Gridless DOA Estimation for Minimum-Redundancy Linear Array in Nonuniform Noise

A gridless direction-of-arrival (DOA) estimation method to improve the estimation accuracy and resolution in nonuniform noise is proposed in this paper. This algorithm adopts the structure of minimum-redundancy linear array (MRA) and can be composed of two stages. In the first stage, by minimizing the rank of the covariance matrix of the true signal, the covariance matrix that filters out nonuniform noise is obtained, and then a gridless residual energy constraint scheme is designed to reconstruct the signal covariance matrix of the Hermitian Toeplitz structure. Finally, the unknown DOAs can be determined from the recovered covariance matrix, and the number of sources can be acquired as a byproduct. The proposed algorithm can be regarded as a gridless version method based on sparsity. Simulation results indicate that the proposed method has higher estimation accuracy and resolution compared with existing algorithms.

Download Full-text

A Novel ULA-Difference-Coarray-Based DOA Estimation Method for General Coherent Signals

Mathematical Problems in Engineering ◽

10.1155/2020/1548016 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Zhang Chen ◽

Hao Wu ◽

Yongxiang Liu

Keyword(s):

Good Accuracy ◽

Linear Array ◽

Estimation Method ◽

Doa Estimation ◽

Estimation Accuracy ◽

Coherent Signals ◽

Low Snr ◽

Sample Covariance ◽

Lower Complexity ◽

The Difference

In this article, a difference-coarray-based direction of arrival (DOA) method is introduced, which utilizes the uniform linear array (ULA) in a novel fashion to address the problem of DOA estimation for coherent signals. Inspired by the coarray-based estimators employed in cases of sparse arrays, we convert the sample covariance matrix of the observed signals into the difference coarray domain and process the signals using a spatial smoothing technique. The proposed method exhibits good accuracy and robustness in both the uncorrelated and coherent cases. Numerical simulations verify that the ULA difference coarray- (UDC-) based method can achieve good DOA estimation accuracy even when the SNR is very low. In addition, the UDC-based method is insensitive to the number of snapshots. Under extremely challenging conditions, the proposed UDC-ES-DOA method is preferred because of its outstanding robustness, while the UDC-MUSIC method is suitable for most moderate cases of lower complexity. Due to its demonstrated advantages, the proposed method is a promising and competitive solution for practical DOA estimation, especially for low-SNR or snapshot-limited applications.

Download Full-text

Direction-of-Arrival Estimation for Coprime Array Using Compressive Sensing Based Array Interpolation

International Journal of Antennas and Propagation ◽

10.1155/2017/6425067 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Aihua Liu ◽

Qiang Yang ◽

Xin Zhang ◽

Weibo Deng

Keyword(s):

Covariance Matrix ◽

Degrees Of Freedom ◽

Linear Array ◽

Estimation Method ◽

Direction Of Arrival ◽

Doa Estimation ◽

Interpolation Algorithm ◽

Estimation Performance ◽

Sample Covariance ◽

Coprime Array

A method of direction-of-arrival (DOA) estimation using array interpolation is proposed in this paper to increase the number of resolvable sources and improve the DOA estimation performance for coprime array configuration with holes in its virtual array. The virtual symmetric nonuniform linear array (VSNLA) of coprime array signal model is introduced, with the conventional MUSIC with spatial smoothing algorithm (SS-MUSIC) applied on the continuous lags in the VSNLA; the degrees of freedom (DoFs) for DOA estimation are obviously not fully exploited. To effectively utilize the extent of DoFs offered by the coarray configuration, a compressing sensing based array interpolation algorithm is proposed. The compressing sensing technique is used to obtain the coarse initial DOA estimation, and a modified iterative initial DOA estimation based interpolation algorithm (IMCA-AI) is then utilized to obtain the final DOA estimation, which maps the sample covariance matrix of the VSNLA to the covariance matrix of a filled virtual symmetric uniform linear array (VSULA) with the same aperture size. The proposed DOA estimation method can efficiently improve the DOA estimation performance. The numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Download Full-text

Underdetermined DOA Estimation for Wideband Signals via Focused Atomic Norm Minimization

Entropy ◽

10.3390/e22030359 ◽

2020 ◽

Vol 22 (3) ◽

pp. 359 ◽

Cited By ~ 1

Author(s):

Juan Shi ◽

Qunfei Zhang ◽

Weijie Tan ◽

Linlin Mao ◽

Lihuan Huang ◽

...

