DOA estimation using sparse array with gain-phase error based on a novel atomic norm

AbstractTwo-dimensional (2D) direction-of-arrival (DOA) estimation with arbitrary planar sparse array has attracted more interest in massive multiple-input multiple-output application. The research on this issue recently has been advanced with the development of atomic norm technique, which provides super resolution methods for DOA estimation, when the number of snapshots is limited. In this paper, we study the problem of 2D DOA estimation from the sparse array with the sensors randomly selected from uniform rectangular array. In order to identify all azimuth and elevation angles of the incident sources jointly, the 2D atomic norm approach is proposed, which can be solved by semidefinite programming. However, the computational cost of 2D atomic norm is high. To address this issue, our work further reduces the computational complexity of the problem significantly by utilizing the atomic norm approximation method based on the concept of multiple measurement vectors. The numerical examples are provided to demonstrate the practical ability of the proposed method to reduce computational complexity and retain the estimation performance as compared to the competitors.

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Sparse Array DOA Estimation Based on Higher-Order Statistics

2020 IEEE 3rd International Conference on Information Systems and Computer Aided Education (ICISCAE) ◽

10.1109/iciscae51034.2020.9236891 ◽

2020 ◽

Author(s):

Zhigang Zhou ◽

Baixiao Chen ◽

Yan Zhang

Keyword(s):

Order Statistics ◽

Doa Estimation ◽

Higher Order ◽

Higher Order Statistics ◽

Sparse Array

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Design And Analysis of the Sparse Array for DoA Estimation of Noncircular Signals

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2018.2883035 ◽

2019 ◽

Vol 67 (2) ◽

pp. 460-473 ◽

Cited By ~ 13

Author(s):

Payal Gupta ◽

Monika Agrawal

Keyword(s):

Doa Estimation ◽

Sparse Array ◽

Noncircular Signals

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Effect of Sparse Array Geometry on Estimation of Co-array Signal Subspace

Applied Computational Electromagnetics Society ◽

10.47037/2020.aces.j.351186 ◽

2021 ◽

Vol 35 (11) ◽

pp. 1435-1436

Author(s):

Mehmet Hucumenoglu ◽

Piya Pal

Keyword(s):

Covariance Matrix ◽

Estimation Error ◽

Doa Estimation ◽

Singular Value ◽

Signal Subspace ◽

Sparse Array ◽

Subspace Estimation ◽

Signal Covariance Matrix ◽

Special Case ◽

Array Geometry

This paper considers the effect of sparse array geometry on the co-array signal subspace estimation error for Direction-of-Arrival (DOA) estimation. The second largest singular value of the signal covariance matrix plays an important role in controlling the distance between the true subspace and its estimate. For a special case of two closely-spaced sources impinging on the array, we explicitly compute the second largest singular value of the signal covariance matrix and show that it can be significantly larger for a nested array when compared against a uniform linear array with same number of sensors.

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Superresolution 2D DOA Estimation for a Rectangular Array via Reweighted Decoupled Atomic Norm Minimization

Mathematical Problems in Engineering ◽

10.1155/2019/6797168 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13

Author(s):

Ming-Ming Liu ◽

Chun-Xi Dong ◽

Yang-Yang Dong ◽

Guo-Qing Zhao

Keyword(s):

Computational Complexity ◽

Optimization Problem ◽

Toeplitz Matrices ◽

Doa Estimation ◽

Rank Minimization ◽

Rectangular Array ◽

Angle Estimation ◽

Norm Minimization ◽

Atomic Norm ◽

Surrogate Function

This paper proposes a superresolution two-dimensional (2D) direction of arrival (DOA) estimation algorithm for a rectangular array based on the optimization of the atomic l0 norm and a series of relaxation formulations. The atomic l0 norm of the array response describes the minimum number of sources, which is derived from the atomic norm minimization (ANM) problem. However, the resolution is restricted and high computational complexity is incurred by using ANM for 2D angle estimation. Although an improved algorithm named decoupled atomic norm minimization (DAM) has a reduced computational burden, the resolution is still relatively low in terms of angle estimation. To overcome these limitations, we propose the direct minimization of the atomic l0 norm, which is demonstrated to be equivalent to a decoupled rank optimization problem in the positive semidefinite (PSD) form. Our goal is to solve this rank minimization problem and recover two decoupled Toeplitz matrices in which the azimuth-elevation angles of interest are encoded. Since rank minimization is an NP-hard problem, a novel sparse surrogate function is further proposed to effectively approximate the two decoupled rank functions. Then, the new optimization problem obtained through the above relaxation can be implemented via the majorization-minimization (MM) method. The proposed algorithm offers greatly improved resolution while maintaining the same computational complexity as the DAM algorithm. Moreover, it is possible to use a single snapshot for angle estimation without prior information on the number of sources, and the algorithm is robust to noise due to its iterative nature. In addition, the proposed surrogate function can achieve local convergence faster than existing functions.

