## 2 System Model
The signal-to-interference plus noise ratio (SINR), and signal-to-noise ratio (SNR) of the signal \(x_{1},x_{2}\), respectively, at the RSU can be formulated by  
\[\gamma_{x_{1}}=\frac{a_{1}P_{S}\left(1-\rho\right)\left|h_{SR_{k}}\right|^{2} }{a_{2}P_{S}\left(1-\rho\right)\left|h_{SR_{k}}\right|^{2}+1}. \tag{3}\]  
It is assumed that SIC is an ideal operation under the situation that several appropriate interference management techniques are included. We also consider imperfect SIC in other work. Due to perfect SIC, \(x_{2}\) can be detected through the SNR below  
\[\gamma_{x_{2}}=a_{2}P_{S}\left(1-\rho\right)\left|h_{SR_{k}}\right|^{2}. \tag{4}\]  
**Remark 1**. : _In this system model, the transmission power at the RSU is able to be achieved once energy harvesting is enabled and signal detection is performed successfully at the RSU as well. Therefore, the transmission power levels for two signals \(x_{1},x_{2}\) at the RSU are determined under the condition of successful detection of these signals \(x_{1},x_{2}\). Then, we denote \(P_{iR},i=1,2\) as transmission power at the RSU serving the first link and second link to \(D_{1},D_{2}\), respectively._  
In the second phase, it is assumed that signals can be forwarded with new power allocation factors. To simplicity in notation, these factors are also \(a_{1},a_{2}\). Thus, the received signal at each vehicle \(D_{i}\) can be expressed as  
\[y_{Di}=\sqrt{P_{iR}}h_{R_{k}D_{i}}\left(\sqrt{a_{1}}x_{1}+\sqrt{a_{2}}x_{2} \right)+n_{Di}, \tag{5}\]  
where \(n_{Di}\) represents AWGN at each receiving vehicle. \(P_{1R}\) is transmission power at the RSU serving to \(D_{1}\) and \(P_{2R}\) is transmission power at the RSU serving to \(D_{2}\). The SINR at the vehicle \(V_{1}\) when detecting the signal \(x_{1}\) can be given as  
\[\gamma_{D,x_{1}}=\frac{a_{1}P_{R}\big{|}h_{R_{k}D_{1}}\big{|}^{2}}{a_{2}P_{1R} \big{|}h_{R_{k}D_{1}}\big{|}^{2}+1} \tag{6}\]  
The SNR at \(D_{2}\) when detecting the signal \(x_{2}\) after performing SIC. It can be given as  
\[\gamma_{D,x_{2}}=a_{2}P_{R}\big{|}h_{R_{k}D_{2}}\big{|}^{2} \tag{7}\]  
where \(P_{R}\) is the transmission power at \(R\). The selection criterion of channel is considered to decide the best RSU. Then, the best RSU is used to forward the signal to a dedicated vehicle. The index of the RSU and corresponding channel gain are determined respectively by  
\[ \begin{array}{c}k^{*}=\begin{array}{c}\arg\\ \end{array}\max\limits_{k=1,\ldots,K}\quad\big{|}h_{SR_{k}}\big{|}^{2},\\ \big{|}h_{SR_{k^{*}}}\big{|}^{2}=\begin{array}{c}\max\limits_{k=1,\ldots,K} \quad\big{|}h_{SR_{k}}\big{|}^{2}\end{array}\end{array}  \tag{8}\]  
The CDF and PDF of such selected channel are formulated respectively from [38]  
\[ \begin{array}{c}F_{\big{|}h_{SR_{k}}\big{|}^{2}}\left(x\right)=\left(1-e^{- \frac{x}{\alpha_{SR}}}\right)^{K}\\ =1-\sum\limits_{k=1}^{K}\left(\begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\left(\mathrm{e}^{-\frac{\mathrm{H}x}{\Omega_{SR} }}\right),\\ \\ f_{\big{|}h_{SR_{k^{*}}}\big{|}^{2}}\left(x\right)=K\sum\limits_{k=0}^{K-1} \left(\begin{array}{c}K-1\\ k\end{array}\right)\frac{(-1)^{k}}{\Omega_{SR_{k}}}\exp\left(-\frac{\left(k+1 \right)x}{\Omega_{SR_{k}}}\right)\end{array}  \tag{9}\]