A computationally efficient method for robust minimum variance beamforming

This paper concerns a robust beamforming problem. Specifically, we consider the problem of maximizing the worst-case signal to interference plus noise ratio (SINR) in the presence of uncertainties in the steering vector. We give a zero-sum game-theoretic interpretation of the problem and prove the existence of a saddle point for the associated zero-sum game. Using this saddle point property, we then show that the problem can be cast as a trust-region problem, which can be solved extremely efficiently. This trust-region formulation leads to a faster algorithm than the second-order cone programming (SOCP) formulation. The game-theoretic interpretation also shows that the robust minimum variance beamforming, which has been a topic of active research, is in fact to maximize the worst-case SINR, although the motivation behind it was not directly related to the worst-case SINR maximization.