A Minimax Regret Approach to Robust Beamforming

Abstract-This article describes a minimax regret approach to robust beamforming with an ellipsoidal uncertainty model for a steering vector, in which the objective is to minimize the worstcase regret over the uncertainty set, where ´worst´ means largest. This problem can be solved efficiently by using an iterative method which uses an alternating sequence of optimization and worst-case analysis steps. Each of the two steps amounts to solving a convex optimization problem. The method typically converges to a solution within 5 iterations. The minimax regret beamforming is illustrated with numerical examples in planar random array antennas. The numerical results show that the minimax regret approach is less pessimistic (less conservative) and provides more robust performance than the worst-case SINR maximization (maximin) approach, where ´worst´ means smallest.