A Tensor-Based Approach to L-Shaped Arrays Processing With Enhanced Degrees of Freedom

Rao, Wei; Li, Dan; Zhang, Jian Qiu

doi:10.1109/lsp.2017.2783370

Cited by 44 publications

(30 citation statements)

References 26 publications

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“…Similar to [ 24 , 25 , 26 ], we also assume here that the K sources are uncorrelated and the source DOA pairs are restricted to satisfy the condition given by Theorem 4 in [ 12 ] so that the signal matrix

(

) with a full column rank is guaranteed. Under these assumptions and considering the Vandermonde structures of

and

, we have

and

, where

represents the Kruskal rank [ 20 ] of the matrix

, which equals to the largest integer such that any set of

columns of

is linearly independent.…”

Section: 2-d Doa and Polarization Parameter Estimationmentioning

confidence: 99%

A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array

Rao

Zhang

2018

Sensors

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In this paper, a novel parallel factor (PARAFAC) model for processing the nested vector-sensor array is proposed. It is first shown that a nested vector-sensor array can be divided into multiple nested scalar-sensor subarrays. By means of the autocorrelation matrices of the measurements of these subarrays and the cross-correlation matrices among them, it is then demonstrated that these subarrays can be transformed into virtual scalar-sensor uniform linear arrays (ULAs). When the measurement matrices of these scalar-sensor ULAs are combined to form a third-order tensor, a novel PARAFAC model is obtained, which corresponds to a longer vector-sensor ULA and includes all of the measurements of the difference co-array constructed from the original nested vector-sensor array. Analyses show that the proposed PARAFAC model can fully use all of the measurements of the difference co-array, instead of its partial measurements as the reported models do in literature. It implies that all of the measurements of the difference co-array can be fully exploited to do the 2-D direction of arrival (DOA) and polarization parameter estimation effectively by a PARAFAC decomposition method so that both the better estimation performance and slightly improved identifiability are achieved. Simulation results confirm the efficiency of the proposed model.

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(

) with a full column rank is guaranteed. Under these assumptions and considering the Vandermonde structures of

and

, we have

and

, where

represents the Kruskal rank [ 20 ] of the matrix

, which equals to the largest integer such that any set of

columns of

is linearly independent.…”

Section: 2-d Doa and Polarization Parameter Estimationmentioning

confidence: 99%

A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array

Rao

Zhang

2018

Sensors

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“…Thus, for a general set A which verifies the conditions of Proposition 2.14, the total cost of the computation is about 59r 6 270 .…”

mentioning

confidence: 92%

“…Indeed the Kruskal's algorithm is used extensively by researchers in technological fields (see e.g. [6]).…”

Section: Introductionmentioning

confidence: 99%

On a geometric method for the identifiability of forms

Mazzon

2019

Boll Unione Mat Ital

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We introduce a new criterion which tests if a given decomposition of a given ternary form T of even degree is unique. The criterion is based on the analysis of the Hilbert function of the projective set of points Z associated to the decomposition, and on the Terracini's Lemma which describes tangent spaces to secant varieties. The criterion works in a range for the length of the decomposition which is equivalent to the range in which the reshaped Kruskal's criterion (see [1]) works. Our criterion determines an algorithm for the identifiability of T which is sensibly faster than algorithms based on the reshaped Kruskal's criterion, especially when the set of points Z is not in general position.

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“…e 2-D DOA estimation has received considerable attention in the past decades and has met many applications in array signal processing society, such as, radar, sonar, and wireless communications [1]. Numerous array structures, such as L-shaped arrays, rectangular arrays, circular arrays, two parallel ULAs, etc., [2][3][4][5][6][7][8][9] are proposed and are applied in different scenario, among which, L-shaped ULA attracts wide concerns due to its simple structure and ease of implementation. Accordingly, researchers developed numerous methods for estimation of 2-D DOA based on L-shaped ULAs [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…ese methods are roughly categorized into two classes: one class is to decouple L-shaped ULA into two separate ULAs, where azimuths and elevations are estimated independently, and the additional 2-D DOA pairing procedure is needed. e other class developed the Vandermonde structure of steering matrix with automatic angles pairing, such as JSVD [18], 2-D MUSIC [20], 2-D PM, 2-D ESPRIT, and their variants [23,25], of tensor techniques, such as PARAFAC [26], CS-PARAFAC [27], and the tensor-based PARAFAC [8]. Compared to other methods, JSVD and 2-D MUSIC can obtain better angle estimation performance at the expense of prohibitive complexity.…”

Section: Introductionmentioning

confidence: 99%

Two 2-D DOA Estimation Methods with Full and Partial Generalized Virtual Aperture Extension Technology

Dong

Zhang

et al. 2019

International Journal of Antennas and Propagation

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We address the two-dimensional direction-of-arrival (2-D DOA) estimation problem for L-shaped uniform linear array (ULA) using two kinds of approaches represented by the subspace-like method and the sparse reconstruction method. Particular interest emphasizes on exploiting the generalized conjugate symmetry property of L-shaped ULA to maximize the virtual array aperture for two kinds of approaches. The subspace-like method develops the rotational invariance property of the full virtual received data model by introducing two azimuths and two elevation selection matrices. As a consequence, the problem to estimate azimuths represented by an eigenvalue matrix can be first solved by applying the eigenvalue decomposition (EVD) to a known nonsingular matrix, and the angles pairing is automatically implemented via the associate eigenvector. For the sparse reconstruction method, first, we give a lemma to verify that the received data model is equivalent to its dictionary-based sparse representation under certain mild conditions, and the uniqueness of solutions is guaranteed by assuming azimuth and elevation indices to lie on different rows and columns of sparse signal cross-correlation matrix; we then derive two kinds of data models to reconstruct sparse 2-D DOA via M-FOCUSS with and without compressive sensing (CS) involvements; finally, the numerical simulations validate the proposed approaches outperform the existing methods at a low or moderate complexity cost.

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A Tensor-Based Approach to L-Shaped Arrays Processing With Enhanced Degrees of Freedom

Cited by 44 publications

References 26 publications

A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array

A Novel PARAFAC Model for Processing the Nested Vector-Sensor Array

On a geometric method for the identifiability of forms

Two 2-D DOA Estimation Methods with Full and Partial Generalized Virtual Aperture Extension Technology

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