DOA Estimation with Sparse Bayesian Learning Using Hierarchical Half-Cauchy Prior with Spectra Refinement Strategy

Advancements in sparse signal recovery (SSR) theory have significantly enhanced direction-of-arrival (DOA) estimation performance, a critical aspect of array signal processing with a wide range of applications. This paper transforms the conventional complex-valued sparse representation for array-received signals into a real-valued problem for covariance coefficients by leveraging the real-valued nature of source powers. A two-stage hierarchical sparsity-induced prior based on the half-Cauchy framework is proposed, which is approximated using an inverse-Gamma structural prior. Building on this prior, an iterative variational Bayesian inference solution is developed that admits a closed-form expression. Additionally, a thresholding-block-matrix iteration method and a mixing prior updating strategy to exploit spatial domain sparsity are proposed. Simulation results demonstrate that our approach minimizes Gaussian noise impact on spatial spectral partitioning and exhibits robustness at high grid resolutions and signal-to-noise ratios (SNRs) compared to state-of-the-art DOA estimation algorithms. Experiments on the SWellEx-96 dataset further validate the effectiveness of our method in practical environments.