Robust Sum Rate Optimization for the Downlink Multiuser MIMO Systems: Worst-Case Design

This paper considers the problem of jointly designing the precoders for the downlink multiuser multiple-input multiple-output (MIMO) systems where imperfect channel state information (CSI) is available at the base station (BS). The multi-antenna users are assumed to employ the linear minimum-mean-square-error (MMSE) receivers. Our objective is to maximize the achievable sum rate under a total BS power constraint and provide robustness against the channel uncertainties. We apply the familiar worst-case performance optimization approach, which in our case turns to be the problem of maximizing the worst-case sum rate constrained with the total BS power. The problem is examined as follows. We first reformulate the expression for the MMSE matrix so that it is conveniently utilized for the worst-case sum rate maximization problem. Then, we solve the resulting robust design problem efficiently by employing the existing mean-square-error (MSE) uplink/downlink duality approach. Computer simulations verify the robustness of the proposed design when compared to the non-robust/naive design.