Probabilistic QoS Constrained Robust Downlink Multiuser MIMO Transceiver Design with Arbitrarily Distributed Channel Uncertainty

We study the robust transceiver optimization in downlink multiuser multiple-input multiple-output (MU-MIMO) systems aiming at minimizing transmit power under probabilistic quality-of-service (QoS) requirements. Owing to the unknown distributed interference, the channel estimation error obtained from the linear minimum mean square error (LMMSE) estimator can be arbitrarily distributed. Under this situation, the QoS requirements should account for the worst-case channel estimation error distribution. While directly finding the worst-case distribution is challenging, two methods are proposed to solve the robust transceiver design problem. One is based on the Markov's inequality, while the other is based on a novel duality method. Two convergence-guaranteed iterative algorithms are proposed to solve the transceiver design problems. Furthermore, for the special case of MU multiple-input single-output (MISO) systems, the corresponding robust transceiver design problems are shown to be convex. Simulation results show that, compared to the non-robust method, the QoS requirement is satisfied by both proposed algorithms. Among the two proposed methods, the duality method shows a superior performance in transmit power, while the Markov method demonstrates a lower computational complexity. Furthermore, the proposed duality method results in less conservative QoS performance than the Gaussian approximated probabilistic robust method and bounded robust method.