Robust Linear MIMO in the Downlink: A Worst-Case Optimization with Ellipsoidal Uncertainty Regions

This paper addresses the joint robust power control and beamforming design of a linear multiuser multiple-input multiple-output (MIMO) antenna system in the downlink where users are subjected to individual signal-to-interference-plus-noise ratio (SINR) requirements, and the channel state information at the transmitter (CSIT) with its uncertainty characterized by an ellipsoidal region. The objective is to minimize the overall transmit power while guaranteeing the users’ SINR constraints for every channel instantiation by designing the joint transmitreceive beamforming vectors robust to the channel uncertainty. This paper first investigates a multiuser MISO system (i.e., MIMO with single-antenna receivers) and by imposing the constraints on an SINR lower bound, a robust solution is obtained in a way similar to that with perfect CSI. We then present a reformulation of the robust optimization problem using S-Procedure which enables us to obtain the globally optimal robust power control with fixed transmit beamforming. Further, we propose to find the optimal robust MISO beamforming via convex optimization and rank relaxation. A convergent iterative algorithm is presented to extend the robust solution for multiuser MIMO systems with both perfect and imperfect channel state information at the receiver (CSIR) to guarantee the worst-case SINR. Simulation results illustrate that the proposed joint robust power and beamforming optimization significantly outperforms the optimal robust power allocation with zeroforcing (ZF) beamformers, and more importantly enlarges the feasibility regions of a multiuser MIMO system.