Robust Beamforming with Magnitude Response Constraints Using Alternating Minimization

We consider the robust beamforming problem with magnitude response constraints to deal with direction-of-arrival (DOA) mismatch in this paper. Because of the non-convex constraints, the traditional convex optimization methods cannot be applied directly. Although semidefinite relaxation (SDR) has been widely applied to tackle non-convex problems, its performance cannot be guaranteed in certain situations. Towards this end, an Alternating Minimization Algorithm (AMA) is proposed. Specifically, the rank-one constraint is first transformed into a trace inequality. Then, this new function is solved by using the proposed alternating optimization method, which converges to the locally optimum rank-one solution. It is verified by simulation results that the proposed beamformer has better robustness.