Output SIR distribution of optimum combining in Rayleigh fading channels with channel estimation errors

This paper investigates the effect of imperfect channel estimates on the distribution of signal to interference ratio (SIR) at the output of the optimum combiner for space diversity reception with multiple interferers in a flat Rayleigh fading environment. Channel estimation errors result in flawed optimum combiner weights degrading the system performance. We consider interference-limited systems in which the number of interferers is no less than the number of antenna elements. It is assumed that the channel estimation errors are circularly symmetric Gaussian distributed, and the interferers have equal powers. The main contribution of the paper is applying multivariate statistical analysis to derive an exact closed-form expression for the probability density function of the output SIR. The analytical result is a useful tool to find the impact of imperfect channel estimation on several measures of performance such as average SIR, outage probability and average bit error probability. The analytical expression is verified by Monte Carlo simulations.