Direction Of Arrival Estimation Of Coherent Signals Research Articles

DOA estimation of coherent signals in underdetermined problems using sparse-based Toeplitz covariance reconstruction

Direction-Of-Arrival (DOA) estimation in environments with coherent sources is a challenging problem, when the number of narrowband sources is more than elements and current coherent algorithms cannot accurately overcome such underdetermined problems. In this paper, we propose the Sparse-based Toeplitz Covariance Reconstruction (STCR) algorithm, which obtains a hole-free extended-aperture array with increased Degrees of Freedom (DOF) by exploiting a minimum redundancy array. This method provides superiority in estimating coherent sources by Toeplitz covariance matrix reconstruction. Also, using a Sparse Signal Representation (SSR) framework makes the DOA estimator stronger in source detection and robust to the noise power. Numerical results show the effectiveness of the proposed method even at low SNRs for over- and underdetermined DOA estimators compared to well-known methods. Also, it has high accuracy in DOA estimation of closely-located coherent sources using a small number of snapshots.

An Enhanced Spatial Smoothing Technique of Coherent DOA Estimation with Moving Coprime Array.

This paper investigates the direction of arrival (DOA) estimation of coherent signals with a moving coprime array (MCA). Spatial smoothing techniques are often used to deal with the covariance matrix of coherent signals, but they cannot be used in sparse arrays. Therefore, super-resolution algorithms such as multiple signal classification (MUSIC) cannot be applied in the DOA estimation of coherent signals in sparse arrays. In this study, we propose an enhanced spatial smoothing method specifically designed for MCA. Firstly, we combine the signals received by the MCA at different times, which can be regarded as a sparse array with a larger number of array sensors. Secondly, we describe how to compute the covariance matrix, derive the signal subspace by eigenvalue decomposition, and prove that the signal subspace is also equivalent to a received signal. Thirdly, we apply enhanced spatial smoothing to the signal subspace and construct a rank recovered covariance matrix. Finally, the DOA of coherent signals are well estimated by the MUSIC algorithm. The simulation results validate the improved performance of the proposed algorithm compared with traditional methods, particularly in scenarios with low signal-to-noise ratios.

L0 Regularization parameter for sparse DOA estimation of coherent signals with modeling errors

Sparse methods have been recently introduced in Direction-Of-Arrival (DOA) estimation as an alternative to subspace-based methods and Maximum Likelihood (ML) techniques. This paper proposes a low complexity sparse L0-regularized method for DOA estimation of coherent signals in multipath environment, a scenario in which subspace-based methods fail. The first eigenvector of the covariance matrix is used as an observation and its statistics in the presence of modeling errors are derived. Thanks to those statistics, we present a theoretical statistical analysis of an interval in which the regularization parameter, usually empirically tuned, should stand. For a regularization parameter in this interval, the global solution of the L0-regularized problem coincides with the solution of the deterministic ML. An off-line selection of the regularization parameter is therefore proposed. Simulations confirm the relevance of this interval and of the proposed method.

Coherent Signal DOA Estimation for MIMO Radar under Composite Background of Strong Interference and Non-Uniform Noise.

To address the problems of low accuracy and low robustness of the conventional algorithm in estimating the direction of arrival (DOA) of coherent signals against a composite background of strong interference and non-uniform noise, in this paper, a coherent signal DOA estimation algorithm based on fixed projection blocking is proposed in conjunction with a multi-input multi-output (MIMO) radar. The covariance matrix of the received signal is first decomposed by eigenvalues, and a fixed projection matrix orthogonal to the interference guidance vector is constructed as the interference blocking matrix. Then, the received array signal is pre-processed to re-form the covariance matrix, and this matrix is rendered decoherent through a Toeplitz reconstruction. Finally, the reconstructed covariance matrix is estimated by DOA using the propagation operator algorithm to reduce the complexity. The simulation verifies that the proposed algorithm has a better robustness and higher accuracy than conventional algorithms for the DOA estimation of coherent signals in composite backgrounds.

