Energy Saving Transmission Time and Power Management for D2D Connection with A Relay Node Using the Same Band with A Cellular Connection

Energy Saving Transmission Time and Power Management for D2D Connection with A Relay Node Using the Same Band with A Cellular Connection | 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 Energy Saving Transmission Time and Power Management for D2D Connection with A Relay Node Using the Same Band with A Cellular Connection Xian Jiang, Yiyao Zhu, Zitian Zhang, Zhenghong Chen, Bin Zhuge, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6217152/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 21 You are reading this latest preprint version Abstract The incorporation of Device-to-Device (D2D) communication, utilizing the same spectral resources as cellular networks, is regarded as a pivotal development for the next generation of wireless communication infrastructures. This is especially relevant when relay nodes are introduced to broaden the transmission distance of D2D links. However, the performance bottleneck persists due to the bidirectional interference stemming from both D2D and conventional cellular links, compelling an escalation in transmission power for these connections. Given the paramount importance of energy conservation for both mobile network operators and users, this study tackles the issue of optimizing transmission time selection and power management (TTSPM) in a scenario where a D2D connection with the rely node and a cellular connection coexist on the same sub-channel, aiming to minimize the overall energy expenditure during transmission. First, we formulate the optimization problem as a NP-hard mixed integer nonlinear programming (MINLP) problem. To solve it, we follow the idea of dividing and conquering and separately investigate four possible resource sharing forms of the two considered links. For the first three resource sharing forms, we prove the TTSPM problem can be transformed into convex optimization problems and then present algorithms to obtain the regional optimal solution corresponding to each form. For the forth resource sharing form, we develop a simulative game-theory based approach to tackle the TTSPM problem since it is still a non-convex optimization problem. As virtual non-cooperative players, cellular connections and D2D connection with the rely nodes are viewed as non-cooperative, we establish the presence of Nash equilibrium within the formulated game and develop algorithms to determine the optimal response of each participant, considering the strategy adopted by their counterpart. Numerical analyses reveal that the TTSPM method, by selecting the optimal regional solution from four potential forms of resource allocation, significantly reduces the overall energy required for transmission across the two analyzed links, outperforming the results documented in prior studies. relay-assisted D2D communication duration time selection power management transmission energy consumption deep neuron network (DNN) Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 20 Apr, 2025 Reviews received at journal 19 Apr, 2025 Reviews received at journal 18 Apr, 2025 Reviews received at journal 16 Apr, 2025 Reviews received at journal 11 Apr, 2025 Reviewers agreed at journal 05 Apr, 2025 Reviews received at journal 04 Apr, 2025 Reviewers agreed at journal 01 Apr, 2025 Reviewers agreed at journal 01 Apr, 2025 Reviewers agreed at journal 01 Apr, 2025 Reviewers agreed at journal 31 Mar, 2025 Reviewers agreed at journal 31 Mar, 2025 Reviewers agreed at journal 30 Mar, 2025 Reviewers agreed at journal 29 Mar, 2025 Reviewers agreed at journal 29 Mar, 2025 Reviewers agreed at journal 29 Mar, 2025 Reviewers agreed at journal 29 Mar, 2025 Reviewers invited by journal 29 Mar, 2025 Editor assigned by journal 14 Mar, 2025 Submission checks completed at journal 14 Mar, 2025 First submitted to journal 13 Mar, 2025 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-6217152","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":443769190,"identity":"80a250ad-b168-4037-b328-6a4dd16b2286","order_by":0,"name":"Xian Jiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYBACxmYwJcHAwN7AYAARSyBWC88BIrUggARcJQEtzO3Mzx5+bbOQN5d8/qDwy5/DDPzsOQYMP3fgcxibubHMGQnDnbMTEoxl2w4zSPa8MWDsPYNPC4OZtESFBOOG2wkHjCUbDjMY3MgxYGZsw6eF/Zu0hIGE/YabBxuMJYAOsyeshcdM8kOFROKGG8wMhh/YgLZIENZSJs1wRiJ5w5k0BmPGtnQeiTPPCg724tFi2H98m+TPtjrbDcePPzP88cdajr89eeODn/i0NAADmgfCZjMGMsDsA7g1MDDIgxz3A8JmfvgDn9JRMApGwSgYsQAAfehOj6iY25sAAAAASUVORK5CYII=","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":true,"prefix":"","firstName":"Xian","middleName":"","lastName":"Jiang","suffix":""},{"id":443769192,"identity":"ee00cd83-0570-4ab4-8a45-4041a167ee61","order_by":1,"name":"Yiyao Zhu","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Yiyao","middleName":"","lastName":"Zhu","suffix":""},{"id":443769194,"identity":"9549db60-824f-4846-b7e4-b50761803e41","order_by":2,"name":"Zitian Zhang","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Zitian","middleName":"","lastName":"Zhang","suffix":""},{"id":443769196,"identity":"3e1ad6dd-d369-4b8c-9d30-f975ee08c597","order_by":3,"name":"Zhenghong Chen","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Zhenghong","middleName":"","lastName":"Chen","suffix":""},{"id":443769198,"identity":"d20a2c37-d492-4722-8b82-35a63314a967","order_by":4,"name":"Bin Zhuge","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Bin","middleName":"","lastName":"Zhuge","suffix":""},{"id":443769201,"identity":"12edd77f-8555-447d-a333-bbb25e1c81ab","order_by":5,"name":"Ligang