A DOA estimation algorithm based on the low computational complexity log-sum sparse recovery

The super-resolution iterative reweighted (SURE-IR) algorithm and the prior-knowledge aided super-resolution iterative reweighted (KA-SURE-IR) algorithm provide an important reference for the research of log-sum sparse recovery. However, even if the matrix inverse lemma is used, SURE-IR and KA-SURE-IR still have the problem of high computational complexity. Therefore, this paper designs a descent direction to achieve low complexity log-sum sparse recovery and direction of arrival (DOA) estimation. Firstly, the received signals are decomposed by singular value decomposition (SVD), and the corresponding log-sum sparse model is established. Then, the log-sum sparse model is relaxed to a convex model, the multiple signal classification (MUSIC) algorithm is used to provide prior information to promote sparse recovery, and the theoretical optimal value of the sparse signals in each iteration calculation is solved. Secondly, a descent direction is designed according to the current value and the theoretical optimal value of the sparse signals in each iteration calculation. Finally, the computational complexity of the proposed algorithm is reduced by selecting the regularization parameters as large as possible to reduce the influence of the residual value and by combining the matrix inverse lemma. The simulation results validated the effectiveness of the proposed algorithm in DOA estimation.