{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T12:10:37Z","timestamp":1780402237366,"version":"3.54.1"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T00:00:00Z","timestamp":1780358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100012905","name":"Key Joint Fund Program of Shandong Province","doi-asserted-by":"publisher","award":["ZR2025LZH001"],"award-info":[{"award-number":["ZR2025LZH001"]}],"id":[{"id":"10.13039\/100012905","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012905","name":"General Program of Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2025MS1063"],"award-info":[{"award-number":["ZR2025MS1063"]}],"id":[{"id":"10.13039\/100012905","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Xinjiang Key Laboratory of Multimodal Intelligent Computing and Large Models"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Low Earth orbit (LEO) satellite systems provide ubiquitous global connectivity for massive grant-free random access Internet of Things (IoT) applications. Full frequency reuse (FFR) improves spectrum efficiency in spectrum sharing scenarios but introduces severe adjacent beam and cross-system co-channel interference. Meanwhile, the high mobility of LEO satellites hinders accurate instantaneous channel state information (iCSI) acquisition, and random direction-of-arrival (DOA) estimation errors cause statistical CSI (sCSI) mismatch, which degrades beamforming performance and makes it difficult to balance transmission robustness, user fairness, and onboard computational complexity. To address these issues, we propose a low-complexity Hybrid Optimized Robust Beamforming (HORBA) algorithm. We first construct a robust joint optimization model to characterize the coupling effects of DOA errors, outdated CSI, and multi-dimensional interference, with constraints on per-user minimum SINR and cross-system interference temperature. Then, based on the block coordinate descent framework, we decouple the original non-convex problem into two convex subproblems, which are solved via generalized eigenvalue decomposition and first-order Taylor expansion, combined with an adaptive sampling mechanism that balances accuracy and complexity. Simulation results verify that our algorithm outperforms typical benchmarks in sum rate and robustness, maintains low onboard processing complexity, and effectively alleviates edge user rate polarization.<\/jats:p>","DOI":"10.3390\/s26113501","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T11:25:31Z","timestamp":1780399531000},"page":"3501","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid Robust Beamforming Optimization for LEO Satellite Communications Under DOA Estimation Errors in Spectrum Sharing Scenarios"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0836-3362","authenticated-orcid":false,"given":"Yunfeng","family":"Wang","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Zaozhuang University, Zaozhuang 277100, China"},{"name":"Xinjiang Key Laboratory of Multimodal Intelligent Computing and Large Models, Kashi University, Kashi 844000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2358-1728","authenticated-orcid":false,"given":"Xuxu","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5902-1736","authenticated-orcid":false,"given":"Jiyang","family":"Jia","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Zaozhuang University, Zaozhuang 277100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6666","DOI":"10.1109\/TWC.2025.3626203","article-title":"Enabling Scalable Distributed Beamforming via Networked LEO Satellites Toward 6G","volume":"25","author":"Zhang","year":"2026","journal-title":"IEEE Trans. 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