High-Resolution Off-Grid Direction-of-Arrival Estimation Using Laplacian Scale Mixture Prior Under Low SNR Conditions

As a crucial branch of array signal processing, direction of arrival (DOA) has been widely applied in various fields and has garnered significant attention in recent years. However, the performance of the DOA estimation is severely affected by low signal-to-noise ratio (SNR) in practical applications. Therefore, how to achieve high-resolution DOA estimation under low SNR conditions is an issue worthy of attention. In this article, an off-grid DOA estimation method based on variational Bayesian inference (VBI) is proposed, denoted as OG-LSMVBI, which can achieve high-resolution DOA estimation results under low SNR conditions by introducing the Laplacian scale mixture (LSM) priors. First, we introduce a hierarchical prior consisting of a Laplacian and an inverse gamma to model sparse signals. Since the Laplacian prior and the Gaussian likelihood are not conjugate, the form of the posterior of the sparse signal cannot be determined directly. Therefore, Laplace approximation is employed in VBI, aiming to derive an approximate posterior distribution obeying a Gaussian distribution through a second-order Taylor expansion. Finally, a grid refinement process is implemented to estimate off-grid errors within the VBI iteration, thus refining the final DOA estimation results. Numerical experimental results based on simulated data have substantiated that the proposed algorithm is more effective under both single-snapshot and multisnapshots compared to other sparse Bayesian learning (SBL) methods, especially in the case of low SNR.