Error performance analysis of differential detection for amplify-and-forward relay systems

We consider a differential amplify-and-forward transmission scheme for a two-user cooperative system with a single relay. We propose a new analytical approach based on first principles, and obtain a closed-form expression for the exact bit error probability (BEP) in Rayleigh fading. This result involves only a single exponential integral function. It applies generally to the case where the channel statistics on different links are non-identical. As expected, the BEP decreases monotonically with the source transmission energy, or the relay transmission energy. The explicit BEP result allows us to study optimum energy allocation between the source and the relay, given a total transmission energy. By lower bounding the exact BEP expression via Jensen´s inequality, we obtain analytically a closedform approximate optimum energy allocation solution between the source and the relay. Numerical results show that the BEP bound and the approximate optimum energy allocation solution are very tight.