## 3 Secrecy Performance Analysis
### MRC-ZFB/MRT-SC-ZFB with FD Scenario
By using MRC-ZFB scheme we can calculate the CDF of \(\gamma_{AR,2}\), which can be derived as  
\[ \begin{split} F_{\gamma_{1}^{MRC-ZFB}}\left(R_{S}\right)& =1-\sum_{k=0}^{N_{R}-1}\frac{1}{k!}\left(\frac{1}{\bar{\gamma}_{B}} \right)^{k}\sum_{i=0}^{k}\left(\begin{array}{c}k\\ i\end{array}\right)\left(2^{R_{S}}-1\right)^{k-i}2^{iR_{S}}\left(\frac{\bar{ \gamma}_{E}}{\bar{\gamma}_{I}}\right)^{i}\Gamma\left(i+1\right)\\ &\times\left[\frac{1}{\bar{\gamma}_{I}}\Psi\left(i+1,4+i-N_{B}, \frac{2^{R_{S}}\bar{\gamma}_{E}+\bar{\gamma}_{B}}{\bar{\gamma}_{B}\bar{\gamma}_ {I}}\right)\right.\left.+\left(N_{B}-2\right)\right.\\ &\times\left.\Psi\left(i+1,3+i-N_{B},\frac{2^{R_{S}}\bar{\gamma}_{E}+ \bar{\gamma}_{B}}{\bar{\gamma}_{B}\bar{\gamma}_{I}}\right)\right]\left[\exp \left(-\frac{\left(2^{R_{S}}-1\right)}{\bar{\gamma}_{B}}\right)\\ &+\frac{\mu}{\lambda_{AP}}\left(\frac{\left(2^{R_{S}}-1\right) \lambda_{AP}+\mu\bar{\gamma}_{B}}{\bar{\gamma}_{B}\lambda_{AP}}\right)^{- \left(k-i+1\right)}\left(1-\exp\left(-\frac{\mu}{\lambda_{AP}}\right)\right) \\ &\times\left.\Gamma\left(k-i+1,\frac{\left(2^{R_{S}}-1\right) \lambda_{AP}+\mu\bar{\gamma}_{B}}{\bar{\gamma}_{B}\lambda_{AP}}\right)\right]. \end{split}  \tag{44}\]In this phase, the proof process of \(F_{\gamma_{1}^{MARC-ZFB}}\left(R_{S}\right)\) for the MRC-ZFB scheme is similar with _Theorem_**1**, and will not be elaborated here. For MRT-SC-ZFB phase, observing from (12) and (13), and by making use of [12], conditional CDF of \(\gamma_{RB,2}\) and conditional PDF of \(\gamma_{RE,2}\) are respectively presented as \(F_{\gamma_{RB,2}}\left(y|G_{1}\right)\) and \(f_{\gamma_{RE,2}}(y|G_{1})\). These processes are similar to (33) and (38). By replacing \(\gamma_{RB,1}\) with \(\gamma_{RB,2}\), which also satisfies the condition of \(\Theta_{N_{R},i}\), \(n_{0}\), \(n_{N_{R}}\) and \(\phi\) in (33). In (38), \(G\to G_{1}\), \(P_{S}\to P_{R}\) and \(\lambda_{AE}\to\lambda_{RE}\). Then, substituting \(F_{\gamma_{RB,2}}\left(y|G_{1}\right)\) and \(f_{\gamma_{RE,2}}(y|G_{1})\) into (15), the conditional \(F_{RB,2}\left(R_{S}|G_{1}\right)\) is written as  
\[ \begin{split} F_{RB,2}\left(R_{S}|G_{1}\right)&= \int_{0}^{\infty}F_{\gamma_{RB,2}}\left(2^{R_{S}}\left(1+y\right)-1\right)f_{ \gamma_{RE,2}}\left(y\right)dy\\ &=\sum_{i=0}^{N_{R}}\binom{N_{B}}{i}(-1)^{i}\exp\left(-\frac{i \left(2^{R_{S}}-1\right)\sigma_{B}^{2}}{P_{S}\lambda_{RB}}\right)\Theta_{N_{ R},i}\bigg{(}\frac{\sigma_{B}^{2}}{P_{S}\lambda_{RB}}\bigg{)}^{\phi}\sum_{j=0}^{ \phi}\left(\begin{array}{c}\phi\\ j\end{array}\right)\\ &\times\left(2^{R_{S}}-1\right)^{\phi-j}\bigg{(}\frac{P_{S}\lambda_{ RE}}{P_{j}\lambda_{JE}}\bigg{)}^{j}\Gamma\left(j+1\right)2^{R_{S}}\left[\Psi \left(j+1,j+4-N_{B},\frac{i2^{R_{S}}P_{S}\lambda_{RE}+P_{S}\lambda_{RB}}{P_{S }\lambda_{RB}P_{J}\lambda_{JE}}\right)\right.\\ &\times\left.\frac{\sigma^{2}}{P_{j}\lambda_{JE}}+\left(N_{B}-2\right)\Psi \left(j+1,j+3-N_{B},\frac{i2^{R_{S}}P_{S}\lambda_{RE}+P_{S}\lambda_{RB}}{P_{ S}\lambda_{RB}P_{J}\lambda_{JE}}\right)\right].\end{split}  \tag{45}\]  
Thus, by using (45) and \(f_{G_{1}}\left(g\right)\), we can write the CDF of \(\gamma_{RB,2}\) for the MRT-SC-ZFB scheme with the FD mechanism in the following theorem. By using MRT-SC-ZFB scheme we can calculate the CDF of \(\gamma_{RB,2}\), which can be derived as  
\[