Performance Analysis of Maximum Likelihood Decode and Forward Cooperative Systems in Rayleigh Fading

The bit error rate (BER) performance analysis of maximum-likelihood (ML) based decode and forward (DF) cooperative diversity systems has been a subject of considerable interest. Exact analysis of ML-DF transmission has been considered a challenging problem due to the nonlinear characteristic of the ML detector. In this paper, we provide exact expressions for the BER of ML-DF cooperative systems employing a single relay. We extend these results to the case of multiple relays for the piecewise linear (PL) combiner, that is known to be a close approximation of the ML detector. This is done by using a novel theory of conditionally Gaussian random variables. By expressing the ML decision variable in terms of functions of conditionally Gaussian variables, exact expressions for the BER of the ML-DF system are obtained. Through simulation results, we verify the validity of the derived analytical expressions.