## 2 Related Works and Main Contributions  
### Related Works  
There is extensive literature regarding user scheduling and beamforming design in the wireless multigroup multicast communication system. In Ref. [11], based on the perfect CSI, taking the throughput maximization as the optimization objective the authors studied the precoding design of the multibeam satellite communication system, and proposed a decoupling scheme of the user scheduling and beamforming design. In Ref. [12], considering the influence of CSI errors and taking the minimizing transmission power as the optimization objective, the robust multigroup multicast transmission scheme of the multibeam satellite communication system was investigated, and the low complexity beamforming algorithm and the user grouping algorithm were proposed, but the length limit of the DVB-S2X frame was not considered. In Ref. [13], based on the perfect CSI and taking the maximizing SE as the optimization objective, the multigroup multicast transmission design scheme of the frame-based multibeam satellite communication system was investigated, and the authors proposed a joint design scheme of the user scheduling and beamforming. However, the influence of CSI errors was not considered, and the user grouping algorithm was simple. In Ref. [14], based on the perfect CSI, the authors studied the user scheduling problem of the multicast transmission in the high-throughput satellite communication system. The user scheduling was decoupled into intra-beam scheduling and inter-beam scheduling, and the correlation degree was calculated by using the equivalent CSI; therefore, the interaction of intra-beam and inter-beam scheduling cannot be fully considered. In Ref. [15], the authors studied the user scheduling problem of the multibeam satellite communication system but did not consider the inter-beam interference caused by scheduling. In Ref. [16], based on the perfect CSI, the authors studied the joint scheduling and beamforming design problem for multiuser MISO downlink, and the message-based user grouping and scheduling algorithm was mainly proposed, but the impact of user grouping on system performance was not fully considered. In Ref. [17], the user scheduling and hybrid beamforming design of the massive MIMO orthogonal frequency division multiple access (OFDMA) communication system was studied, in scheme design. First, a joint design algorithm of user scheduling and analog beamforming was proposed; then, the digital beamforming matrix was solved by the weighted minimum mean-square error (WMMSE) algorithm. In Ref. [18], the authors studied the design of user scheduling and subcarrier allocation in the downlink of a massive MIMO OFDMA communication system and proposed a hybrid beamforming scheme. First, based on the optimal solution of digital beamforming, the analog beamforming matrix was obtained by a singular value decomposition algorithm. Then, the authors proposed an algorithm to solve the digital beamforming matrix and its corresponding scheduling users.  
Most of the above research took the geosynchronous earth orbit (GEO) satellite or the terrestrial cellular network as the research object, and less used the LEO satellite. In addition, the optimization objectives mainly focused on maximizing SE and minimizing transmission power, and less on the EE optimization. Meanwhile, the analysis of CSI errors was insufficient, as some research considered the CSI errors, but did not analyze the influence of the Doppler shift. In terms of the user scheduling, the common idea was to adopt the decoupling scheme of user scheduling and beamforming design, without fully considering the coupling relationship between the user scheduling and the beamforming design.