## 2 Modeling of UAV-Assisted Communication  
### UAV Air-to-Ground Channel Model  
In dense urban environments, communication is primarily supported by ground-based stations serving mobile users distributed across cellular networks. However, during certain emergencies such as earthquakes, urban communication infrastructure may fail. When the ground-based station in the earthquake-stricken area malfunctions, it results in the loss of signal coverage within the community. This disruption complicates communication for ground users, leading to panic and impeding emergency relief efforts. Therefore, unmanned aerial vehicles (UAVs) are introduced as temporary aerial base stations to provide communication services in emergency scenarios. In this section, we present the basic model of UAV-assisted A2G communication. When the ground base station malfunctions, the UAV can be utilized as an aerial base station to serve urgent communication. Before establishing a UAV-assisted emergency communication model, it is necessary to discuss the air-to-ground channel. In A2G communication, there are LoS (line of sight) paths and NLoS (not line of sight) paths, in which the NLoS is obstructed by obvious obstacles. While A2G communication can enjoy LoS channel in common cases, NLoS channel occurs when obstacles exist. As Figure 1 demonstrates, urban architecture and natural landscape both perform as obstacles in UAV-assisted communication. The occurrence probability for LoS/NLoS channel differs according to the location of UAV and the density of obstacles. It can be seen that the ratio of LoS and NLoS path varies with the height of UAV. Therefore, a probabilistic LoS/NLoS channel model is applied [21] with parameter \(p_{LoS}\) to denote the occurrence probability of LoS channel and \(p_{NLoS}\) for that in NLoS channel. Inconsideration of varied environmental factors, \(p_{LoS}\) and \(p_{NLoS}\) for a single A2G link can be calculated by Equations (1) and (2). \[p_{LOS}=\alpha(\frac{180\theta}{\pi}-15)^{\gamma}, \tag{1}\]  
\[p_{NLOS}=1-\alpha(\frac{180\theta}{\pi}-15)^{\gamma}, \tag{2}\]  
in which \(\theta\) refers to the elevation angle between each user equipment and UAV, reflecting the impact of UAV height and position on the link. Parameters \(\alpha\) and \(\gamma\) are influenced by environmental characteristics at the same time. In the discussed earthquake-stricken cellular cells, mobile users evacuate from buildings and move toward certain exits. The ground base station breaks, interrupting communication. To plan a UAV for urgent communication, we need to model the environment of the cell, and then adjust the UAV's resources and location to maximize communication quality. As Figure 2 displays, the path of a UAV can be planned according to ground users' evacuation trajectory in order to enhance communication quality and increase coverage. Figure 1: **LoS/NLoS A2G channels in UAV-assisted communication. ** The model consists of a UAV aerial base station, ground user equipment, urban obstacles, and natural obstacles, which can influence LoS probability and then determine the A2G channel. Figure 2: **UAV-assisted emergency communication with malfunctioned ground base station and moving users. ** The model considers obstacles that impact both the trajectory of users and the signal transmission with the UAV base station, and our research is dedicated to the scheduling of UAV trajectory and resources to optimize the efficiency of communication during the evacuation. The LoS path of UAV is obstructed by several obstacles, including compound buildings and greenery such as trees. Buildings are also regarded as obstacles for mobile users to evacuate from. Moreover, at each communication timeslot, transmission power and spectrum division of the UAV are determined. As the proposed problem mainly focuses on the path planning and resource allocation algorithm of the UAV base station, a number of assumptions are introduced to simplify the model with no influence on algorithm construction.