## 4 Secrecy Outage Performance of MISO-CR-NOMA Network
### The Space-Time Transmission Scheme  
First, BS uses space-time coding [15] technology to encode the secondary user signal. All antennas of BS participate in signal coding and send the signal to the secondary users receiving node. To ensure the QoS of PD, the total transmit power of all antennas are limited to \(P_{s}\). To simplify the calculation, consider the equal power distribution method, and assume that the transmitting power of each antenna of BS is \(P_{s}/M\)[16]. The CDF of \(\gamma_{C_{ij}}^{ST}\) (\(G\in\{U,E\}\,j=1,2,3\)) and \(\left|h_{PD}^{ST}\right|^{2}\) are expressed as \[F^{\text{ST}}_{\gamma_{C_{1}}}(x) =\left\{ \begin{array}{ll}1+\sum\limits_{k=1}^{M}\left(\begin{array} []{c}M\\ k\end{array}\right)(-1)^{k}e^{-\frac{\lambda\text{M}^{2}x}{\lambda_{C_{1}}P_{ \text{\tiny{$\left|{1-(2+\alpha_{3})}\right|}^{2}}}}},&x<\frac{a_{1}}{a_{2}+a_ {3}}\\ 1,&x\geq\frac{a_{1}}{a_{2}+a_{3}}\end{array} \right. \tag{36}\] \[F^{\text{ST}}_{\gamma_{C_{2}}}(x) =\left\{ \begin{array}{ll}1+\sum\limits_{k=1}^{M}(-1)^{k}\left( \begin{array}{c}M\\ k\end{array}\right)e^{-\frac{\lambda\text{M}^{2}x}{\lambda_{C_{2}}P_{\text{ \tiny{$\left|{2-\alpha_{3}}\right|}^{2}}}}},&x<\frac{a_{2}}{a_{3}}\\ 1,&x\geq\frac{a_{2}}{a_{3}}\end{array} \right.\] (37) \[F^{\text{ST}}_{\gamma_{C_{3}}}(x) =1+\sum\limits_{k=1}^{M}(-1)^{k}\left( \begin{array}{c}M\\ k\end{array} \right)e^{-\frac{\lambda\text{M}^{2}x}{\lambda_{C_{3}}P_{\text{ \tiny{$\left|{3}}\right|}^{2}}}}\] (38) \[F^{\text{ST}}_{\left|h_{PD}\right|^{2}}(x) =1+\sum\limits_{k=1}^{M}(-1)^{k}\left( \begin{array}{c}M\\ k\end{array} \right)e^{-\frac{\lambda\text{M}}{NDD}}\] (39) \[f^{\text{ST}}_{\gamma_{C_{1}}}(x) =\left\{ \begin{array}{ll}\sum\limits_{k=1}^{M}(-1)^{k}\left( \begin{array}{c}M\\ k\end{array}\right)\frac{k\lambda\text{M}^{2}a_{1}a^{2}}{\lambda_{C_{1}}P_{ \text{\tiny{$\left|{1-(2+\alpha_{3})}\right|}^{2}}}}e^{-\frac{\lambda\text{M} ^{2}x}{\lambda_{C_{1}}P_{\text{\tiny{$\left|{1-(2+\alpha_{3})}\right|}^{2}}}}},&x<\frac{a_{1}}{a_{2}+a_{3}}\\ 0,&x\geq\frac{a_{1}}{a_{2}+a_{3}}\end{array} \right.\] (40) \[f^{\text{ST}}_{\gamma_{C_{2}}}(x) =\left\{ \begin{array}{ll}\sum\limits_{k=1}^{M}\left(\begin{array} []{c}M\\ k\end{array}\right)(-1)^{k+1}\frac{k\lambda\text{M}^{2}a_{2}a^{2}}{\lambda_{C_{ 2}}P_{\text{\tiny{$\left|{2-\alpha_{3}}\right|}^{2}}}}e^{-\frac{\lambda\text{M }^{2}x}{\lambda_{C_{2}}P_{\text{\tiny{$\left|{2-\alpha_{3}}\right|}^{2}}}}},&x< \frac{a_{2}}{a_{3}}\\ 0,&x\geq\frac{a_{2}}{a_{3}}\end{array} \right.\] (41) \[f^{\text{ST}}_{\gamma_{C_{3}}}(x) =\sum\limits_{k=1}^{M}(-1)^{k}\left( \begin{array}{c}M\\ k\end{array} \right)\frac{k\lambda\text{M}^{2}a^{2}}{\lambda_{C_{3}}a_{3}P_{ \text{\tiny{$\left|{3}}\right|}^{2}}}e^{-\frac{\lambda\text{M}^{2}x}{\lambda_ {C_{3}}P_{\text{\tiny{$\left|{3}}\right|}^{2}}}}\] (42) \[f^{\text{ST}}_{\left|h_{PD}\right|^{2}}(x) =\sum\limits_{k=1}^{M}(-1)^{k+1}\left( \begin{array}{c}M\\ k\end{array} \right)\frac{k}{\lambda_{PD}}e^{-\frac{\lambda\text{M}}{NDD}} \tag{43}\]  
Similar to the derivation of the SOP with MCC scheme, we can obtain Theorem 3. Theorem 3: _The SOP of secondary users \(U_{1}\), \(U_{2}\) and \(U_{3}\) with ST scheme in the MISO-CR-NOMA network are expressed as_  
\[ \begin{split} P^{\text{ST}}_{U_{1}\_{\text{-}}sp}=& 1+\sum\limits_{k=1}^{M}\sum\limits_{s=1}^{M}\sum\limits_{l=1}^{M}\sum\limits_{n= 1}^{N}\left(\begin{array}{c}M\\ k\end{array}\right)\left(\begin{array}{c}M\\ s\end{array}\right)\left(\begin{array}{c}M\\ l\end{array}\right)(-1)^{k+s+l}\\ &\times\frac{s\sigma^{2}\alpha_{1}\omega_{1}\pi M\sqrt{1-{\tau_{ \text{\tiny{$\left|{2}\right|}^{2}}}}}}{\lambda_{E}2N[\alpha_{1}-(\alpha_{2}+ \alpha_{3})\
u_{1}]}\left(\frac{e^{-C_{1}}}{P_{t}}\left(1-e^{-\frac{lQ}{ \lambda_{PD}P_{t}}}\right)+\frac{\Gamma\left(2,\frac{Q}{P_{t}}\left(C_{4}+ \frac{l}{\lambda_{PD}}\right)\right)}{\lambda_{PD}Q\left(C_{2}+\frac{l}{ \lambda_{PD}}\right)^{2}}\right)\end{split} \] (44) \[