Asymptotic performance analysis for two-way opportunistic relaying based on amplify-and-forward network coding

This study mainly focuses on the asymptotical performance of two-way amplify-and-forward network coding opportunistic relaying (TWOR-AFNC) where the nodes have the same transmission powers, and there is (no) direct link between two sources, that is, TWOR-AFNC-Dir and TWOR-AFNC-Nodir. Firstly, based on the max-min criterion, the authors obtain the closed-form expressions to the probability density function (PDF), the cumulative distribution function (CDF) and the moment-generating function (MGF) of the equivalent end-to-end signal-to-noise ratio (SNR). These results are given with very simple analytical expressions by defining an auxiliary variable omega(eq-k)(theta), 2 <= theta <= 3. Secondly, the comparison analyses of the outage probability and symbol error probability (SEP) between the two systems are presented. The comparison analysis shows that the derived results are the tight lower bound when theta = 2, and are the upper bound when theta = 3. Finally, to obtain the exact estimation of the performance, the authors obtain the optimisation values of theta. The results show that the optimisation values of theta are a little greater than 2 in lower SNR, whereas are equal to 2 in high SNR. Moreover, the feasible SNR regime for theta = 2 is expanding with the increasing of the asymmetry between relay channels. Besides of this, the authors also present the closed-form expressions to CDF and PDF when the nodes have different transmission powers. The results indicate that the closed-form expressions to CDF and PDF are similar for the two cases where the nodes transmission powers are same or different.