## 6 Conclusions
\begin{array}{ll}P^{11}&=Pr\Big{\{}R_{5U_{1}}^{x_{2}}\geq R_{2},R_{5U_{1}}^ {x_{1}}\geq R_{1}\Big{\}}\\ &=Pr\Bigg{\{}\frac{a_{2\Theta}s_{1\omega_{1}}|^{2}}{\sigma_{1}\left|h_{7U_{1}} \right|^{2}+\alpha_{1}\Theta s_{1\omega_{1}}\right|^{2}+1}\geq\gamma_{2},\frac {a_{1\Theta}s_{1\omega_{1}}|^{2}}{\sigma_{1}\left|h_{7U_{1}}\right|^{2}+1} \geq\gamma_{1}\Bigg{\}}\\ &=Pr\Big{\{}\rho s_{5}\left|h_{5U_{1}}\right|^{2}\geq\left(\rho_{T}\left|h_{7U _{1}}\right|^{2}+1\right)\varphi_{1}\Big{\}}\\ &=\int_{0}^{\infty}\!\!\left[1-F_{\rho s_{1}\left|h_{5U_{1}}\right|^{2}}( \varphi_{1}y)\right]\cdot f_{\rho_{T}\left|h_{7U_{1}}\right|^{2}+1}(y)dy\\ &=\frac{\sigma^{2}}{\lambda_{7U_{1}}\Gamma_{T}}exp\Big{(}\frac{\sigma^{2}}{ \lambda_{7U_{1}}\Gamma_{T}}\Big{)}\cdot(Q_{1}-Q_{2}).\end{array}  \tag{2}\]  
where \(Q_{1}\) and \(Q_{2}\) are given, respectively, as  
\[ \begin{array}{ll}Q_{1}=\int_{1}^{\infty}exp(-a_{1}y)dy=\frac{1}{a_{1}}exp(-a _{1}),\\ Q_{2}&=exp\Big{(}-\frac{I_{0}}{\lambda_{5R}\Gamma_{1}}\Big{)}\int_{1}^{\infty }\frac{y}{b_{1}+y}exp(-a_{1}y)dy\\ &\stackrel{{ t=b_{1}+y}}{{=}}exp\Big{(}-\frac{I_{0}}{\lambda_{5R }\Gamma_{1}}\Big{)}\int_{1+b_{1}}^{\infty}\frac{t-b_{1}}{t}exp(-a_{1}(t-b_{1 }))dy\\ &=exp\Big{(}-\frac{I_{0}}{\lambda_{5R}\Gamma_{1}}\Big{)}exp(a_{1}b_{1})\left[ \int_{1+b_{1}}^{\infty}exp(-a_{1}t)dy-\int_{1+b_{1}}^{\infty}\frac{b_{1}}{t} exp(-a_{1}t)dy\right]\\ &=exp\Big{(}-\frac{I_{0}}{\lambda_{5R}\Gamma_{1}}\Big{)}exp(a_{1}b_{1})\left[ \frac{1}{a_{1}}exp(-a_{1}-a_{1}b_{1})-b_{1}E_{1}(a_{1}+a_{1}b_{1})\right].\\ \end{array} \]  
In \(Q_{1}\) and \(Q_{2}\), \(a_{1}=\frac{\sigma^{2}\left(\varphi_{1}\lambda_{7U_{1}}\Gamma_{T}+\lambda_{5U _{1}}\Gamma_{T}\right)}{\left(\lambda_{5U_{1}}\Gamma_{T}\lambda_{7U_{1}} \Gamma_{T}\right)},b_{1}=\frac{\left(\lambda_{5U_{1}}I_{0}\right)}{\left( \lambda_{5R}\sigma^{2}\varphi_{1}\right)}\), \(\varphi_{1}=max\Big{\{}\gamma_{4x}\frac{\gamma_{1}}{\alpha_{1}}\Big{\}},\gamma _{4x}=\frac{\gamma_{2}}{\left(\alpha_{2}-\alpha_{1}\gamma_{2}\right)}\), and \(q\) is obtained by exponential integral function \(E_{1}(x)=-E_{i}(-x)=\int_{1}^{\infty}\frac{1}{t}exp(-a_{1}t)dt\) and Equation (3.352.2) in [35]. The probability of the event that \(\Theta\) = '10' is given by  
