## 2 System Model  
We consider a V2X-NOMA depicted as in Figure 1. The CR architecture provides the downlink of secondary network from the base station (BS) to vehicles \(D_{1},D_{2}\) under the support of many RSUs. The secondary network containing the BS and RSU can share the spectrum with the primary network without disturbing its normal communication. However, the BS can access the spectrum only when the primary network does not occupy that spectrum and such situation is associated with spectrum sensing. The RSUs are able to harvest wireless energy from the BS, shown in Figure 1. In the traditional scheme, the RSU directly transmits data to the vehicle; however, degraded performance occurs since vehicles move to several locations with a weak received signal. In this paper, the best RSU can be selected to serve the downlink. We denote \(h_{SR_{k}}\) as the channel from the BS to \(k\)-th RSU. It is assumed that the primary and secondary networks employ channels with independent, flat, and block Rayleigh fading. This means that the system state will independently vary in different time slots and keep invariance in one time slot. The channel from the RSU to the primary receiver and the secondary vehicles are denoted by \(\left|h_{R_{k}P}\right|^{2}\) and \(\left|h_{R_{k}D_{1}}\right|^{2}\), respectively. The channel \(h_{ab}\) for link from node \(a\) to node \(b\) follows an exponential distribution with parameters \(\Omega_{ab}\). To guarantee the operation of the considered network, the BS is required to opportunistically serve the vehicles with respect to securing the primary user's QoS. The transmission procedure is occurred within two epochs in the considered system. In the first epoch, the BS sends the superimposed signal to the RSU node. To keep stable performance of the primary receiver, the transmission power of the  
Figure 1: The model of the V2X-NOMA system. BS is controlled. The interference power at the primary user is not allowed to exceed the maximum tolerable power level \(I\), and, therefore, the power of the BS should satisfy  
\[P_{S}=\min\left\{P,\frac{I}{\left|h_{SP}\right|^{2}}\right\} \tag{1}\]  
where \(P\) is the maximum transmission power of source in the primary network. It is worth noting that the interference from the primary network induces worse performance on the secondary network. Fortunately, interference can be reduced by adjusting an interference guard zone to each secondary user with a radius. This means that the interference from the primary network is dominated by the large scale path-loss. As a result, the interference from the primary network can be neglected for large distances [37]. NOMA signal at the BS, \(x_{1},x_{2}\) are message signals dedicated to the first vehicle \(V_{1}\) and the second vehicle \(V_{2}\) and the corresponding power allocations are \(a_{1},a_{2}\) with the constraint of \(a_{1}>a_{2},a_{1}+a_{2}=1\). Regarding energy harvesting in terms of SWIPT, \(\rho\) is the power splitting factor in the power splitting based relaying protocol (\(0<\rho<1\)). It means that \(P_{S}\left(1-\rho\right)\) corresponds to the power for signal processing from the BS to the RSU. Therefore, the received signal at the selected RSU is given by  
\[y_{R}=\left(\sqrt{a_{1}}x_{1}+\sqrt{a_{2}}x_{2}\right)\sqrt{P_{S}\left(1-\rho \right)h_{SR_{k}}}+n_{R}, \tag{2}\]  
where \(n_{R}\) stands for the additive white Gaussian noise (AWGN), and it follows \(\omega\sim\mathcal{CN}\left(0,1\right)\). \(h_{SR}\) is the gain of channel from the \(BS\) to \(k\)-th RSU. At the RSU, \(x_{1},x_{2}\) need to be decoded before forwarding to distant vehicles. As the assumption above, \(a_{1}>a_{2}\) condition means that \(x_{1}\) is decoded firstly, then subtracting \(x_{1}\) from the received mixture signal to detect signal \(x_{2}\) thanks to SIC.