressions for the CRB remain valid. This paper derives a new expression for the CRB to fill this gap. The conditions for validity of this expression are expressed as the rank condition of a matrix defined based on the difference coarray. The rank condition and the closed-form expression lead to a number of new insights. For example, 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 conditions are valid. In particular, for nested arrays, coprime arrays, and MRAs, the new expressions remain valid for D=O(N^2), the precise detail depending on the specific array geometry.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gqq3c-46f43One-bit sparse array DOA estimation
https://resolver.caltech.edu/CaltechAUTHORS:20170621-155418409
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2017
DOI: 10.1109/ICASSP.2017.7952732
One-bit quantization has become an important topic in massive MIMO systems, as it offers low cost and low complexity in the implementation. Techniques to achieve high performance in spite of the coarse quantizers have recently been advanced. In the context of array processing and direction-of-arrival (DOA) estimation also, one bit quantizers have been studied in the past, although not as extensively. This paper shows that sparse arrays such as nested and coprime arrays are more robust to the deleterious effects of one-bit quantization, compared to uniform linear arrays (ULAs); in fact, sparse arrays with one-bit quantizers are often found to be as good as ULAs with unquantized data. Nested and coprime arrays without quanitzers are known to be able to resolve more DOAs than the number of sensors, when sources are uncorrelated. It will be demonstrated that this continues to be true even with one-bit quantization.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kyzw5-wyg40Hourglass arrays: Planar sparse arrays with hole-free coarrays and reduced mutual coupling
https://resolver.caltech.edu/CaltechAUTHORS:20170620-133144745
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'Palghat'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2017
DOI: 10.1121/1.4988557
Linear (1D) sparse arrays such as nested arrays have hole-free difference coarrays with O(N^2) virtual sensor elements, where N is the number of physical sensors. This property implies that O(N^2) monochromatic and uncorrelated sources can be identified. For the 2D case, planar sparse arrays with hole-free coarrays having O(N^2) elements have also been known for a long time. These include billboard arrays, open box arrays (OBA), and 2D nested arrays. Their merits are similar to those of the 1D sparse arrays mentioned above, although identifiability claims regarding O(N^2) sources have to be handled with more care in 2D. In this presentation, we propose hourglass arrays, which have closed-form 2D sensor locations and hole-free coarrays with O(N^2) elements just like the OBA. Furthermore, the mutual coupling effect, which is the undesired interaction between sensors, is reduced since the number of sensor pairs with small spacings such as λ/2 decreases. Among the planar arrays mentioned above, simulations show that hourglass arrays have the best estimation performance in the presence of mutual coupling.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n0sfs-sc311Hourglass Arrays, and Other Novel 2-D Sparse Arrays with Reduced Mutual Coupling
https://resolver.caltech.edu/CaltechAUTHORS:20170405-151504238
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2017
DOI: 10.1109/TSP.2017.2690390
Linear [one-dimensional (1-D)] sparse arrays such as nested arrays and minimum redundancy arrays have hole-free difference coarrays with O(N^2) virtual sensor elements, where N is the number of physical sensors. The hole-free property makes it easier to perform beamforming and DOA estimation in the coarray domain which behaves like an uniform linear array. The O(N^2) property implies that O(N^2) uncorrelated sources can be identified. For the 2-D case, planar sparse arrays with hole-free coarrays having O(N^2) elements have also been known for a long time. These include billboard arrays, open box arrays (OBA), and 2-D nested arrays. Their merits are similar to those of the 1-D sparse arrays mentioned above, although identifiability claims regarding O(N^2) sources have to be handled with more care in 2-D. This paper introduces new planar sparse arrays with hole-free coarrays having O(N^2) elements just like the OBA, with the additional property that the number of sensor pairs with small spacings such as λ/2 decreases, reducing the effect of mutual coupling. The new arrays include half-open box arrays, half-open box arrays with two layers, and hourglass arrays. Among these, simulations show that hourglass arrays have the best estimation performance in presence of mutual coupling.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0a8k7-fyv09Correlation Subspaces: Generalizations and Connection to Difference Coarrays
https://resolver.caltech.edu/CaltechAUTHORS:20170705-151126529
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2017
DOI: 10.1109/TSP.2017.2721915