Keyword(s):

Information Theory ◽

Signal Processing ◽

Covariance Matrix ◽

Estimation Method ◽

Doa Estimation ◽

Estimation Methods ◽

Estimation Accuracy ◽

Norm Minimization ◽

Atomic Norm ◽

Virtual Array

In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

Download Full-text

An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix

Sensors ◽

10.3390/s21134403 ◽

2021 ◽

Vol 21 (13) ◽

pp. 4403

Author(s):

Ji Woong Paik ◽

Joon-Ho Lee ◽

Wooyoung Hong

Keyword(s):

Covariance Matrix ◽

Phased Array ◽

Null Space ◽

Estimation Method ◽

Direction Of Arrival ◽

Estimation Algorithm ◽

Doa Estimation ◽

Direction Of Arrival Estimation ◽

Improve Performance ◽

Space Projection

An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

Download Full-text

A covariance matrix shrinkage method with Toeplitz rectified target for DOA estimation under the uniform linear array

AEU - International Journal of Electronics and Communications ◽

10.1016/j.aeue.2017.06.026 ◽

2017 ◽

Vol 81 ◽

pp. 50-55 ◽

Cited By ~ 8

Author(s):

Yanyan Liu ◽

Xiaoying Sun ◽

Shishun Zhao

Keyword(s):

Covariance Matrix ◽

Linear Array ◽

Doa Estimation ◽

Uniform Linear Array ◽

Matrix Shrinkage ◽

Shrinkage Method

Download Full-text

Compressed Sensing-Based DOA Estimation with Unknown Mutual Coupling Effect

Electronics ◽

10.3390/electronics7120424 ◽

2018 ◽

Vol 7 (12) ◽

pp. 424 ◽

Cited By ~ 11

Author(s):

Peng Chen ◽

Zhenxin Cao ◽

Zhimin Chen ◽

Linxi Liu ◽

Man Feng

Keyword(s):

Compressed Sensing ◽

Mutual Coupling ◽

Linear Array ◽

State Of The Art ◽

Coupling Effect ◽

Estimation Method ◽

Doa Estimation ◽

System Model ◽

Reconstruction Problem ◽

Uniform Linear Array

The performance of a direction-finding system is significantly degraded by the imperfection of an array. In this paper, the direction-of-arrival (DOA) estimation problem is investigated in the uniform linear array (ULA) system with the unknown mutual coupling (MC) effect. The system model with MC effect is formulated. Then, by exploiting the signal sparsity in the spatial domain, a compressed-sensing (CS)-based system model is proposed with the MC coefficients, and the problem of DOA estimation is converted into that of a sparse reconstruction. To solve the reconstruction problem efficiently, a novel DOA estimation method, named sparse-based DOA estimation with unknown MC effect (SDMC), is proposed, where both the sparse signal and the MC coefficients are estimated iteratively. Simulation results show that the proposed method can achieve better performance of DOA estimation in the scenario with MC effect than the state-of-the-art methods, and improve the DOA estimation performance about 31.64 % by reducing the MC effect by about 4 dB.

Download Full-text

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.

Download Full-text

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.

Download Full-text

Estimation accuracy of covariance matrices when their eigenvalues are almost duplicated

APSIPA Transactions on Signal and Information Processing ◽

10.1017/atsip.2018.22 ◽

2018 ◽

Vol 7 ◽

Author(s):

Kantaro Shimomura ◽

Kazushi Ikeda

Keyword(s):

Covariance Matrix ◽

Estimation Method ◽

Estimation Accuracy ◽

Essential Information ◽

The Matrix ◽

The Difference ◽

Processing Techniques ◽

Monotonic Property ◽

Signal Processing Techniques ◽

Special Case

The covariance matrix of signals is one of the most essential information in multivariate analysis and other signal processing techniques. The estimation accuracy of a covariance matrix is degraded when some eigenvalues of the matrix are almost duplicated. Although the degradation is theoretically analyzed in the asymptotic case of infinite variables and observations, the degradation in finite cases are still open. This paper tackles the problem using the Bayesian approach, where the learning coefficient represents the generalization error. The learning coefficient is derived in a special case, i.e., the covariance matrix is spiked (all eigenvalues take the same value except one) and a shrinkage estimation method is employed. Our theoretical analysis shows a non-monotonic property that the learning coefficient increases as the difference of eigenvalues increases until a critical point and then decreases from the point and converged to the distinct case. The result is validated by numerical experiments.

Download Full-text