Exact error analysis for decode and forward cooperation with maximal ratio combining

In this paper, we provide exact expressions for the bit error rate (BER) for single relay maximal ratio combining (MRC) based decode and forward (DF) cooperative systems in Nakagami-m fading. This is done by expressing the decision variable as a sum of gamma conditionally Gaussian (CG) random variables. The characteristic function (CF) of gamma CG variables is then derived and used to obtain the BER expressions using the Gil-Pelaez inversion formula. A tight closed form approximation for the BER is also derived and used to obtain the diversity order. Numerical results, including simulations, are provided to verify the validity of the derived analytical expressions.