Direction-of-arrival (DOA) estimation finds applications in many areas of science and engineering. In these applications, sparse arrays such as minimum redundancy arrays, nested arrays, and coprime arrays can be exploited to resolve uncorrelated sources using physical sensors. Recently, 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 paper 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. It is demonstrated through examples that using sparse arrays and generalized correlation subspaces, DOA estimators with source priors exhibit better estimation performance than those without priors, in extreme cases like low SNR and limited snapshots.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wkjy7-z2j27The role of difference coarrays in correlation subspaces
https://resolver.caltech.edu/CaltechAUTHORS:20180419-095825149
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2017
DOI: 10.1109/ACSSC.2017.8335536
The concept of correlation subspaces was recently introduced in array processing literature by Rahmani and Atia. Given a sensor array, its geometry determines the correlation subspace completely, and the covariance matrix of the array output is constrained in a certain way by the correlation subspace. It has been shown by Rahmani and Atia that this knowledge about the covariance constraint can be exploited to improve the performance of DOA estimators. In this paper, it is shown that there is a simple closed form expression for the basis vectors of the correlation subspace. Thus, computation of this subspace is greatly simplified. Another fundamental observation is that, this expression is closely related to the difference coarray. Thirdly, the paper also shows an interesting logical connection between correlation subspaces, redundancy averaging, and rectification, which are popularly used in DOA estimation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7wg09-jyb70Maximally economic sparse arrays and Cantor arrays
https://resolver.caltech.edu/CaltechAUTHORS:20180419-082338809
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2017
DOI: 10.1109/CAMSAP.2017.8313139
Sparse arrays, where the sensors are properly placed with nonuniform spacing, are able to resolve more uncorrelated sources than sensors. This ability arises from the property that the difference coarray, defined as the differences between sensor locations, has many more consecutive integers (hole-free) than the number of sensors. In some implementations, it might be preferable that a) the arrays be symmetric, b) that the arrays be maximally economic, that is, each sensor be essential, and c) that the coarray be hole-free. The essentialness property of a sensor means that if it is deleted, then the difference coarray changes. Existing sparse arrays, such as minimum redundancy arrays (MRA), nested arrays, and coprime arrays do not satisfy these three criteria simultaneously. It will be shown in this paper that Cantor arrays meet all the desired properties mentioned above, based on a comprehensive study on the structure of the difference coarray. Even though Cantor arrays were previously proposed in fractal array design, their coarray properties have not been studied earlier. It will also be shown that the Cantor array has a hole-free difference coarray of size N^(log_2^3) ≈ N^(1.585) where N is the number of sensors. This is unlike the sizes of difference coarrays of the MRA, nested array, coprime array (all O(N^2)), and uniform linear arrays (O(N))^1.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h9dr5-7a306Robustness of Coarrays of Sparse Arrays to Sensor Failures
https://resolver.caltech.edu/CaltechAUTHORS:20180920-112433763
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2018
DOI: 10.1109/ICASSP.2018.8462643
Sparse arrays can identify O(N^2) uncorrelated sources using N physical sensors. This property is because the difference coarray, defined as the differences between sensor locations, has uniform linear array (ULA) segments of length O(N^2) . It is empirically known that, for sparse arrays like minimum redundancy arrays, nested arrays, and coprime arrays, this O(N^2) segment is susceptible to sensor failure, which is an important issue in practical systems. This paper presents the (k-)essentialness property, which characterizes the combinations of the failing sensors that shrink the difference coarray. Based on this, the notion of fragility is proposed to quantify the reliability of sparse arrays with faulty sensors, along with comprehensive studies of their properties. It is demonstrated through examples that there do exist sparse arrays that are as robust as ULA and at the same time, they enjoy O(N^2) consecutive elements in the difference coarray.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yzch4-gym35Comparison of Sparse Arrays From Viewpoint of Coarray Stability and Robustness
https://resolver.caltech.edu/CaltechAUTHORS:20180906-142258359
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2018
DOI: 10.1109/SAM.2018.8448465
