Article records
https://feeds.library.caltech.edu/people/Liu-Chun-Lin/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 23:49:14 +0000Remarks 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.edu/records/cbdvf-yfj49Discrete 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.edu/records/rgehe-b1872Super 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.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.edu/records/8y2a4-16y07Cramér–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.edu/records/gqq3c-46f43Hourglass 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.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.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.edu/records/wkjy7-z2j27Robustness 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.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.edu/records/awy5c-16w94Novel 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.edu/records/fst8j-my548