{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T14:27:32Z","timestamp":1785421652127,"version":"3.56.0"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T00:00:00Z","timestamp":1775952000000},"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":["62301431"],"award-info":[{"award-number":["62301431"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["62301431"],"award-info":[{"award-number":["62301431"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004750","name":"The Aeronautical Science Foundation of China","doi-asserted-by":"crossref","award":["2024M051053001"],"award-info":[{"award-number":["2024M051053001"]}],"id":[{"id":"10.13039\/501100004750","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper investigates the secrecy energy efficiency (SEE) maximization problem in a downlink multiple-input single-output (MISO) wireless communication system assisted by an intelligent reflecting surface with movable elements (ME-IRS). Unlike a conventional IRS, which has fixed-position elements, the proposed ME-IRS enables dynamic adjustment of element positions to exploit additional spatial degrees of freedom for performance enhancement. However, such flexibility introduces new challenges due to the strong coupling among transmit beamforming, IRS phase shifts, and element positions, as well as the additional power consumption caused by element movement. To address these issues, we formulate an SEE maximization problem by jointly optimizing the transmit beamforming, phase shift matrix, and element positions. The resulting problem is highly non-convex owing to the fractional objective function and coupled variables. To address this challenge, an efficient alternating optimization (AO) framework is developed by leveraging semidefinite relaxation (SDR), successive convex approximation (SCA), and gradient-based methods. Simulation results demonstrate that the proposed ME-IRS configuration significantly outperforms conventional fixed-position and discrete-position IRS configurations in terms of SEE, providing valuable insights into the impact of movable region size and system parameters.<\/jats:p>","DOI":"10.3390\/e28040432","type":"journal-article","created":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T10:19:14Z","timestamp":1776075554000},"page":"432","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Energy Efficiency Maximization for ME-IRS-Enabled Secure Communications"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-5016-2670","authenticated-orcid":false,"given":"Chenxi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0455-9608","authenticated-orcid":false,"given":"Limeng","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8290-3910","authenticated-orcid":false,"given":"Yong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0874-9927","authenticated-orcid":false,"given":"Wei","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/MCOM.001.1900107","article-title":"Towards smart and reconfigurable environment: Intelligent reflecting surface aided wireless network","volume":"58","author":"Wu","year":"2020","journal-title":"IEEE Commun. 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