## 4 Secrecy Outage Performance of MISO-CR-NOMA Network
### The Maximum Channel Capacity Scheme
#### 4.1.1 max-\(U_{1}\)  
In this one, the \(i\)-th transmit antenna at the BS is selected such that the channel capacity of the BS-\(U_{1}\) is maximized, which means \(\gamma_{U_{1}}^{\text{M1}}=\underset{1\leq i\leq M}{\text{max}}\left\{\gamma_{ SiU_{1}}\right\}\), \(\gamma_{SiU_{1}}\) is the received instantaneous SINR at \(U_{1}\) from the \(i\)-th antenna at S, and the symbol \"M1\" represents max-\(U_{1}\). The CDF and PDF of \(\gamma_{SiU_{1}}\) correspond identically to Equations (10) and (14). Then, the CDF and PDF of \(\gamma_{U_{1}}^{\text{M1}}\) can be obtained as  
\[F_{\gamma_{U_{1}}^{\text{M1}}}(x)=\left(F_{\gamma_{U_{1}}}(x)\right)^{M}=\left\{ \begin{array}{ll}1+\sum\limits_{k=1}^{M}\left(\begin{array}{c}M\\ k\end{array}\right)(-1)^{k}e^{-\frac{k^{2}x}{\lambda_{U_{1}}\mathbb{E}[u_{1}-( \alpha_{2}+\alpha_{3})x]}},&x<\frac{a_{1}}{a_{2}+a_{3}}\\ 1,&x\geq\frac{a_{1}}{a_{2}+a_{3}}\end{array}\right. \tag{22}\]  
\[f_{\gamma_{U_{1}}^{\text{M1}}}(x)=\left\{\begin{array}{ll}\sum\limits_{k=1} ^{M}\left(\begin{array}{c}M\\ k\end{array}\right)(-1)^{k+1}\frac{k^{2}x}{\lambda_{U_{1}}\mathbb{E}[u_{1}-( \alpha_{2}+\alpha_{3})x]}e^{-\frac{k^{2}x}{\lambda_{U_{1}}\mathbb{E}[u_{1}-( \alpha_{2}+\alpha_{3})x]}},&x<\frac{a_{1}}{a_{2}+a_{3}}\\ 1,&x\geq\frac{a_{1}}{a_{2}+a_{3}}\end{array}\right. \tag{23}\]  
It is noteworthy that the selection of the \(i\)-th transmits antenna for \(U_{1}\) entails the random selection of a transmit antenna for \(U_{2}\), \(U_{3}\), PD, and E. As a result, the CDF and PDF of \(\gamma_{U_{2}}^{\text{M1}}\), \(\gamma_{U_{3}}^{\text{M1}}\) and \(\left|h_{PD}^{\text{M1}}\right|^{2}\) in this scenario are identical to those of the SISO-CR-NOMA network, i.e., (11)-(13) and (15)-(17), respectively. Similar to the derivation of the single-antenna case, we can obtain Theorem 2.  
**Theorem 2**.: _The SOP of secondary users \(U_{1}\), \(U_{2}\) and \(U_{3}\) with max-\(U_{1}\) of MCC scheme in the MISO-CR-NOMA network are expressed as_  
\[P_{U_{1},sp}^{\text{M1}}=1+\sum\limits_{k=1}^{M}\sum\limits_{n=1}^{N}\left( \begin{array}{c}M\\ k\end{array}\right)(-1)^{k}\frac{\sigma^{2}\alpha_{1}\omega_{1}\pi\sqrt{1- \tau_{n}{}^{2}}}{\lambda_{E}2N[\alpha_{1}-(\alpha_{2}+\alpha_{3})\
u_{n1}]^{2 }}\left(\frac{e^{-B_{1}}}{P_{t}}\left(1-e^{-\frac{Q}{\lambda_{PD}\
u_{1}}T} \right)+\frac{\Gamma\left(2,\frac{Q}{\lambda_{PD}}\left(B_{2}+\frac{1}{ \lambda_{PD}}\right)\right)}{\lambda_{PD}Q\left(B_{2}+\frac{1}{\lambda_{PD}} \right)^{2}}\right) \tag{24}\]  
\[P_{U_{2},sp}^{\text{M1}} =P_{U_{2},sp} \tag{25}\] \[P_{U_{3},sp}^{\text{M1}} =P_{U_{3},sp}\] (26) \[P_{overall,sp}^{\text{M1}} =\frac{1}{3}\left(P_{U_{1},sp}^{\text{M1}}+P_{U_{2},sp}^{\text{ M1}}+P_{U_{3},spp}^{\text{M1}}\right) \tag{27}\]where \(B_{1}=\frac{\rho^{2}\
u_{\alpha_{1}}}{\lambda_{L}P[\alpha_{1}-(\alpha_{2}+\alpha_ {3})\
u_{\alpha}]}\ +\ \frac{k\
u^{2}(\theta_{1}\
u_{\alpha}+\theta_{1}-1)}{\lambda_{U_{1}}P[ \alpha_{1}-(\alpha_{2}+\alpha_{3})(\theta_{1}\
u_{\alpha}+\theta_{1}-1)]},\ \ \ B_{2}=\frac{e^{2 }\
u_{\alpha_{1}}}{\lambda_{L}Q[\alpha_{1}-(\alpha_{2}+\alpha_{3})v_{\alpha}]} \ +\ \frac{k\
u^{2}(\theta_{1}\
u_{\alpha}+\theta_{1}-1)}{\lambda_{U_{1}}Q[ \alpha_{1}-(\alpha_{2}+\alpha_{3})(\theta_{1}\
u_{\alpha}+\theta_{1}-1)]}.\)