\[\begin{array}{ll}P^{10}&=Pr\Big{\{}R_{SU_{1}}^{x_{2}}\geq R_{2},R_{SU_{1}}^{x_{1} }<R_{1}\Big{\}}\\ &=Pr\Big{\{}\frac{a_{2}\rho_{S}|h_{SU_{1}}|^{2}}{\rho_{T}|h_{U_{1}}|^{2}+a_{1} \rho_{S}|h_{SU_{1}}|^{2}+1}\geq\gamma_{2},\frac{a_{1}\rho_{S}|h_{SU_{1}}|^{2}}{ \rho_{T}|h_{TU_{1}}|^{2}+1}<\gamma_{1}\Big{\}}\\ &=\Big{[}F_{\rho_{S}|h_{SU_{1}}|^{2}}\Big{(}\Big{(}\rho_{T}|h_{TU_{1}}|^{2}+1 \Big{)}\varphi_{1}\Big{)}-F_{\rho_{S}|h_{SU_{1}}|^{2}}\Big{(}\Big{(}\rho_{T}|h_ {TU_{1}}|^{2}+1\Big{)}\varphi_{2}\Big{)}\Big{]}I_{\{\gamma_{a}<\frac{\gamma_{ 2}}{\alpha_{1}}\}}\\ &=\frac{\sigma^{2}}{\lambda_{TU_{1}}P_{T}}exp\Big{(}\frac{\sigma^{2}}{\lambda _{TU_{1}}P_{T}}\Big{)}\cdot\big{[}(Q_{2}-Q_{1})-(Q_{4}-Q_{3})\big{]}I_{\{a_{2}> 1-\frac{\gamma_{1}}{\gamma_{0}}\}}\\ &\text{where}\,Q_{3}=1/a_{2}exp(-a_{2}),Q_{4}=exp\Big{(}-\frac{I_{0}}{\lambda_{ SR_{1}}R_{1}}\Big{)}exp(a_{2}b_{2})\Big{[}\frac{1}{a_{2}}exp(-a_{2}-a_{2}b_{2})-b_{2}E_{1 }(a_{2}+a_{2}b_{2})\Big{]}.\\ &\text{In}\,\,Q_{3}\text{ and}\,\,Q_{4},\,a_{2}=\frac{\sigma^{2}\big{(}\rho_{2} \lambda_{TU_{1}}P_{T}+\lambda_{SU_{1}}P_{1}\big{)}}{\big{(}\lambda_{SU_{1}}P_{ 1}\lambda_{TU_{1}}P_{T}\big{)}},\,\,b_{2}=\big{(}\frac{\lambda_{SU_{1}}I_{0}}{ \lambda_{SR}\sigma^{2}\varphi_{2}}\big{)},\,\,\varphi_{2}=min\{\gamma_{a}, \gamma_{1}/\alpha_{1}\}\) and \(\gamma_{0}=\gamma_{1}+\gamma_{2}+\gamma_{1}\gamma_{2}\). The probability of the event that \(\Theta\) = '01' is given by  
\[ \begin{array}{ll}P^{01}&=Pr\Big{\{}R_{SU_{1}}^{x_{2}}<R_{2},R_{SU_{1}}^{x_{1} }\geq R_{1}\Big{\}}\\ &=\frac{\sigma^{2}}{\lambda_{TU_{1}}P_{T}}exp\Big{(}\frac{\sigma^{2}}{\lambda _{TU_{1}}P_{T}}\Big{)}\cdot\big{[}(Q_{2}-Q_{1})-(Q_{4}-Q_{3})\big{]}I_{\{a_{2} \leq 1-\frac{\gamma_{1}}{\gamma_{0}}\}}\\ \end{array}  \tag{10}\]  
The probability of the event that \(\Theta\) = '00' is given by  
\[