Single snapshot direction of arrival estimation using the EP-SURE-SBL algorithm

Grid-based methods in sparse signal reconstruction (SSR) are well-regarded for their efficacy in direction-of-arrival (DoA) estimation. This paper presents the EP (Expectation Propagation)-SURE (Stein's Unbiased Risk Estimate)-SBL (Sparse Bayesian Learning) algorithm, designed for single snapshot DoA estimation. The algorithm divides DoA estimation into two parts: grid-on estimation and off-grid error estimation, employing first-order and second-order Taylor expansions. In grid-on estimation, sparse Bayesian learning is employed for sparse modeling. To tackle hyperparameter estimation challenges within sparse Bayesian learning, the algorithm adopts SURE estimator instead of the commonly-used expectation-maximization (EM) approach. For off-grid error estimation, the algorithm utilizes the EP technique to handle high-dimensional, non-tractable integration in posterior mean calculations. The feasibility and effectiveness of the proposed algorithm are validated through extensive simulations.