Complex Multisnapshot Sparse Bayesian Learning for Offgrid DOA Estimation

Direction of arrival (DOA) estimation has recently been developed based on sparse signal reconstruction (SSR). Sparse Bayesian learning (SBL) is a typical method of SSR. In SBL, the two-layer hierarchical model in Gaussian scale mixtures (GSMs) has been used to model sparsity-inducing priors. However, this model is mainly applied to real-valued signal models. In order to apply SBL to complex-valued signal models, a general class of sparsity-inducing priors is proposed for complex-valued signal models by complex Gaussian scale mixtures (CGSMs), and the special cases correspond to complex versions of several classical priors are provided, which is helpful to analyze the connections with different modeling methods. In addition, the expression of the SBL form of the real- and complex-valued model is unified by parameter values, which makes it possible to generalize and improve the properties of the SBL methods. Finally, the SBL complex-valued form is applied to the offgrid DOA estimation complex-valued model, and the performance between different sparsity-inducing priors is compared. Theoretical analysis and simulation results show that the proposed algorithm can effectively process complex-valued signal models and has lower algorithm complexity.