## 2 System Model  
Based on Figure 1, we contemplate a downlink CR-NOMA network including a secondary base station (BS), a primary user (PD), a set of secondary users: \(U_{1}\) (the farthest user), \(U_{2}\) (the remote user) and \(U_{3}\) (the near user), a passive eavesdropper (E). Because BS has strong computing power and volume, we assume that BS is equipped with \(M\)-antennas; instead, PD, \(U_{1}\), \(U_{2}\), \(U_{3}\) and E are equipped with a single antenna because of their limited spatial and power consumption. The model is founded on the following assumptions, which are without loss of generality:  
1. Considering the channel from BS to the \(D\), where \(D\in\{\mathrm{PD},U_{1},U_{2},U_{3},\mathrm{E}\}\), let \(\bar{h}_{SD}\) and \(L_{SD}\) represent the small-scale fading and large-scale path-loss of the BS\(\rightarrow\)\(D\), channel. It is assumed that all channels are independent of each other and exhibit Rayleigh block flat fading. Therefore, the channel gain of small-scale fading (\(|\bar{h}_{D}|^{2}\)) follows independent exponential distribution with the mean of \(\tilde{\lambda}_{D}\). The model of large-scale fading is \(L_{D}=\mathrm{L}(d_{D}/d_{0})^{-\kappa}\), where L means the path-loss constant, \(d_{D}\) represents the distance between BS and \(D\), \(d_{0}\) means the reference distance, and \(\kappa\) means the path-loss exponent. To simplify symbols, we refer to the modeling of [24], let \(h_{D}\triangleq\bar{h}_{D}L_{D}\), \(\left|\bar{h}_{D}\right|^{2}\) follows an exponential distribution with unit mean. Consequently, the channel coefficient \(\left|h_{D}\right|^{2}\) follows an independent exponential distribution with the mean of \(\lambda_{D}=\mathrm{L}(d_{D}/d_{0})^{-\kappa}\). 2. All channels are subjected to an additive white Gaussian noise (AWGN) characterized by a zero mean and a variance of \(\sigma_{1}^{2}\). In line with [25], we consider the absence of channel state information (CSI) of the primary base station (PBS) at the secondary users. Consequently, owing to the Central Limit Theorem, we can regard the interference resulting from PBS as AWGN having a zero mean and a variance of \(\sigma_{p}^{2}\). To simplify symbols, let \(\sigma^{2}\stackrel{{\Delta}}{{=}}\sigma_{1}^{2}+\sigma_{p}^{2}\). In this network, the superimposed signal sent by BS in NOMA mode is  
\[x_{BS}=\sqrt{\alpha_{1}}x_{1}+\sqrt{\alpha_{2}}x_{2}+\sqrt{\alpha_{3}}x_{3} \tag{1}\]  
where \(x_{1}\), \(x_{2}\) and \(x_{3}\) represents the signals sent by BS to secondary users \(U_{1}\), \(U_{2}\) and \(U_{3}\), respectively. \(\alpha_{1}\), \(\alpha_{2}\) and \(\alpha_{3}\) are power distribution coefficients (\(\alpha_{1}+\alpha_{2}+\alpha_{3}=1\)). According to the NOMA transmission principle, since the distance from \(U_{3}\) to BS is closer than \(U_{2}\) to BS, \(U_{2}\) is also closer than \(U_{1}\), and it is assumed that \(\alpha_{1}>\alpha_{2}>\alpha_{3}\). When BS sends signals to secondary users, the signal received by secondary users \(U_{j}(j=1,2,3)\) can be expressed as  
\[y_{U_{j}} = h_{U_{j}}P_{s}(\sqrt{\alpha_{1}}x_{1}+\sqrt{\alpha_{2}}x_{2}+ \sqrt{\alpha_{3}}x_{3})+z_{U_{j}} \tag{2}\]  
where \(h_{U_{j}}\) is the channel coefficient from BS to \(U_{j}\) link, \(P_{s}\) is BS transmit power, and \(z_{U_{j}}\) is AWGN with the variance of \(\sigma^{2}\). In order to ensure the QoS of the primary user, we consider the transmit power \(P_{s}\) of the BS to be constrained by both BS peak transmission power and peak interference power, which is expressed as  
\[P_{s} = \left\{ \begin{array}{cc}P_{t},&|h_{PD}|^{2}\leq\frac{Q}{K}\\ \frac{Q}{|h_{PD}|^{2}},&|h_{PD}|^{2}>\frac{Q}{P_{t}}\end{array} \right. \tag{3}\]  
where \(P_{t}\) is BS peak transmission power, \(Q\) is interference temperature, and \(|h_{PD}|^{2}\) indicates the interference channel gain between BS to PD. Firstly, we describe the signal-to-interference-plus-noise ratio (SINR) and signal-to-noise ratio (SNR) at \(U_{j}\) and E according to successive interference cancellation (SIC) technology. 1.