## Appendix C  
Based on MRC scheme, when \(\overline{\gamma}_{B1}\rightarrow\infty\), the conditional CDF of \(\gamma_{AB,1}\) is given by  
\[F_{\gamma_{AR,1}}\left(x|G\right)\approx\frac{1}{N_{R}!}\Bigg{(}\frac{\sigma_{ R}^{2}x}{P_{S}\lambda_{AR}}\Bigg{)}^{N_{R}}. \tag{36}\]  
Also, the conditional PDF of \(\gamma_{AE,1}\) is written as  
\[f_{\gamma_{AE,1}}\left(y|G\right)=\frac{1}{\overline{\gamma}_{E1}}\exp\left(- \frac{1}{\overline{\gamma}_{E1}}y\right). \tag{37}\]By substituting (A5) and (A6) into (15), the asymptotic conditional \(F_{\gamma_{AR,1}}\left(R_{S}|G\right)\) is given by  
\[F_{\gamma_{AR,1}}\left(R_{S}|G\right)=\frac{1}{N_{R}!}\Bigg{(}\frac{\sigma_{R}^{ 2}}{P_{S}\lambda_{AR}}\Bigg{)}^{N_{R}}\sum\limits_{q=0}^{N_{R}}\Bigg{(}\begin{array} []{c}N_{R}\\ q\end{array}\Bigg{)}\Big{(}2^{R_{S}}\Big{)}^{q}\Big{(}2^{R_{S}}-1\Big{)}^{N_{R }-q}q!(\overline{\gamma}_{E1})^{q}.\] (A7)  
Now, On the basis of (31), the desired result \(F_{\gamma_{1}^{MRC}}\left(R_{S}\right)\) can be derived as  
\[\begin{split} F_{\gamma_{1}^{MRC}}\left(R_{S}\right)&= \left(\frac{1}{\tilde{\gamma}_{B1}}\right)^{N_{R}}\sum\limits_{q=0}^{N_{R}} \Bigg{(}\begin{array}{c}N_{R}\\ q\end{array}\Bigg{)}\Big{(}2^{R_{S}}-1\Big{)}^{N_{R}-q}q!\Big{(}2^{R_{S}} \Big{)}^{q}(\gamma_{E1})^{q}\frac{1}{N_{R}!}\\ &\times\left[\left(1-\exp\left(-\frac{\mu}{\lambda_{AP}}\right) \right)+\left(\frac{\lambda_{AP}}{\mu}\right)^{N_{R}}\;\Gamma\left(N_{R}+1, \frac{\mu}{\lambda_{AP}}\right)\right].\end{split}\] (A8)  
Based on MRT-SC phase, the MRT-SC scheme is similar with MRC scheme description process of the (A8), and when \(\overline{\gamma}_{B1}\rightarrow\infty\), the conditional CDF of \(\gamma_{RB,1}\) can be approximated as  
\[F_{\gamma_{RB,1}}\left(y|G_{1}\right)\approx\left(\frac{1}{N_{R}!}\right)^{N_{ B}}\Bigg{(}\frac{\sigma_{R}^{2}x}{P_{R}\lambda_{RB}}\Bigg{)}^{N_{R}N_{B}}.\] (A9)  
\(f_{\gamma_{RE,1}}\left(y|G_{1}\right)\) is the same as \(f_{\gamma_{AE,1}}\left(y|G\right)\) of (A6).  
Similarly, the asymptotic conditional \(F_{\gamma_{RB,1}}\left(R_{S}|G_{1}\right)\) is given by  
\[F_{\gamma_{RB,1}}\left(R_{S}|G_{1}\right)=\Big{(}\frac{1}{N_{R}!}\Big{)}^{N_{ B}}\bigg{(}\frac{\sigma_{R}^{2}}{P_{R}\lambda_{RB}}\Bigg{)}^{N_{R}N_{B}}\sum \limits_{j=0}^{N_{R}N_{B}}\Bigg{(}\begin{array}{c}N_{R}N_{B}\\ j\end{array}\Bigg{)}\big{(}2^{R_{S}}-1\big{)}^{N_{R}N_{B}-j}2^{R_{S}j}j!\Big{(} \frac{1}{\overline{\gamma}_{E1}}\Big{)}^{-j}.\] (A10)  
Now, on the basis of \(f_{G_{1}}\left(g\right)\), the desired result \(F_{\gamma_{2}^{MRT-SC}}\left(R_{S}\right)\) is written as  
\[\begin{split} F_{\gamma_{2}^{MRT-SC}}\left(R_{S}\right)&= \left(\frac{1}{\overline{\gamma}_{B1}}\right)^{N_{R}N_{B}}\sum\limits_{j=0}^{N _{R}N_{B}}\Bigg{(}\begin{array}{c}N_{R}N_{B}\\ j\end{array}\Bigg{)}2^{R_{S}j}\Big{(}2^{R_{S}}-1\Big{)}^{N_{R}N_{B}-j}j!\left( \frac{1}{\overline{\gamma}_{E1}}\right)^{-j}\!\left(\frac{1}{N_{R}!}\right)^{ N_{B}}\\ &\times\left[\left(1-\exp\left(-\frac{\mu}{\lambda_{RP}}\right) \right)+\left(\frac{\lambda_{RP}}{\mu\epsilon}\right)^{N_{R}N_{B}}\Gamma \left(N_{R}N_{B}+1,\frac{\mu}{\lambda_{RP}}\right)\right].\end{split}\] (A11)  
By using (A8) and (A11), \(\Delta_{1}\) and \(\Delta_{2}\) are given by (49) and (50).