Interference-Aware Complex Phasor Message Passing Network for Joint Beamforming Optimization in Multi-User IRS-Assisted 6G Systems

Interference-Aware Complex Phasor Message Passing Network for Joint Beamforming Optimization in Multi-User IRS-Assisted 6G Systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Interference-Aware Complex Phasor Message Passing Network for Joint Beamforming Optimization in Multi-User IRS-Assisted 6G Systems Mustafa Ihsan MUSTAFA, Osman Nuri Ucan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9283835/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Intelligent Reflecting Surface (IRS)-assisted communication has emerged as a key enabler for next-generation 6G wireless networks, offering enhanced spectral efficiency through programmable propagation environments. However, joint optimization of active transmit beamforming and passive IRS phase shifts remains a challenging non-convex problem due to the coupled amplitude–phase interactions and multi-user interference. In this paper, we propose an Interference-Aware Complex Phasor Message Passing Network (CPMPN) for joint beamforming optimization in multi-user IRS-assisted systems. The proposed framework introduces a novel complex-valued graph representation that preserves the intrinsic amplitude and phase structure of wireless channels, enabling accurate modeling of signal superposition and interference dynamics. An interference-aware message passing mechanism is developed to adaptively weight channel interactions based on propagation strength, while a feasibility-preserving phase output layer ensures physically valid IRS configurations. In addition, a joint prediction module simultaneously generates transmit beamforming vectors and IRS phase shifts within a unified learning framework. The proposed method is evaluated using the DeepMIMO ray-tracing dataset under realistic millimeter-wave propagation conditions. Simulation results demonstrate that CPMPN achieves an average achievable sum rate of 26.3 bps/Hz, outperforming state-of-the-art optimization and learning-based methods including deep unfolding, Transformer-based beamforming, and graph neural networks. Furthermore, the proposed framework approaches the semidefinite relaxation upper bound with a small optimality gap of approximately 3%, while significantly reducing computational complexity through single-pass inference. Comprehensive ablation and statistical analyses confirm the effectiveness and robustness of the proposed design. These results highlight the potential of physics-aware complex graph learning for scalable and real-time beamforming optimization in future 6G wireless systems. Intelligent Reflecting Surface Graph Neural Network Complex-Valued Learning Achievable Rate Maximization 6G Wireless Networks Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 17 May, 2026 Reviews received at journal 14 May, 2026 Reviews received at journal 13 May, 2026 Reviewers agreed at journal 01 May, 2026 Reviews received at journal 01 May, 2026 Reviewers agreed at journal 01 May, 2026 Reviewers agreed at journal 30 Apr, 2026 Reviewers invited by journal 17 Apr, 2026 Editor assigned by journal 08 Apr, 2026 Submission checks completed at journal 08 Apr, 2026 First submitted to journal 31 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9283835","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627752321,"identity":"fa5e5368-0195-4641-919a-6276e3dfca06","order_by":0,"name":"Mustafa Ihsan MUSTAFA","email":"data:image/png;base64,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","orcid":"","institution":"Altinbas University","correspondingAuthor":true,"prefix":"","firstName":"Mustafa","middleName":"Ihsan","lastName":"MUSTAFA","suffix":""},{"id":627752325,"identity":"01fbdf97-7ae1-4cd0-9bfd-bbcdcfd26003","order_by":1,"name":"Osman Nuri Ucan","email":"","orcid":"","institution":"Altinbas University","correspondingAuthor":false,"prefix":"","firstName":"Osman","middleName":"Nuri","lastName":"Ucan","suffix":""}],"badges":[],"createdAt":"2026-03-31 19:38:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9283835/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9283835/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107702020,"identity":"de4c39e1-2dc6-4c1b-9a2c-de58d9f8bbef","added_by":"auto","created_at":"2026-04-24 08:11:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1479484,"visible":true,"origin":"","legend":"","description":"","filename":"paper2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9283835/v1_covered_67a14e16-70cc-4296-8137-0f3bd15f4bfb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eInterference-Aware Complex Phasor Message Passing Network for Joint Beamforming Optimization in Multi-User IRS-Assisted 6G Systems\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Computing](https://link.springer.com/journal/10791)","snPcode":"10791","submissionUrl":"https://submission.springernature.com/new-submission/10791/3","title":"Discover Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Intelligent Reflecting