Robust SLNR downlink beamforming based on Markov´s inequality

This paper considers the multi-user multiple-input and multiple-output (MU-MIMO) downlink system where each user is equipped with multiple receive antennas. Due to the inevitable channel imperfection, the system performance may degrade significantly. A robust signal-to-leakage-and-noise ratio (SLNR)-based beamforming is developed to provide robustness against channel uncertainties, which maximizes the expectation of the signal power and maintains a low probability of the severe leakage. Two types of errors are taken into account, that is, the estimation Gaussian error in time division duplexing (TDD) system and the quantization error in frequency division duplexing (FDD) system. In order to solve the underlying problem efficiently, the probabilistic constraint is transformed into a convex one by using Markov´s inequality, which places an upper bound of the robust scheme based on channel statis-tics. Furthermore, the proposed design is applicable to general error distributions, rather than restricted to Gaussian errors or quantization errors. Simulation results show that the proposed approach with probabilistic constraint can achieve high SLNR performance and prevent a pessimistic result by considering the leakage power proportionally.