Robust Adaptive Beamforming via Block Sparse Bayesian Learning and Covariance Matrix Reconstruction in the Presence of Gain-Phase Errors

This letter addresses the problem of robust adaptive beamforming for linear arrays impaired by gain-phase errors. We propose a joint calibration and estimation method based on block sparse Bayesian learning, in which all unknown parameters - including gain-phase errors and those required for covariance matrix reconstruction - are incorporated into a unified Bayesian inference framework. By reparameterizing the steering vector with gain-phase perturbations, the error structure is decoupled from the overcomplete dictionary, resulting in a fully deterministic dictionary that requires no further learning. An expectation-maximization procedure is employed to iteratively estimate these parameters. The estimates are then used to reconstruct the interference-plus-noise covariance matrix. Based on the minimum variance distortionless response principle, a novel robust adaptive beamformer is developed for partially calibrated arrays. Simulation results demonstrate that the proposed beamformer significantly enhances output performance and exhibits strong robustness under gain-phase error mismatches, achieving an output SINR improvement of up to 3 dB over state-of-the-art methods in low SNR scenarios.