{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T04:37:40Z","timestamp":1778215060796,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T00:00:00Z","timestamp":1776297600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Hebei Province, China","award":["F2024523005"],"award-info":[{"award-number":["F2024523005"]}]},{"DOI":"10.13039\/100017938","name":"Postdoctoral Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["B2023005001"],"award-info":[{"award-number":["B2023005001"]}],"id":[{"id":"10.13039\/100017938","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Laboratory of Wireless Communications Foundation","award":["IFN202404"],"award-info":[{"award-number":["IFN202404"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Reconfigurable intelligent surface (RIS) emerges as a promising paradigm and offers a new perspective for physical layer security. In practice, imperfect eavesdropper channel state information (CSI) represents a critical challenge for RIS-aided physical layer security design. To tackle this issue, this paper investigates RIS-aided physical layer security enhancement under imperfect eavesdropper CSI and formulates a robust weighted sum secrecy rate maximization problem. To efficiently solve this problem, a model-driven deep learning approach is proposed. We begin by introducing the gradient descent\u2013ascent algorithm to solve the optimization problem. Then we unfold this algorithm into a gated recurrent unit (GRU)-aided deep unfold network with trainable parameters. The proposed GRU-aided deep unfold network leverages GRU to adaptively generate gradient ascent\u2013descent step sizes. Different from the existing deep unfold network that commonly has a fixed number of iteration, the proposed deep unfold network integrates the sequential learning capability of GRU and enables adaptive iteration adjustment. The simulation results demonstrate that compared to existing non-robust optimization algorithm and traditional deep unfold network with fixed number of iteration, the proposed method exhibits robustness against imperfect CSI and achieves higher weighted sum secrecy rate.<\/jats:p>","DOI":"10.3390\/e28040457","type":"journal-article","created":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T11:35:42Z","timestamp":1776339342000},"page":"457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["RIS-Aided Physical Layer Security with Imperfect CSI: A Robust Model-Driven Deep Learning Approach"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-2395-5761","authenticated-orcid":false,"given":"Ruikai","family":"Miao","sequence":"first","affiliation":[{"name":"The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China"},{"name":"National Key Laboratory of Advanced Communication Networks, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiqun","family":"Song","sequence":"additional","affiliation":[{"name":"The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China"},{"name":"National Key Laboratory of Advanced Communication Networks, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Li","sequence":"additional","affiliation":[{"name":"The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China"},{"name":"National Key Laboratory of Advanced Communication Networks, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0668-7080","authenticated-orcid":false,"given":"Xingjian","family":"Li","sequence":"additional","affiliation":[{"name":"The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China"},{"name":"National Key Laboratory of Advanced Communication Networks, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lizhe","family":"Liu","sequence":"additional","affiliation":[{"name":"The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China"},{"name":"National Key Laboratory of Advanced Communication Networks, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoyuan","family":"Shao","sequence":"additional","affiliation":[{"name":"North Automatic Control Technology Institute, Taiyuan 030006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China"},{"name":"National Key Laboratory of Advanced Communication Networks, Shijiazhuang 050081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,16]]},"reference":[{"key":"ref_1","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":"Wang","year":"2023","journal-title":"IEEE Commun. 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