Direction-of-Arrival Estimation for Coprime Array via Covariance Matrix Reconstruction

In this paper, to improve the utilization of noncontiguous virtual sensors of the coprime array, we propose a covariance matrix reconstruction method for underdetermined direction-of-arrival (DOA) estimation. Firstly, the distribution characteristic of virtual sensors is analyzed from the perspective of the difference coarray. According to the correspondence between the difference coarray and the wave path difference, the covariance matrix is extended to a high-dimensional Toeplitz covariance matrix with missing data. Then, based on the matrix completion theory, we employing the mapping matrix, further use trace norm instead of the rank norm for convex relaxation to recover the matrix, thereby realizing the filling of the virtual sensor holes. Compared with the sparsity- based methods, the proposed method can eliminate the effect of the discretization of the angle domain.