# Outdoor Visible Light Communication in Intelligent Transportation Systems: Impact of Snow and Rain
## 3 Simulation Results and Discussion
### Optical Power Received (\(P_{rx-los}\))  
Assuming that the distance between two traffic lights on the same lane is 300 m, as mentioned in [13] and based on the tables given in this paper, simulation results are obtained and displayed in the figures. The minimum distance between the transmitter and receiver for the first lane is 18 m, and for the second lane this distance is 25 m, under which there is no LoS between the traffic light and receiver. All numerical parameters are listed in Table 6.  
Figure 9 depicts \(\mathrm{p_{rx}}\) for clear and snowy weather as a function of coverage area. As it appears, \(\mathrm{p_{rx}}\) has a different behavior for clear and snowy weather in large distances (max = 300 m) and has a similar behavior reaching the minimum distance for two lanes (18 m, 25 m). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Transmission optical power & \(\mathrm{P_{t}}\) & 314 [mW] \\ Detector physical area & A & 0.79 [cm\({}^{2}\)] \\ Gain of optical filter & \(\mathrm{T_{s}(\psi)}\) & 1.0 \\ Refractive index of concentrator & n & 1.7 \\ Electron charge & q & 1.602e-19 [C] \\ Photodetector responsivity & r & 0.35 [A/W] \\ [PERSON]’s constant & \(\mathrm{k_{B}}\) & 1.3811e-23 [J/K] \\ Absolute temperature & T & 298 [\({}^{\circ}\)K] \\ Open-loop voltage gain & G & 10 \\ FET transconductance & \(\mathrm{g_{m}}\) & 30 [mS] \\ FET channel noise factor & \(\Gamma\) & 1.5 \\ Bandwidth of band-pass optical filter & \(\Delta\lambda\) & 10 [nm] \\ Background irradiance per unit bandwidth & \(P_{\mathrm{bg}}\) & 5.8 [\(\mathrm{\mu W/cm^{2}\cdot nm}\)] \\ Capacitance per unit area & \(\eta\) & 112 [pF/cm\({}^{2}\)] \\ Noise bandwidth factors & \(\mathrm{I_{2}}\) & 0.562 \\ Wavelength of LED & \(\lambda\) & 505 [nm] \\ Vehicle velocity & \(\mathrm{v_{s}}\) & 60 [km/h] \\ Transmission data rate & \(\mathrm{T_{d}}\) & 10 M [bit/s] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Numerical analysis parameters [13]. FET: field-effect transistor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Weather Condition** & **Attenuation [dB/km] for Different Precipitation Rates** \\ \hline Snow & Light & Moderate & Heavy \\
2 mm/h & 4 mm/h & 8 mm/h \\ Wet & 6 & 10 & 17 \\ Dry & 14 & 37 & 97 \\ Rain & Light & Moderate & Heavy \\
2 mm/h & 10 mm/h & 25 mm/h \\ Marshall model & 0.7 & 1.5 & 3 \\ France model by & 2 & 5 & 9 \\ Carbonneau & 2.5 & 7 & 12 \\ Japan model & 2.5 & 0.911 & \\ Very clear & & 0.911 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Attenuation for various weather conditions. From the values listed in Table 5 and Figure 9, it is obvious that the dry snow has a significant effect on \(\mathrm{p_{rx}}\) comparing with wet snow due to the high attenuation. The \(\mathrm{p_{rx}}\) value decreases with the increase in the snow perception rate. The maximum power received is \(-15.98\) dBm at 18 m, while the minimum power received is approximately \(-35\) dBm at 300 m in very clear weather for the first lane. For wet and dry snow at different precipitation rates, the range is, respectively, from \(-16.4\) dBm to \(-17.9\) dBm and \(-17.08\) dBm to \(-23.08\) dBm at 18 m ranging from lower rates to higher rates. The difference in \(\mathrm{p_{rx}}\) from the second lane to the first lane is approximately \(-3\) dBm lower. There are two important factors affecting the system performance: \(\theta\) and FOV. The performance is tested at different values of \(\theta\) and FOV and the obtained results suggest setting \(\theta\geq 40^{\circ}\) and FOV \(\leq 40^{\circ}\) to enhance the system outage. According to the non-imaging receiver part that was discussed before, to reach the best performance set, FOV = \(\Delta\lambda\) then \(\theta\) will be calculated according to Equation (8).