The Limited Aperture Sparse Array for DOA Estimation of Coherent Signals: A Mutual-Coupling-Optimized Array and Coherent DOA Estimation Algorithm

The paper investigates DOA estimation of coherent Signals with the limited aperture sparse array. Mutual coupling between the sensors of the array cannot be ignored in practical radar with a limited aperture of array sensors, which will result in a degradation in the performance of Direction of Arrival (DOA) estimation. This paper proposes a Mutual-coupling-optimized array (MCOA) with a limited aperture in this scenario to reduce the mutual coupling effect. Firstly, we prove the sparse uniform linear array (SULA) has the smallest mutual coupling leakage when the array aperture and the number of sensors is determined. Secondly, we modify the spacing of the array sensors in SULA to make sure that the spacing between all array sensors and the reference sensor are coprime aiming to estimate DOA without spatial aliasing. Thirdly, we give an expression for the array element spacing arrangement with reduced mutual coupling leakage. Finally, the coherent signals are well resolved by the Sparse Bayesian Learning (SBL) algorithm. Numerous simulations are conducted to validate the advantages of the proposed array compared to several sparse arrays for estimating coherent signals in the presence of mutual coupling.

Fast and Accurate Approach for DOA Estimation of Coherent Signals

An algorithm for estimation of direction of arrival (DOA) based on QR decomposition is proposed for coherent signals in this paper. When coherent is present, the rank of the signal covariance matrix is generally less than the signal number, making the estimation of the signal or noise subspace inaccurate. Therefore, we need to eliminate the spatial covariance matrix rank loss. According to the idea of matrix reconstruction, we try to construct three different data matrices, one is the signal covariance matrix, the other is the eigenvector reconstruction matrix of the signal covariance matrix, and the other is reconstructed matrix with the addition of spatial smoothing technology. Based on the resulting data matrix, whereafter, QR decomposition with the iteratively weighted least squares (IWLS) as solver is proposed to reduce the computational complexity of DOA estimation. Compared with other existing algorithms, the simulation results show that our method has high accuracy and great increase in the computational efficiency.

DOA estimation of the coherent signals using beamspace matrix reconstruction

The matrix reconstruction technique can effectively estimate the direction-of-arrival (DOA) of coherent signals with a relatively small computational complexity. However, the existing methods are affected by the phase perturbation or the fact that the eigenvalue ratio of the signal subspace to noise subspace is linearly related to the square of input signal-to-noise ratio (SNR). This results in a significant decrease in the DOA estimation performance for the cases with a low SNR. To address these problems, we propose a new method for DOA estimation of coherent signals based on the beamspace matrix reconstruction. The array is firstly divided into multiple subarrays, and the data received is transformed from the element space into the beamspace via beamforming, which can eliminate the phase perturbation caused by the mutual impact between the coherent signals and improve the SNR. Then, we add the output covariance matrices from several beam directions to realize the beamspace matrix reconstruction, this results in the eigenvalue ratio of the signal subspace to the noise subspace is the linear transformation of the input SNR in the beamspace domain, which can enhance the eigenvalue ratio of beamspace signal to noise at low SNRs. Finally, the DOAs can be resolved by combining it with the subspace-based methods. Theoretical analysis and simulation results verify the effectiveness of the proposed method at low input SNRs due to beamspace processing, even in the cases where the DOAs between the coherent signals are closely spaced and low snapshot number, our proposed method significantly provides better performance on estimation and resolution.

Off-grid DOA estimation for passive radar

To solve the problem that the true target direction of arrival (DOA) is not on the discrete grid points, we adopt a new off-grid sparse strategy to estimate the target DOA of passive radar. This strategy is the root sparse Bayesian learning method, which utilizes a coarse grid and treats the sampling position in the coarse grid as an adaptive parameter. Then, the coarse mesh is iteratively refined using the expectation maximization algorithm, and the estimated angle is the root of a certain polynomial. Simulation results show that the method has higher estimation accuracy and lower computational complexity in DOA estimation of passive radar. In addition, this method can not only estimate the DOA of multi-target signals in a single snapshot, but also provide new ideas for DOA estimation of coherent signals.

