Sparse and low-rank decomposition of covariance matrix for efficient DOA estimation

In order to enhance the performance of the existing beamformer-based direction-of-arrival (DOA) estimation methods, a novel DOA estimation method based on the sparse and low-rank decomposition of the sample covariance matrix is proposed. First, the sample covariance matrix is divided into the covariance matrix of the desired signal and interference as well as that of noise. The first component is shown to have the property of low-rank and meanwhile, the second component can be approximately regarded as a sparse matrix. Second, a convex optimization problem to decompose the sample covariance matrix is constructed, which can be efficiently solved using the interior point method or the augmented Lagrange multiplier method. Finally, the reconstructed covariance matrix of the desired signal and interference is suitably diagonal loaded and then used to replace the sample covariance matrix in the minimum variance distortionless response method. Several computer simulations demonstrate that the proposed sparse and low-rank decomposition based DOA estimation method can achieve higher direction resolution and lower direction estimation error than other beamformer-based DOA estimation methods.