{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:12Z","timestamp":1787337012085,"version":"build-2736575974"},"reference-count":37,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T00:00:00Z","timestamp":1787270400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>This paper investigates a reconfigurable intelligent surface (RIS)-aided hybrid beamforming (HBF) framework for downlink multi-user millimeter-wave (mmWave) systems operating under practical hardware constraints. Given the severe path-loss disparity and blockage sensitivity inherent in mmWave propagation, RIS-assisted systems often suffer from pronounced user-rate imbalance, a challenge further exacerbated by the restricted spatial degrees of freedom in overlapped sub-array (OSA) hybrid architectures. To explicitly mitigate this disparity, we formulate a hardware-constrained optimization problem to maximize the geometric mean (GM) of user rates, thereby enforcing instantaneous fairness and service reliability. At the base station, an OSA-based HBF architecture is adopted to balance spatial flexibility and RF-chain efficiency, while the RIS operates with discrete phase shifts. Distinctive from conventional sum-rate-driven or idealized fully-digital designs, the proposed framework integrates GM-rate maximization with a manifold-theoretic optimization approach, enabling a realizable mapping from the fully-digital benchmark to a practical hybrid analog-digital structure. A two-block block coordinate descent (BCD) algorithm is developed, wherein the active precoder update admits an exact power-constrained solution and the passive phase optimization is executed on a Riemannian manifold to handle unit-modulus and discrete constraints. Numerical simulations demonstrate that the proposed approach effectively exploits OSA connectivity to achieve robust fairness across users. Specifically, an interference-aware warm-start strategy significantly accelerates convergence and yields an objective value improvement of up to 18.18% compared with existing methods, confirming both mathematical superiority and practical computational efficiency. Moreover, the results validate that low-resolution (e.g., 3-bit) phase shifters are sufficient to approach continuous-phase performance, underscoring the feasibility of the proposed framework for cost- and energy-efficient RIS-assisted mmWave deployments.<\/jats:p>","DOI":"10.1371\/journal.pone.0354965","type":"journal-article","created":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:40:36Z","timestamp":1787334036000},"page":"e0354965","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Scalable RIS-aided hybrid beamforming for mmWave systems enables multiple sub-array architectures: A Geometric Mean Approach"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0572-2091","authenticated-orcid":true,"given":"Hoang M.","family":"Tran","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3908-8690","authenticated-orcid":true,"given":"Tung V.","family":"Dinh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hoa T.","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3226-250X","authenticated-orcid":true,"given":"Huy T.","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,8,21]]},"reference":[{"key":"pone.0354965.ref001","doi-asserted-by":"crossref","first-page":"148191","DOI":"10.1109\/ACCESS.2021.3124812","article-title":"6G Wireless Communications Networks: A Comprehensive Survey","volume":"9","author":"M Alsabah","year":"2021","journal-title":"IEEE Access"},{"issue":"2","key":"pone.0354965.ref002","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1109\/COMST.2023.3249835","article-title":"On the Road to 6G: Visions, Requirements, Key Technologies, and Testbeds","volume":"25","author":"C-X Wang","year":"2023","journal-title":"IEEE Commun Surv Tutorials"},{"key":"pone.0354965.ref003","doi-asserted-by":"crossref","first-page":"116753","DOI":"10.1109\/ACCESS.2019.2935192","article-title":"Wireless Communications Through Reconfigurable Intelligent Surfaces","volume":"7","author":"E Basar","year":"2019","journal-title":"IEEE Access"},{"issue":"11","key":"pone.0354965.ref004","doi-asserted-by":"crossref","first-page":"2450","DOI":"10.1109\/JSAC.2020.3007211","article-title":"Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces: How It Works, State of Research, and The Road Ahead","volume":"38","author":"M Di Renzo","year":"2020","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"4","key":"pone.0354965.ref005","doi-asserted-by":"crossref","first-page":"2283","DOI":"10.1109\/COMST.2020.3004197","article-title":"Toward Smart Wireless Communications via Intelligent Reflecting Surfaces: A Contemporary Survey","volume":"22","author":"S Gong","year":"2020","journal-title":"IEEE Commun Surv Tutorials"},{"issue":"1","key":"pone.0354965.ref006","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1109\/MNET.2024.3482571","article-title":"Multi-Functional RIS for a Multi-Functional System: Integrating Sensing, Communication, and Wireless Power Transfer","volume":"39","author":"A Magbool","year":"2025","journal-title":"IEEE Network"},{"key":"pone.0354965.ref007","doi-asserted-by":"crossref","unstructured":"Wang D, Bazzi A, Chafii M. 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