Sparse arrays, such as minimum redundancy arrays (MRA), nested arrays, and coprime arrays, can resolve O(N^2), uncorrelated sources with N physical sensors, since they possess an O(N2) -long uniform segment in the difference coarray, which is defined as the differences between sensor locations. Empirically, this O(N^2), property is susceptible to sensor failures. On the other hand, uniform linear arrays (ULA) are known to be robust, but they possess only O(N) elements in the difference coarray. This paper compares the size and the robustness of the difference coarray for a wide variety of array geometries. It is observed from numerical examples that, for a fixed N, increasing the size of the difference coarray typically makes it less robust to faulty sensors. Furthermore, it is noticed from examples that given two arrays with the same N and the same difference coarray, one could be much more robust than the other.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ytphh-3y451Optimizing Minimum Redundancy Arrays for Robustness
https://resolver.caltech.edu/CaltechAUTHORS:20190301-153800720
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2018
DOI: 10.1109/ACSSC.2018.8645482
Sparse arrays have received considerable attention due to their capability of resolving O(N^2)uncorrelated sources with N physical sensors, unlike the uniform linear array (ULA) which identifies at most N−1 sources. This is because sparse arrays have an O(N^2)−long ULA segment in the difference coarray, defined as the set of differences between sensor locations. Among the existing array configurations, minimum redundancy arrays (MRA) have the largest ULA segment in the difference coarray with no holes. However, in practice, ULA is robust, in the sense of coarray invariance to sensor failure, but MRA is not. This paper proposes a novel array geometry, named as the robust MRA (RMRA), that maximizes the size of the hole-free difference coarray subject to the same level of robustness as ULA. The RMRA can be found by solving an integer program, which is computationally expensive. Even so, it will be shown that the RMRA still owns O(N^2) elements in the hole-free difference coarray. In particular, for sufficiently large N, the aperture for RMRA, which is approximately half of the size of the difference coarray, is bounded between 0.0625N^2 and 0.2174N^2.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5qp96-phn05Composite Singer Arrays with Hole-free Coarrays and Enhanced Robustness
https://resolver.caltech.edu/CaltechAUTHORS:20190424-103509340
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2019
DOI: 10.1109/ICASSP.2019.8683563
In array processing, minimum redundancy arrays (MRA) can identify up to O(N^2) uncorrelated sources (the O(N^2) property) with N physical sensors, but this property is susceptible to sensor failures. On the other hand, uniform linear arrays (ULA) are robust, but they resolve only O(N) sources. Recently, the robust MRA (RMRA) was shown to possess the O(N^2) property and to be as robust as ULA. But finding RMRA is computationally difficult for large N. This paper proposes a novel array geometry called the composite Singer array, which is related to a classic paper by Singer in 1938, and to other results in number theory. For large N, composite Singer arrays could own the O(N^2) property and are as robust as ULA. Furthermore, the sensor locations for the composite Singer array can be readily computed by the proposed recursive procedure. These properties will also be demonstrated by using numerical examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mvjd3-5cq67Robustness of Difference Coarrays of Sparse Arrays to Sensor Failures - Part II: Array Geometries
https://resolver.caltech.edu/CaltechAUTHORS:20190425-131914048
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2019
DOI: 10.1109/TSP.2019.2912877
In array processing, sparse arrays are capable of resolving O(N^2) uncorrelated sources with N sensors. Sparse arrays have this property because they possess uniform linear array (ULA) segments of size O(N^2) in the difference coarray, defined as the differences between sensor locations. However, the coarray structure of sparse arrays is susceptible to sensor failures and the reliability of sparse arrays remains a significant but challenging topic for investigation. In the companion paper, a theory of the k -essential family, the k -fragility, and the k -essential Sperner family were presented not only to characterize the patterns of k faulty sensors that shrink the difference coarray, but also to provide a number of insights into the robustness of arrays. This paper derives closed-form characterizations of the k -essential Sperner family for several commonly used array geometries, such as ULA, minimum redundancy arrays (MRA), minimum holes arrays (MHA), Cantor arrays, nested arrays, and coprime arrays. These results lead to many insights into the relative importance of each sensor, the robustness of these arrays, and the DOA estimation performance in the presence of sensor failure. Broadly speaking, ULAs are more robust than coprime arrays, while coprime arrays are more robust than maximally economic sparse arrays, such as MRA, MHA, Cantor arrays, and nested arrays.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6w17h-1jy28Robustness of Difference Coarrays of Sparse Arrays to Sensor Failures - Part I: A Theory Motivated by Coarray MUSIC
