## 3 Performance Evaluation
### Outage Probability
\begin{array}{l}{\rm OP_{C-ORS}}=1\\ -\sum\limits_{m=0}^{M-1}\sum\limits_{t=0}^{K-1}\sum\limits_{n=0}^{N}\sum \limits_{w=0}^{K-1}\sum\limits_{q=0}^{N}(-1)^{m+n+q}C_{M-1}^{m}\frac{C_{N}^{m} C_{N}^{m}}{\hbar\pi!}\left(\frac{\lambda_{\rm BS}}{\kappa}\right)^{t}\left( \frac{\lambda_{\rm BS}}{\kappa}\right)^{w}\frac{M\lambda_{\rm RD}}{\kappa_{\rm RD }+m\Omega}\\ \times\int_{0}^{+\infty}\int_{0}^{z_{2}}\left(\frac{\lambda_{\rm BS}}{\kappa}z _{1}^{t}-n\lambda_{\rm SP}\delta z_{1}^{t-2}-tz_{1}^{t-1}\right)\left(\frac{ \lambda_{\rm BS}}{\kappa}z_{2}^{w}-q\lambda_{\rm RP}\delta z_{2}^{w-2}-wz_{2} ^{w-1}\right)\\ \times\exp\left(-\frac{\lambda_{\rm SP}}{\Delta}\frac{1}{z_{1}}\right)\exp \left(-\frac{(\lambda_{\rm RD}+m\Omega)}{\Delta}\frac{1}{z_{2}}\right)\exp \left(-\frac{\lambda_{\rm BS}}{\kappa}z_{1}-\frac{n\lambda_{\rm SP}\delta}{z_ {1}}\right)\\ \times\exp\left(-\frac{\lambda_{\rm BS}}{\kappa}z_{2}-\frac{q\lambda_{\rm RP} \delta}{z_{2}}\right)dz_{1}dz_{2}\\ -\sum\limits_{m=0}^{M-1}\sum\limits_{t=0}^{K-1}\sum\limits_{n=0}^{N}\sum \limits_{w=0}^{K-1}\sum\limits_{q=0}^{N}(-1)^{m+n+q}C_{M-1}^{m}\frac{C_{N}^{m} C_{N}^{m}}{\hbar\pi!}\left(\frac{\lambda_{\rm BS}}{\kappa}\right)^{t}\left(\frac{ \lambda_{\rm BS}}{\kappa}\right)^{w}\frac{m}{m+1}\frac{M\lambda_{\rm SB}}{ \lambda_{\rm RD}+m\Omega}\\ \times\int_{0}^{+\infty}\int_{0}^{z_{2}}\left(\frac{\lambda_{\rm BS}}{\kappa}z _{1}^{t}-n\lambda_{\rm SP}\delta z_{1}^{t-2}-tz_{1}^{t-1}\right)\left(\frac{ \lambda_{\rm BS}}{\kappa}z_{2}^{w}-q\lambda_{\rm RP}\delta z_{2}^{w-2}-wz_{2} ^{w-1}\right)\\ \times\exp\left(-\frac{(m+1)\Omega}{\Delta}\frac{1}{z_{1}}\right)\exp\left(- \frac{\lambda_{\rm BS}}{\kappa}z_{1}-\frac{n\lambda_{\rm SP}\delta}{z_{1}} \right)\exp\left(-\frac{\lambda_{\rm BS}}{\kappa}z_{2}-\frac{q\lambda_{\rm RP} \delta}{z_{2}}\right)dz_{1}dz_{2}\\ -\sum\limits_{m=0}^{M-1}\sum\limits_{t=0}^{K-1}\sum\limits_{n=0}^{N}\sum \limits_{w=0}^{K-1}\sum\limits_{q=0}^{N}(-1)^{m+n+q}C_{M-1}^{m}\frac{C_{N}^{m} C_{N}^{m}}{\hbar\pi!}\left(\frac{\lambda_{\rm BS}}{\kappa}\right)^{t}\left(\frac{ \lambda_{\rm BS}}{\kappa}\right)^{w}\frac{M\lambda_{\rm SB}}{\lambda_{\rm SR}+m \Omega}\\ \times\int_{0}^{+\infty}\int_{0}^{z_{1}}\left(\frac{\lambda_{\rm BS}}{\kappa}z _{1}^{t}-n\lambda_{\rm SP}\delta z_{1}^{t-2}-tz_{1}^{t-1}\right)\left(\frac{ \lambda_{\rm BS}}{\kappa}z_{2}^{w}-q\lambda_{\rm RP}\delta z_{2}^{w-2}-wz_{2} ^{w-1}\right)\\ \times\exp\left(-\frac{\lambda_{\rm RD}}{\Delta}\frac{1}{z_{2}}\right)\exp \left(-\frac{(\lambda_{\rm SB}+m\Omega)}{\Delta}\frac{1}{z_{1}}\right)\exp \left(-\frac{\lambda_{\rm BS}}{\kappa}z_{1}-\frac{n\lambda_{\rm SP}\delta}{z_ {1}}\right)\\ \times\exp\left(-\frac{\lambda_{\rm BS}}{\kappa}z_{2}-\frac{q\lambda_{\rm RP} \delta}{z_{2}}\right)dz_{1}dz_{2}\\ -\sum\limits_{m=0}^{M-1}\sum\limits_{t=0}^{K-1}\sum\limits_{n=0}^{N}\sum \limits_{w=0}^{K-1}\sum\limits_{q=0}^{N}(-1)^{m+n+q}C_{M-1}^{m}\frac{C_{N}^{m} C_{N}^{m}}{\hbar\pi!}\left(\frac{\lambda_{\rm BS}}{\kappa}\right)^{t}\left(\frac{ \lambda_{\rm BS}}{\kappa}\right)^{w}\frac{m}{m+1}\frac{M\lambda_{\rm RD}}{ \lambda_{\rm SR}+m\Omega}\\ \times\int_{0}^{+\infty}\int_{0}^{z_{2}}\left(\frac{\lambda_{\rm BS}}{\kappa}z _{1}^{t}-n\lambda_{\rm SP}\delta z_{1}^{t-2}-tz_{1}^{t-1}\right)\left(\frac{ \lambda_{\rm BS}}{\kappa}z_{2}^{w}-q\lambda_{\rm RP}\delta z_{2}^{w-2}-wz_{2} ^{w-1}\right)\\ \times\exp\left(-\frac{(m+1)\Omega}{\Delta}\frac{1}{z_{2}}\right)\exp\left(- \frac{\lambda_{\rm BS}}{\kappa}z_{1}-\frac{n\lambda_{\rm SP}\delta}{z_{1}} \right)\exp\left(-\frac{\lambda_{\rm BS}}{\kappa}z_{1}-\frac{n\lambda_{\rm SP} \delta}{z_{1}}\right)\\ \times\exp\left(-\frac{\lambda_{\rm BS}}{\kappa}z_{2}-\frac{q\lambda_{\rm RP} \delta}{z_{2}}\right)dz_{1}dz_{2}\\ \end{array}  \tag{56}\]  
Proof. : In the C-ORS protocol, the end-to-end OP can be calculated by  
\[