## 3 System Model  
Figure 1 previews the under-investigation system model of integrating LEO-Sat and aerials to cover post-disaster regions where all nearby GBSs are destroyed or malfunctioned. The management and control (M&C) center orders the nearest survival GBS to the post-disaster area to manage the aerials' deployment assisted by LEO-Sat. To ensure that only one aerial covers a specific post-disaster location, the whole region is virtually divided into a number of clusters. These are depicted as dashed blue lines in Figure 1, with a total number of \(M\) clusters. Each cluster comprises \(K_{i}\) UDs, \(1\leq i\leq M\). LEO-Sat facilitates communication between the closest survival GBS and aerials for both traffic and control data. Also, \(\mathcal{N}\) refers to the set of aerials, with a total number of \(N\) aerials, \(N=5\) in Figure 1, where \(1\leq j\leq N\) and \(N<M\), are used to cover the post-disaster area. LEO-Sat continuously covers these aerials and can easily switch between satellites. The effects of this handover on network performance will be the subject of future investigations. At each time step \(t\), the survival GBS determines which clusters the aerials should cover and assigns  
them accordingly. This is then relayed to the aerials via LEO-Sat backhauling. Relaying and multi-hop transmissions among aerials are out of the scope of this paper and will be the subject of our future investigations. The goal is to properly allocate the aerials to clusters that maximize their attainable data rates while ensuring fair coverage based on UDs' densities in the distributed clusters. This allocation is subject to constraints such as the limited aerial battery budget and the limited LEO-Sat bandwidth resources. In the proposed system model, both rescue workers' and victims' devices are assumed to operate using the same frequency band for simplicity as the main focus is on the LEO-Sat assisted fair aerials distribution. However, we can assume that victims and rescue workers use two different communication bands to mitigate interference. In this case, aerials should be capable of using two different bands' interfaces, one for the workers and the other for the victims, which will complicate the aerials' communication task and put more burdens on their energy consumption. For sure, workers can communicate among themselves using device-to-device (D2D) communications, but they definitely need aerial connectivity to reach the ground monitoring/control center for management and control via LEO-Sat relaying. This interesting point will be a subject of our future investigations by using two different bands, one for workers and the other for victims, including its challenges and possible solutions. Also, this paper proposes a fully centralized scenario for aerial deployment carried out by the M&C center in the survival area, as shown in Figure 1. A decentralized scenario, where rescue workers control aerials deployment, will be the subject of our future investigations due to its numerous challenges, including the limited information on rescue workers, their limited battery capacities that cannot handle the complicated task of aerials deployment, the lack of connectivity to all aerials simultaneously, etc. In the following subsections, the link models of aerial-UD and LEO-aerial are described in detail, and the optimization problem is formulated.