## 4 Parameterization and Analysis of the Proposed TDL Model
### Delay-Doppler Spectrum  
The Doppler frequencies at different time instants can be obtained using Equation (2). Given that the receiver is fixed, the Doppler shift can be rewritten as [29]  
\[f=-\frac{\
u_{t}}{\lambda}\cdot\cos(\varphi)\cdot\cos(\theta), \tag{14}\]  
where \(\
u_{t}\) is speed of the UAV as listed in Table 2, and \(\varphi\) and \(\theta\) are the azimuth and elevation angles between the velocity vector and propagation direction of the signal, respectively. These two angles are calculated based on their position, which is obtained from the navigational equipment on the receiver and the UAV. Thus, the maximum Doppler frequency \(f_{m}\) and the Doppler frequency of the LoS component \(f_{los}\) for each flight phases can be calculated by the angle information and the UAV's speed. Figure 6 shows the normalized delay-Doppler spectrum of the considered UAV flight phases from FS1 to FS6. The UAV descends vertically, as shown in Figure 1b, with a speed of 1.2 m/s, which results in a maximum Doppler frequency 10.8 Hz. In such a scenario, the azimuth angle remains nearly constant, whereas the elevation angle changes dramatically resulting in the Doppler frequency of the LoS component within the range between 1.9 Hz and 9.7 Hz. In addition, the steady variation of the UAV can be also observed in the Doppler domain with fewer MPCs, which can be verified in Figure 6a. Figure 6b shows an example of the averaged Doppler spectrum for low approach scenario, where the UAV flies in from a distance to the takeoff point. The altitude of UAV slowly decreases from 100 m down to 40 m, with speed reduced from 27 m/s down to 1.2 m/s. It can be observed from the Doppler spectrum that there exists diffuse scattered MPCs spreading in delay from approximately 100 ns to 1000 ns, and in Doppler frequency from \(-200\) Hz to 200 Hz. In scenario FS3, the UAV is within the hovering flight mode, where the UAV speed remains constant at \(27\,\mathrm{m/s}\). In this scenario, the Doppler frequency is determined by the angles \(\varphi\) and \(\theta\). The effective one-dimension (1D) Doppler angle varies from \(0^{\circ}\) to \(180^{\circ}\), resulting in the Doppler frequency from \(-f_{max}\) and \(f_{max}\). Figure 6c shows the obtained delay-Doppler spectrum at the \"inflexion point\", where the distance between UAV and receiver is the minimum within current flight route. As such, the Doppler frequency of the LoS component at this particular instant is \(0\,\mathrm{Hz}\). The Doppler frequency of LoS component varies between \(89\,\mathrm{Hz}\) and \(-152\,\mathrm{Hz}\), while the UAV travels along the flight route. Similar delay-Doppler spectrum can be found as the fist two scenarios, where a typical \"U-shape\" delay-Doppler spectrum is observed. It indicates the fact that there exists dense scattered MPCs. In A2G propagation scenarios FS4 to FS6, the propagation environment is expanded from traditional two-dimensional (2D) to three-dimensional (3D), implying that the UAV altitude needs careful attentions. Therefore, we considered in the model the influence of UAV at different altitudes on the Doppler spectrum of A2G channels. Figure 6d-f show the delay-Doppler spectrum for the scenario where the UAV flying steadily along a straight line at altitudes of \(300\,\mathrm{m}\), \(500\,\mathrm{m}\), and \(800\,\mathrm{m}\), respectively. With the increase in UAV altitude, the MPC caused by ground reflection and scattering becomes less dominant. In the meanwhile, the LoS path is less effected by ground objects and becomes dominant, as also reported in [34]. In addition, the Doppler shift of the LoS component remains constant at approximately \(201\,\mathrm{Hz}\). The delay-Doppler spectrum for scenarios FS4 to FS6 show essentially the same variation patterns.