Diversity Loss Due to Suboptimal Relay Selection

The performance of relay selection is degraded when the channel estimates used for relay selection are imperfect. Considering that the channel estimates are obtained via practical channel estimation techniques, we quantify the effects of imperfect channel state information (CSI) on the diversity order of relay selection. The analysis involves combining the effects of noise, time-varying channels, and feedback delays on the CSI used for relay selection into a unified model. Based on this model, the correlation between the actual and the estimated channel values, n, is expressed as a function of the signal-to-noise ratio (SNR), providing interesting insight into the behavior of the outage probability in high SNR. The resulting expression for the diversity order reveals that the behavior of the correlation in high SNR crucially affects the asymptotic performance of relay selection. In summary, based upon expressing n as a function of the SNR, we answer the following question: How fast should n tend to one, as the SNR tends to infinity, so that relay selection does not experience any diversity loss?