Robust Beamforming Using Multiple Constraints Relaxation
Yang Feng, Guisheng Liao, Jingwei Xu, Shengqi Zhu, Cao Zeng · 2018
The conventional robust beamformers based on worst-case performance optimization suffer from difficulty in selecting an appropriate size of the uncertainty set. Besides, their performances degrade dramatically if large steering vector mismatch occurs. In this paper, we propose a semidefinite programming (SDP) based robust beamformer using multiple small uncertainty sets where these sets are used to describe the desired steering vector in the possible large uncertainty region. To solve the nonconvex original problem, we relax the constraints and then recast it in high dimension. By using multiple constraints relaxation, we obtain the optimal solution of the beamformer. Simulation results indicate that the proposed method offers a significant performance improvement in case of large steering vector mismatch.