A Real-Valued Off-Grid DOA Estimator Via Sparse Bayesian Learning Exploiting Wishart prior

For sparse Direction-of-Arrival (DOA) estimation problems, sparse Bayesian learning (SBL) has achieved excellent performance. As a combination of observation and priors, SBL-based methods exploit priors as regularization constraint to promote sparsity. Unfortunately, canonical Gaussian priors cannot enhance sparsity well, while hierarchical priors show satisfactory sparsity performance. However, most developed methods based on hierarchical priors use Gamma priors, which cannot model the correlation between different variables to be solved and cannot promote sparsity performance to a high level. On this basis, the paper uses Wishart prior to model the correlation and enhance sparsity further, yielding a novel Bayesian framework. Based on the framework, we rigorously deduce the corresponding SBL iterative algorithm by an expectation-maximization (EM) procedure. Moreover, to avoid the unrobust complex operations and intractable off-grid gaps, a real-valued transformation is adopted and the off-grid compensation is completed. Extensive simulations are presented to illustrate the superiority of the proposed method beyond state-of-the-art methods.