## 3 System Model and Optimization Formulation  
### System Model  
This paper explores an uplink scenario where the multibeam LEO constellation provides services for heterogeneous remote IoT terminals with various QoS requirements. As shown in Figure 1, each multibeam of LEO satellites provides data transmission services for remote IoT terminals within its beam coverage, such as forest fire monitoring sensors and hydrological sensors. As network access selection has not been studied in this paper, it is assumed that all IoT terminals access their nearest satellite. Therefore, for IoT terminals, it can be assumed that there is only one satellite above it, regardless of other satellites in the LEO constellation. LEO satellites share the spectrum of the Ka-band and implement a direct forwarding mechanism. Furthermore, another assumption in this scenario is that the terminal remains stationary and is equipped with a single antenna. Multiple power amplifiers on satellites receive uplink signals from IoT terminals, which are located in the geographical area of multiple corresponding beams. Let \(K\) and \(N\) denote the number of IoT terminals and beams, respectively. Consequently, the sets of IoT terminals and beams can be denoted by \(U=\{u_{k}|k=1,2,\cdots,K\}\) and \(B=\{b_{n}|n=1,2,\cdots,N\}\), respectively. More specifically, the terminal's beam allocation depends on their location and can be represented by \(\mathbf{x}_{k}=[x_{k,1},x_{k,2},\cdots x_{k,N}],x_{k,n}\in\{0,1\}\), where \(x_{k,n}=1\) denotes that terminal \(u_{k}\) is located in the coverage of the \(n\)th beam and accordingly transmits data to the \(n\)th antenna element of the satellite. The maximum forwarding power of a single beam antenna is \(P_{B}\), while the maximum forwarding power of the whole satellite is \(P_{total}\). The overall transmission process of \(u_{k}\)'s intermittent uplink data transmission request can be divided into the following processes. Firstly, \(u_{k}\) employs a control channel to send access requests in the access process, containing its specific QoS requirements \(QoS_{k}\) and the amount of data \(D_{k}\) to be transmitted. Then, the Centralized transmission control unit (CTCU) on the satellite will take charge of channel assignment and power control to allocate specific channel \(c_{k,S}\) and power \(p_{k,S}\) for \(u_{k}\). Subsequently, \(u_{k}\) transmits its data with power  
Figure 1: S-IoT scenario based on multibeam LEO satellite constellation. \(p_{k,S}\) on channel \(c_{k,S}\) in the data transmission process. This paper focuses on the joint channel allocation and power control decision in the second step of the process. For spectrum resources, the total bandwidth is divided into an independent control channel and \(M\) data transmission channels according to the frequency division multiple access (FDMA) paradigm. The available channel set for transmission can be denoted as \(C=\{c_{m}|m=1,2,\cdots,M\}\), where each channel enjoys the bandwidth of \(B\). Therefore, the channel allocation aims to select a channel from the channel set \(\mathcal{C}\) for IoT terminal \(u_{k}\), which can be denoted as a channel allocation vector \(\mathbf{w}_{k}=[w_{k,1},w_{k,2},\cdots w_{k,M}]^{T}w_{k,m}\in\{0,1\}\), where \(w_{k,m}=1\) indicates that the \(m\)th channel \(c_{m}\) is allocated to IoT terminal \(u_{k}\). Hence the channel allocation result of all the terminals can be expressed as \(\mathbf{W}=[\mathbf{w}_{1},\mathbf{w}_{2},\cdots,\mathbf{w}_{M}],\mathbf{W} \in\mathbb{R}^{K\times M}\). In terms of power resource, \(P_{k}\) denotes the maximum transmission power of the IoT terminal \(u_{k}\). Though power is theoretically a continuous variable, it is usually discretized in practice in satellite communication scenarios to reduce the computational complexity of a satellite control system.