Underdetermined Wideband Source Localization via Sparse Bayesian Learning modeling ℓ2,1-norm

Abstract

The issue of underdetermined direction-of-arrival (DOA) estimation, where the number of sensors is less than that of sources, for wideband sources by employing a nonuniformly spaced sensor array is addressed in this paper. The joint sparsity among multiple frequency bins and the nonnegativity of source variances are considered and hence a Bayesian hierarchical model is established, leading to a sparse Bayesian learning (SBL) method, which is realized by expectation-maximization (EM). Specifically, the ℓ2,1-norm of the source data at multiple frequency bins is involved in the proposed Bayesian model to enforce sparsity, which was not considered in any existing wideband DOA estimation methods involving SBL. It is shown that the proposed DOA estimation method achieves superior performance in low signal-to-noise ratio (SNR) or when the number of snapshots is small, via numerical simulations.