Sparsity-Based Two-Dimensional DOA Estimation for Co-Prime Planar Array via Enhanced Matrix Completion

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem is explored for the sum-difference co-array (SDCA) generated by the virtual aperture expansion of co-prime planar arrays (CPPA). Since the SDCA has holes, this usually causes the maximum virtual aperture of CPPA to be unavailable. To address this issue, we propose a complex-valued, sparse matrix recovery-based 2-D DOA estimation algorithm for CPPA via enhanced matrix completion. First, we extract the difference co-arrays (DCA) from SDCA and construct the co-array interpolation model via nuclear norm minimization to initialize the virtual uniform rectangular array (URA) that does not contain the entire rows and columns of holes. Then, we utilize the shift-invariance structure of the virtual URA to construct the enhanced matrix with a two-fold Hankel structure to fill the remaining empty elements. More importantly, we apply the alternating direction method of the multipliers (ADMM) framework to solve the enhanced matrix completion model. To reduce the computational complexity of the traditional vector-form, sparse recovery algorithm caused by the Kronecker product operation between dictionary matrices, we derive a complex-valued sparse matrix-recovery model based on the fast iterative shrinkage-thresholding (FISTA) method. Finally, simulation results demonstrate the effectiveness of the proposed algorithm