On the average capacity of rate adaptive single-relay selection decode-and-forward dual-hop relaying in Rayleigh fading channels

The exact average capacities of rate adaptive single-relay selection decode-and-forward dual-hop relaying for block Rayleigh fading with two cooperation schemes, called parallel channel cooperation and repetition-based cooperation (RC), are obtained. General, dissimilar fading channels and the effect of the source-destination link are considered. Accurate approximations to the average capacity in the RC case are derived for large and small signal-to-noise ratio (SNR) regimes. The approximations characterize the cooperative power gain of the system, and show that the power gain almost increases with half the logarithm of the number of relays, and that the capacity is logarithmic in SNR in both large and small SNR scenarios. In the scenarios with the SD link, the power gain in dB is always positive. In the scenarios without the SD link, the gain is positive only for more than 3 to 5 relays. The small SNR power gain is greater than the large SNR power gain for any number of relays.