## 3 Secrecy Outage Performance of SISO-CR-NOMA Network  
In this section, we consider the circumstance of the SISO-CR-NOMA network, i.e., \(M=1\), the BS is equipped with one antenna. The SOP results obtained in this section can replace many complex expressions in the MISO network, which is easier to understand more intuitively, and it can be used as a benchmark for comparison, making it easier to understand the secrecy outage performance improvement brought by TAS schemes. First, we explain the secrecy capacity and SOP, then derive the exact closed-form of the secondary user's SOP in the SISO-CR-NOMA network. Secrecy capacity can be defined as the disparity between the channel capacity of the BS-User transmission link and the BS-E eavesdropping link [14]. Therefore, the secrecy capacity of \(U_{j}\) is  
\[C_{s_{j}}=\Big{[}C_{j}-C_{E_{j}}\Big{]}^{+} \tag{8}\]  
where \([t]^{+}=\max\{t,0\}\), \(C_{j}=\log_{2}\Big{(}1+\gamma_{U_{j}}\Big{)}\), \(C_{E_{j}}=\log_{2}\Big{(}1+\gamma_{E_{j}}\Big{)}\). SOP is defined as the probability that secrecy capacity is less than the secrecy communication rate [16]. The SOP of \(U_{j}\) can be expressed as  
\[P_{U_{j}\_{SOP}}=\Pr\Big{[}C_{s_{j}}\leq R_{j}^{s}\Big{]} \tag{9}\]  
where \(R_{j}^{s}\) is the secrecy communication rate of \(U_{j}\). In order to derive the SOP of \(U_{j}\), we first need to obtain the cumulative distribution function (CDF) of \(\gamma_{U_{j}}\), \(\gamma_{E_{j}}\), and BS-PD interference channel gain \(\left|h_{PD}\right|^{2}\), the CDF of \(\gamma_{G_{j}}(G\in\{U,\text{E}\},\,j=1,2,3)\) and \(\left|h_{PD}\right|^{2}\) expressed as  
\[F_{\gamma_{G_{1}}}(x) = \left\{ \begin{array}{ll}1-e^{-\frac{\sigma^{2}x}{\lambda_{G_{1} }P_{S}\big{|}h_{1}-(\alpha_{2}+\alpha_{3})\big{|}}},&x<\frac{a_{1}}{a_{2}+a_{3} }\\ 1,&x\geq\frac{a_{1}}{a_{2}+a_{3}}\end{array} \right. \tag{10}\] \[F_{\gamma_{G_{2}}}(x) = \left\{ \begin{array}{ll}1-e^{-\frac{\sigma^{2}x}{\lambda_{G_{2} }P_{S}\big{|}h_{2}-a_{3}\big{|}}},&x<\frac{a_{2}}{a_{3}}\\ 1,&x\geq\frac{a_{2}}{a_{3}}\end{array} \right.\] (11) \[F_{\gamma_{G_{3}}}(x) = 1-e^{-\frac{\sigma^{2}x}{\lambda_{G_{3}}a_{3}}}\] (12) \[F_{|h_{PD}|^{2}}(x) = 1-e^{-\frac{\tau}{\lambda_{PD}}} \tag{13}\]By deriving the CDF above (10)-(13), the probability density function (PDF) of the variable \(\gamma_{\text{G}_{j}}\) and \(|h_{PD}|^{2}\) can be obtained, respectively. \[f_{\gamma_{\text{G}_{1}}}(x) =\left\{ \begin{array}{ll}\frac{a_{1}\omega^{2}}{\lambda_{\text{G }_{1}}P_{\text{s}}[a_{1}-(a_{2}+a_{3})x]^{2}}e^{-\frac{\sigma^{2}x}{\lambda_{ \text{G}_{1}}P_{\text{s}}[a_{1}-(a_{2}+a_{3})x]}},&x<\frac{a_{1}}{a_{2}+a_{3}} \\ 0,&x\geq\frac{a_{1}}{a_{2}+a_{3}}\end{array} \right. \tag{14}\] \[f_{\gamma_{\text{G}_{2}}}(x) =\left\{ \begin{array}{ll}\frac{a_{2}\sigma^{2}}{\lambda_{\text{G }_{2}}P_{\text{s}}(a_{2}-a_{3}x)^{2}}e^{-\frac{\sigma^{2}x}{\lambda_{\text{G}_ {2}}P_{\text{s}}(a_{2}-a_{3}x)}},&x<\frac{a_{2}}{a_{3}}\\ 0,&x\geq\frac{a_{2}}{a_{3}}\end{array} \right.\] (15) \[f_{\gamma_{\text{G}_{3}}}(x) =\frac{\sigma^{2}}{\lambda_{\text{G}_{3}}P_{\text{s}}}e^{-\frac{ \sigma^{2}x}{\lambda_{\text{G}_{3}}P_{\text{s}}}}\] (16) \[f_{|h_{PD}|^{2}}(x) =\frac{1}{\lambda_{PD}}e^{-\frac{x}{\lambda_{PD}}} \tag{17}\]  
Substituting the above CDF and PDF into Equations (8) and (9), the following conclusions can be obtained:  
**Theorem 1**.