Robust Broadband Adaptive Beamforming Based on Probability Constraint

Broadband adaptive beamformers suffer from severe performance degradation in the presence of array imperfections. To solve this problem, a robust broadband beamforming algorithm based on probability constraint is proposed. Firstly, steering vector error model is established under the hypothesis that array steering errors follow the Gaussian distribution. Secondly, the cost function is constructed by minimizing the array output power while guaranteeing the array response undistorted with sufficiently high probability, which could assure the robustness and ability of suppressing interference. Lastly, we show that the design problem can be formulated as the second-order cone programming (SOCP), which could be solved efficiently via the well-established interior point method. Compared with the worst-case optimization algorithm, the parameters in the proposed algorithm can be better specified by chi-square distribution table, which led to higher performance. Theoretical analysis and simulation results show the effectiveness of the proposed method.