Surface, Graph Neural Network, Complex-Valued Learning, Achievable Rate Maximization 6G Wireless Networks","lastPublishedDoi":"10.21203/rs.3.rs-9283835/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9283835/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIntelligent Reflecting Surface (IRS)-assisted communication has emerged as a key enabler for next-generation 6G wireless networks, offering enhanced spectral efficiency through programmable propagation environments. However, joint optimization of active transmit beamforming and passive IRS phase shifts remains a challenging non-convex problem due to the coupled amplitude\u0026ndash;phase interactions and multi-user interference. In this paper, we propose an Interference-Aware Complex Phasor Message Passing Network (CPMPN) for joint beamforming optimization in multi-user IRS-assisted systems. The proposed framework introduces a novel complex-valued graph representation that preserves the intrinsic amplitude and phase structure of wireless channels, enabling accurate modeling of signal superposition and interference dynamics. An interference-aware message passing mechanism is developed to adaptively weight channel interactions based on propagation strength, while a feasibility-preserving phase output layer ensures physically valid IRS configurations. In addition, a joint prediction module simultaneously generates transmit beamforming vectors and IRS phase shifts within a unified learning framework. The proposed method is evaluated using the DeepMIMO ray-tracing dataset under realistic millimeter-wave propagation conditions. Simulation results demonstrate that CPMPN achieves an average achievable sum rate of 26.3 bps/Hz, outperforming state-of-the-art optimization and learning-based methods including deep unfolding, Transformer-based beamforming, and graph neural networks. Furthermore, the proposed framework approaches the semidefinite relaxation upper bound with a small optimality gap of approximately 3%, while significantly reducing computational complexity through single-pass inference. Comprehensive ablation and statistical analyses confirm the effectiveness and robustness of the proposed design. These results highlight the potential of physics-aware complex graph learning for scalable and real-time beamforming optimization in future 6G wireless systems.\u003c/p\u003e","manuscriptTitle":"Interference-Aware Complex Phasor Message Passing Network for Joint Beamforming Optimization in Multi-User IRS-Assisted 6G Systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-24 08:10:45","doi":"10.21203/rs.3.rs-9283835/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"241961686934656753084198321043928576351","date":"2026-05-17T23:53:15+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-14T15:21:04+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-13T12:26:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"192549078938689229375005804483358167095","date":"2026-05-01T13:14:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-01T07:42:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"239489764650249966112257486730776651600","date":"2026-05-01T06:16:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"31380793769610894928445040881467770464","date":"2026-04-30T16:42:33+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-17T11:13:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-08T14:12:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-08T14:12:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Computing","date":"2026-03-31T19:21:14+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Computing](https://link.springer.com/journal/10791)","snPcode":"10791","submissionUrl":"https://submission.springernature.com/new-submission/10791/3","title":"Discover Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"96303d05-e116-4817-abdf-be82890e016e","owner":[],"postedDate":"April 24th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"241961686934656753084198321043928576351","date":"2026-05-17T23:53:15+00:00","index":52,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-14T15:21:04+00:00","index":51,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-13T12:26:08+00:00","index":48,"fulltext":""},{"type":"reviewerAgreed","content":"192549078938689229375005804483358167095","date":"2026-05-01T13:14:29+00:00","index":41,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-01T07:42:50+00:00","index":40,"fulltext":""},{"type":"reviewerAgreed","content":"239489764650249966112257486730776651600","date":"2026-05-01T06:16:47+00:00","index":39,"fulltext":""},{"type":"reviewerAgreed","content":"31380793769610894928445040881467770464","date":"2026-04-30T16:42:33+00:00","index":37,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-24T08:10:46+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-24 08:10:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9283835","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9283835","identity":"rs-9283835","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}