https://resolver.caltech.edu/CaltechAUTHORS:20190426-105059411
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2019
DOI: 10.1109/TSP.2019.2912882
In array processing, sparse arrays are capable of resolving O(N^2) uncorrelated sources with N sensors. Sparse arrays have this property because they possess uniform linear array (ULA) segments of size O(N^2) in the difference coarray, defined as the differences between sensor locations. However, the coarray structure of sparse arrays is susceptible to sensor failures, and the reliability of sparse arrays remains a significant but challenging topic for investigation. Broadly speaking, ULAs whose difference coarrays only have O(N) elements, are more robust than sparse arrays with O(N^2) coarray sizes. This paper advances a theory for quantifying such robustness by introducing the k-essentialness of sensors and the k-essential family of arrays. The proposed theory is motivated by the coarray MUSIC algorithm, which estimates source directions based on difference coarrays. Furthermore, the concept of essentialness not only characterizes the patterns of k faulty sensors that shrink the difference coarray, but also leads to the notion of k-fragility, which assesses the robustness of array geometries quantitatively. However, the large size of the k-essential family usually complicates the theory. It will be shown that the k-essential family can be compactly represented by the so-called k-essential Sperner family. Finally the proposed theory is used to provide insights into the probability of change of the difference coarray, as a function of the sensor failure probability and array geometry. In a companion paper, the k-essential Sperner family for several commonly used array geometries will be derived in closed-form, resulting in a quantitative comparison of the robustness of these arrays.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/awy5c-16w94One-Bit Normalized Scatter Matrix Estimation For Complex Elliptically Symmetric Distributions
https://resolver.caltech.edu/CaltechAUTHORS:20210304-101834311
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2020
DOI: 10.1109/icassp40776.2020.9053956
One-bit quantization has attracted attention in massive MIMO, radar, and array processing, due to its simplicity, low cost, and capability of parameter estimation. Specifically, the shape of the covariance of the unquantized data can be estimated from the arcsine law and onebit data, if the unquantized data is Gaussian. However, in practice, the Gaussian assumption is not satisfied due to outliers. It is known from the literature that outliers can be modeled by complex elliptically symmetric (CES) distributions with heavy tails. This paper shows that the arcsine law remains applicable to CES distributions. Therefore, the normalized scatter matrix of the unquantized data can be readily estimated from one-bit samples derived from CES distributions. The proposed estimator is not only computationally fast but also robust to CES distributions with heavy tails. These attributes will be demonstrated through numerical examples, in terms of computational time and the estimation error. An application in DOA estimation with MUSIC spectrum is also presented.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ewhqf-b1g46Novel Algorithms for Analyzing the Robustness of Difference Coarrays to Sensor Failures
https://resolver.caltech.edu/CaltechAUTHORS:20200131-154057752
Authors: {'items': [{'id': 'Liu-Chun-Lin', 'name': {'family': 'Liu', 'given': 'Chun-Lin'}, 'orcid': '0000-0003-3135-9684'}, {'id': 'Vaidyanathan-P-P', 'name': {'family': 'Vaidyanathan', 'given': 'P. P.'}, 'orcid': '0000-0003-3003-7042'}]}
Year: 2020
DOI: 10.1016/j.sigpro.2020.107517
Sparse arrays have drawn attention because they can identify O(N²) uncorrelated source directions using N physical sensors, whereasuniform linear arrays (ULA) find at most N−1 sources. The main reason is that the difference coarray, defined as the set of differences between sensor locations, has size of O(N²) for some sparse arrays. However, the performance of sparse arrays may degrade significantly under sensor failures. In the literature, the k-essentialness property characterizes the patterns of k sensor failures that change the difference coarray. Based on this concept, the k-essential family, the k-fragility, and the k-essential Sperner family provide insights into the robustness of arrays. This paper proposes novel algorithms for computing these attributes. The first algorithm computes the k-essential Sperner family without enumerating all possible k-essential subarrays. With this information, the second algorithm finds the k-essential family first and the k-fragility next. These algorithms are applicable to any 1-D array. However, for robust array design, fast computation for the k-fragility is preferred. For this reason, a simple expression associated with the k-essential Sperner family is proposed to be a tighter lower bound for the k-fragility than the previous result. Numerical examples validate the proposed algorithms and the presented lower bound.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fst8j-my548