Linear Multiuser Transceivers: Robustness Via Worst Scenario MSE Approach

We consider the design of linear transceivers for multiuser communication systems in the presence of uncertain channel state information (CSI), with an emphasis on the downlink. We consider a deterministically-bounded model for the channel uncertainty, and we study the design of robust downlink transceivers that minimize the worst-case MSE over all admissible channels. While we show that the design problem is NP-hard, we also propose an iterative local optimization algorithm that is based on efficiently-solvable convex conic formulations. Our framework is quite flexible, and can incorporate different bounded uncertainty models as well as a variety of power constraints. In particular, we study a “system-wide” uncertainty model, and although the resulting design problem is still NP hard, it does result in a significantly simpler iterative local design algorithm than the “per-user” uncertainty model. Our approaches to the minimax design for the downlink can be extended to the uplink, and we provide explicit formulations for the resulting uplink designs. Simulation results indicate that the proposed designs can significantly reduce the sensitivity of the downlink to uncertain CSI.