## 3 Secrecy Outage Performance of SISO-CR-NOMA Network
: _The SOP of secondary users \(U_{1}\), \(U_{2}\) and \(U_{3}\) in the SISO-CR-NOMA network are expressed as_  
\[P_{U_{1}\_{sop}} =1-\sum_{n=1}^{N}\frac{\sigma^{2}\alpha_{1}\omega_{1}\tau\sqrt{1- \tau_{n}{}^{2}}}{\lambda_{\text{E}}2N[\alpha_{1}-(\alpha_{2}+\alpha_{3})v_{n 1}]^{2}}\left(\frac{e^{-A_{1}}}{P_{\text{t}}}\bigg{(}1-e^{-\frac{Q}{\lambda_{PD }P_{\text{t}}}}\bigg{)}-\frac{\Gamma\Big{(}2,\frac{Q}{P_{\text{t}}}\Big{(}A_{ 2}+\frac{1}{\lambda_{PD}}\Big{)}\Big{)}}{\lambda_{PD}Q\Big{(}A_{2}+\frac{1}{ \lambda_{PD}}\Big{)}^{2}}\right) \tag{18}\] \[P_{U_{2}\_{sop}} =1-\sum_{n=1}^{N}\frac{\sigma^{2}\alpha_{2}\omega_{2}\tau\sqrt{1 -\tau_{n}{}^{2}}}{\lambda_{\text{E}}2N[\alpha_{2}-\alpha_{3}v_{n2}]^{2}} \left(\frac{e^{-A_{3}}}{P_{\text{t}}}\bigg{(}1-e^{-\frac{Q}{\lambda_{PD}P_{ \text{t}}}}\bigg{)}+\frac{\Gamma\Big{(}2,\frac{Q}{P_{\text{t}}}\Big{(}A_{4}+ \frac{1}{\lambda_{PD}}\Big{)}\Big{)}}{\lambda_{PD}Q\Big{(}A_{4}+\frac{1}{ \lambda_{PD}}\Big{)}^{2}}\right)\] (19) \[P_{U_{3}\_{sop}} =1-\frac{\lambda_{U_{3}}}{\lambda_{\text{E}}\theta_{3}+\lambda_{ U_{3}}}\Bigg{[}\bigg{(}1-e^{-\frac{Q}{\lambda_{PD}P_{\text{t}}}}\bigg{)}e^{-\frac{ \sigma^{2}(\theta_{3}-1)}{\lambda_{U_{3}}P_{\text{t}}}}-\frac{\lambda_{U_{3}} \alpha_{3}Qe^{-\left(\frac{\sigma^{2}(\theta_{3}-1)}{\lambda_{U_{3}}P_{\text{ t}}}\right)}\frac{Q}{P_{\text{t}}}}{\lambda_{PD}\sigma^{2}(\theta_{3}-1)+ \lambda_{U_{3}}\alpha_{3}Q}\Bigg{]} \tag{20}\]  
_where \(\omega_{1}=\frac{1}{(\alpha_{2}+a_{3})\theta_{1}}-1<\frac{\alpha_{1}}{a_{2}+a_{3 }}\), \(\theta_{1}=2R_{1}^{\text{s}}\), \(\tau_{n}=\cos\Bigl{(}\frac{2n-1}{2N}\tau\Bigr{)}\
u_{n1}=\frac{\omega_{1}(\tau_{n }+1)}{2}\), \(\omega_{2}=\frac{a_{2}+a_{3}}{a_{3}\theta_{2}}-1<\frac{\alpha_{2}}{a_{3}}\), \(\theta_{2}=2R_{2}^{\text{s}}\), \(\
u_{n2}=\frac{\omega_{2}(\tau_{n}+1)}{\alpha_{2}R_{1}^{\text{s}}(a_{2}+a_{3 })v_{n1}}=\frac{\sigma^{2}v_{n1}}{\lambda_{\text{E}}P_{\text{s}1}(a_{1}-(a_{2 }+a_{3})v_{n1})}+\frac{\sigma^{2}(\theta_{1}v_{n1}+\theta_{1}-1)}{\lambda_{ U_{1}}P_{\text{s}1}(a_{1}-(a_{2}+a_{3})(\theta_{1}v_{n1}+\theta_{1}-1))}\), \(A_{2}=\frac{\sigma^{2}v_{n1}}{\lambda_{\text{E}}\mathcal{Q}[a_{1}-(a_{2}+a_{3})v _{n1}]}+\frac{\sigma^{2}(\theta_{1}v_{n1}+\theta_{1}-1)}{\lambda_{U_{1}} \mathcal{Q}[a_{1}-(a_{2}+a_{3})(\theta_{1}v_{n1}+\theta_{1}-1)]}\), \(A_{3}=\frac{\sigma^{2}v_{n2}}{\lambda_{\text{E}}P_{\text{t}}(a_{2}-a_{3}v_{n2}) }+\frac{\sigma^{2}(\theta_{2}v_{n2}+\theta_{2}-1)}{\lambda_{U_{1}}P_{\text{t}}[a_ {2}-a_{3}(\theta_{2}v_{n2}+\theta_{2}-1)]}\), \(A_{4}=\frac{\sigma^{2}v_{n2}}{\lambda_{\text{E}}Q(\alpha_{2}-a_{3}v_{n2})}+ \frac{\sigma^{2}(\theta_{1}v_{n2}+\theta_{2}-1)}{\lambda_{U_{1}}\mathcal{Q}[a_{2}-a _{3}(\theta_{2}v_{n2}+\theta_{2}-1)]}\). Proof. : Please see Appendix A. According to [26; 27], given the assumption that [PERSON]'s interest lies solely in the information of a particular user within the system, the probability of selecting said user is equal among all users, i.e., \(P=1/3\). However, BS lacks knowledge regarding which user [PERSON] intends to eavesdrop on. Therefore, the overall SOP of three secondary users in the CR-NOMA network can be expressed as  
\[P_{overall\_{sop}}=\frac{1}{3}\big{(}P_{U_{1}\_{sop}}+P_{U_{2}\_{sop}}+P_{U_{3}\_ {sop}}\big{)} \tag{21}\]  
Proof. : Please see Appendix B.