Efficient sparse parameter estimation based methods for two‐dimensional DOA estimation of coherent signals

This study addresses the problem of direction-of-arrival (DOA) estimation of coherent signals via sparse parameter estimation. Since many sparse methods provide good performances regardless of signal correlations and array geometry, they can be considered as candidates for DOA estimation of coherent signals impinging on a sensor array with arbitrary geometry. However, their straightforward applications require high computational loads especially for two-dimensional (2D) DOA estimation. Two efficient methods based on sparse parameter estimation are herein presented; one is a combined approach of sparse estimation and the RELAX algorithm extended for 2D DOA estimation and the other relies on the adaptive 2D grid refinement and power update control. Numerical simulations are performed to demonstrate the efficiency of the proposed methods using a uniform circular array for both 1D and 2D DOA estimation cases. It is shown that sparse asymptotic minimum variance (SAMV)-RELAX, a combined approach of SAMV and RELAX, outperforms SAMV and multi-stage SAMV in 2D scenarios without suffering from plateau effects for off-grid signals and that its computational load is significantly lower than those of SAMV and multi-stage SAMV. In addition, SAMV-RELAX does not require the difficult selection of grid parameters for fine DOA estimation unlike the multi-stage approach.

DOA Estimation for Coherent Signals With Improved Sparse Representation in the Presence of Unknown Spatially Correlated Gaussian Noise

In this paper, a new method is proposed for direction-of-arrival (DOA) estimation of coherent signals with improved sparse representation in unknown spatially correlated Gaussian noise. To be specific, leveraging a symmetric uniform linear array, the entries of the signal covariance matrix is firstly recasted to eliminate the spatially correlated noise. Subsequently, it is shown that an equivalent source vector can be obtained by squaring any row of the noise-free signal covariance matrix, irrespective of the coherency between the signals. Finally, an improved sparse representation, which enhances signal sparsity via utilizing a designed weight vector, is derived to determine the DOAs of the signals. Numerical examples are provided to demonstrate its superiority of DOA estimation performance in low signal-to-noise ratio (SNR) environments. Besides, it is computationally efficient, which is critical for large array and/or real-time data processing systems.

Two‐dimensional DOA estimation for coherent signals using a novel covariance‐like matrix

AbstractThis paper addresses a two‐dimensional (2‐D) direction of arrival (DOA) estimation of coherent signals problem. To do so, we first reconstruct a covariance‐like matrix, and then apply forward and backward spatial smoothing (FBSS) method as a preprocessor to remedy the rank deficiency problem. By utilizing the covariance‐like matrix instead of outputs sensors in the FBSS method, the noise and small fading factor influences are reduced in the DOA estimation problem. Afterward, two matrix pencil pairs are exploited to extract 2‐D DOA of impinging signals. This two matrix pencil pairs method can estimate 2‐D DOA with repeated eigenvalues efficiently and also pair the estimated parameters automatically. The proposed algorithm not only has all the privileges of the estimation of signal parameters via rotational invariant techniques (ESPRIT)‐like algorithm but also increases the array aperture. By mathematical tractability, we derive Cramer‐Rao bounds for azimuth and elevation angles for coherent signals received by uniform rectangular array to compare the performance of the estimation algorithms with a lower bound. Simulation results show that the proposed algorithm outperforms the symmetric configuration of uniform rectangular array (SC‐URA), the FBSS–multiple‐signal classification (FBSS‐MUSIC) and the ESPRIT‐like algorithms in terms of root mean squared error (RMSE).

