An Exact Analytical Method for Performance Analysis of Maximal-Ratio and Equal-Gain Combining Diversity Schemes over Rayleigh Fading Channels in the Presence of Gaussian Channel Estimation Error

In this paper, the probability of error of maximal-ratio combining (MRC) and equal-gain combining (EGC) diversity schemes with coherent binary phase shift keying (BPSK) is analyzed over Rayleigh fading channels in the presence of channel estimation error. The channel estimation errors cause errors in the required weighting coefficients of the diversity receivers. Such errors are generally modeled as complex Gaussian random variables. Based on this assumption, we develop novel exact analytical equations for the calculation of the probability of error in the presence of Gaussian errors in the weighting coefficients. Results show that the exact probability of error can be derived using the existing equations under the assumption of perfect channel estimation and by replacing the SNR with an effective SNR, which is due to the weighting coefficients errors.