Off-Grid DOA Estimation With Mutual Coupling via Block Log-Sum Minimization and Iterative Gradient Descent

Mutual coupling (MC) effect between antennas can deteriorate the direction of arrival (DOA) estimation performance. Block sparse signal representation (BSSR) is an effective solution to mitigate the MC effect. Nevertheless, continuous angle space has to be discretized into a finite set of grid points, which lead to the grid mismatch. In this letter, we present an iterative block sparsity reconstruction algorithm for off-grid DOA estimation with MC. First, by exploiting the banded symmetric Toeplitz structure of MC matrix, a reduced BSSR model is formulated to preferably mitigate the MC effect. Then, an iterative block sparsity reconstruction algorithm with multiple measurement vectors (MMV) is proposed. Due to the NP-hard property of block l(0) norm minimization, a block log-sum minimization method is developed to encourage sparsity for such a block sparse recovery problem, and a surrogate objective function is derived via the majorization-minimization approach. Finally, an iterative gradient descent algorithm is explored to refine the DOAs. Simulations verify that the proposed off-grid algorithm has robustness under limited snapshots and coherent sources.