Sparsity-Inducing DOA Estimation of Coherent Signals Under the Coexistence of Mutual Coupling and Nonuniform Noise

The sparse reconstruction techniques can improve the accuracy and resolution of the direction of arrival (DOA) estimation using sensor arrays. However, due to reflective objects and nonidealities of the antennas and circuitry, the received signals may be coherent and coupled to each other in nonuniform noise environments, causing severe performance degradation of the signal sparse reconstruction. In this paper, a novel sparsity-inducing DOA estimation method is proposed to adapt to such a challenging scenario. To mitigate the nonuniform noise, its power components are first eliminated by a linear transformation. Then, leveraging the steering vector parametrization based on the banded symmetric Toeplitz structure of the mutual coupling matrix (MCM), a reweighted l 1 -norm minimization subject to an error-constrained l 2 -norm is designed to determine the DOA estimates, further enhancing the sparsity and providing robustness against the noise. In addition, a new stochastic Cramer-Rao lower bound (CRLB) of the DOA estimation is derived for the considered adverse condition. The simulation results demonstrate the superiority of the proposed method over its state-of-the-art counterparts.

Efficient method of two-dimensional DOA estimation for coherent signals

An effective decoherence method called the fourth-order cumulants-based improved Toeplitz matrices reconstruction (FOC-ITMR) is addressed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. To avoid the loss of the array’s physical aperture, the FOC-ITMR method fully utilizes the information of received data from the whole two parallel uniform linear arrays (ULAs) and the changing reference element based on FOC. Compared with previous works, the proposed method can offer excellent decoherence performance in both white noise and color noise environments. In addition, the proposed algorithm can achieve automatic pair-matching without additional computation. The theoretical analysis and simulation results confirm the effectiveness of the proposed algorithm.

A NEW HIGH-RESOLUTION AND STABLE MV-SVD ALGORITHM FOR COHERENT SIGNALS DETECTION

The performance of smart antenna greatly relies on the e-cient use of direction-of-arrival (DOA) estimation techniques for both coherent and non-coherent signals. In practice, DOA estimation problems and di-culties increase when the signals in multipath propagation environments are highly correlated or coherent. Therefore exploring an algorithm which is capable of estimating coherent signals is of great importance. To overcome this problem a new high-resolution modifled virtual singular value decomposition (MVSVD) algorithm for DOA estimation of coherent signals is proposed. It is based on the hybrid combination of the virtual array extension singular value decomposition (SVD), and modifled MUSIC algorithms. The proposed algorithm provides many features such as: decorrelation of the coherence between the signals without reducing the rank of the covariance matrix or losing the array aperture size; high-resolution and more stability especially at low SNR values; and an increase in the maximal number of detectable signals to M i 1, where M is the number of antenna elements.

Spatial smoothing for direction of arrival estimation of coherent signals in the presence of unknown mutual coupling

There is rarely a method that can deal with the direction of arrival (DOA) estimation of coherent signals in the presence of unknown mutual coupling. Based on the special structure of mutual coupling matrix for uniform linear array (ULA), an improved spatial smoothing algorithm for DOA estimation of coherent signals is proposed. The DOAs can be accurately estimated without any calibration sources since the effects of mutual coupling can be eliminated by the inherent mechanism of the proposed algorithm. Simulation results demonstrate the effectiveness of the algorithm.

Improved spatial smoothing techniques for DOA estimation of coherent signals

In the context of coherent signal classification, spatial smoothing is necessary for the application of the eigen-based direction of arrival (DOA) estimation methods. However, the currently known spatial smoothing algorithms not only reduce the effective aperture of the array, but also do not consider the cross correlations of the subarray outputs. An improved spatial smoothing algorithm which can fully utilize the correlations of the array outputs and produce a more stable estimate of the covariance matrix is presented. Simulation results are provided to verify the theoretical prediction. The superiority of this method over the conventional methods is obvious, especially when the SOSR (subarray to overall size ratio) is small. >