An Off-Grid DOA Estimation Method Using Proximal Splitting and Successive Nonconvex Sparsity Approximation

Direction-of-arrival (DOA) estimation is a fundamental problem in many signal processing. Recently, a variety of sparsity-aware methods have been proposed for DOA estimation. The discrimination of grid in these methods often suffers from grid mismatch problem, which degrades the performance of DOA estimation, when the true unknown DOAs are not on the potential angular grids. To deal with grid mismatch problem in conventional sparsity-based methods, a novel off-grid model is proposed via Taylor interpolation that jointly estimates the sparse signals and grid offset parameters, using a family of successive nonconvex sparsity approximation penalties on the sparse signals. Then an iterative alternating optimization strategy is utilized to tackle this nonconvex problem with respect to sparse signals and grid offset parameters, and the proposed algorithm is solved by the proximal splitting algorithm in each iteration, where the optimization problem is split into two parts: sparsity and projection. The proposed framework in this paper is universal and also can be extended to other off-grid sparsity-based algorithms. The extensive simulations are conducted to verify that the proposed method achieves superior resolution and more accurate DOA estimation performance than other conventional sparsity-based method and the state-of-the-art off-grid methods in many cases of practical interest.