Marginal Likelihood Maximization Based Fast Array Manifold Matrix Learning for Direction of Arrival Estimation

Abstract

By exploiting the sparsity of signal sources in the spatial domain, compressive sensing (CS) based directional 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 maximization of a simple cost function over a sole variable (angle), which enables the learning of the manifold matrix and the development of an efficient solver. The grid mismatch problem is circumvented and the manifold matrix during learning is kept in a small size (slightly larger than the number of sources), leading to low computational complexity. Simulations results demonstrate the merits of the proposed method in terms of performance and computational complexity, compared to state-of-the-art SBL-based methods.