## 4 Results
### Average Path Loss  
In this subsection, the performance of the proposed V2I-VLC model in terms of path loss is presented. Since the proposed V2I-VLC model is based on short-range communication over LEDs, the path loss has a significant impact on the model. Figure 6 illustrates the path loss under different transmission distances \(I_{V_{1}-PD}\) in LOS and NLOS links given in (12), (13), and (14) for different weather conditions. The simulation curves are also incorporated to confirm the accuracy of the derived closed-form expression for the average path loss. It is worth noting that the negative sign indicates that the path loss is in the form of a penalty. As a result, the path loss in both the LOS and NLOS links increases with the transmission distance, as shown in Figure 6. From the comparison, it is obvious that the LOS and NLOS links have the highest channel gain in clear weather conditions and the worst gain in dense fog conditions. As an example, for \(I_{V_{1}-PD}=50\) m in the LOS link, the average path loss value is about \(-52\) dB for clear weather conditions, \(-53.8\) dB for moderate fog conditions, and \(-55\) dB for dense fog conditions. The difference in channel gain between moderate fog and dense fog versus clear weather conditions is \(1.8\) dB and \(3\) dB, respectively. In addition, the further \(V_{1}\) is from Rx (the larger the value of \(I_{V_{1}-PD}\)), the larger the difference in channel gain described above. Therefore, the transmission distance and the weather factor have significant impacts on the average path loss of the V2I-VLC.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Variable Name** & **Value** \\ \hline \(D_{R}\) & Aperture Diameter of PD & \(0.02\) m \\ \hline \(L_{w}\) & Road Width & \(4.5\) m \\ \hline \(v_{w}\) & Vehicle Width & \(1.8\) m \\ \hline \(c\) (Clear Weather) & Extinction Coefficient (Clear Weather) & \(0\) \\ \hline \(c\) (Moderate Fog) & Extinction Coefficient (Moderate Fog) & \(0.00782\) \\ \hline \(c\) (Dense Fog) & Extinction Coefficient (Dense Fog) & \(0.01565\) \\ \hline \(\varepsilon\) (Clear Weather) & Weather Correction Factor 1 (Clear Weather) & \(0.0175\) \\ \hline \(\varepsilon\) (Moderate Fog) & Weather Correction Factor 1 (Moderate Fog) & \(0.0172\) \\ \hline \(\varepsilon\) (Dense Fog) & Weather Correction Factor 1 (Dense Fog) & \(0.0170\) \\ \hline \(\zeta\) (Clear Weather) & Weather Correction Factor 2 (Clear Weather) & \(0.1585\) \\ \hline \(\zeta\) (Moderate Fog) & Weather Correction Factor 2 (Moderate Fog) & \(0.1600\) \\ \hline \(\zeta\) (Dense Fog) & Weather Correction Factor 2 (Dense Fog) & \(0.1550\) \\ \hline \(L_{PD}\) & Height of Headlights and PD & \(0.7\) m \\ \hline \(\sigma_{o}\) 2 & Variance of the Zero Mean AWGN Noise & \(1\) \\ \hline \(\sigma_{l}\) 2 & Variance of the Lognormal Distribution & \(0.2\) \\ \hline \(\eta\) & Photoelectric Conversion Efficiency of PD & \(1\) \\ \hline \(P_{L,l}\) & Output Power of a Single Tx & \(30\) W \\ \hline \(B\) & System Bandwidth & \(20\) MHz \\ \hline \hline \end{tabular}
\end{table}
Table 2: Modeling and simulation parameters of the proposed V2I–VLC system.  
The average V2I-VLC path loss in different links under dense fog conditions is shown in Figure 7. It is worth noting that the path loss of NLOS-M links is higher than those of NLOS-RS links when the values of \(I_{V_{1}-PD}\) range from 10 to 50 m. However, after 60 m, \(PL_{av}^{NLOS\_RS}\approx PL_{av}^{NLOS\_M}\). It shows that, when \(V_{1}\) is close to Rx, the reflection effect of the road surface plays the leading role compared to the reflection of the mountain, i.e., most of the optical power received by Rx from the NLOS link is reflected by the road surface. Additionally, when \(V_{1}\) is far away from Rx, the road surface and mountain reflection have basically the same effect on the performance of V2I-VLC.