## 3 Performance Analysis
### Op  
According to [18], OP is an important performance measurement, which is known as the SNDER falls below a predefined threshold \(\gamma_{0}\), namely:  
\[P_{out}\left(\gamma_{0}\right)=\Pr\left({\gamma_{R}\leq\gamma_{0}}\right)+ \Pr\left({\gamma_{D}\leq\gamma_{0}}\right)-\Pr\left({\gamma_{R}\leq\gamma_{0} }\right)\Pr\left({\gamma_{D}\leq\gamma_{0}}\right). \tag{24}\]  
In what follows, \(\Pr\left({\gamma_{R}\leq\gamma_{0}}\right)\) and \(\Pr\left({\gamma_{D}\leq\gamma_{0}}\right)\) will be given, respectively. Firstly, we get the closed-form expression of \(\Pr\left({\gamma_{R}\leq\gamma_{0}}\right)\). From Equation (9), when \(\gamma_{0}<1/k_{1}^{2}\), we have:  
\[ \begin{split}\Pr\left({\gamma_{R}\leq\gamma_{0}}\right)& =\Pr\left({\frac{{\gamma_{SR}Q}}{{\gamma_{SR}Qk_{SR}^{2}+\gamma_{ SP}\left({1+k_{SP}^{2}}\right)\delta_{R}^{2}}}\leq\gamma_{0}}\right)\\ &=\int_{0}^{\infty}{\int_{0}^{C_{2}y+C_{3}}{f_{\gamma_{SR}}\left( x\right)f_{\gamma_{SP}}\left(y\right)dxdy}}\\ &=\int_{0}^{\infty}{F_{\gamma_{SR}}\left(y{C_{2}+C_{3}}\right)f_{ \gamma_{SP}}\left(y\right)dy},\end{split}  \tag{25}\]  
where \(C_{2}=\frac{{\delta_{R}^{2}\left({1+k_{SP}^{2}}\right)\gamma_{0}}}{{\sigma \left({1-k_{1}^{2}\gamma_{0}}\right)}}\) and \(C_{3}=\frac{{A\gamma_{0}}}{{\mathcal{Q}\left({1-k_{1}^{2}\gamma_{0}}\right)}}\). By taking Equations (20) and (23) into Equation (25), we can get Equation (26), which is shown at the top of this page. \[ \begin{split}&\Pr\left({\gamma_{R}\leq\gamma_{0}}\right)\\ &=\sum\limits_{\xi_{1}=0}^{m_{SP}-1}\cdots\sum\limits_{\xi_{M}=0}^ {m_{SP}-1}\Xi\left(M\right)\left[{\left({\Lambda_{SP}-1}\right)!\Omega_{SP}^{- \Lambda_{SP}}-\sum\limits_{t=1}^{m_{SE}-1}\sum\limits_{s=0}^{t}{\frac{{\alpha_{ SR}\xi\left(t\right)t!}}{{\gamma_{SR}^{t+1}s!\alpha_{SR}^{t-s+1}}}\sum\limits_{\
u=0}^{s}{ \left({s}\right)\frac{{C_{3}^{-\
u}\mathbb{C}_{2}^{\sigma}e^{-\Lambda_{SR}C_{3} }\left({\Lambda_{SP}-1+\
u}\right)!}}{{\left({C_{2}\Delta_{SR}+\Delta_{SP}} \right)^{-\Lambda_{SP}-\
u}}}}}\right]\\ &=1-\sum\limits_{\xi_{1}=0}^{m_{SP}-1}\cdots\sum\limits_{\xi_{M}=0 }^{m_{SP}-1}\Xi\left(M\right)\sum\limits_{t=1}^{m_{SE}-1}\sum\limits_{s=0}^{t} {\frac{{\alpha_{SR}\xi\left(t\right)t!}}{{\gamma_{SR}^{t+1}s!\alpha_{SR}^{t-s+ 1}}}\sum\limits_{\
u=0}^{s}{\left({s}\right)\frac{{C_{3}^{-\
u}\mathbb{C}_{2 }^{\sigma}e^{-\Lambda_{SR}C_{3}}\left({\Lambda_{SP}-1+\
u}\right)!}}{{\left({C_ {2}\Delta_{SR}+\Delta_{SP}}\right)^{-\Lambda_{SP}-\
u}}}}}.\end{split}  \tag{26}\]Then, with similar manners, when \(\gamma_{0}<1/k_{2}^{2}\), \(\Pr\left(\gamma_{D}\leq\gamma_{0}\right)\) is given by:  
\[ \begin{split}\Pr\left(\gamma_{D}\leq\gamma_{0}\right)& =\Pr\left(\frac{\gamma_{RD}Q}{\gamma_{RD}Qk_{2}^{2}+\delta_{D}^{2} \gamma_{RP}\left(1+k_{RP}^{2}\right)+B}\leq\gamma_{0}\right)\\ &=\int_{0}^{\infty}\int_{0}^{y_{D}+D_{2}}f_{\gamma_{RD}}\left(x \right)f_{\gamma_{RP}}\left(y\right)dxdy\\ &=\int_{0}^{\infty}F_{\gamma_{RD}}\left(yD_{1}+D_{2}\right)f_{ \gamma_{RP}}\left(y\right)dy,\end{split}  \tag{27}\]  
where \(D_{1}=\frac{\delta_{D}^{2}\left(1+k_{RP}^{2}\right)\gamma_{0}}{\sigma\left(1- k_{2}^{2}\gamma_{0}\right)Q}\) and \(D_{2}=\frac{B\gamma_{0}}{\left(1-k_{2}^{2}\gamma_{0}\right)Q}\). Then, substituting Equations (12) and (13) into Equation (27), we can obtain Equation (28), which is presented at the top of this page. \[ \begin{split}\Pr\left(\gamma_{D}\leq\gamma_{0}\right)& =\sum_{i=1}^{\rho\left(\text{A}_{RP}\right)}\sum_{j=1}^{\gamma_{ \left(\text{A}_{RP}\right)}}\chi_{i,j}\left(\text{A}_{RP}\right)-\sum_{i=1}^{ \rho\left(\text{A}_{RP}\right)}\sum_{j=1}^{\gamma_{\left(\text{A}_{RP}\right) }}\frac{\chi_{i,j}\left(\text{A}_{RP}\right)\mu_{\left\langle j\right\rangle}^{ -j}}{\left(1/\mu_{\left\langle j\right\rangle}+D_{2}/\gamma_{RD}\right)^{j}}\\ &=1-\sum_{i=1}^{\rho\left(\text{A}_{RP}\right)}\sum_{j=1}^{\gamma _{\left(\text{A}_{RP}\right)}}\frac{\chi_{i,j}\left(\text{A}_{RP}\right)\mu_{ \left\langle j\right\rangle}^{-j}}{\left(1/\mu_{\left\langle j\right\rangle}+D _{2}/\gamma_{RD}\right)^{j}}.\end{split}