## 3 System Model and Problem Formulation
### Problem Formulation  
In this section, a multi-objective optimization problem is introduced to address the uplink channel resource allocation challenge. The decision variables for this multi-objective optimization problem encompass UAV deployment locations, bandwidth allocation ratios for different categories of IoT devices, bandwidth allocation ratios for IoT devices within a category, and UAV-IoT device selection association. The objective is to maximize the minimum channel capacity within each category of IoT devices, with the the number of objective functions equal to the number of IoT device categories. The multi-objective optimization problem can be formulated as follows:  
\[\max_{\mathbf{L}}\left\{ \begin{aligned} & min(R_{n}^{1}),& \forall n\in\{1,\dots,N_{1}\}\\ &\dots\\ & min(R_{n}^{t}),&\forall n\in\{1,\dots,N_{t}\},\forall t \in\{1,\dots,T\}\\ &\dots\\ & min(R_{n}^{T}),&\forall n\in\{1,\dots,N_{T}\}\\ \end{aligned} \right. \tag{6}\] \begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & **Description** \\ \hline \(T\), \(I_{t}\) & The number of types of IoT devices, the \(t\)-th category of IoT devices. \\ \hline \(N_{t}\), \(N^{l}\), \(N^{l}\) & The number of the \(t\)-th category of IoT devices, the total number of IoT devices, the number of UAVs. \\ \hline \((x_{n}^{t},y_{n}^{t})\) \((x_{n}^{UI},y_{n}^{UI},t^{U})\) & Coordinate of the \(n\)-th device in \(I_{t}\), coordinate of the \(n\)-th UAV. \\ \hline \(B\) & The total available bandwidth of the system. \\ \hline \(\mathbf{j},\mathbf{k}^{t},\mathbf{K}\) & The set of bandwidth ratios occupied by different types of IoT devices, the set of the bandwidth ratios occupied by each device in the t-th category of IoT devices, the set of \(\mathbf{k}^{t}\) for each category of IoT devices. \\ \hline \(j_{t}\), \(k_{n}^{t}\) & The proportion of total bandwidth occupied by the \(t\)-th category of IoT devices, the proportion of bandwidth occupied by the \(n\)-th device in the \(t\)-th category of IoT devices. \\ \hline \(\mathbf{a}_{t}\), \(\mathbf{A}\) & The set of UAV serial numbers selected by each device in the \(t\)-th category of IoT devices, the set of \(\mathbf{a}_{t}\) for each category of IoT devices. \\ \hline \(\alpha_{tt}\), \(C_{tn}^{LI}\) & The UAV sequence number selected by the \(n\)-th device in the \(t\)-th-category IoT devices, the number of IoT devices associated with the UAV selected by the \(n\)-th device in the \(t\)-th-category IoT devices. \\ \hline \(P^{l}\), \(P^{U}\) & Signal transmission power of IoT devices, total forwarding power per UAV. \\ \hline \((x^{L},y^{L},h^{L})\) & The three-dimensional coordinate of an LEO satellite. \\ \hline \(h^{LI}\), \(h^{L}\) & The fixed height at which the drone flies, the altitude of the LEO satellite. \\ \hline \(g_{n}\) & The channel gain per unit distance. \\ \hline \(g_{n}^{l_{t}\to l_{u_{n}}}\) & \(g_{n}^{U_{u_{n}}\to L}\) & The channel gain between the \(n\)-th device in \(I_{t}\) and the selected UAV, the channel gain between the UAV selected by the \(n\)-th device in \(I_{t}\) and LEO satellite. \\ \hline \(\gamma_{n}^{l_{t}\to l_{u_{n}}}\) & \(\gamma_{n}^{U_{u_{n}}\to L}\) & The signal-to-noise ratio between the \(n\)-th device in \(I_{t}\) and the selected UAV, the signal-to-noise ratio between the UAV selected by the \(n\)-th device in \(I_{t}\) and LEO satellite. \\ \hline \(N_{0}\) & The power spectral density of additive white Gaussian noise. \\ \hline \(B_{n}^{t}\), \(P_{n}^{t}\) & The bandwidth occupied by the \(n\)-th device in \(I_{t}\), the forwarding power obtained by the \(n\)-th device in \(I_{t}\) from the selected UAV. \\ \hline \(R_{n}^{t}\) & The channel rate of the \(n\)-th device in \(I_{t}\) forwarded to the LEO satellite via a UAV. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notation summary.