Average SNR and Ergodic Capacity Analysis for Proactive and Reactive DF Relaying over Rayleigh Fading Channels

In this paper, we focus on single-selection opportunistic relaying with the decode-and-forward protocol over Rayleigh fading channels. The end-to-end average signal-to-noise ratios (SNR) and ergodic capacities of both proactive and reactive opportunistic relaying are analyzed as a closed form in a high source-to-relay SNR regime where all link qualities satisfy the required SNR. The derived results are then used to prove that the end-to-end average SNR for the proactive scheme is greater than or equal to that of the reactive scheme. In addition, it is proven that the SNR and ergodic capacity differences of these schemes are broaden as the number of relays increases. The end-to-end ergodic capacities of the two methods are investigated both with and without the threshold using simulations.