## 3 Outage Performance Analysis
### Outage Probability of \(\mathrm{D}_{2}\)
\begin{split} B_{2}&=\left(\underbrace{\Pr\left\{P \big{|}h_{SR_{k}}\big{|}^{2}>\gamma,\big{|}h_{R_{k}D_{2}}\big{|}^{2}<\frac{ \gamma}{\eta\left(P\big{|}h_{SR_{k}}\big{|}^{2}-\gamma\right)},\big{|}h_{R_{k} P}\big{|}^{2}<\frac{I}{\eta\left(P\big{|}h_{SR_{k}}\big{|}^{2}-\gamma\right)} \right\}}_{B_{21}}\right.\\ &+\underbrace{\Pr\left\{P\big{|}h_{SR_{k}}\big{|}^{2}>\gamma, \big{|}h_{R_{k}D_{2}}\big{|}^{2}<\frac{\gamma\big{|}h_{R_{k}P}\big{|}^{2}}{I}, \big{|}h_{R_{k}P}\big{|}^{2}>\frac{I}{\eta\left(P\big{|}h_{SR_{k}}\big{|}^{2}- \gamma\right)}\right\}}_{B_{22}}\right)\Pr\left\{\big{|}h_{SP}|^{2}<\frac{I}{ \mathbb{P}}\right\}\\ &+\underbrace{\Pr\left\{\frac{I\big{|}h_{SR_{k}}\big{|}^{2}}{|h_ {SP}|^{2}}>\gamma,\big{|}h_{SP}\big{|}^{2}>\frac{I}{\mathbb{P}},\big{|}h_{R_{k }D_{2}}\big{|}^{2}<\frac{\gamma}{\eta\left(\frac{\big{|}h_{SR_{k}}\big{|}^{2}} {|h_{SP}|^{2}}-\gamma\right)},\big{|}h_{R_{k}P}\big{|}^{2}<\frac{I}{\eta\left( \frac{\big{|}h_{SR_{k}}\big{|}^{2}}{|h_{SP}|^{2}}-\gamma\right)}\right\}}_{B_{2 3}}\right.\\ &+\underbrace{\Pr\left\{\frac{I\big{|}h_{SR_{k}}\big{|}^{2}}{|h_ {SP}|^{2}}>\gamma,\big{|}h_{SP}\big{|}^{2}>\frac{I}{\mathbb{P}},\big{|}h_{R_{k }D_{2}}\big{|}^{2}<\frac{\gamma\big{|}h_{R_{k}P}\big{|}^{2}}{I},\big{|}h_{R_{k }P}\big{|}^{2}>\frac{I}{\eta\left(\frac{\big{|}h_{SR_{k}}\big{|}^{2}}{|h_{SP}| ^{2}}-\gamma\right)}\right\}}_{B_{24}}\right.\end{split}  \tag{29}\]  
It is noted that the first term \(B_{21}\) can be calculated as  
\[ \begin{split}& B_{21}=\sum_{k=1}^{K}\left(\begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\exp\left(-\frac{\gamma k}{P\Omega_{SR}}\right) \left(1-2\sqrt{\frac{lk}{p\eta\Omega_{RP}\Omega_{SR}}}K_{1}\left(2\sqrt{\frac {lk}{\eta P\Omega_{RP}\Omega_{SR}}}\right)\right.\\ &\left.-2\sqrt{\frac{\gamma k}{\eta P\Omega_{RD_{2}}\Omega_{SR}}}K_{1} \left(2\sqrt{\frac{\gamma k}{\eta P\Omega_{RD_{2}}\Omega_{SR}}}\right)+2\sqrt{ \frac{\left(\gamma\Omega_{RP}+I\Omega_{RD_{2}}\right)k}{\Omega_{RD_{2}}p\eta \Omega_{RP}\Omega_{SR}}}K_{1}\left(2\sqrt{\frac{\left(\gamma\Omega_{RP}+I\Omega _{RD_{2}}\right)k}{\Omega_{RD_{2}}\eta\Omega_{RP}P\Omega_{SR}}}\right)\right). \end{split}  \tag{30}\]  
The second term \(B_{22}\) can be expressed by \[ \begin{split} B_{22}&=2\sum\limits_{k=1}^{K}\left( \begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\text{e}^{-\frac{k\gamma}{\Omega_{SR}P}}\left( \sqrt{\frac{lk}{\Omega_{RP}\Omega_{SR}P\eta}}K_{1}\left(2\sqrt{\frac{lk}{ \Omega_{RP}\Omega_{SR}P\eta}}\right)\right.\\ &-\left.\frac{I\Omega_{RD_{2}}}{\gamma\Omega_{RP}+I\Omega_{RD_{2}}}\sqrt{ \frac{\left(\gamma\Omega_{RP}+I\Omega_{RD_{2}}\right)k}{\Omega_{RD_{2}}\Omega_ {RP}\Omega_{SR}P\eta}}K_{1}\left(2\sqrt{\frac{\left(\gamma\Omega_{RP}+I\Omega _{RD_{2}}\right)k}{\Omega_{RD_{2}}\Omega_{RP}\Omega_{SR}P\eta}}\right)\right) \end{split}  \tag{31}\]  
The third term \(B_{23}\) can be calculated as  
\[ \begin{split} B_{23}&=\Pr\left\{\frac{\left|h_{SR_{ k}}\right|^{2}}{\left|h_{SP}\right|^{2}}>\frac{\delta}{I},\left|h_{SP}\right|^{2}> \frac{I}{P},\left|h_{R_{k}D_{2}}\right|^{2}<\frac{\delta}{\eta\left(\frac{ \left|h_{SR_{k}}\right|^{2}}{X_{SP}}-\delta\right)},\left|h_{RP}\right|^{2}< \frac{I}{\eta\left(\frac{\left|h_{SR_{k}}\right|^{2}}{X_{SP}}I-\delta\right)} \right\}\\ &=\int_{\frac{1}{P}}^{\infty}\int_{\frac{\omega}{T}}^{\infty}F_{ \left|h_{R_{k}D_{2}}\right|^{2}}\left(\frac{\delta}{\eta\left(\frac{1}{y}- \delta\right)}\right)F_{\left|h_{SP}\right|^{2}}\left(\frac{I}{\eta\left( \frac{lx}{y}-\delta\right)}\right)f_{\left|h_{SR_{k}}\right|^{2}}\left(x \right)dxf_{\left|h_{SP}\right|^{2}}\left(y\right)dy\end{split}  \tag{32}\]  
Similarly, \(B_{23}\) is rewritten as  
\[