Multiple Constraints Robust Beamforming Algorithm Under Steering Vector Mismatch Conditions

‍ ‍With the development of digital signal processing technology， adaptive beamforming has been widely employed in many applications including radar， microphone array speech/audio processing， and medical imaging. However， when the array is disturbed， it causes the disturbance to deviate from the null position， and even causes the algorithm to fail completely. To solve the disturbance and steering vector mismatch occurring at the interference position， we proposed a multiple constraints robust beamforming algorithm based on the alternating direction multiplier method （ADMM）. More constraints were introduced according to the actual situation， including the bilateral norm perturbation constraint， and the quadratic similarity constraint， which were added to allow the range of error generation. In addition， we ensured that the direction of arrival （DOA） of the signal of interest （SOI） was far away from the DOA region of all linear combinations of interfering steering vectors， which ensured that the DOA of the optimal steering vector lay in the angular sector region of the SOI. First， based on the maximum output power criterion and practical constraints， an optimization model of the steering vector was designed. Next， the covariance matrix was reconstructed using the defined interference range to widen the null and enhance the ability of resisting motion interference. Finally， the interior point method was used to obtain the solution of the substitute variable， to solve the quadratic inequality constraint problem for the guiding vector. Substitute variables were then inserted into the constraint model， and the directional vector was iteratively solved using the alternating direction multiplier method. The explicit solution was obtained in each iteration. Meanwhile， we also analyzed the time complexity and convergence of the algorithm. The experimental results showed that， compared to traditional beamforming algorithms， the proposed method widens the nulls at the interference point， improves the robustness of the algorithm against system errors， and effectively corrects the mismatched steering vector.