Exact BEP Analysis for Coherent M-ary PAM and QAM over AWGN and Rayleigh Fading Channels

A novel and unified framework is presented to evaluate the exact bit error probability (BEP) of
M
-ary pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) over additive white Gaussian noise (AWGN) channel for any bit-mapping techniques. Tight approximations are also provided for both of them. Using these results, we obtain the exact and tight approximate BEP expressions for maximal-ratio combining (MRC) and selection combining (SC) in Rayleigh fading.