## 1 Introduction
### Literature Review
By cooperatively utilizing the advantages of GEO and LEO satellites, the SATCOM service could be significantly enhanced [13]. The GEO satellite is able to provide wide coverage while LEO satellites offer low latency service. In a GEO-LEO network, ground users have choices to access the GEO satellite or the LEO one. For the transmission techniques in GEO-LEO networks, the authors in [14] proposed an uplink NOMA in GEO-LEO network. In the novel scheme, ground users transmit signals to GEO and LEO satellites within one resource block. Simulation results showed that the ergodic sum-rate of NOMA is superior compared with the conventional orthogonal multiple access (OMA). Further, the ergodic sum-rate grows with the increase in elevation angle. To provide deep insight on the GEO-LEO transmission, our previous work in [15] proposed two uplink schemes for a two-user two-satellite scenario. The LEO satellite can serve beam-center and beam-edge users with one signal carrier by realizing the significant difference of the channel gain. As another solution, the beam-edge user can choose to access the GEO satellite while the beam-center user is still served by the LEO satellite. Simulation results found out that the LEO NOMA can provide a promising outage probability performance compared with the GEO-LEO OMA in low signal-to-noise ratio (SNR) regions. When the channel condition of the beam-center user is assumed to be superior to the beam-edge user, LEO NOMA outperforms the GEO-LEO OMA. In [16], the authors consider a downlink transmission method in a GEO and multiple LEO satellites scenario where ground users are classified as GEO users and LEO users. In detail, LEO users receive signals from LEO satellites by applying maximal ratio combining. To improve the LEO downlink transmission sum-rate, the signal power for each user is further optimized. Meanwhile, SINRs for GEO users are considered as optimization limitations in order to guarantee the quality of service. Since the transmission environment of GEO SATCOM is significantly different from that of LEO SATCOM, a unified framework of GEO and LEO satellites is difficult to be realized--especially the physical layer. In this case, LEO-LEO cooperation has become a widely studied theme. The authors in [17] proposed a decoding protocol under multi-satellite background. At first, LEO satellites in a certain area could receive uplink signals simultaneously. Then, each satellite processes received signals and linearly maps to a value range. Further, all the processed signals would be transmitted to the gateway while the signals could be enhanced. Our previous work in [18] considered a three-user two-satellite scenario and developed a cooperative downlink NOMA scheme. Recognizing that there exists a huge channel gain gap between the beam-edge user and the beam-center user, the two satellites could serve two beam-center users and one beam-edge user cooperatively within the same resource block. The ergodic sum-rate showed the advancement of the new method. Under the same background, the authors in [19] investigated a cooperative NOMA in a Shadowed-Rician channel model. Outage probability is considered as the evaluation criteria where the superiority of NOMA is demonstrated by simulations. In addition to providing wide range communication, LEO constellation could also offer additional services like satellite positioning. The authors in [20] studied a multiple satellite cooperative positioning scheme where positioning accuracy for ground users could be enhanced by exploiting the diversity of the satellite. In detail, a UT receives useful signals from numerous satellites, and each satellite is able to generate several beams. Unfortunately, interference from other cells would be incurred since frequency reusing is applied onboard. To improve the positioning accuracy, the authors optimized the beamforming vectors and beam generating scheme. As one of the main concerns, carrying out full digital beamforming may not be possible since the computing ability onboard is quite limited.