## 3 Link Budget and Dual-Slope Path Loss Measurement Results
### Dual-Slope Path Loss Model Results  
To process the data sets obtained during the measurement campaign, a selection was made according to the propagation scenarios, analyzing the behavior of the path loss propagation as a function of the separation distance between the Tx and Rx. A further process of data filtering was carried out to obtain more accurate values for the parameters of the dual-slope path loss model. According to [25], a linear relationship can be established between the mean path loss expressed in logarithmic units, \(PL(d)\), and \(log_{10}(d)\) in V2V radio channels, analogous to traditional F2M channels, given by the following:  
\[PL(d)=L_{0}+10\gamma log_{10}\left(\frac{d}{d_{0}}\right)+S,\ \ \ d\geq d_{0}, \tag{5}\]  
where \(L_{0}\) represents the average path loss propagation at a separation distance \(d_{0}\), the term \(10\gamma log_{10}\left(\frac{d}{d_{0}}\right)\) refers to the average path loss propagation referring to the Tx/Rx distance \(d_{0}\), \(\gamma\) is the PLE related to the type of propagation environment, and \(S\) is a Gaussian distributed random variable with zero mean and standard deviation \(\sigma_{S}\) in dB that is used to model long-term fading or shadowing. However, there are environments in which a dual-slope model can more accurately fit the measured data. A dual-slope model is characterized by a path loss exponent of \(\gamma_{1}\) and a standard deviation of \(\sigma_{S_{1}}\) above a reference distance up to critical distance \(d_{C}\), a path loss exponent of \(\gamma_{2}\), and a standard deviation of \(\sigma_{S_{2}}\) for a distance higher than the critical distance. Using this model, the average path loss value can be estimated as the following:  
\[PL(d)[dB]=\left\{ \begin{matrix}L_{0}+10\gamma_{1}log_{10}\left(\frac{d}{d_{0}} \right)+S,\ \ \ d_{0}\leq d\leq d_{C};\\ L_{0}+10\gamma_{1}log_{10}\left(\frac{d_{C}}{d_{0}}\right)+10\gamma_{2}log_{1 0}\left(\frac{d}{d_{C}}\right)+S,\ \ \ d\geq d_{C}.\end{matrix} \right. \tag{6}\]  
On the other hand, the behavior of the path loss propagation based on a dual-slope model was observed for some of the analyzed routes. It should be noted that this behavior did not appear in all propagation scenarios or in the two frequency bands (700 MHz and 5.9 GHz) in which the measurements were made. Figure 8 shows the path loss as a function of the Tx/Rx separation distance for an urban environment with high traffic density at 700 MHz. A double-slope behavior was observed; thus, applying a linear least squares fit (magenta curve for the first slope and red curve for the second slope in Figure 8) yields values of \(L_{0}\) = 36.83 dB, \(\gamma_{1}\) = 1.65, \(\sigma_{S_{1}}\) = 4.73 dB, \(\gamma_{2}\) = 3.26, and \(\sigma_{S_{2}}\) = 5.1 dB, with a \(d_{C}\) = 39.67 m.  
Similarly, Figure 9 shows the path loss as a function of the Tx/Rx separation distance for an urban environment with low traffic density at 5.9 GHz. We thus obtained \(L_{0}\) = 59.88 dB, \(\gamma_{1}\) = 1.61, \(\sigma_{S_{1}}\) = 4.00 dB, \(\gamma_{2}\) = 4.42, \(\sigma_{S_{2}}\) = 5.26 dB, and \(d_{C}\) = 134.56 m. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Channel Sounder at 700 MHz** & **Channel Sounder at 5.9 GHz** \\ \hline Transmitted power & \(-20\) dBm & \(-10\) dBm \\ Points number & 401 & 5000 \\ Resolution bandwidth & 30 kHz & 100 kHz \\ SPAN & 0 & 0 \\ Dynamic range & 80 dB & 80 dB \\ \hline \end{tabular}
\end{table} 
Table 1: Measurement system configuration parameters at 700 MHz and 5.9 GHz. The mean parameters that characterize the path loss propagation for the dual-slope model are summarized in Table 2. The PLE values for the first slope range from 1.04 to 2.13 and 1.72 to 2.46 at 700 MHz and 5.9 GHz, respectively. The highest PLE values for the first slope occurred in urban environments with low traffic density at 700 MHz and 5.9 GHz. Similarly, the PLE values for the second slope range from 3.43 to 4.92 and from 6.26 to 9.69 at 700 MHz and 5.9 GHz, respectively.