Outage probability-based power and time optimization for relay networks

In the context of cooperative wireless networks that convey data on slow fading channels, outage probability P_o is the relevant performance index from the point of view of information theory. Derivation and minimization of this probability with respect to the relaying protocol parameters is of central importance. However, it is often hard to derive its expression, let alone to find its exact minimum for all possible values of the signal-to-noise ratio (SNR). This problem can be simplified by studying the behavior of P_o in the asymptotic regime where the SNR ρ converges to infinity. In this regime, usually ρ_N+1 P_o converges to a constant ξ where N is the number of relays. In this paper, a simple and general method for deriving and minimizing ξ with respect to the power distribution between the source and the relays, and with respect to the durations of the slots specified by the relaying protocol, is developed. While the proposed approach is designed for the high SNR regime, simulations show that outage probability is reduced in a similar proportion at moderate SNR. The method applies to a general class of radio channels that includes the Rayleigh and the Rice channels as particular cases. Convexity of ξ with respect to the design parameters is shown. Decode-and-forward, as well as amplify-and-forward protocols are considered in the half duplex mode.