## 4 High SNR Analysis and Secrecy Throughput  
### High SNR Analysis  
Although the derivation of the closed-form expressions of the SOP has been finished above, the analysis of the asymptotic SOP in the high SNR will be conducted in this subsection to obtain more insights. Specifically, consider two different scenarios: (1) \(\overline{\tau}_{Bj}\rightarrow\infty\) and _fixed_\(\overline{\tau}_{Ej}\), that a scenario in which the SNR of main link outperforms the SNR of the eavesdropper's link, also known as the eavesdropper's channel, suffers from heavy shadowing effect. (2) \(\overline{\tau}_{Bj}\rightarrow\infty\) and \(\overline{\tau}_{Ej}\rightarrow\infty\), that a scenario where both the receiver and the eavesdropper can be closer to the transmitter, namely both the wiretap channel and main channel are equipped with better SNR. ST is also one of the indicators to verify the secrecy performance of the considered system. Finally, the secrecy performance can be expressed by the high SNR slope, the secrecy diversity gain and coding gain. In the section, for \(\overline{\gamma}_{Bj}\) and \(\overline{\gamma}_{Ej}\), \(j\in(1,2)\) represent MRC/MRT-SC, MRC-ZFB/MRT-SC-ZFB, respectively. 1.1 Scenario I: \(\overline{\gamma}_{Bj}\rightarrow\infty\) and Fixed \(\overline{\gamma}_{Ej}\)  
In this scenario, \(P_{out}\left(R_{S}\right)\) is approximated as  
\[P_{out}\left(R_{S}\right)\approx\Delta_{\theta^{\prime}\mathcal{T}_{B}}^{- \min\left(N_{R},N_{R}N_{B}\right)}, \tag{47}\]  
and \(\Delta_{\theta}\) is given by  
\[\Delta_{\theta}=\left\{ \begin{array}{cc}\Delta_{1},&N_{B}\
eq 1\\ \Delta_{1}+\Delta_{2},&N_{B}=1,\end{array} \right. \tag{48}\]  
where \(\Delta_{1}\) and \(\Delta_{2}\) represent the first phase and second phase of the MRC/MRT-SC and MRC-ZFB/MRT-SC-ZFB schemes, respectively. _(1) MRC/MRT-SC scheme:_  
**Corollary 1**. : _The asymptotic SOP of the different time-slots with MRC/MRT-SC scheme under \(\overline{\gamma}_{B1}\rightarrow\infty\) and fixed \(\overline{\gamma}_{E1}\) is given by_  
\[ \begin{split}\Delta_{1}&=\sum_{q=0}^{N_{R}}\left( \begin{array}{c}N_{R}\\ q\end{array}\right)\left(2^{R_{S}}-1\right)^{N_{R}-q}\left(2^{R_{S}}\right)^{ q}q!\frac{1}{N_{R}!}(\gamma_{E1})^{q}\\ &\times\left[\left(1-\exp\left(-\frac{\mu}{\lambda_{AP}}\right) \right)+\left(\frac{\lambda_{AP}}{\mu}\right)^{N_{R}}\ \Gamma\left(N_{R}+1,\frac{\mu}{\lambda_{AP}}\right) \right],\end{split}  \tag{49}\]  
_and_  
\[ \begin{split}\Delta_{2}&=\sum_{j=0}^{N_{R}N_{B}} \left(\begin{array}{c}N_{R}N_{B}\\ j\end{array}\right)\left(2^{R_{S}}-1\right)^{N_{R}N_{B}-j}\!\!2^{R_{S}j}\! \left(\frac{1}{\overline{\gamma}_{E1}}\right)^{-j}\!\left(\frac{1}{N_{R}!} \right)^{N_{B}}j!\left[\left(1-\exp\left(-\frac{\mu}{\lambda_{RP}}\right) \right)\right.\\ &\left.+\!\left(\frac{1}{\mu}\right)^{N_{R}N_{B}}\Gamma\left(N_{R}N_{B }+1,\frac{\mu}{\lambda_{RP}}\right)\right]\left(\frac{1}{\epsilon}\right)^{N_ {R}N_{B}}.\end{split}  \tag{50}\]  
**Proof of Corollary 1. ** See Appendix C.  
_(2) MRC-ZFB/MRT-SC-ZFB scheme:_  
**Corollary 2**. : _The asymptotic SOP of the different phases with MRC-ZFB/MRT-SC-ZFB scheme under \(\overline{\gamma}_{B2}\rightarrow\infty\) and fixed \(\overline{\gamma}_{E2}\) is given by_  
\[ \begin{split}\Delta_{1}&=\frac{1}{N_{R}!}\left( \Xi 1+\Xi 2\right)\left[\left(1-\exp\left(-\frac{\mu}{\lambda_{AP}}\right) \right)\right.+\left(\frac{1}{\mu}\right)^{N_{R}}\!\left(\frac{1}{\lambda_{AP} }\right)^{-N_{R}}\!\!\Gamma\left(N_{R}+1,\frac{\mu}{\lambda_{AP}}\right)\right].\end{split}  \tag{51}\]  
_Then \(\Delta_{2}\) is given by_  
\[