Optimal power allocation for layered broadcast over amplify-and-forward relay channels

In this paper, we consider a fading relay channel where the source uses multilayer source coding with successive refinement. The source layers are transmitted using superposition coding at the source with optimal power allocation. The relay uses the simple half-duplex amplify-and-forward strategy. The destination applies successive interference cancellation after optimally combining the direct and relayed signals. The power allocation for the source layers at the source 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 propose an approximation for the distribution of the end-to-end channel quality. We assume that only the channel statistics are known. We characterize the expected utility function in terms of the channel statistics of the fading channels, and we solve the optimization problem for any number of source layers. We provide 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.