## 3 UAV AG Communication Channel Modeling and Characterization  
### A UAV AG Multi-Mobility Multi-Trajectories Channel Model  
The propagation channel between a UAV and a ground BS is affected by large-scale fading and small-scale fading: for this paper, we mainly studied the influence of the latter. Small-scale fading is mainly caused by the multipath components (MPCs) of the channel between the UAV and the vehicle, which can be abstracted as lots of static and moving clusters. The transmission signal between the UAV and the vehicle consists of LoS components and NLoS components, and the NLoS components contain SB components and MB components. Figure 2 gives the model framework of a 3D non-stationary GBSM abstracted by an AG channel with multi-mobility multi-trajectories. The representation of angles, distances, and other parameters is basically the same for the SB case and the MB case; therefore, in order to simplify the content, our article basically shows the parameters of the MB case. The subscripts \(l,k\) and \(l^{\prime},k^{\prime}\) were used to represent the MB case and the SB case, respectively. In particular, the distances of the ray between the Tx/Rx and the clusters were distinguished, using the superscript \(MB\) and \(SB\). The UAV was set as the Tx, and the vehicle was set as the Rx. For the MB case, the AAoD and EAoD of the \(l\)th ray in cluster \(\mathbf{C}_{k}^{A}(t)\) transmitted from the Tx were denoted by \(\phi_{A,I_{k}}^{T}(t)\) and \(\phi_{E,I_{k}}^{T}(t)\), respectively. \(\phi_{A,I_{k}}^{R}(t)\) and \(\phi_{E,I_{k}}^{R}(t)\) were defined as the AAoA and EAoA of the \(l\)th ray in cluster \(\mathbf{C}_{k}^{Z}(t)\) transmitted from Rx, respectively. The relevant angles of the antenna array are also provided, i.e., \(\beta_{E}^{T}\) was the elevation angle, and \(\beta_{A}^{T}\) was the azimuth angle. The angle of the ground Rx end was the same as the above, and is not shown in the figure, due to the low height of the Rx end. Figure 1: UAV-assisted emergency communication scenarios. The channel coefficients for each cluster and each Tx and Rx element pair were characterized by an \(N_{T}\times N_{R}\) matrix \(\mathbf{H}_{small}=\left[h_{pq}(t,\tau)\right]_{N_{T}\times N_{R}}\). The channel impulse response (CIR) between the \(p\)th Tx and the \(q\)th Rx was represented by LoS and NLoS components, expressed as  
\[h_{pq}(t,\tau)=\sqrt{\frac{K_{R}}{K_{R}+1}}h_{pq}^{LoS}(t,\tau)+\sqrt{\frac{1}{ K_{R}+1}}\Big{(}h_{pq,SB}^{NLoS}(t,\tau)+h_{pq,MB}^{NLoS}(t,\tau)\Big{)} \tag{1}\]  
where \(K_{R}\) was the K-factor, and \(\tau\) was the time delay. The NLoS components \(h_{pq}^{NLoS}(t,\tau)\) were expressed as  
\[ \begin{split} h_{pq,SB}^{NLoS}(t,\tau)&=\sum_{k^{ \prime}=1}^{K_{pq}^{\prime}(t)}\sum_{l^{\prime}=1}^{L_{k^{\prime}}^{\prime}} \Bigg{[}F_{q,V}(\phi_{E,l^{\prime}}^{R}(t),\phi_{A,l^{\prime}_{l^{\prime}}}^{ R}(t))\Bigg{]}^{T}\Bigg{[}\begin{matrix}e^{i\theta_{V}^{VV}}&\sqrt{ \kappa_{l^{\prime}}^{-1}}e^{i\theta_{V}^{VH}}\\ \sqrt{\kappa_{l^{\prime}}^{-1}}e^{i\theta_{V}^{HV}}&e^{i\theta_{V}^{HH}}\\ \end{matrix}\Bigg{]}\\ &\times\Bigg{[}F_{p,V}(\phi_{E,l^{\prime}}^{T}(t),\phi_{A,l^{ \prime}_{l^{\prime}}}^{T}(t))\\ F_{p,H}(\phi_{E,l^{\prime}}^{T}(t),\phi_{A,l^{\prime}_{l^{\prime}}}^{T}(t)) \Bigg{]}\sqrt{P_{pq,l^{\prime}_{l^{\prime}}}(t)}e^{2\pi f_{c}((D_{p,l^{\prime} }^{T,SB}(t)+D_{q,l^{\prime}_{l^{\prime}}}^{R,SB}(t))/c+\tau)}\\ &\cdot\delta(\tau-((D_{p,l^{\prime}_{l^{\prime}}}^{T,SB}(t)+D_{q,l^{ \prime}_{l^{\prime}}}^{R,SB}(t))/c+\tau))\end{split}  \tag{2}\]  
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