A Sparse-Based Approach for DOA Estimation and Array Calibration in Uniform Linear Array

This paper aims at achieving a joint estimation of direction-of-arrival (DOA) and array perturbations, such as gain and phase uncertainty, mutual coupling, and sensor location error, which deteriorate the performance of the DOA estimation if not carefully handled. To that end, in this paper, the array perturbations represented by a perturbation matrix as multiplicative noise to the array manifold are then reformulated to facilitate the perturbation compensations. One great finding on the perturbation matrix is that it is a sparse matrix, which contains a lot of zero elements and only few nonzero elements. With this reformulation, the perturbation compensation problems turn into sparse matrix completion problems. Then, by utilizing the sparsity of both the DOAs and perturbation matrix, a joint estimation of DOAs and array perturbations is proposed under a unified optimization framework. In addition, numerical studies are presented to demonstrate the effectiveness of the joint estimation.