# A Survey of Vehicular VLC Methodologies
## 6 Vehicular VLC Channel Modeling and Propagation Characteristics
### Existing Vehicular VLC Channel Models  
This section discusses the existing vehicular VLC channel models for V2V with headlights and taillights and I2V with either streetlights or traffic lights. 1. V2V with High-Beam Headlights  
* Linear model  
For perfect alignment [39], the linear model of path loss between vehicles VLC can be written as  
\[P_{r}\ =P_{t}(\alpha d+\beta) \tag{7}\]  
where \(P_{r}\) represents the received optical power, \(P_{t}\) represents the transmission power, \(\alpha\) and \(\beta\) represent weather coefficients, and d represents the inter-vehicle distance. * Exponential Model  
The exponential path loss for vehicle-to-vehicle VLC can be written as  
\[Pr=\ Pt\ \underbrace{Ad^{-2B}\ \exp(-cd)}_{p} \tag{8}\]  
where \(Pt\) represents the transmission power, A represents the geometrical loss value at a reference distance specified as \(d_{0}\), B is the decaying factor as determined by \(\{A=P_{0}\ d_{0}^{2B}\text{exp}(cd_{0})/Pt\}\), c represents the extinction coefficient for clear, rainy, and foggy weather, and p is the optical channel coefficient. * Comprehensive Model  
For lateral shift and receiver aperture effect, we can obtain the overall path loss as [76]\(PL=10 log_{10}\)  
\[\frac{1}{2}\sum_{i=1}^{2}\left(\left(\frac{D_{R}\left(d/\sqrt{d^{2}+{d_{h_{i}}}^{ 2}}\right)^{\frac{1}{2}}}{\xi\sqrt{d^{2}+{d_{h_{i}}}^{2}}}\right)^{2}exp\left(-c \sqrt{d^{2}+{d_{h_{i}}}^{2}}\ \left(\frac{D_{R}}{\xi\sqrt{d^{2}+{d_{h_{i}}}^{2}}} \right)^{\epsilon/2}\right)\right) \tag{9}\]  
where \(D_{R}\) represents an aperture diameter, \(\zeta\) and \(\epsilon\) are two correction coefficients that consider the pattern of the headlamp light to be asymmetrical, in addition to the weather conditions, \(\sqrt{d^{2}+{d_{h_{i}}}^{2}}\) represents the distance of propagation between the \(i_{th}\) TX, \(i=1,2\), and RX. 2. V2V with Low-Beam Headlight  
The optical channel model for the asymmetric low beam headlight pattern (\(h_{opt}\)) is given as  
\[h_{opt}[dB]\approx 10 log_{10}\left(\frac{4D_{R}}{3\left(d+d_{h}^{2}\right)} \right)^{2} \tag{10}\]  
where \(D_{R}\) refers to the diameter of the power meter's effective area, \(d_{h}\) represents stands for the lateral displacement, and d represents stands for the distance between vehicles. Based on computation, it was determined that the loss of the geometric shape dominates the failure of the trajectory. Additionally, because the beam is parallel, the lateral distance has a more significant influence than the distance between vehicles by a factor of two [31]. It is essential to emphasize the fact that the model relies on there being a low-beam headlight present in the vehicle. The photodetector on the receiving vehicle is perfectly aligned with the headlight that is being assessed, and there is no evidence of any lateral displacement. 3. V2V with Taillights  
The formula for the path loss model, an explicit function of both d and the distance from vehicle to vehicle in terms of its taillights, is as follows [73]:  
\[PL_{i}(d)=PL_{0,i}+10 log_{10}\left(d^{-2\epsilon_{i}}\right)-\zeta_{i}d,i\in\{ a,b,c\} \tag{11}\]  
where \(PL_{0}\) represents the reference \(PL\) at \(d_{0}\) of one meter, and \(\zeta_{i}\) and \(\epsilon_{i}\) represent correction coefficients values. 4. IZV with Traffic Lights  
The model of loss of the infrastructure to vehicle (IZV) connection with traffic lights is given as follows [135]:  
\[PL_{IZV}=10 log_{10}\left(h_{IZV}\right)=a\ exp\left(-\left(\frac{d_{IZV}-b}{c} \right)^{2}\right) \tag{12}\]  
where \(h_{IZV}\) denotes the optical channel coefficient, equal to the loss computed on a linear standard; \(\{a,b,\) and \(c\}\) are denoted coefficients that were acquired using ray tracing for each \(d_{h}\) (which demonstrate the horizontal shift that occurred within IZV). I2V with Street lights  
Due to the regular distribution of streetlights over a distance and the assigned area between them, a car traveling approaches a lamp and then passes away from it.