Input-distribution optimization for estimate-and-forward relaying

We investigate the design of optimized input distributions for the two-hop Gaussian relay channel under an average power constraint. In our study, the relay is confined to implement an estimate-and-forward strategy. We demonstrate that the rate achievable by an optimized discrete input distribution can significantly outperform that achievable by a Gaussian codebook. The lower bound obtained by the optimized EF scheme is also used to establish an improved lower bound on the rates achievable by compress-and-forward.