Two-Dimensional DOA estimation via matrix completion and sparse matrix recovery for coprime planar array

The coprime planar array (CPPA) can obtain a larger virtual aperture using the sum-difference co-array (SDCA). Nonetheless, the holes in the SDCA always cause the virtual aperture to be not fully utilized. In order to solve this issue, a two-dimensional (2-D) directional of arrival (DOA) estimation algorithm with CPPA via matrix completion and sparse matrix recovery is proposed in this paper. To accurately complete the missing elements in the SDCA, we construct an optimization problem based on the truncated nuclear norm regularization (TNNR) by constraining the conjugate flip symmetry property of the virtual array and the noise term. Moreover, we derive a complex-valued sparse matrix recovery algorithm based on the fast iterative shrinkage-thresholding (FISTA) method avoiding using Kronecker product operations between dictionary matrices, which aims to reduce the computational complexity of the conventional vector-form sparse recovery algorithms. Therefore, the proposed algorithm can achieve a larger virtual aperture and lower computational complexity, improving the angle estimation performance. Simulation results demonstrate the effectiveness of the proposed algorithm for CPPA.