Amplify-and-Forward Relay Selection with Outdated Channel Estimates

We study the effect of outdated channel state information on the outage and error rate performance of amplify-and-forward (AF) relay selection, where only one out of the set of available relays is activated. We consider two variations of AF relay selection, namely best relay selection and partial relay selection, when the selection is based upon outdated channel estimates. For both these variations, closed-form expressions for the outage probability are obtained, along with approximate expressions for the symbol error rate in the medium to high signal-to-noise-ratio (SNR) regime. The diversity gain and coding gain of the above schemes are also explicitly derived. Numerical results manifest that the outage performance of AF relay selection is highly dependent on the level of correlation between the actual channel conditions and their corresponding (outdated) estimates. This result has a significant impact on the deployment of relay selection in practical applications, implying that a high feedback rate may be required in practice in order to attain the full benefits of relay selection. It is further shown that it may be preferable, in terms of outage and symbol error probability, not to include links in the relay selection process that experience a sufficiently high maximum Doppler shift, since in those cases partial relay selection outperforms best relay selection.