## 3 Outage Performance Analysis  
### Outage Probability of \(\mathrm{D_{1}}\)  
In this section, the outage performance of each vehicle is investigated. It is equivalent to the probability of successful detection of signal \(x_{1},x_{2}\) at these vehicles. In principle, the outage probability of a signal is defined as the probability that the achievable rate is below a threshold target rate. We denote \(R_{1},R_{2}\) as a target rate for D1, D2, respectively. Such an outage probability for D1 is given by  
\[P_{out\_D1}=\underbrace{\Pr\left\{P_{S}\big{|}h_{SR_{k}}\big{|}^{2}<\delta \right\}}_{A_{1}}+\underbrace{\Pr\left\{P_{S}\big{|}h_{SR_{k}}\big{|}^{2}> \delta,P_{1R}\big{|}h_{R_{k}D_{1}}\big{|}^{2}<\delta\right\}}_{A_{2}}, \tag{11}\]  
where \(P_{S}=\min\left\{P,\frac{I}{\big{|}h_{SP}\big{|}^{2}}\right\}\), \(\delta=\frac{\omega_{1}}{a_{1}-\omega_{1}a_{2}}\), in which \(\omega_{1}=2^{2R_{1}}-1\). In this situation, the transmission power obtained at the RSU \(P_{1R}\) after performing energy harvesting can be determined as the following analysis. It is worth noting that the RSU can detect the message successfully from the BS if the following condition occurs:  
\[\frac{1}{2}\log\left(1+\frac{a_{1}P_{S}\left(1-\rho\right)\big{|}h_{SR_{k}} \big{|}^{2}}{a_{2}P_{S}\left(1-\rho\right)\big{|}h_{SR_{k}}\big{|}^{2}+1} \right)\geqslant R_{1} \tag{12}\]  
Thus, the power splitting factor \(\rho_{1}\leqslant 1-\frac{\omega_{1}}{\left(a_{1}-\omega_{1}a_{2}\right)P_{S} \big{|}h_{SR_{k}}\big{|}^{2}}\), and \(R_{1}\) denotes the targeted data rate. Firstly, \(A_{21}\) can be computed by  
\[ \begin{split} A_{21}&=\Pr\left\{\left|h_{SR_{k}}\right|^ {2}>\frac{\delta}{P^{\prime}},\left|h_{R_{k}D_{1}}\right|^{2}<\frac{\delta}{ \eta\left(P\big{|}h_{SR_{k}}\big{|}^{2}-\delta\right)},\left|h_{R_{k}P}\right|^ {2}<\frac{I}{\eta\left(P\big{|}h_{SR_{k}}\big{|}^{2}-\delta\right)}\right\}\\ &=\int_{\frac{\delta}{P}}^{\infty}F_{\left|h_{R_{k}D_{1}}\right|^ {2}}\left(\frac{\delta}{\eta\left(Px-\delta\right)}\right)F_{\left|h_{R_{k}P} \right|^{2}}\left(\frac{I}{\eta\left(Px-\delta\right)}\right)f_{\left|h_{SR_{k }}\right|^{2}}\left(x\right)dx\\ &=\sum_{k=1}^{K}\left(\begin{array}{c}K\\ k\end{array}\right)\left(-1\right)^{k-1}\exp\left(-\frac{\delta k}{P\Omega_{ SR}}\right)\left(1-2\sqrt{\frac{Ik}{P\eta\Omega_{RP}\Omega_{SR}}}K_{1}\left(2 \sqrt{\frac{Ik}{\eta P\Omega_{RP}\Omega_{SR}}}\right)\right.\\ &-2\sqrt{\frac{\delta k}{\eta P\Omega_{RD_{1}}\Omega_{SR}}}K_{1}\left(2\sqrt{ \frac{\delta k}{\eta P\Omega_{RD_{1}}\Omega_{SR}}}\right)\\ &+\left.2\sqrt{\frac{\left(\delta\Omega_{RP}+I\Omega_{RD_{1}}\right)k}{\Omega_ {RD_{1}}P\eta\Omega_{RP}\Omega_{SR}}}K_{1}\left(2\sqrt{\frac{\left(\delta \Omega_{RP}+I\Omega_{RD_{1}}\right)k}{\Omega_{RD_{1}}\eta\Omega_{RP}\Omega_{SR} }}\right)\right)\end{split}  \tag{17}\]  
The term \(A_{22}\) can be calculated as [20]  
\[ \begin{split} A_{22}&=2\sum_{k=1}^{K}\left( \begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\mathbf{e}^{-\frac{k\beta}{\Omega_{SR}P}}\left( \sqrt{\frac{Ik}{\Omega_{RP}\Omega_{SR}P\eta}}K_{1}\left(2\sqrt{\frac{Ik}{ \Omega_{RP}\Omega_{SR}P\eta}}\right)\right.\\ &-\left.\frac{I\Omega_{RD_{1}}}{\delta\Omega_{RP}+I\Omega_{RD_{1}} \sqrt{\frac{\left(\delta\Omega_{RP}+I\Omega_{RD_{1}}\right)k}{\Omega_{RD_{1}} \Omega_{RP}\Omega_{SR}P\eta}}}K_{1}\left(2\sqrt{\frac{\left(\delta\Omega_{RP}+ I\Omega_{RD_{1}}\right)k}{\Omega_{RD_{1}}\Omega_{RP}\Omega_{SR}P\eta}}\right) \right).\end{split}  \tag{18}\]  
See in Appendix B. Similarly, \(A_{23}\) can be calculated as  
\[