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Central DOA Estimation Method for Exponential-Type Coherent Distributed Source Based on Fourth-Order Cumulant

International Journal of Antennas and Propagation ◽

10.1155/2020/8968136 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Hao Li ◽

Weijia Cui ◽

Bin Ba ◽

Haiyun Xu ◽

Yankui Zhang

Keyword(s):

Fourth Order ◽

Exponential Type ◽

Complexity Analysis ◽

Estimation Method ◽

Doa Estimation ◽

Estimation Accuracy ◽

Distributed Source ◽

Sparse Array ◽

Fourth Order Cumulant ◽

Array Aperture

The performance of direction-of-arrival (DOA) estimation for sparse arrays applied to the distributed source is worse than that applied to the point source model. In this paper, we introduce the coprime array with a large array aperture into the DOA estimation algorithm of the exponential-type coherent distributed source. In particular, we focus on the fourth-order cumulant (FOC) of the received signal which can provide more useful information when the signal is non-Gaussian than when it is Gaussian. The proposed algorithm extends the array aperture by combining the sparsity of array space domain with the fourth-order cumulant characteristics of signals, which improves the estimation accuracy and degree of freedom (DOF). Firstly, the signal-received model of the sparse array is established, and the fourth-order cumulant matrix of the received signal of the sparse array is calculated based on the characteristics of distributed sources, which extend the array aperture. Then, the virtual array is constructed by the sum aggregate of physical array elements, and the position set of its maximum continuous part array element is obtained. Finally, the center DOA estimation of the distributed source is realized by the subspace method. The accuracy and DOF of the proposed algorithm are higher than those of the distributed signal parameter estimator (DSPE) algorithm and least-squares estimation signal parameters via rotational invariance techniques (LS-ESPRIT) algorithm when the array elements are the same. Complexity analysis and numerical simulations are provided to demonstrate the superiority of the proposed method.

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A Gridless Wideband DOA Estimation Based On Atomic Norm Minimization

2020 IEEE 11th Sensor Array and Multichannel Signal Processing Workshop (SAM) ◽

10.1109/sam48682.2020.9104308 ◽

2020 ◽

Author(s):

Yuanyuan Jiang ◽

Dan Li ◽

Xiaohuan Wu ◽

Wei-Ping Zhu

Keyword(s):

Doa Estimation ◽

Norm Minimization ◽

Atomic Norm

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DOA Estimation Using Compressed Sparse Array

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2018.2847645 ◽

2018 ◽

Vol 66 (15) ◽

pp. 4133-4146 ◽

Cited By ~ 28

Author(s):

Muran Guo ◽

Yimin D. Zhang ◽

Tao Chen

Keyword(s):

Doa Estimation ◽

Sparse Array

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Atomic Norm-Based DOA Estimation with Dual-Polarized Radar

Electronics ◽

10.3390/electronics8091056 ◽

2019 ◽

Vol 8 (9) ◽

pp. 1056 ◽

Cited By ~ 3

Author(s):

Min Han ◽

Wenbin Dou

Keyword(s):

Doa Estimation ◽

Spatial Domain ◽

Estimation Problem ◽

Semidefinite Program ◽

Sparse Reconstruction ◽

Reconstruction Problem ◽

Estimation Performance ◽

Atomic Norm ◽

Dual Polarized ◽

Definition Of

In the dual-polarized radar system, the horizontally and vertically polarized signals can be exploited to improve the direction of arrival (DOA) estimation performance. In this paper, the DOA estimation problem is considered in the dual-polarized radar. By exploiting the target sparsity in the spatial domain, the sparse-based method is proposed after formulating the DOA estimation problem as a sparse reconstruction problem. In the traditionally sparse methods using the compressed sensing (CS) theory, the spatial domain is discretized into grids to establish a dictionary matrix and solve the sparse reconstruction problem, but the off-grid error is introduced in the discretized grids. Therefore, we formulate a novel definition of atomic norm for the dual-polarized signals and give an atomic norm-based method to denoise the received signals. Then, an efficient semidefinite program (SDP) is derived, and the DOA is estimated by searching the peak values of the denoised signals. Simulation results show that the proposed method can significantly improve the DOA estimation performance in the dual-polarized radar. Additionally, compared with the state-of-art methods, the proposed method has better estimation performance with relatively low computational complexity.

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Sparsity-Based DOA Estimation with Gain and Phase Error Calibration of Generalized Nested Array

Mathematical Problems in Engineering ◽

10.1155/2020/1720310 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Ziang Feng ◽

Guoping Hu ◽

Hao Zhou

Keyword(s):

Degrees Of Freedom ◽

Phase Error ◽

Doa Estimation ◽

Model Errors ◽

Multiple Sources ◽

Sparse Arrays ◽

Estimation Algorithms ◽

Phase Errors ◽

Representation Method ◽

Cramer Rao Bound

Sparse arrays, which can localize multiple sources with less physical sensors, have attracted more attention since they were proposed. However, for optimal performance of sparse arrays, it is usually assumed that the circumstances are ideal. But in practice, the performance of sparse arrays will suffer from the model errors like mutual coupling, gain and phase error, and sensor’s location error, which causes severe performance degradation or even failure of the direction of arrival (DOA) estimation algorithms. In this study, we follow with interest and propose a covariance-based sparse representation method in the presence of gain and phase errors, where a generalized nested array is employed. The proposed strategy not only enhances the degrees of freedom (DOFs) to deal with more sources but also obtains more accurate DOA estimations despite gain and phase errors. The Cramer–Rao bound (CRB) derivation is analyzed to demonstrate the robustness of the method. Finally, numerical examples illustrate the effectiveness of the proposed method from DOA estimation.

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