Source localization for sparse array using nonnegative sparse Bayesian learning

• DOA estimation via sparse arrays is discussed in the framework of SBL.
• A nonnegative SBL algorithm involving nonnegative sparse prior is proposed.
• An EM procedure is employed to give the Bayesian inference.
• The proposed method yields superior performance in the underdetermined scenario.

The problem of source localization is addressed for sparse arrays, which have the special array geometry to increase the degree of freedom (DOF), and a nonnegative sparse signal recovery (SSR) problem is formulated for the virtual array response model of sparse arrays. A novel method is developed in the framework of nonnegative sparse Bayesian learning (NNSBL), which obviates presetting any hyperparameter, and an expectation-maximization (EM) algorithm is exploited for solving this NNSBL problem. Without a priori knowledge of the source number, the proposed method yields superior performances in the underdetermined condition illustrated by numerical simulations.