Power optimization for layered transmission over decode-and-forward relay channels

In this paper, we consider a fading relay channel where the source uses two layers source coding with successive refinement. The two source layers are transmitted using superposition coding at the source and relay with optimal power allocation, and successive interference cancellation at the receivers (i.e. relay and destination). The power allocation for the two layers at the source and relay is subject to optimization in order to maximize the expected user satisfaction that is defined by a utility function of the total decoded rates at the destination. We assume that only the channel statistics are known. The relay is half-duplex and applies decode and forward. We characterize the expected utility function in terms of the channel statistics of the fading channels, and we solve the optimization problem using the numerical random search method. We provide many numerical examples to show the prospected gains of using the relay on the expected utility for different channel conditions. Furthermore, we obtain that for some conditions, it is optimal to send only one layer.