## 1 Introduction  
As a significant part of space information networks, satellite communication (SAT-COM) has been widely applied to provide global wireless links [1]. Motivated by the seamless coverage character of SATCOM, researchers began to study how the SATCOM helps the terrestrial wireless networks, especially the 5G and beyond [2, 3, 4, 5]. As one of the significant achievements, the nonterrestrial network (NTN) was proposed in Release 16 and formally defined in Release 17 by 3 GPP [6]. In NTN, one or more satellites work as relays which can help exchange data among user terminals (UTs). Meanwhile, gateways are required to manage the NTN, and can connect the NTN with terrestrial networks [7, 8]. Due to the severe signal attenuation of space-to-ground links, gateways are often equipped with high transmit-receive gain antennas, which have the ability to amplify UTs' signals in SATCOM star networks [9, 10, 11]. A typical SATCOM star network consists of a gateway, called hub station (HS) in this scenario, and multiple UTs. Two UTs could communicate with each other in a UT-to-HS-to-UT two-hop-wise manner, where the HS works in the amply-and-forward mode. As another usage of the star network, the HS broadcasts to UTs and collects information in the backward link. This mechanism has been widely applied in multimedia and Internet of Things [12, 13]. To meet the transmission requirements of extensive UTs, multiple access (MA) technologies have been studied. The authors in [14] provided possible application scenarios of SATCOM star networks. In addition, commonly used MA techniques, such as time division multiplexing and time division multiple access (TDM/TDMA) and frequency division multiple access (FDMA), are also investigated. In order to give instructions for MA techniques in the SATCOM star network, the authors in [15] studied measurement methods in terms of the transmitting performance. By building a ground-based measurement system with a UT, ref. [15] gave testing results of TDMA and multi-frequency TDMA (MF-TDMA) on the aspects of power consumption and spectrum envelope. Motivated by the advanced MA schemes in terrestrial wireless networks, high-spectral-efficiency MA solutions such as nonorthogonal multiple access (NOMA) were developed. The authors in [16] gave deep insights into the terrestrial-satellite integrated network, where the SATCOM works as a supplemental means for the terrestrial NOMA network. Users with poor channel conditions would be served by the satellite. To maximize the channel capacity, ref. [16] further proposed the user-pairing strategy, and the power allocation scheme was also studied. Realizing that the SATCOM would be fully integrated in ground-based wireless network in the future, the same authors discussed a terrestrial-satellite jointly beamforming method in their work [17]. Specially, optimal beamforming vectors were derived to improve the channel capacity. In [18], the authors proposed a two-phase NOMA in two-user SATCOM networks. The co-channel users decode NOMA signals in the first phase, where the strong user could obtain the weak user's signal as well. Then, the strong user pushes forward useful signals to the weak user to enhance the signal-to-noise ratio (SNR). For the sake of analyzing how the NOMA behaves in a shadow fading environment, the authors in [19] investigated multi-user NOMA over shadowed Rician fading channels. The outage probability was derived to validate the advancement compared with conventional MA schemes. Inspired by NOMA, we developed a co-carrier transmission method in our previous work [20]. Different from the works in the above, the co-carrier method occupies partial bandwidth instead of the whole spectral resource acquired in conventional NOMA. Particularly, ref. [20] further gave instructions on pairing suitable users for co-carrier transmission. Recognizing the benefits of the multi-antenna technique, researchers launched the development of multiple antennas in SATCOM.