You just include the noise in the SNR term, and yes it is constant, this is the characteristic of white noise, that it has a flat power spectral density.
Regarding the AF relaying, the end-to-end SNR is:
\[\frac{\frac{E_1|h_{sr}|^2}{N_0}\frac{E_2|h_{rd}|^2}{N_0}}{\frac{E_1|h_{sr}|^2}{N_0}+\frac{E_2|h_{rd}|^2}{N_0}+1}=\frac{\gamma_1\gamma_2}{\gamma_1+\gamma_2+1}\]
Actually, I am looking for this simulation, too. So, if you come up with some thing new, please post it here.
Note: Why you continue to use \[P\] instead of \[E\]? In bandlimited channel of bandwidth \[W\], the SNR is given in one of two equivalent forms: \[\frac{P}{N_0W}\] or \[\frac{E}{N_0}\], where \[W\approx\frac{1}{T} \], which means that \[\frac{P}{N_0W}=\frac{PT}{N_0}\], where \[PT=E\].
Thanks