Off-Grid DOA Estimation in Mutual Coupling via Robust Sparse Bayesian Learning

This paper concerns direction of arrival (DOA) estimation based on a sparse Bayesian learning (SBL) approach. We address two inherent problems of this class of DOA estimation methods: (i) a predefined dictionary can generate off-grid problems to a SBL DOA estimator; (ii) a parametric prior generally enforces the solution to be sparse, but the existence of noise can greatly affect the sparsity of the solution. Both of these issues may have a negative impact on the estimation accuracy. In this paper, we propose an improved root SBL (IRSBL) method for off-grid DOA estimation that adopts a coarse grid to generate an initial dictionary. To reduce the bias caused by dictionary mismatch, we integrate the polynomial rooting approach into the SBL method to refine the spatial angle grid. Then, we integrate a constant false alarm rate rule in the SBL framework to enforce sparsity and improve computational efficiency. Finally, we generalize the IRSBL method to the case of non-uniform linear arrays. Numerical analysis demonstrates that the proposed IRSBL method provides improved performance in terms of both estimation accuracy and computational complexity over the most relevant existing method.

The limited space of a conformal array may lead to a serious mutual coupling effect, which will significantly affect the performance of direction of arrival (DOA) estimation algorithms. In this paper, an efficient 2-D direction finding method is developed in the presence of unknown mutual coupling for the uniform cylindrical conformal array (CCA). To avoid the time-consuming two-dimensional spectral peak searching, the 2-D DOA estimation is decoupled and divided into two 1-D DOA estimations. Elevation is first estimated based on a subarray estimation of signal parameters via rotation invariant technique (ESPRIT), and then azimuth is estimated based on the rank reduction (RARE) method by using the elevation estimation result. Consequently, the mutual coupling coefficients can be estimated after getting the DOA estimates. The proposed method can well calibrate the mutual coupling effect of a cylindrical array with a low computational complexity. The final simulation results corroborate our analysis.

In this proposed work, a subspace based method of Direction of Arrival (DOA) estimation with Mutual Coupling (MC) compensation and wavelet denoising for Uniform Linear Array (ULA) is addressed. A preprocessing technique of denoising by Wavelet Transform (WT) is accomplished and followed by Mutual Coupling compensation algorithm to improve DOA estimation. A complex symmetric Toeplitz matrix is modeled and based on this matrix, mutual coupling between sensors is compensated. By denoising and mutual coupling compensation, this method accomplishes a satisfactory performance for weak signals in DOA estimation without array calibration. The effectiveness of the proposed method is studied through simulations.

This paper addresses the degradation in direction of departure (DOD) and direction of arrival (DOA) estimation performance caused by array mutual coupling in bistatic MIMO sonar systems. A joint DOD-DOA estimation algorithm based on smoothed Atomic Norm Minimization (ANM) is proposed. The method mitigates the effects of array mutual coupling by applying a decoupling smoothing matrix to preprocess the received signals. The processed signals exhibit a structure resembling line spectral signals, which allows for the formulation of an ANM optimization problem. By exploiting the inherent sparsity of the signals, the proposed algorithm effectively reconstructs a high signal-to-noise ratio (SNR) covariance matrix, even with a limited number of snapshots, enabling accurate estimation of DOD and DOA. Simulation results validate the algorithm’s performance under mutual coupling conditions in MIMO sonar transmit and receive arrays. The algorithm maintains high estimation accuracy even with a limited number of received snapshots, making it suitable for rapid target localization in real underwater detection applications. Compared to existing gridless sparse recovery methods for covariance matrix estimation, the proposed algorithm achieves lower computational dimensions and faster execution. Additional simulation experiments further demonstrate the effectiveness and superiority of the proposed method under varying SNR and target angle separation conditions.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

Direction of arrival (DOA) estimation is a classic problem in array processing. It has wide applications in wireless communications, radar, acoustics, and smart antennas, to name just a few. In this paper, we present a novel comparative study of six array geometries and their impact on mutual coupling and DOA estimation performance. Two scenarios are presented: with and without mutual coupling. A numerical software package was used to simulate the array geometries with dipole antennas. The mutual coupling matrix was calculated from the S‐parameters of the simulated arrays at the operating frequency based on specific sensor locations. The MUSIC algorithm was used to resolve the source location using the difference coarray technique. A well‐known smoothing technique was used to improve the rank of the covariance matrix, allowing MUSIC to compute the DOA using the sparse arrays. Several properties of each array are described, such as the physical sensor location, difference coarray, weight function, and coupling matrix. The sparse array HFCA and UACA achieved an RMSE below 2 degrees (for both 9 and 16 sources and the whole SNR range) and 0.5 degrees (for both 9 and 16 sources and SNR equals to 30 dB), respectively. The performance of the DOA estimation was compared using RMSE as a metric, considering the environment configuration with different number of sources and SNR conditions.

Direction of arrival (DOA) estimation is an important issue for monostatic MIMO radar. A DOA estimation method for monostatic MIMO radar based on unitary root-MUSIC is presented in this article. In the presented method, a reduced-dimension matrix is first utilised to transform the high dimension of received signal data into low dimension one. Then, a low-dimension real-value covariance matrix is obtained by forward–backward (FB) averaging and unitary transformation. The DOA of targets can be achieved by unitary root-MUSIC. Due to the FB averaging of received signal data and the eigendecomposition of the real-valued matrix covariance, the proposed method owns better angle estimation performance and lower computational complexity. The simulation results of the proposed method are presented and the performances are investigated and discussed.

