A Multiuser MIMO Transmit Beamformer Based on the Statistics of the Signal-to-Leakage Ratio

A multiuser multiple-input multiple-output (MIMO) downlink communication system is analyzed in a Rayleigh fading environment. The approximate closed-form expressions for the probability density function (PDF) of the signal-to-leakage ratio (SLR), its average, and the outage probability have been derived in terms of the transmit beamformer weight vector. With the help of some conservative derivations, it has been shown that the transmit beamformer which maximizes the average SLR also minimizes the outage probability of the SLR. Computer simulations are carried out to compare the theoretical and simulation results for the channels whose spatial correlations are modeled with different methods.