Comparison of average symbol error rate and optimal power allocation for two‐way opportunistic relaying with amplify‐and‐forward protocol

In this paper, we investigate the statistical characteristics of the equivalent end‐to‐end signal‐to‐noise ratios (SNRs), the average symbol error ratios (SERs), and the optimal power allocation (OPA) for two‐way amplify‐and‐forward opportunistic relaying (TWOR‐AF) systems. First, with strict mathematic manipulation, we obtain the closed‐form solutions to the PDF, CDF, and moment generating function of the end‐to‐end SNRs. Then, based on the obtained statistical results, we present the total average SER of the Non‐OPA TWOR‐AF systems by using the appropriate approximation, in which only the greater segment of the two terminal SERs is considered. Finally, by aiming at minimizing the total average SER and using the SNRs balancing condition at both transceivers, we study the OPA problem subject to a total transmission power constraint. The comparison analysis shows that, for the Non‐OPA TWOR‐AF systems, we can only evaluate exactly the greater segment of the two SERs of the received signals at two transceivers by using the derivations. However, for the OPA TWOR‐AF systems, with our derivations we can evaluate exactly not only each segment of the two terminal SERs but also the sum SER (exact total SER). Moreover, the simulations show the OPA TWOR‐AF systems outperform the Non‐OPA TWOR‐AF systems. Copyright © 2012 John Wiley & Sons, Ltd.