# Trajectories and Resource Management of Flying Base Stations for C-V2X
## 3 System Model
### Radio Channel and Physical Layer  
As far as the radio interface is concerned, we considered an LTE scenario where vehicles were using C-V2X technology. Table 1 shows the parameters related to the technology and scenario. Both the TBSs and the UAV operated within the same carrier of 2600 MHz and had the same quantity of RRs available. From the TBSs side, we considered a typical radio channel of an urban scenario, with the propagation exponent, \(\beta\), of 3.6 [44] and a shadowing variable, \(S_{\sigma}\) with log-normal distribution and variance \(\sigma=6\) dB. Given the equivalent radiated power \(EIRP_{\text{tx,TBS}}=P_{\text{tx,TBS}}\cdot G_{\text{tx, TBS}}\), with \(P_{\text{tx,TBS}}\) and \(G_{\text{tx,TBS}}\) being the transmission power and gain of the TBSs, respectively, the received power \(P_{\text{tx,TBS}}\) is computed as  
\[P_{\text{rx,TBS}}=EIRP_{\text{tx,TBS}}\cdot\left(\frac{c}{4\pi \cdot f_{\text{c,TBS}}}\right)^{2}\cdot\frac{1}{d}^{-\beta}\cdot S_{\sigma} \tag{1}\]  
where \(c\) is the speed of light, \(f_{\text{c,TBS}}\) is the TBSs carrier frequency and \(d\) is the link distance. See Table 1 for implementation details. Differently, the UAV encounters less impairments thanks to its height, and therefore we applied the model of the air-to-ground (ATG) channel proposed in [45]. It mainly consists of extracting the probability of LOS or Non-LOS depending on the height and the angle \(\theta\) between the ground \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter Definition** & **Value** \\ \hline Rectangular area, \(A\) & \(1.8\times 1.6\) m\({}^{2}\) \\ Average number of vehicles in the scenario & 600 \\ Number of TBSs in the area, \(N_{\text{TBS}}\) & 16 \\ TBSs equivalent radiated power, \(EIRP_{\text{tx,TBS}}\) & 43 dBm \\ UAV transmit power, \(P_{\text{tx,UAV}}\) & 20 dBm \\ Bilateral noise density, \(N_{0}\) & \(4\times 10^{-20}\) W/Hz \\ Single carrier frequency on UAV and TBS, \(f_{\text{c,TBS}}=f_{\text{c,drone}}\) & 2600 MHz \\ Subcarrier spacing, \(B_{\text{subc}}\) & 15 kHz \\ Number of subcarriers of a resource block & 12 \\ Maximum capacity, \(T_{\text{max}}\) & 100 Mb/s \\ Time slot interval & 0.5 ms \\ Frame time duration & 10 ms \\ Bandwidth of TBSs & [5; 6; 7; 8; 9; 10] MHz \\ Reuse factor & 1 \\ UAV speed, \(s\) & 20 m/s \\ UAV altitude, \(h\) & 120 m \\ UAV antenna aperture angle, \(\alpha\) & 120 deg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mobile network parameters. and the line connecting the UAV to the user. The larger is \(\theta\), the closer to one is the probability of LOS. Depending on this, the ATG path loss, \(PL\), is computed. In particular, the LOS probability \(P_{\text{LOS}}(\theta)\) follows  
\[P_{\text{LOS}}(\theta)=\frac{1}{1+a\exp(-b[\theta-a])} \tag{2}\]  
where \(a\) and \(b\) are parameters defined in [45] that depend on the environment. The ATG channel has for both the LOS and NLOS cases an excessive path loss [45], \(\eta\), to be added to the free space loss, \(FSPL\). Then, the following equations can be applied  
\[PL_{\text{dB}}=FSPL_{\text{dB}}+\eta \tag{3}\]  
\[FSPL_{\text{dB}}=20\log(d)+20\log(f_{\text{c,drone}\text{MHz}})-27.55 \tag{4}\]  
\[Pr=\frac{P_{\text{b,UAV}}}{PL}, \tag{5}\]  
where the subscript dB denotes that the variable is expressed in decibels. In (4), the free-space loss was computed (in dB) as a function of the distance \(d\) between the vehicle and the UAV and a value of \(f_{\text{c,drone}}\) expressed in MHz. Those nodes that have an elevation angle \(\theta\) below \(15^{\circ}\) were not considered in the UAV coverage range as in [45], since their heavy path loss value would not allow a correct signal reception. This implies that the UAV coverage range is limited depending on \(\theta\). We assumed the UAV is equipped with a directional antenna that employs a fixed aperture angle \(\alpha\) pointing towards the terrain as in [46].