# Modeling and Performance Analysis of mmWave and WiFi-Based Vehicle Communications
## 2 System Model
### WiFi Communications  
This work focuses on examining the 802.11p WiFi communication standard. 802.11p is a short-range communication (SRC) technology that allows data transmission at rates ranging from 6 to 27 Mbps, covering distances of a few hundred meters. It ensures dependable, strong communication with minimal delay. Nevertheless, the 802.11p standard has limitations, including a low throughput during peak loads due to limited available frequency bandwidth.  
To evaluate the reliability of the WiFi transmission link, the following path-loss model is considered.  
\[PL_{WiFi}(r)=PL_{WiFi}(r_{0})+\sum_{\xi=1}^{2}P_{\xi}\beta_{\xi}10\log_{10} \left(\frac{r}{r_{0}}\right), \tag{1}\]  
where \(P_{1}\) and \(P_{2}\) present the LoS and NLoS probabilities, respectively, \(\beta_{\xi}\) is the path-loss exponent, \(r\) denotes the 3D spatial distance between \(Tx\) and \(Rx\), and \(PL_{WiFi}(r_{0})\) indicates the path loss at the reference distance \(r_{0}\) (usually is equal to 1 m), which is presented as follows  
\[PL_{WiFi}(r_{0})=20\log_{10}\left(\frac{4\pi f_{c_{WiFi}}}{C}\right), \tag{2}\]  
here, \(f_{c_{WiFi}}\) is the WiFi carrier frequency, and \(C\) denotes the speed of light.  
Accordingly, the corresponding instantaneous received signal-to-noise ratio (SNR) can be expressed as follows  
\[SNR_{WiFi}=\sum_{\xi=1}^{2}\frac{P_{\xi}\mathcal{P}_{\tau}\mathcal{H}_{\xi}{A _{w}}^{-\beta_{\xi}}}{\mathcal{P}_{N}}, \tag{3}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Definition** \\ \hline \(h_{T_{x}}\) & The \(Tx\)’s height \\ \(h_{Rx}\) & The \(Rx\)’s height \\ \(h_{a}\) & The threshold height \\ \(a\) & The distance between \(Tx\) and a given vehicle \(V\) \\ \(h_{r}\) & The obstacle vehicle’s height \\ \(h_{mm}\) & The maximum vehicle’s height \\ \(h_{min}\) & The minimum vehicle’s height \\ \(d\) & The 2D distance between \(Tx\) and \(Rx\) \\ \(r\) & The 3D distance between \(Tx\) and \(Rx\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The used notations throughout the paper.  
In this equation, \(\xi\) is equal to 1 for the LoS case and is equal to 2 for the NLoS case, \(\beta_{\xi}\) indicates the associated path-loss exponent, \(P_{1}\) (\(P_{2}\)) represents the LoS (NLoS) probabilities, \(\mathcal{P}_{T}\) denotes the vehicles' transmission power, \(\mathcal{H}_{\xi}\) represents the channel gain, \(\mathcal{P}_{N}\) designates the additive white Gaussian noise (AWGN) power, and \(A_{W}\) stands for the coefficient of WiFi channel attenuation, which is given by  
\[A_{W}=\left(\frac{C}{4\pi f_{\epsilon_{W WiFi}}}\right)^{2}, \tag{4}\]  
In this work, we assume that the signals are transmitted through Rice fading channels in the case of LOS, while NLoS scenarios incorporate Rayleigh fading channels. Consequently, the probability density function (PDF) of \(\mathcal{H}1\) follows a non-central Chi Square distribution, where its closely approximate PDF expression is provided by [32]  
\[p_{{}_{H_{1}}}(x)\approx\frac{\mathcal{K}+1}{\mu_{1}}\exp\left(-\mathcal{K}- \frac{[\mathcal{K}+1]}{\mu_{1}}x\right)\times\sum_{n=0}^{N}\left(\frac{ \mathcal{K}[\mathcal{K}+1]}{\mu_{1}}\right)^{n}\frac{x^{n}}{n!\ \Gamma(n+1)}, \tag{5}\]  
here, \(\mathcal{K}\) represents the ratio between the LoS and NLoS power components, and \(\mu_{1}\) denotes the average of \(\mathcal{H}_{1}\). For the NLoS case, \(\mathcal{H}_{2}\) adheres to an exponential distribution, with mean \(\mu_{2}\) and a PDF \(p_{{}_{H_{2}}}\) that is expressed as follows  
\[p_{{}_{\mathcal{H}_{2}}}(x)=\frac{1}{\mu_{2}}\exp\left(-\frac{x}{\mu_{2}} \right). \tag{6}\]