Nonconvex Group Sparse Reconstruction-Based Robust Adaptive Beamforming Under Limited Training Samples

Existing robust adaptive beamforming (RAB) methods usually employ schemes including uncertainty set constraints and worst-case performance optimization to enhance interference suppression performance. However, these methods generally require a large number of training samples, incur high computational complexity and fail to leverage prior knowledge of array steering vector errors. To address this issue, this paper focuses on adaptive beamforming in the presence of array gain-phase errors under limited samples, and proposes a -norm sparsity-regularized processing method for joint estimation of interferences and gain-phase errors. First, a group-sparse representation of interferences is established in the existence of gain-phase errors. Then a joint recovery problem for interferences and gain-phase errors is formulated based on the group-sparsity constraint using -norm. Finally, the alternating direction method of multipliers is leveraged to accurately estimate the interferences and gain-phase errors, reconstruct the interference-plus-noise covariance matrix (INCM), and yield an adaptive beamformer based on the maximum signal-to-interference-plus-noise ratio (SINR) criterion. Numerical results demonstrate that the proposed method effectively improves the estimation accuracy of INCM and the output SINR of beamformer.