# Deterministic Propagation Modeling for Intelligent Vehicle Communication in Smart Cities
## 3 Simulation Results  
### Large Scale Spatial Path Loss  
The Ray Launching technique is a well-recognized tool for the accurate estimation of the propagation model parameters useful in the radio-planning phase of the V2I communication projects. This large-scale spatial path loss characterization subsection presents a detailed spatial representation of the Received Signal Strength (RSS) as a function of the Euclidean distance from the transmitter (TX) to the receiver (RX) (TX height: 3.5 m, RX height: 1.5 m), along the avenues and streets. For illustrative purposes, the left (x-axis) and top (y-axis) distances from TX were prefixed with a negative sign, while the right and bottom distances remain positive. The RSS data generated by 3D-RL simulation is represented with a dotted line, while a Least Square (LS) fitting is represented with a dashed line. The LS fitting (first order polynomial) is robust for minimizing the effect of the outliers in the 3D-RL raw data and could be used for comparison purposes with theoretical path loss models. The Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) regions had been properly identified. The TX1-RSS along AV1, AV2, ST1, ST2 and ST3 is depicted in Figure 7 while Table 3 summarizes the PLE and STD values along AV1, AV2, ST1, ST2 and ST3. Figure 7a illustrates the TX1-RSS along AV1  
Figure 5: Communication devices for V2I and V2V communication: **(a)** laptop used to store the _iperf_ traces; **(b)** AC/DC inverter plugged into the vehicle; **(c)** antenna placed on the vehicle; **(d)** spectrum analyzer; **(e-g)** antenna placed on the infrastructure; **(h–i)** antenna placed on the vehicle. Figure 6: Communication protocol stack implemented for the experiments. and its comparison with a Path Loss Model (PLM) [34]. This PLM describes the random shadowing effects over many measurements that have the same TX-RX separation, but different levels of clutter on the propagation path. The PLM received power \(\mathrm{P_{r}}\), is defined by Equation (1):  
\[\mathrm{P_{r}(d)[dBm]=P_{t}[dBm]+G_{t}[dB]+G_{r}[dB]-\left[\mathrm{PL(d_{o})[dB ]+10n\log 10\left(\frac{d}{d_{o}}\right)[dB]+X_{\sigma}[dB]\right]} \tag{1}\]  
where:  
- \(\mathrm{P_{t}}\) is the power transmitted by the TX. - \(\mathrm{G_{t}}\) and \(\mathrm{G_{r}}\) are the gain of RT and RX respectively. - \(\mathrm{PL(d_{o})}\) is the free space path loss (reference distance \(\mathrm{d_{o}=1\ m}\)), defined by Equation (2):  
\[\mathrm{PL(d_{o})[dB]=-10\log_{10}\left(\frac{\lambda^{2}}{{(4\pi)^{2}}{d_{o}}^ {2}}\right)} \tag{2}\]  
where  
- \(\lambda=c/f\) is the wavelength, where \(\mathrm{c=3\ \times\ 10^{8}\ m/s\ and\ f=5\ \times\ 10^{9}\ Ghz}\)  
- \(\mathrm{d_{o}}\) is the close-in distance from the TX (considered 1 m). - \(\mathrm{X_{\sigma}}\) is a zero-mean Gaussian distributed random variable with standard deviation \(\sigma\). - \(\mathrm{d}\) is the TX-RX distance. - \(\mathrm{n}\), is the path loss exponent (PLE) and together with the standard deviation (STD) were estimated from the 3D-RL raw data, using Maximum Likelihood (ML) [35], according Equations (3) and (4):  
\[\mathrm{PLE}=\frac{-\sum_{i=1}^{n}(P_{i}[dBm]-P_{o}[dBm])\log_{10}\left(\frac{ d_{i}}{d_{o}}\right)}{\sum_{i=1}^{n}10\left(\log_{10}\left(\frac{d_{i}}{d_{o}} \right)\right)^{2}} \tag{3}\]  
\[\mathrm{STD}\left[dB\right]=\frac{1}{\sqrt{n}}\left\{\sum_{i=1}^{n}\left[P_{i} [dBm]-P_{0}[dBm]+10\log_{10}\left(\frac{d_{i}}{d_{o}}\right)\right]^{2}\right\} ^{\frac{1}{2}} \tag{4}\]