Asymptotic Analysis of Opportunistic Relaying Based on the Max-Generalized-Mean Selection Criterion

In an opportunistic relaying mechanism, the "best" relay is selected to forward a received signal to the destination. In this paper, we propose a novel criterion to choose the "best" relay, namely the max-generalized-mean (MGM) selection criterion, which encompasses the max-min and the max-harmonic-mean (MHM) selection criteria. We then analyze the asymptotic outage probability of the selection decode-and-forward opportunistic relaying (SDF-OR) protocol under the proposed MGM selection criterion. Based on the asymptotic results, we show the conditions under which the MGM selection framework provides the full diversity. We further optimize the asymptotic outage probability by adjusting the parameters associated with the MGM selection criterion. We show that at high signal-to-noise-ratio (SNR), a lower outage probability can be accomplished by the MGM selection criterion compared with the max-min or the MHM selection criterion for the SDF-OR protocol.