The Diversity Potential of Relay Selection with Practical Channel Estimation

We investigate the diversity order of decode-and-forward relay selection in Nakagami-m fading, in cases where practical channel estimation techniques are applied. In this respect, we introduce a unified model for the imperfect channel estimates, where the effects of noise, time-varying channels, and feedback delays are jointly considered. Based on this model, the correlation between the actual and the estimated channel values, ρ, is expressed as a function of the signal-to-noise ratio (SNR), yielding closed-form expressions for the overall outage probability as a function of ρ. The resulting diversity order and power gain reveal a high dependence of the performance of relay selection on the high SNR behavior of ρ, thus shedding light onto the effect of channel estimation on the overall performance. It is shown that when the channel estimates are not frequently updated in applications involving time-varying channels, or when the amount of power allocated for channel estimation is not sufficiently high, the diversity potential of relay selection is severely degraded. In short, the main contribution of this paper lies in answering the following question: How fast should ρ tend to one, as the SNR tends to infinity, so that relay selection does not experience any diversity loss?