By exploiting the sparsity of signal sources in the spatial domain, compressive sensing (CS) based direction of arrival (DOA) estimation has emerged as a promising approach especially in the case of a limited number of snapshots. However, due to the use of a large overcomplete dictionary obtained from a predefined grid, CS-based DOA estimation methods normally suffer from high computational complexity and the grid mismatch problem. Many methods, in particular sparse Bayesian learning (SBL) based off-grid methods, have been developed to address the grid mismatch problem at the cost of high complexity. In this work, we develop a new method for DOA estimation based on marginal likelihood maximization, where the array manifold matrix is learned incrementally, which is in contrast to the use of overcomplete dictionaries or grid matrices in existing CS or SBL based methods. We show that the problem of marginal likelihood maximization over multiple variables can be greatly simplified to maxim
Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it does not work well for a generic measurement matrix, which may cause AMP to diverge. Damped AMP has been used for SBL to alleviate the problem at the cost of reducing convergence speed. In this work, we propose a new SBL algorithm based on structured variational inference, leveraging AMP with a unitary transformation (UAMP). Both single measurement vector and multiple measurement vector problems are investigated. It is shown that, compared to stateof- the-art AMP-based SBL algorithms, the proposed UAMPSBL is more robust and efficient, leading to remarkably better performance.