Robust adaptive beamforming with optimal covariance matrix estimation in the presence of gain-phase errors

An adaptive beamformer is sensitive to model mismatch, especially when the desired signal exists in the training samples. Focusing on the problem, this paper proposed a novel adaptive beamformer based on the interference-plus-noise covariance (INC) matrix reconstruction method, which is robust with gain-phase errors for uniform or sparse linear array. In this beamformer, the INC matrix is reconstructed by the estimated steering vector (SV) and the corresponding individual powers of the interference signals, as well as noise power. Firstly, a gain-phase errors model of the sensors is deduced based on the first-order Taylor series expansion. Secondly, sensor gain-phase errors, the directions of the interferences, and the desired signal can be accurately estimated by using an alternating descent method. Thirdly, the interferences and noise powers are estimated by solving a quadratic optimization problem. To reduce the computational complexity, we derive the closed-form solutions of the second and third steps with compressive sensing and total least squares methods. Simulation results and measured data demonstrate that the performance of the proposed beamformer is always close to the optimum, and outperforms other tested methods in the case of gain-phase errors.