## 3 System Model and Problem Formulation  
### System Model  
The system model addressed in this article is depicted as a three-layer network structure, comprising IoT devices located on the ground, UAV clusters deployed in the air, and LEO satellites. The corresponding schematic diagram is illustrated in Figure 1. Our emphasis is solely on the uplink transmission of the signal. Specifically, the data collected by ground IoT sensors are relayed by drones and transmitted to the LEO satellite in space. Subsequently, the LEO satellite transfers the data to the remote data center via the satellite network, a feature not considered in the model. \(T\) different types of IoT devices are taken into account, denoted as \(I_{1},\ldots,I_{l},\ldots,I_{T}\), and their quantities are defined as \(N_{1},\ldots,N_{t},\ldots,N_{T}\). The total number of IoT devices is defined as \(\sum_{t=1}^{T}N_{t}=N^{l}\). We use \((x_{n}^{l},y_{n}^{l})\) to denote the coordinate of the \(n\)-th device in the \(t\)-th category of IoT devices. The set of UAVs is represented by \(\mathbf{U}=[U_{1},\ldots,U_{N^{l}}]\), where \(N^{l}\) is the number of UAVs. The coordinate of the \(n\)-th drone is denoted as \(\mathbf{L}_{m}^{U}=(x_{n}^{l},y_{n}^{l},h^{U})\), where \(h^{U}\) is the fixed flight height of the drone. UAV relays are assumed to facilitate multiple-input multiple-output communications, enabling the simultaneous existence of multiple uplinks. The UAV relay is equipped with a robust signal receiver. Given the limited deployment range of IoT devices in this study, it is assumed that the UAV can effectively receive signals from all the ground IoT devices. The total available bandwidth of the entire communication system is defined as \(B\). To prevent signal interference among IoT devices, we allocated the bandwidth into different shares, ensuring that the bandwidth resources occupied by each IoT device do not overlap. Correspondingly, we initially partition the bandwidth into \(T\) segments for various categories of IoT devices, with the ratio represented by \(\mathbf{j}=[j_{1},\ldots,j_{l},\ldots,j_{T}]\), \(\sum_{t=1}^{T}j_{t}=1\). Next, we further subdivided the allocated bandwidth for IoT devices within each category. Specifically, for the \(t\)-th category of IoT devices, the bandwidth reallocation ratio is defined as \(\mathbf{k}^{t}=[k_{1}^{t},\ldots,k_{n}^{t},\ldots,k_{N_{t}}^{t}]\), \(\sum_{t=1}^{N_{t}}k_{t}^{t}=1\). And the intra-class bandwidth allocation set for all categories of IoT devices is represented as \(\mathbf{k}=[\mathbf{k}^{1},\ldots,\mathbf{k}^{T}]\). \(\mathbf{a}_{t}=[\alpha_{t1},\ldots,\alpha_{tn},\ldots,\alpha_{N_{t}}]\) is utilized to denote the selection association of the \(t\)-th type of IoT devices to the drone, where \(\alpha_{tn}\in\{1,\ldots,N_{u}\}\), \(n\in\{1,\ldots,N_{t}\}\). In other words, the serial number of the associated drone for the \(n\)-th IoT device in \(l_{l}\) is \(\alpha_{tn}\). \(\mathbf{A}=[\mathbf{a}_{1},\ldots,\mathbf{a}_{l},\ldots,\mathbf{a}_{T}]\) is used to represent the relationship between all types of IoT devices and UAVs. Simultaneously, \(C_{tn}^{U}\) is defined as the number of IoT devices associated with the UAV selected by the \(n\)-th IoT device in \(l_{l}\). It should be noted that one IoT device can only select one UAV for data transmission. Additionally, the transmit power of each ground IoT device is set to \(P^{l}\). The total forwarding power of the drone is set to \(P^{l}\), evenly distributed for signal forwarding to each connected IoT device. Furthermore, we consider an LEO satellite to stably receive the UAV's forwarded signal, disregarding LEO satellite switching. The coordinate of the LEO satellite is denoted as \((x^{L},y^{L},h^{L})\), where the altitude of LEO satellite is fixed at \(h^{L}\).