###### Abstract  
In the satellite multigroup multicast communication systems based on the DVB-S2X standard, due to the limitation of the DVB-S2X frame structure, user scheduling and beamforming design have become the focus of academic research. In this work, we take the massive multi-input multi-output (MIMO) low earth orbit (LEO) satellite communication system adopting the DVB-S2X standard as the research scenario, and the LEO satellite adopts a uniform planar array (UPA) based on the fully connected hybrid structure. We focus on the coupling design of user scheduling and beamforming; meanwhile, the scheme design takes the influence of residual Doppler shift and phase disturbance on channel errors into account. Under the constraints of total transmission power and quality of service (QoS), we study the robust joint user scheduling and hybrid beamforming design aimed at maximizing the energy efficiency (EE). For this problem, we first adopt the hierarchical clustering algorithm to group users. Then, the semidefinite programming (SDP) algorithm and the concave convex process (CCCP) framework are applied to tackle the optimization of user scheduling and hybrid beamforming design. To handle the rank-one matrix constraint, the penalty iteration algorithm is proposed. To balance the performance and complexity of the algorithm, the user preselected step is added before joint design. Finally, to obtain the digital beamforming matrix and the analog beamforming matrix in a hybrid beamformer, the alternative optimization algorithm based on the majorization-minimization framework (MM-AltOpt) is proposed. Numerical simulation results show that the EE of the proposed joint user scheduling and beamforming design algorithm is higher than that of the traditional decoupling design algorithms. LEO satellite communications; massive MIMO; multigroup multicast; user scheduling; hybrid beamforming; robust; joint design; energy efficiency +
Footnote †: journal: 10 September 2022  
Therefore, the multigroup multicasting principle can be used in the beamformer design. In this paper, we concentrate on the massive MIMO LEO satellite communication system forward link multigroup multicasting beamforming scheme [7]. In the beamforming design of the massive MIMO LEO satellite multigroup multicast communication system, the following issues need to be considered:  
* User scheduling: Due to that only a few users can be bound into a DVB-S2X frame, and there are a large number of active users in each multicast group, it is necessary to design the user scheduling algorithm. Meanwhile, it should be noted that the interference between scheduled users depends on the beamforming design, which in turn depends on the scheduled users in other beams. Therefore, user scheduling and beamforming design are coupled, and the joint design scheme of user scheduling and beamforming needs to be considered. * Channel errors: The LEO satellite has high orbital speed, which will produce a large Doppler shift and result in the channel phase deviation [8]. Meanwhile, the factors such as distortion of high-frequency devices, expiration of the CSI and large propagation delay also can cause the channel phase disturbance. Therefore, it is difficult to obtain accurate channel state information (CSI) at the LEO satellite transmitter. Due to the existence of CSI errors, the designed beamforming vector does not match the actual CSI, resulting in the reduction in the receiving gain and signal to interference plus noise ratio (SINR) of the user terminal. Then, the QoS will not be guaranteed. Thus, it is of practical significance to study the robust user scheduling and beamforming design. * EE optimization: Due to the limited energy load of LEO satellites, to prolong the service life of the LEO satellite and improve the stability of the LEO satellite communications system, under the consideration of green communications and economic benefits, we need to pay attention to the EE optimization [9].