## 2 System Model  
The Model of the Multi-Dimensional Hybrid Multiple-Access Method for Space-Time-Frequency-Code Division  
Ground user terminals of the S-IoT are in a dormant state most of the time to reduce energy consumption and prolong their service life. Therefore, when a satellite receives a message from the ground terminal, it first sends a wake-up command to the ground terminal and then allocates a channel for the user. The S-IoT is based on narrowband communication. Thus, we establish a MH-STDF model under the condition of limited frequency resources. It includes a single satellite and several different beams, with the sub-beams arranged in a cellular pattern, as shown in Figure 1. The LEO satellite cellular beam layout can be regarded as consisting of multiple small cells. Except for the circular coverage area of the main beam, the coverage areas of the other beams are elliptical. For the ease of analysis, the elliptical coverage areas are proportionally equivalent to circular coverage areas of equal area. Furthermore, the shape of the coverage areas is equivalent to a regular hexagon. The user distribution within the coverage areas is also equivalent proportional. The coverage areas of beams are multiplexed using three colors. Within a single beam cell, frequency division multiple access (FDMA), time division multiple access (TDMA), and CDMA are used to further multiplex the frequencies within the beam. In this model, when the satellite sends a wake-up command, it assigns information such as the frequency point, time slot, and code pattern to the terminal. In order to increase the maximum number of users that can be connected to a single satellite, each beam cell needs to allocate as much frequency resources as possible to improve the overall spectrum utilization. Therefore, in this model, the beam cells are divided into central and edge areas according to the distance from the center of the sub-beam. The edge area is used as a protection interval to avoid user channel interference in the overlapping area between adjacent beams. The central area allocates more frequency resources according to user needs as much as possible. The frequency allocation principle for a single satellite multi-beam cell is as follows: First, the available frequency is divided into multiple sub-bands according to FDMA. Then, the frequency band resources are allocated to the central and edge areas of the cell. It is ensured that the frequency bands allocated to the central area do not overlap with those allocated to the edge area in the same beam. The edge area serves as a protection interval, and the frequency band resources allocated to adjacent edge areas cannot overlap. The allocation of frequency resources to users in the same region is random to ensure that all users can get services fairly. The principle of time slot allocation is as follows: Since the LEO satellite beam is fast-moving, it faces the problem of beam switching [30; 31]. Therefore, when dividing time slots, some channels are reserved for users not currently under the beam. The remaining channels are allocated to users close to the edge of the beam according to their location. The time slot allocation of users among different satellite beams can be transmitted via the intersatellite link [32; 33]. The frequency resource allocation of the MHSTFC-UD model is shown in Figure 2. Full-frequency multiplexing is implemented in different beams, and three-color multiplexing is implemented between adjacent edge cells to avoid frequency interference. After a single beam cell has divided the time slot through organized time division multiple access (OTDMA) and allocated a certain amount of frequency resources, the model further implements frequency reuse by using PN codes through CDMA to expand the spectrum, thereby further increasing the number of users that can be accessed to the satellite. The MHSTFC-UD model distinguishes different access users in four dimensions: space, time, frequency and code.