On the performance of diversity combining schemes on Rayleigh fading channels with noisy channel estimates

In this paper, we analyze the error probability performance of maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) diversity schemes with coherent BPSK signaling on Rayleigh fading channels with Gaussian channel estimation errors. We first show that, with weighting errors, the conditional probability of error is not an explicit function of the signal-to-noise ratio (SNR) at the output of the diversity combiner. We then show that averaging the conditional probability of error with the density function of the SNR at the output of the combiner yields a lower bound on the exact probability of error, independent of the underlying diversity combining scheme. Later, we derive the exact probability of error for MRC, EGC, and SC diversity schemes and show that the exact probability of error with weighting errors is very similar to the case of perfect channel estimation, but with the average SNR per diversity branch, γ_, for the case of perfect channel estimation, replaced by the effective SNR, γ__ρ, due to weighting errors, which is a function of both γ_ and ρ, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as ρ → 0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity combining rule.