## 2 System Model and Problem Formulation
### Problem Description  
Assuming all links are independent block fading channels, CSI can be approximately constant in each time interval. At the beginning of each time interval, CUEs use uplink resources to report the cellular link CSI to the BS. For the VUEs, during the V2V discovery phase, the receiving end of VUEs reports the CSI of the vehicle link to the BS using uplink resources. However, due to the Doppler effect brought about by the high mobility of vehicles, the vehicle link will undergo rapid changes in small-scale fading. In this case, if CSI is continuously updated to the BS, it will result in high signaling overhead [48]. Therefore, the system model in this article only considers large-scale fading to reduce the network overhead. In addition, this article assumes that the vehicle speeds are all the same, so the Doppler effect between vehicles can be ignored. We define VUEi as the \(i\)-th VUE; similarly, CUEj is the \(j\)-th CUE.  
We define \(a_{j,i}^{v}\) as the channel power gain of the interference link between the transmitting end of CUEj and the receiving end of VUEi on the \(v\)-th subcarrier, represented as  
\[a_{j,i}^{v}=A\delta_{j,i}dis_{j,i}^{-\omega}, \tag{1}\]  
In the equation, \(A\) is the path loss constant, with \(\delta_{j,i}\) representing the shadow fading between VUEi and CUEj. This shadow fading follows a lognormal distribution. The parameter \(dis_{j,i}\) is the distance between the receiving end of VUEi and the transmitting end of CUEj, and \(\omega\) is the path loss index. Additionally, \(a_{j}^{v}\) is defined as the communication link channel power gain from CUEj to the BS, \(a_{i}^{v}\) is the channel power gain of the communication link of VUEi, \(a_{i,D}^{v}\) is the interference channel power gain from VUEi sharing subcarrier \(v\) to the BS, and \(a_{j,i}^{v}\) is the interference channel power gain between the transmitting end of VUEi\({}^{\prime}\) and the receiving end of VUEi sharing subcarrier \(v\).  
The signal-to-interference plus noise ratio (SINR) of VUEi is represented as  
\[\psi_{i}^{v}=\frac{W_{i}^{v}a_{i}^{v}}{\theta^{2}+\sum_{i^{\prime},i^{\prime},i}^{X}C_{i^{\prime}}^{v}W_{i}^{v}a_{i^{\prime},j}^{v}+\sum_{j}^{Y}C_{j}^{v} W_{j}^{v}a_{j,i}^{v}}, \tag{2}\]  
\(W_{j}^{v}\) represents the transmission power of VUEi on the v-th subcarrier. \(C_{i^{\prime}}^{v}\) represents the binary variable that represents the mapping relationship between the subcarrier \(v\) and VUEi\({}^{\prime}\). If VUEi\({}^{\prime}\) allows the use of the subcarrier \(v\), then \(C_{i^{\prime}}^{v}=1\); otherwise \(C_{i^{\prime}}^{v}=0\). \(\theta^{2}\) is the variance of zero mean Gaussian noise. Since a subcarrier is allowed to be used by multiple VUEs, therefore, interference to VUEi includes other VUEs and CUE using the subcarrier \(v\).  
The SINR of CUEj is represented as  
\[\psi_{j}^{v}=\frac{W_{j}^{v}a_{j}^{v}}{\theta^{2}+\sum_{i}^{X}C_{i}^{v}W_{i}^ {v}a_{i,D}^{v}}\, \tag{3}\]  
In the formula, we represent the SINR of CUEj when using the \(v\)-th subcarrier, where \(W_{j}^{v}\) represents the transmission power of CUEj on the \(v\)-th subcarrier. Due to the orthogonal spectral resources between CUEs, the interference to CUEs is only caused by VUEs that jointly use the subcarrier \(v\).