Jointly optimal power and rate allocation for layered broadcast over amplify-and-forward relay channels

We investigate the optimal power and rate allocation for multilayer transmission using the broadcast approach over a fading amplify-and-forward relay channel. The source uses multilayer source coding with successive refinement where the layers are transmitted using superposition coding at the source with optimal rate and power allocation. The destination applies successive interference cancellation after optimally combining the direct and relayed signals. The optimization objective is to maximize the expected user satisfaction which is usually defined by a differentiable concave increasing utility function of the total decoded rate. We propose a simple approximation for the end-to-end channel quality. This approximation is used to apply the power and rate allocation algorithm, which has a linear complexity with respect to the number of source layers. We provide many numerical examples to show the prospected gains of using the relay on the expected utility for different channel conditions.