Gridless postprocessing for sparse signal reconstruction based DOA estimation

Recently, many sparse signal reconstruction (SSR) based methods have been proposed for direction-of-arrival (DOA) estimation. However, these methods often suffer from the off-grid problem caused by the discretization of the potential angle space. Most of them employ iterative grid refinement (IGR) method to alleviate this problem. However, IGR requires a high computational load and may not comply with the restricted isometry property (RIP) condition. In this paper, we propose a novel postprocessing scheme named as gridless postprocessing (GPP) for the SSR-based DOA estimation. GPP solves a convex optimization problem with an alternate procedure to obtain the bias estimate. To accelerate the convergence, a closed-form expression is derived for the bias estimation. The proposed scheme enjoys much smaller computational load than IGR while provides comparable performance. Furthermore, by avoiding further dividing the grids, the GPP is superior to IGR in the correlated signal scenario. Simulations are carried out to verify the performance of our proposed method.