## 3 Statistics of the SNR of an Equivalent End-to-End Communication Link
### CDF of the End-to-End SNR
\bigg{]} \tag{10}\]  
where \(\psi_{1}=\{(1-a_{1},r_{1}),\big{(}1-z_{1}^{2},r_{1}\big{)}\}\), \(\psi_{2}=\{(b_{1},r_{1}),(0,1),\\ \big{(}z_{2}^{2},r_{1}\big{)}\}\), \(\psi_{3}=\{(1,r_{2}),(1-b_{2},r_{2}),\big{(}1+z_{2}^{2},r_{2}\big{)}\}\), \(\psi_{4}=\{(1,1),(a_{2},r_{2}),\big{(}z_{2}^{2},r_{2}\big{)},(0,r_{2})\}\), and \(H_{p,q;p_{1},q_{1};p_{2},q_{2}}^{\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H },\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H },\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H },\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H },\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H },\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H },\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H },\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H},\text{H}, \text{H},\text{H},\text{H},\text{H},\text{H},\textwhere \(\psi_{6}=\big{\{}(1,1),\psi_{1},(1-a_{2},r_{2}),\big{(}1-z_{2}^{2},r_{2}),(1,r_{2}) \big{\}}\) and \(\psi_{7}=\{(b_{1},r_{1}),(b_{2},r_{2}),(0,1),\)\(\big{(}-z_{1}^{2},r_{1}),\big{(}-z_{2}^{2},r_{2})\big{\}}\). By applying Equation (1.5.9) in [14] to (12) and using elementary functions, the OP in the asymptotic regime can be expressed as  
\[F_{\gamma_{e2e}}(\gamma)\rightarrow \phi_{1}+\frac{\theta_{2}\gamma^{\frac{a_{1}}{7}}_{1}}{\gamma^{ \frac{a_{1}}{7}}_{1}}+\frac{\theta_{3}\gamma^{\frac{a_{1}^{2}}{7}}_{1}}{\gamma ^{\frac{a_{1}}{7}}_{1}}+\frac{\theta_{4}\gamma^{\frac{a_{1}}{7}}_{1}}{\gamma^{ \frac{a_{1}}{7}}_{1}}+\frac{\theta_{5}\gamma^{\frac{a_{1}^{2}}{7}}_{1}}{\gamma ^{\frac{a_{1}^{2}}{7}}_{1}} \tag{13}\] \[+\frac{\theta_{6}\gamma^{\frac{a_{2}}{7}}_{2}}{\gamma^{\frac{a_{2 }}{7}}_{2}}+\frac{\theta\gamma\gamma^{\frac{a_{2}^{2}}{7}}_{1}}{\gamma^{\frac{ a_{2}^{2}}{7}}_{2}},\]  
where \(\theta_{i}\) for \(i=1,2,\ldots,7\) are constants that can be easily obtained from Equation (1.5.10) in [14].