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.

I. Introduction

COOPERATIVE communication is a promising technique to provide transmit diversity by using multiple relays as a virtual antenna array while meeting the space constraints on the relays [1]. By utilizing this mechanism, cooperative communication can inherit many desirable properties of multiple-input-multiple-output (MIMO) systems [2]. However, synchronization is a challenge in most relaying protocols [2]–[4]. Opportunistic relaying is shown to be an effective scheme to overcome the synchronization problem while achieving a performance close to that of the distributed space-time coding [5]. It selects the “best” relay to transmit instead of letting all relays cooperate simultaneously. Conventional ways of selecting the “best” relay include (i) maximizing the minimum of the source-relay channel gain and the relay-destination channel gain or (ii) maximizing the harmonic mean of the two channel gains. The two selection criteria are referred to as max-min selection criterion and max-harmonic-mean (MHM) selection criterion, respectively.