Covariance matrix reconstruction for source localization over impaired uniform linear array

In this paper, a novel trace norm minimization optimization method for Direction of arrival (DOA) estimation is proposed under array element failure case. In the proposed method, we design a selection matrix according to the positions of failed elements firstly. Utilizing low rank structure of the covariance matrix and covariance fitting criteria, a convex optimization problem is proposed to reconstruct the covariance matrix that is observed before failure. Finally, we exploit the root-MUSIC method to estimate the DOAs. Simulations demonstrate the improved performance of the proposed method over the conventional subspace method under impaired array case.