Max-flow min-cut outage characterization of dual-hop relay channels

Employing the max-flow min-cut method, this paper derives a new closed-form lower bound expression on the outage probability of dual-hop relaying channels which is valid for arbitrary signal-to-noise ratios (SNRs). Based on this result, we investigate the performance in the low and high-SNR regimes. At low SNR, the optimal relay position, as well as the optimal power allocation between the source and relay, to maximize the upper bound on the -outage capacity are obtained in closed-form. Our analysis shows that under the optimal power allocation, when the relay is closely located near the destination, the corresponding -outage capacity is about twice of that when the relay is closely located near the source. At high SNR, the derived lower bound on the outage probability is approximated, from which the diversity-multiplexing tradeoff of the relay channel is extracted. Quite surprisingly, the derived high SNR approximation is shown to be very accurate for a wide range of SNRs of practical interest, not simply in the high-SNR regime.