## 3 Air-to-Air Channel Models
### Theoretical Studies and Simulations for Channel Modeling
This can also be applied, as a simple rule of thumb, in other terrain types (e.g., suburban and rural areas). A simple A2A path-loss model that takes into account the mobility of UAVs is presented in [50] for rugged terrains. It is based on the Stanford University Interim (SUI) model [51; 52], extending its usage by incorporating additional losses due to the induced Doppler shift. The path loss, in decibels, is expressed as  
\[PL=20\log_{10}(\frac{4\pi d_{0}}{\lambda})+10(a-bh_{\mathrm{Tx}}+\frac{c}{h_{ \mathrm{Tx}}})\log_{10}(\frac{d}{d_{0}})+\Delta L_{f}+\Delta L_{h}+s+PL_{ \mathrm{Doppler}}, \tag{15}\]  
where \(\lambda\) is the transmitted wavelength, in meters, \(d_{0}\) stands for the reference distance, \(h_{\mathrm{Tx}}\) designates the Tx height, and \(d\) is the Tx-Rx distance, all of which are provided in meters. Furthermore, \(\Delta L_{f}=6\mathrm{log}10(f/2000)\) denotes the frequency-correction factor, in which the frequency, \(f\), is given in MHz, \(s\) indicates the shadowing parameter, in decibels, due to NLOS conditions, and \(\Delta L_{h}\) is the Rx correction height, which is given by  
\[\Delta L_{h}= \begin{cases}-10.8\log_{10}(h_{\mathrm{Rx}}/2),&\text{Terrain Type A, B}\\ -20\log_{10}(h_{\mathrm{Rx}}/2),&\text{Terrain Type C}\end{cases} , \tag{16}\]  
where \(h_{\mathrm{Rx}}\) is the Rx height, in meters. The coefficients \(a\), \(b\), and \(c\), are terrain-specific and can be obtained experimentally [51]. The shadowing parameter is optional and is usually left to users (between 8.2 dB and 10.6 dB). Finally, the excess loss, in decibels, due to the Doppler is provided by  
\[PL_{\mathrm{Doppler}}=-3.72+5\log_{10}(f_{d})+5.01\log_{10}(d), \tag{17}\]  
where \(f_{d}\) is the Doppler shift (\(f_{d}=u/\lambda\)) in Hz, and \(u\) is the velocity of the Rx towards Tx, in m/s. Figure 10: Indicative paradigm of LOS probability in Athens city center, when varying the elevation angle and the Rx flight altitude. The following scenarios are presented in the form of a case study, in order to examine the impact of different parameters on the path loss. Applying (15) for a type-A terrain at 5.8 GHz and \(s\) = 8.2 dB, the variation in the path loss is examined in Figure 10 as a function of the UAV separation, Rx height, and speed. Figure 11 presents the path-loss variations for the UAV-separation distance, and Rx flight altitudes between 200 m and 5 km. The Rx is assumed to fly at a constant speed of 108 km/h, whereas the Tx hovers steadily at 200 m above the ground. The plot indicates that the path loss is influenced more by the Rx height because, at higher altitudes, it reduces drastically. This is attributed to the Rx correction factor \(\Delta L_{h}\), which has a negative impact by decreasing the path loss as the Rx flies at higher altitudes. For example, even at the greatest separation between the two UAVs, of 5 km, the path loss is reduced by about 20 dB as the Rx height increases from 200 m up to 5 km. This observation is directly associated with the ground-terrain effects (e.g., reflection, diffraction, and scattering), as also mentioned previously, and at lower altitudes, the communication channel has a lower probability of establishing a LOS link and the signal-fading variations are also increased due to multipath, which entails increased attenuation. Furthermore, Figure 11b demonstrates the Doppler effect on the path loss, based on the speed of the Rx. In this specific scenario, both UAVs are positioned 200 m above the ground, whereas the Rx moves away from the Tx at various speeds, between 1 m/s and 70 m/s (i.e., from 3.6 km/h up to 252 km/h). The induced Doppler effect is more than evident, since, at higher speeds, the path loss escalates significantly. The specific variation can reach up to 10 dB and is virtually constant for distances of 200 m or 5 km between the two UAVs. The wireless-link range is influenced the most by the movement.