## 3 Air-to-Air Channel Models
### Theoretical Studies and Simulations for Channel Modeling
The corresponding results are presented in Figure 12.  
The flat area in the mesh plots corresponds to the NLOS condition, whereas the remaining area with the rapidly varying path loss and peaks is attributable to the behavior of the two-ray model in the LOS condition. The effect of the environment is more than evident, since in suburban locations, the probability of the NLOS condition is limited, as can be observed in Figure 12b. The Rx flight altitude is the primary parameter that controls the path loss. In urban locations, NLOS conditions are encountered for low flying altitudes (below 40 m) as the elevation angle approaches 90\({}^{\circ}\), but as \(h_{\rm Rx}\) increases, the transition from NLOS to LOS can be achieved at lower elevation angles and at distances greater than 40 m and up to 100 m. These are the Rx height limits after which the LOS condition is dominant. On the other hand, in suburban areas, these heights are much lower and LOS conditions can be achieved for Rx heights above 20-40 m, almost independent from the elevation angle. The path-loss behavior in both plots is directly associated with the mixed excess loss given by (19) and the LOS probability provided by (14). It is worth mentioning that LOS conditions are exhibited for Rx flight altitudes between 2 and 5 times, and between 2.5 and 5 times, the areas' average building height, in urban and suburban locations, respectively. In addition to measurements, stochastic models for the A2A channel have also been developed. For this purpose, geometry-based stochastic models (GBSMs) have been employed to investigate the non-stationary characteristics of the wideband A2A wireless link. A three-dimensional (3D)-cylinder geometrical model that combined a LOS path with single- and double-reflected components was recommended in [55,56]. The specific model involved two moving UAVs in the 3D space, with two antenna elements 0.5A apart in both the Tx and the Rx. The simulations were conducted at 3 GHz, considering a cylinder radius of 300 m, a separation distance of 150 m between the UAVs, and a Tx height of 150 m. Two different scenarios were examined, yielding the time-frequency correlation of the channel (from the time-varying transfer functions). In the first, a constant speed (10 m/s) and trajectory were considered (linear motion), whereas, in the second, a variable speed and trajectory were involved (applying a Gauss-Markov model for the randomness). In both cases, the Tx and Rx moved vertically and horizontally in the 3D space. In the first scenario, based on the time-correlation function, it was observed that when the UAV moved vertically, the correlation time decreased faster compared with the horizontal movement (between 1 ms and 2.5 ms, depending on the selected reflections). This was true for both single- and double-bounce cases, implying that the vertical movement affected the channel stationarity more significantly. In this case, non-stationary characteristics were induced in the channel much earlier. In the case of double-buncing reflections, the time correlation decreased faster in both the vertical and the horizontal movements of the UAVs. These observations indicated that, generally, the direction of movement affected the channel stationarity less in the double-bounce reflections; however, it demonstrated that the vertical movement affected the channel stationarity more significantly. In this case, non-stationary characteristics were induced in the channel much earlier. In the case of double-buncing reflections, the time correlation decreased faster in both the vertical and the horizontal movements of the UAVs. These observations indicated that, generally, the direction of movement affected the channel stationarity less in the double-bounce reflections is more pronounced in the double-bounce reflections. Figure 12: Indicative path-loss results when varying the Rx flight altitude and the elevation angle for two different propagation scenarios: (**a**) dense urban environment; (**b**) suburban environment.