## 1 Introduction  
### Literature Review  
Due to its wide coverage characteristic, satellite communication (SATCOM) is able to provide long distance data transmission services. In 6G wireless communication systems, SATCOM has been recognized as an efficient way to spread terrestrial coverage [1, 2]. Specifically, user terminals (UTs) can be expected to access the wireless network by connecting to the satellite. Satellites are able to relay the information directly to the target UT or to the gateway, which has wired connections with the ground-based networks [3]. To provide stable links between the satellite and UTs, SATCOM systems are often built on geostantly Earth orbit (GEO) satellites. Due to the extremely high signal path loss in GEO-based systems, large-size antennas are expected to be equipped at UTs. However, UTs are always designed in small-size terminals for Internet of Everything (IoE) uses. In this case, low Earth orbit (LEO) SATCOM has been widely studied in the scenario of IoE. Since LEO satellites have the advantages of short transmission delay and low signal path loss, many companies have turned their attention to LEO SATCOM. As one of the pioneers, SpaceX launched the project of Starlink in 2014, which aims to built a SATCOM network with over ten thousand LEO satellites [4; 5; 6]. In the Starlink system, LEO satellites are connected by inter-satellite links. Then, multiple satellites could provide global service where users are able to connect to the internet by deploying a satellite terminal. Dynamic strategies have been widely studied in SATCOM. The authors of [7] proposed a dynamic selection method in satellite-terrestrial networks where a power and server execution rate joint-optimization scheme is developed. UTs are able to access the proper node with the minimum expense. To alleviate the inter-beam interference in LEO SATCOM, ref. [8] proposed a dynamic beam illumination method. The number of simultaneously illuminated beams could be minimized while guaranteeing the coverage range. One of the main concerns of the LEO SATCOM is determining how to efficiently develop the satellite resource, which has drawn significant attention. In this paper, we provide a literature review of high efficiency transmission methods under single and multiple nodes backgrounds. High efficiency transmission methods have been widely discussed in existing works. In [9], the authors proposed a two time-slots transmission method in satellite-ground integrated systems. To fully utilize the channel diversity, the user with a strong channel condition could forward the useful information to the weak user after running the successive interference cancellation (SIC). In this case, the outage probability of the weak user could be improved. For the multi-beam scenario, the authors in [10] studied a non-orthogonal multiple access (NOMA)-based multi-beam transmission scheme in a terrestrial-satellite network. The beamforming vectors of the satellite and base stations were jointly optimized to boost the signal that arrived at the users. For the LEO NOMA, the authors in [11] proposed a channel condition feedback-based NOMA transmission method. To relieve the computational complexity onboard, LEO satellites generate random beams without calculating the exact beamforming vectors. Users could transmit the channel condition of each beam through the uplink channel. Then, the LEO could allocate users in the beams by considering the threshold of signal-to-interference-noise ratio (SINR). Generally speaking, the number of simultaneously generated beams on LEO satellites would be limited. In this case, our previous work in [12] studied a beamhopping-based NOMA transmission scheme where ground cells can be illuminated sequentially according to the requirements. We proposed a unified framework for code domain or power domain beamhopping NOMA. To satisfy the service requirements of users, the illuminating duration of beams and power factor are optimized. The work analyzed the outage behavior of beamhopping NOMA as well.