Off-grid DOA Estimation with Unknown Nonuniform Noise via Covariance SBL Strategy

In this paper, a sparse Bayesian learning (SBL) strategy based on array covariance vector is proposed for off-grid DOA estimation with the unknown non-uniform noise. In the proposed method, the covariance matrix of array received signal is firstly vectorized and a reduced dimensional matrix is adopted to eliminate the redundant terms in the covariance vector for constructing a new covariance-based signal model. Then an off-grid sparse model is formulated to realize the off-grid DOA estimation with unknown non-uniform noise, where the signal variance and off-grid error are estimated by the expectation-maximization (EM) algorithm, and the covariance matrix of non-uniform noise is reconstructed by the least square (LS) strategy. Finally, numerical simulation experiments are conducted to verify the effectiveness and superiority of the proposed method.

I. Introduction

Recently, the sparse signal reconstruction (SSR) technique [1] is booming development, which provides a new perspective for DOA estimation. Based on the SSR technique, there are many methods have been proposed for the DOA estimation, such as the sparse Bayesian learning (SBL) algorithm [2]. The estimation accuracy of the SBL-based DOA estimation method is largely dependent on the discretization degree of spatial. The higher the discretization degree of spatial is, the higher the DOA estimation accuracy will be. When the spatial discretization degree is low, the off-grid error will seriously affect the accuracy of DOA estimation [1]. However, it is unrealistic that all target signals fall on the spatial discrete grid points, and there exists off-grid error between the true DOA and spatial discrete grid points, especially under the coarse grid condition. Hence, aiming at the off-grid DOA estimation, an off-grid sparse Bayesian inference (OGSBI) method is proposed in [3], where the off-grid error is assumed to obey a non-prior uniform distribution, and the real DOA is approximated by linear transformation. Furthermore, in order to reduce the computational complexity, a root SBL algorithm is proposed in [4], where the spatial grid points are iteratively updated by a polynomial root procedure. But, both of these two algorithms are on the premise that the spatial noise is uniformly white, which is hard to be satisfied in practice. For the DOA estimation in non-uniform noise scenario, a covariance sparsity-aware method is reported in [5], and a named OGVSBL-PVA method is proposed in [6], they eliminate covariance of non-uniform noise by utilizing a select matrix, which will result in the loss of degree of freedom (DOF). Furthermore, Wang et al. report a SBL-based method [7] for Multiple Input Multiple Output (MIMO) radar in the case of unknown non-uniform noise by using a Least Squares (LS) strategy to reconstruct the covariance of noise, which can maintain the entire array DOF, but the performance under the coarse grid condition is not satisfactory.