## 1 Introduction  
Due to their flying, maneuvering, and hovering merits, aerials have been increasingly used as wireless communication platforms, especially for post-disaster aid services. This is due to their ability to quickly reach remote and hard-to-access areas [1, 2, 3]. In post-disaster situations, aerials can offer wireless connection for user devices (UDs) owned by survivors and rescue teams where the terrestrial wireless communication networks are completely damaged or malfunctioned [4, 5, 6, 7]. Deploying multiple aerials in such scenarios is challenging, requiring multi-objective optimization, including coverage, limited aerial battery life times, heights, and communication performance. Also, the limited transmission coverage of aerials might hinder their ability to establish communication links with the closest ground base station (GBS) or even among themselves, affecting their arrangement and data collection abilities in post-disaster zones. Therefore, this paper proposes the usage of low earth orbit satellite (LEO-Sat) to assist aerials in rescue missions by creating backhaul links with the nearest survival GBS. Recently, LEO-Sat has garnered significant interest and is currently the subject of ongoing research in diverse wireless communication applications [8, 9, 10, 11, 12, 13, 14, 15]. However, limited research studies have explored the potential integration of LEO-Sat and aerial technologies to leverage both benefits and establish more efficient wireless communication platforms [16; 17; 18]. In the proposed post-disaster scenario, LEO-Sat effectively assists disseminating/collecting control information and data traffic to/from nearby GBSs via aerials, where only indirect communication links between GBSs and aerials exist. The primary difficulty in this system is how to effectively distribute aerials in the sparsely populated sub-areas, i.e., disaster area clusters/grids. In this scenario, the main objective is to maximize the area's total achievable sum data rates plus maintaining fairness in post-disaster cluster coverage. Also, the bounded aerials' battery capacity and LEO-Sat bandwidth should be anticipated. To ensure fairness in post-disaster cluster coverage, higher user density clusters/grids should be served more frequently than the less-populated ones. This optimization problem has three main challenges. Firstly, coverage fairness should be maintained among post-disaster clusters according to their users' densities, where the wireless infrastructure is entirely malfunctioning, which involves the difficulty of knowing victims' information. Secondly, aerials should conserve their battery energy while maximizing the collected data from the post-disaster zone to prolong their critical rescue operation cycle before recharging. Finally, optimizing aerials' transmit (TX) communication powers as well as LEO-Sat bandwidth resources according to the aerials' traffic reflects another critical challenge. To deal with this highly challenging problem, this work presents the following main contributions:  
* We propose to split the LEO-Sat assisted aerials deployment problem into two sub-problems. This is enabled by aerials' TX powers towards the LEO-Sat, and the LEO-Sat bandwidth resources should be allocated based on aerials' traffic needs after deployment. In this regard, the first sub-problem deals with the limited battery budget fair aerials deployment, and the second one deals with optimizing the aerials' TX powers and LEO-Sat bandwidth resources according to the aerials' traffic needs. * A budget-constrained combinatorial multi-armed bandit (MAB) game with arms' fairness (CB-BFC) [19] will be proposed to address the first sub-problem. In this context, MAB is an advanced online learning tool where a player intends to increase his achievable profit via playing over the bandit's arms. Only through the exploitation-exploration process, without knowing any prior knowledge about the game, the player learns how to always play with the highest-profitted arm.