A robust linear receiver for uplink multi-user MIMO systems based on probability-constrained optimization and second-order cone programming

Traditional receiver algorithms developed for multiple-input multiple-output (MIMO) wireless communication systems are based on the assumption that the channel state information (CSI) is perfectly known at the receiver. However, in real environments the exact CSI is unavailable. In this paper, we address the problem of robustness of multiuser space-time block coded MIMO systems against imperfect CSI and develop a simple linear receiver which guarantees robustness against CSI errors with a certain selected probability. The proposed receiver is formulated via a probability-constrained optimization problem which is further relaxed using Chebyshev inequality to a much simpler second-order cone programming (SOCP) problem. Simulations demonstrate that the proposed receiver has a moderate performance degradation as compared to the exact solution to the original probability-constrained optimization problem, while offering much simpler implementation.