Robust Adaptive Beamforming Based on Deep Unfolded ADMM Network

The gain-phase errors between different array channels lead to steering vector mismatch, which seriously degrades the performance of adaptive beamforming. The current robust adaptive beamforming (RAB) methods improve beamforming performance by introducing worst-case steering vector mismatch error constraints or jointly estimating gain-phase errors and beamformer weight vector. However, these methods consume high computational overhead and have poor performance under limited snapshot scenes. Owing to this, this article proposes an alternating direction multiplier method (ADMM)-based RAB network under the deep unfolding framework to quickly achieve joint estimation of gain-phase errors and interference covariance matrix. The sparse representation model of interference signals is first established in the presence of gain-phase errors. Then, according to the ADMM-based joint estimation method of gain-phase errors and sparse coefficients of interferences, a deep unfolding ADMM (DU-ADMM) network is proposed. Its input is the received interference signals and its output is gain-phase errors and interference sparse coefficients. Finally, the interference plus noise covariance matrix is recovered based on the network output and then used to generate a robust adaptive beamformer. Simulation results show that the DU-ADMM network can achieve RAB in a single snapshot scene. Moreover, it can estimate the gain-phase errors more accurately with fewer network layers, leading to reduced computational cost, and yield higher output signal-to-interference-plus-noise ratio.