## 3 Air-to-Air Channel Models
### Theoretical Studies and Simulations for Channel Modeling
For example, considering a viable link established at 4 km for a low-speed UAV (3.6 km/h), if the airborne vehicle accelerates up to 200 km/h, then the corresponding range should be reduced by about 91.2% (down to 351 m) in order to achieve convenient communication (i.e., to encounter the same path loss). Figure 11: Path-loss effects with different parameters: (**a**) Tx–Rx distance and Rx height; (**b**) Tx–Rx distance and Rx speed; (**c**) Rx height and speed. Finally, Figure 11c demonstrates how both the Rx speed and the height influence the path loss. The Tx is assumed to hover steadily at 200 m above the ground. The path-loss variation can reach up to 13 dB with the adjustment of these two parameters. However, the Rx speed is the most critical factor. As the UAV accelerates, the path loss escalates rapidly compared with its flying height. At low flying altitudes, the ground effect is still present, providing higher attenuation values. The corresponding path-loss variations are in the order of 2.5-3 dB, which is much lower than those induced by the speed of the UAV, indicating that the Rx speed is more dominant. Another analytical A2A channel model that takes into consideration both LOS and NLOS conditions for dense urban environments was proposed in [53]. The specific model was developed using the elevation angle and the height difference between the transmitting and receiving UAVs. It is based on the two-ray-reflection model, as well as on knife-edge diffraction. The corresponding path loss is calculated, in decibels, according to  
\[PL=20\log_{10}(h_{\rm Tx}-h_{\rm Rx})+20\log_{10}(f)-20\log_{10}(\sin\theta)-14 7.55+L_{\rm excess}, \tag{18}\]  
where \(f\) is the frequency in Hz, \(\theta\) corresponds to the elevation angle, and \(h_{\rm Tx}\) and \(h_{\rm Rx}\) denote the flight altitudes of the Tx and Rx UAV, respectively. The additional term, \(L_{\rm excess}\), denotes the extra losses induced by the terrain, in either LOS or NLOS conditions. The excess loss is given by  
\[L_{\rm excess}=20\log_{10}\Bigl{(}10^{(L_{\rm LOS}/20)}p_{\rm LOS}+10^{(L_{\rm NLOS }/20)}(1-p_{\rm LOS})\Bigr{)}, \tag{19}\]  
where \(L_{\rm LOS}\) and \(L_{\rm NLOS}\) denote the extra losses, in decibels, if the LOS or NLOS condition is encountered, respectively, and \(p_{\rm LOS}\) is the LOS probability provided by (14). The extra loss in the LOS condition can be calculated based on the two-ray model and can be expressed by the following relationship:  
\[L_{\rm LOS}=-20\log(2\sin(\frac{2\pi}{\lambda}\frac{h_{\rm Tx}h_{\rm Rx}}{h_{ \rm Tx}-h_{\rm Rx}}\sin(\theta))), \tag{20}\]  
where \(h_{\rm Tx}\) and \(h_{\rm Rx}\) denote the flight altitude of the Tx and Rx UAV, respectively, \(\theta\) stands for the elevation angle, and \(\lambda\) is the transmitting wavelength. The excess loss for the NLOS condition can be found by using the Ikegami knife-edge diffraction model [54], and it can be calculated as follows:  
\[L_{\rm NLOS}=10\log_{10}(f)+10\log_{10}(h_{\rm Tx}-h_{\rm Rx})+20\log_{10}( \cos(\theta))-10\log_{10}(1+\frac{\sqrt{2}}{L_{r}^{2}})-68.8, \tag{21}\]  
where \(L_{r}\) is the reflection loss, and the rest of the parameters were described previously. The reflection loss takes values between 4 dB and 15 dB, on average [54]. The aforementioned model is applicable if the flight altitude of one of the UAVs is higher than the average building height in the area (i.e., \(h_{\rm Tx}>\gamma\)). Let \(h_{\rm Tx}=250\) m, \(f=5.8\) GHz, and \(L_{r}=6\) dB; the path loss is calculated for variable \(h_{\rm Rx}\) distance and elevation angles, applying (18)-(21). Two different propagation scenarios are considered. A dense urban environment in Athens' city center, and Marousi, a suburban area a few kilometers north of Athens. The parameters for the LOS probability are selected according to [49], with \(a=0.5\), \(\beta=300\) and \(\gamma=20\) for the first scenario and \(a=0.1\), \(\beta=750\) and \(\gamma=8\) for the second.