## 1 Introduction  
The integration of terrestrial space and aerial access networks is a key use of sixth-generation (6G) technology, which is garnering increasing interest from academics and businesses. This integration greatly enhances the capabilities of the Internet of Remote Things (IoRT) [1, 2, 3]. IoRT networks have gained widespread use, such as remote surveillance systems for monitoring wild animals, natural disasters, and climate change [4, 5, 6]. Due to the limitation of the geographical environment, it is difficult to deploy terrestrial base stations in mountains, deserts, and other remote areas, but environmental monitoring data are crucial in such areas. Meanwhile, terrestrial base stations cannot change their fixed locations without incurring high cost. To meet the requirements of IoRT, non-terrestrial networks (NTNs) represent a promising future application of wireless networks, especially for extending connectivity to remote and underserved areas and providing new communication options [7]. NTN technologies like satellites, high-altitude communication platforms (HAPs), and unmanned aerial vehicles (UAVs) can bring temporary or long-term connectivity to regions where terrestrial infrastructure is lacking [8, 9, 10]. In particular, UAVs fly at a low altitude, are equipped with sensors and monitoring equipment, and can be quickly launched to collect the data of IoRT sensors, which are then transmitted to the core network (CN) [11]. However, due to the limitation of the storage capacity and data processing capability of UAVs, the collected data can be conveyed to satellites in space and then transmitted to remote ground stations [12]. Compared with medium-orbit satellites and synchronous satellite systems, LEO satellites have the advantages of low transmission delay, low launch cost, and global coverage. Combining the advantages of the flexible distribution of UAVs and the long-distance transmission of LEO satellites, a network architecture is proposed in which UAVs serve as base stations and low-orbit satellites serve as relays. This structure belongs to fifth-generation new radio (5G-NR) networks and is a kind of integrated access and backhaul (IAB). However, NTNs have not yet been taken into consideration, and the present standards only specify IABs for the terrestrial domain [13]. UAV-assisted and satellite-terrestrial IAB networks are the two categories of existing research on non-terrestrial IAB networks. A system model is proposed for forward link broadcasts in an in-band IAB HetNet by incorporating UAVs as drone BSs into the IAB network [14]. The work in [15] solved a path selection problem for a multi-hop IAB network using UAV assistance. In order to determine the best path scheduling strategy and maximize the overall transmission rate, the authors devised and solved a binary linear optimization algorithm. A satellite-terrestrial IAB network design for data offloading was examined in [16]. In order to optimize the overall backhaul capacity, the authors suggested modifying the swap-matching method. Above these studies, the aim is to design the optimal network deployment to achieve economic wide-area connectivity. However, due to the mobility of both the UAV BSs and the LEO relays, there are many crucial challenges to the backhaul links. The fast and continuous movement of both UAVs and satellites results in rapid topological changes, which break data transmission and degrade system reliability [17]. Moreover, the deployment of UAVs varies based on the specific circumstances and needs of IoT sensors [9; 18]. For example, in rescue operations following an earthquake, UAV-assisted remote control varies from a few kilometers to several hundred kilometers around, whereas UAVs are distributed on multiple lines for the inspection of outdoor high-voltage transmission lines. Therefore, backhaul link selection for a UAV to a group of LEO relays is very complicated.