Outage probability optimization of certain wireless relaying protocols

In the context of wireless relay networks operating on slow fading channels, the outage probability optimization is of central importance. It is often hard to give a closed form expression of the outage probability P_o for all possible values of the Signal to Noise Ratio (SNR). On the other hand, it is possible to analyze the behaviour of P_o in the asymptotic regime where the SNR rho converges to infinity. In this regime, rho^N+1P_o usually converges to a constant xi where N is the number of relays. This paper presents a general method for deriving and minimizing xi 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. Convexity of xi with respect to the design parameters is shown. The method applies to a general class of radio channels that includes the Rayleigh and the Rice channels as particular cases. Decode-and-forward as well as amplify-and-forward protocols are considered in the half duplex mode. 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.