## 4 Numerical Results and Analysis  
For this section, some key statistical properties of the channel model, related to the Tx and Rx, were analyzed and compared. The moving trajectories of the Tx, the Rx, and the clusters are presented. Furthermore, the influences of different trajectories on the statistical properties of the channel model were further investigated. The impact of motion trajectory on the PDP in the simulation was supposed to be observed, so the number of Tx and Rx antenna were set to one. The trajectory of the UAV was mainly determined by the speed \(V_{P}\) and angle, where the angle was controlled by the azimuth angle \(\alpha\) and by the elevation angle \(\gamma\), and the random change of trajectory was realized by setting the random change of the two angles. The ST mobility model was used to achieve smooth turns in the RX trajectories, where \(\delta_{s}^{2}\) were used to control the smoothness of the turns. A small variance \(\sigma_{s}^{2}\) indicated a greater likelihood of a very large turn radius, which would show a straighter trajectory. Setting \(\sigma_{s}\to 0\) meant the generation of a trajectory that was close to a straight line. The time interval \(\tau_{i}\) represented the length of time that the Rx moved along the fixed steering center. Smaller time intervals meant that the trajectory would change turn centers frequently, which could lead to wavy trajectories. As shown in Figure 3a, a Markov chain was used to create the Tx trajectories, the \(\alpha\) was random, and the \(\gamma\) was set as \(\pi/8\) and \(\pi/3\) for simulating the random flight. There are three trajectories shown in Figure 3b. For smooth-turning trajectories, the \(\sigma_{s}^{2}\) was set to 0.007 m\({}^{-1}\), and the time interval was set to 4 s.  
In the simulation of the MB case, the basic parameters were set as follows: \(f_{c}\) = 3.5 GHz; \(v_{UAV}=v_{R}\) = 5 m/s, \(a_{UAV}=a_{R}\) = 0 m/s\({}^{2}\). As shown in Figure 4a, the Tx trajectory was set as a line, to emulate the level-flight trajectory; a Tx trajectory based on a Markov chain was generated, as shown in Figure 4b. Based on the ST mobility model, the Rx trajectory was set as trajectory I, as shown in Figure 4a; the Rx trajectory was set as trajectory II, as shown in Figure 4b. From the time-variant PDP, there is a bright red line in Figure 4, representing the LoS path. Some subpaths were arranged to the right of the LoS path. The delay of the LoS path reflected the relative distance between the Tx and the Rx. From the PDP diagram, we can see the drift of power, the delay, and other parameters, as well as the birth and death of clusters. The changes of multiple sub-paths reflected the influence of the changes of the scattering environment on the signal during transmission. The random trajectory in dual-mobility had a greater degree of curvature and a greater time delay than the linear trajectory from the PDP diagram. The results indicated that the trajectories of the Tx would have effects on the PDP. As shown in Figure 5, a simulation of a PDP diagram for the SB case was created. The trajectory of the cluster was assumed to be the same as that of the Rx during the simulation. In order to simulate urban transportation emergency communication scenarios, there were a large number of vehicles blocking the vehicles at the Rx, with the same vehicle trajectory. Figure 6 shows the temporal ACF. A temporal ACF can reflect the stationary characteristics of the AG channel. The time variation of the temporal ACF was caused by the time-variant MPCs between the Tx and the Rx, due to the motion of the UAV and theground BS. For the simulated parameters of Figure 6a, the UAV speed was 4 m/s, the acceleration was 3 m/s\({}^{2}\), and the Rx speed was 4 m/s. The random track of the Tx was formed by a Markov chain, and the Rx trajectory was set as linear. For the simulated parameters of Figure 6b, the UAV speed was 4 m/s or 2 m/s, the acceleration was 1 m/s\({}^{2}\), and the Rx speed was 2 m/s, using the same trajectory.