{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T00:58:20Z","timestamp":1778806700549,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,10]],"date-time":"2022-09-10T00:00:00Z","timestamp":1662768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62001516"],"award-info":[{"award-number":["62001516"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/s22186858","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T04:05:41Z","timestamp":1663041941000},"page":"6858","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Joint User Scheduling and Hybrid Beamforming Design for Massive MIMO LEO Satellite Multigroup Multicast Communication Systems"],"prefix":"10.3390","volume":"22","author":[{"given":"Yang","family":"Liu","sequence":"first","affiliation":[{"name":"Graduate School, Space Engineering University, Beijing 101416, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5260-0794","authenticated-orcid":false,"given":"Changqing","family":"Li","sequence":"additional","affiliation":[{"name":"Space Information School, Space Engineering University, Beijing 101416, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiong","family":"Li","sequence":"additional","affiliation":[{"name":"Space Information School, Space Engineering University, Beijing 101416, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu","family":"Feng","sequence":"additional","affiliation":[{"name":"Graduate School, Space Engineering University, Beijing 101416, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jin, L., Wang, L., Jin, X., Zhu, J., Duan, K., and Li, Z. 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