Piece-wise linear approximation solution to the estimate-and-forward relay with the Bayesian estimator

In this paper, we extend our previous work on Bayesian Estimate-and-Forward (BEF) relaying scheme. The probabilistic relationship between the original symbol and its Bayesian estimate at the relay is investigated, since it is important when combining the cooperative information from both the source and the relay. Unlike the rough Gaussian noise modeling in priori art, we first derive an optimal relationship of BEF based on a MAP detector. Then, we propose a piecewise linear approximation relationship to form the symbol estimate, so that the original symbol can be detected simply at the destination in block-fading rayleigh channels. In the simulations, the piecewise linear approximation strategy performs well and achieves similar performance with the optimal relationship approach at high signal-to-noise ratio regime.