Analysis of selection combining schemes on Rayleigh fading channels with noisy channel estimates

The optimum selection combining (SC) scheme, proposed recently by Kim, requires estimation of complex channel fades on every diversity channel for minimizing the average probability of error. In this paper, we quantify the effect of imperfect channel estimation on the performance of the optimum SC receiver. By modeling the estimation errors as independent Gaussian random variables, we obtain a simple closed-form expression for the average probability of error. We also analyze a simple sub-optimum SC scheme, based on the output of the coherent matched filter alone, without requiring the knowledge of the fade amplitudes, in the presence of channel estimation errors. Finally, we provide some numerical results to illustrate the comparative performances of various SC receivers with pilot-aided minimum mean-square error (MMSE) channel estimation.