A Robust Adaptive Beamformer Based on Semidefinite Programming with Quadratic Constraints

A robust beamforming with quadratic constraints, formulated as a semidefinite programming (SDP) problem, is proposed in this paper. With this formulation, the constraints on magnitude response can be easily imposed on the adaptive beamformer. And the non-convex quadratic constraints can be transformed into linear constraints. Therefore, the proposed method can be robust against the steering direction error. In practice, there are many array imperfections except steering direction error. In order to resist all kinds of array imperfections, the adaptive beamformer based on worst-case optimization technique is proposed by minimizing the array output power with respect to the worst-case array imperfections. Simulation results demonstrate that the proposed method is effective and can achieve a better performance.