Fast DOA estimation algorithm for MIMO sonar based on ant colony optimization

DOA (Direction of Arrival) estimation is a major problem in array signal processing applications. Recently, compressive sensing algorithms, including convex relaxation algorithms and greedy algorithms, have been recognized as a kind of novel DOA estimation algorithm. However, the success of these algorithms is limited by the RIP (Restricted Isometry Property) condition or the mutual coherence of measurement matrix. In the DOA estimation problem, the columns of measurement matrix are steering vectors corresponding to different DOAs. Thus, it violates the mutual coherence condition. The situation gets worse when there are two sources from two adjacent DOAs. In this paper, an algorithm based on OMP (Orthogonal Matching Pursuit), called ILS-OMP (Iterative Local Searching-Orthogonal Matching Pursuit), is proposed to improve DOA resolution by Iterative Local Searching. Firstly, the conventional OMP algorithm is used to obtain initial estimated DOAs. Then, in each iteration, a local searching process for every estimated DOA is utilized to find a new DOA in a given DOA set to further decrease the residual. Additionally, the estimated DOAs are updated by substituting the initial DOA with the new one. The simulation results demonstrate the advantages of the proposed algorithm.

Due to the existence of dense subarray, nested array (NA) is susceptible to mutual coupling, which seriously degrades the parameter estimation performance. To deal with this problem, we propose an improved scheme to obtain direction of arrival (DOA) and mutual coupling estimation in this paper. Specifically, a new sparse subarray can be formed by moving specific sensors of the nested array, which enables well-performed estimation free from severe mutual coupling effect. Subsequently, the contaminated steering vector of the whole non-uniform sparse array is constructed and a quadratic optimization problem is established to simultaneously eliminate DOA estimation ambiguity and estimate mutual coupling coefficients (MCCs). Numerical simulations demonstrate the superiority of the proposed scheme in terms of estimation accuracy and computation complexity.

Collaborative Direction of Arrival estimation by using Alternating Direction Method of Multipliers in distributed sensor array networks employing Sparse Bayesian Learning framework

We propose a Taylor expansion multiple signal classification (TE MUSIC) method for joint direction of departure (DOD) and direction of arrival (DOA) estimation in a bistatic multiple-input multiple-output (MIMO) array. First, using a Taylor expansion of the steering vector, a two-dimensional (2D) search in the conventional MUSIC method for MIMO arrays is reduced to a two-step one-dimensional (ID) search in the proposed TE MUSIC method. Second, DOAs of the targets can be achieved via Lagrange multiplier by a ID search. Finally, substituting the DOA estimates into the 2D MUSIC spectrum function, DODs of the targets are obtained by another ID search. Thus, the DOD and DOA estimates can be automatically paired. The performance of the proposed method is better than that of the MIMO ESPRIT method, and is similar to that of the 2D MUSIC method. Furthermore, due to the ID search, the TE MUSIC method avoids the high computational complexity of the 2D MUSIC method. Simulation results are presented to show the effectiveness of the proposed method.

Recently, popular machine learning algorithms have successfully been applied to the direction of arrival (DOA) estimation. An implementation of determination of DOA estimation is presented based on deep neural networks (DNNs) to reduce the computational complexity of traditional superresolution DOA estimation methods. The classical DOA estimation algorithms have limitations due to unforeseen effects, such as array perturbations. Instead of computing an inverse mapping based on the incomplete forward mapping that relates the signal directions to the array outputs, the DOA problem is approached as a mapping, which can be approximated using a suitable DNN trained with input output pairs. The neural network architecture is based on a multilayer perception and a group of parallel DNNs to perform detection and DOA estimation, respectively. Simulation results are performed to investigate the effect of network parameters on estimation accuracy so that they can be roughly determined in the case of one signal scenario. Based on a set of simulations and experimental measurements, the performance of the optimum network is also assessed and compared to that of the classical DOA estimation methods for multiple signals. It has been shown that the proposed method can not only achieve reasonably high DOA estimation accuracy, but also dramatically reduce the computational complexity and the memory space.

A full-space unambiguous direction of arrival (DOA) estimation can be achieved by only using one single vector hydrophone. And it provides spatial advantage for solving the DOA estimation. The paper proposes a novel method for DOA estimation of single vector hydrophone based on the steered minimum variance (STMV) algorithm, which applies the STMV algorithm of the array signal processing to the single vector hydrophone. With the 3×1 dimensional steered matrix, the single vector hydrophone not only has the ability of high-resolution DOA estimation, but also improves the robustness of the algorithm and reduces the calculation amount of the algorithm. The simulation data and lake test data are used for experimental verification, and STMV algorithm is compared with the cross-spectrum method and the conventional beamforming (CBF) method. The research results have shown that the STMV algorithm has higher DOA estimation capability, better robustness, and lower computational complexity.

It is well known that accurate direction of arrival (DOA) estimation can help to improve the performance of MIMO systems. However, when large scale MIMO systems are considered, the DOA estimation becomes very difficult due to the large dimension of DOAs. Based on the observation that correlation exists between the neighboring antennas due to the limited size of the antenna array, we propose a correlation based DOA estimation method for the large scale multi-user (MU) MIMO system in this paper. It is verified that the proposed DOA estimation method can obtain a better performance than the existing methods with a much lower computational complexity.