## 1 Introduction  
The space-based Internet of Things (S-IoT) is a network that uses various space-based platforms to acquire, process, transmit and apply Internet of Things (IoT) information [1]. It connects various devices and sensors through a satellite network to enable large-scale connection and data transmission between devices and sensors on a global scale [2]. It has the characteristics of working in all weather conditions and across all regions and is not easily disrupted [3, 4]. Nowadays, it is widely used in the ship automatic identification system (AIS), automatic dependent surveillance-broadcast (ADS-B), and data collection system (DCS) [5]. The S-IoT not only makes up for the shortcomings of ground-based IoT [6] but also combines with ground-based IoT, which is one step further from realizing the interconnection of everything. However, the further development of S-IoT is being limited by insufficient allocable frequency resources and low spectrum utilization [7]. With the rapid development of mobile communications and IoT, the number of terrestrial terminals and users showed explosive growth. Global System for Mobile Communication Association (GSMA) and Transforma Insights predict that the global scale of IoT connections in 2030 will reach 30 billion [8] and access to satellite terminals will reach more than 100 million users. The demand for spectrum resources is growing. The Ku band, as the \"golden band\" for LEO satellite communication, has almost been allocated. The remaining LEO satellite communication bands that can be allocated are Ka and V bands. Although the communication band is higher and the available band is wider, the rain fade of Ka and V communication bands is also larger, and the requirements for the receiver are also higher. The remaining available spectrum resources in the L, S and C frequency bands, where meteorological and maritime communication satellites work, are limited. The existing technologies can no longer meet the increasing communication needs. The low utilization of an allocated spectrum is another constraint for the development of space-based IoT. According to a survey conducted by the Federal Communications Commission (FCC) in the United States, the resource utilization rate of the licensed frequency bands is between 15% and 85% under the preset spectrum allocation model [9]. Moreover, in Finland, more than 90% of the spectrum is idle [10]. Therefore, under the condition of limited frequency resources, improving the utilization of spectrum resources by combining different multiple-access technologies, optimizing spectrum allocation, and frequency multiplexing will be the key to expanding the system capacity and the development of satellite communication technology [7]. To improve the utilization of a spectrum, the combination of multiple-access techniques can achieve frequency multiplexing. Ref. [11] combines code division multiple access (CDMA) with space division multiple access (SDMA), but the access user capacity is more significantly affected by the spreading sequence length and the size of the spreading gain. Then, the K-means clustering algorithm is used to cluster and group users to each SDMA group to improve throughput [12]. Ref. [13] proposes a MIMO transmission scheme for full-frequency multiplexing (FFR), but it needs to know the channel information of the users for precoding. Further, a single-frequency multi-beam transmission (SF-MBT) algorithm allocates different beams more carefully for different geographic regions to avoid the interference generated by full frequency multiplexing [14]. Therefore, improving the beam layout is also one of the ways to improve spectrum utilization, such as concentric space division multiplexing (CSDM) based on orbital angular momentum (OAM) [15], dividing the beam into central and edge regions [16; 17], designing multicolor frequency multiplexing layouts [18; 19], and designing square coverage layouts by using polygonal splitting strategies [20]. However, most are only used in terrestrial networks. Ref.