Robust transmit beamforming for multi-user MIMO systems using a probabilistic constraint approach

This paper considers the multi-user multiple-input and multiple-output (MU-MIMO) downlink system where each user is equipped with multiple receive antennas. As the design of transmit beamformers relies heavily on perfect channel state information, channel uncertainties may cause substantial performance degradation. Here we suggest a solution based on a probabilistic constraint approach. The suggested method maximizes the average signal power and keeps leakage power below an acceptable level, leading to an upper bound on signal to leakage noise ratio (SLNR). To solve the underlying problem efficiently, the probabilistic constraint is transformed to a deterministic, convex one through the application of the Markov inequality. Simulation results show that the probabilistic constraint approach provides excellent performance in terms of signal-to-interference and noise ratio (SINR) and bit error rate (BER) for large channel errors and various error distributions.