Robust beamforming with magnitude response constraints and conjugate symmetric constraint

In this letter, a novel robust adaptive beamformer is proposed with magnitude response constraints and conjugate symmetric constraint. With the constraints on magnitude response, we can flexibly control the robust response region with specified beamwidth and response ripple. However, due to the non-convex lower bound magnitude response constraint, conventional convex optimization techniques cannot be applied directly. To overcome this, we exploit the symmetric structure of the array weights to transform the non-convex constraint into a convex one without any relaxation or approximation. In order to obtain a more robust beamformer against all kinds of array imperfections, we further extend the proposed approach to deal with the optimization of worst-case performance.