A Low-Complexity Sparse Representation Algorithm for DOA Estimation of Coherent Signals with Unknown Mutual Coupling

This paper proposes a low-complexity sparse representation algorithm for direction-of-arrival (DOA) estimation of coherent signals under mutual coupling for uniform linear arrays (ULAs). At first, the problem is formulated as a block sparse signal recovery problem from array measurements based on the Toeplitz structure of the mutual coupling matrix. Then, it is addressed by the expectation-maximization (EM)-Gaussian scale mixture (GSM)-damping generalized approximate message passing (DGAMP) algorithm at each snapshot. Finally, the DOA estimates are obtained by applying a block norm operation to the signals from all snapshots and identifying the peaks of the resulting vector. By directly utilizing the array measurements, the algorithm successfully avoids the rank deficiency in the array covariance matrix resulting from coherent signals. The proposed algorithm has significantly lower complexity than existing sparse representation algorithms, and enables hardware concurrency for real-time DOA estimation since each snapshot is processed independently. Simulation results demonstrate that the performance of the proposed method is superior to state-of-the-art methods.