Dong","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Ligang","middleName":"","lastName":"Dong","suffix":""},{"id":443769203,"identity":"f515788a-c58c-49d6-9986-f4b874b4d8ef","order_by":6,"name":"Yipin Wang","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Yipin","middleName":"","lastName":"Wang","suffix":""},{"id":443769204,"identity":"37a56da1-526c-45cb-aa78-5652c7b7ca7c","order_by":7,"name":"Yingqi Sun","email":"","orcid":"","institution":"Children’s Hospital of Fudan University","correspondingAuthor":false,"prefix":"","firstName":"Yingqi","middleName":"","lastName":"Sun","suffix":""},{"id":443769205,"identity":"b2cb38d0-9a5c-4d0f-a857-9457f2649519","order_by":8,"name":"Jie Zhang","email":"","orcid":"","institution":"University of Sheffield","correspondingAuthor":false,"prefix":"","firstName":"Jie","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2025-03-13 06:53:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6217152/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6217152/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80883300,"identity":"e348f3e2-1203-4552-9e4a-aa8f7ac751c9","added_by":"auto","created_at":"2025-04-18 08:08:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4470179,"visible":true,"origin":"","legend":"","description":"","filename":"submittedmanuscriptforTheJournalofSupercomputing.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6217152/v1_covered_809669bf-e882-4c79-aef7-3ef134a09a38.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Energy Saving Transmission Time and Power Management for D2D Connection with A Relay Node Using the Same Band with A Cellular Connection","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"relay-assisted D2D communication, duration time selection, power management, transmission energy consumption, deep neuron network (DNN)","lastPublishedDoi":"10.21203/rs.3.rs-6217152/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6217152/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe incorporation of Device-to-Device (D2D) communication, utilizing the same spectral resources as cellular networks, is regarded as a pivotal development for the next generation of wireless communication infrastructures. This is especially relevant when relay nodes are introduced to broaden the transmission distance of D2D links. However, the performance bottleneck persists due to the bidirectional interference stemming from both D2D and conventional cellular links, compelling an escalation in transmission power for these connections. Given the paramount importance of energy conservation for both mobile network operators and users, this study tackles the issue of optimizing transmission time selection and power management (TTSPM) in a scenario where a D2D connection with the rely node and a cellular connection coexist on the same sub-channel, aiming to minimize the overall energy expenditure during transmission. First, we formulate the optimization problem as a NP-hard mixed integer nonlinear programming (MINLP) problem. To solve it, we follow the idea of dividing and conquering and separately investigate four possible resource sharing forms of the two considered links. For the first three resource sharing forms, we prove the TTSPM problem can be transformed into convex optimization problems and then present algorithms to obtain the regional optimal solution corresponding to each form. For the forth resource sharing form, we develop a simulative game-theory based approach to tackle the TTSPM problem since it is still a non-convex optimization problem. As virtual non-cooperative players, cellular connections and D2D connection with the rely nodes are viewed as non-cooperative, we establish the presence of Nash equilibrium within the formulated game and develop algorithms to determine the optimal response of each participant, considering the strategy adopted by their counterpart. Numerical analyses reveal that the TTSPM method, by selecting the optimal regional solution from four potential forms of resource allocation, significantly reduces the overall energy required for transmission across the two analyzed links, outperforming the results documented in prior studies.\u003c/p\u003e","manuscriptTitle":"Energy Saving Transmission Time and Power Management for D2D Connection with A Relay Node Using the Same Band with A Cellular Connection","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-18 07:44:40","doi":"10.21203/rs.3.rs-6217152/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-20T18:28:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-19T23:02:48+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-18T16:17:20+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-16T10:13:07+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-11T15:07:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"224349023755272165320102345777908827837","date":"2025-04-05T11:39:25+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-04T19:02:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"296114919580018470624218627711974188769","date":"2025-04-02T03:12:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"264166065901291304065582550638405769863","date":"2025-04-01T12:36:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"297856298670972830729672995560663212718","date":"2025-04-01T07:43:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"116318066486402906365091224170307142746","date":"2025-03-31T22:52:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"28558651377318134515207782674724317250","date":"2025-03-31T10:02:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"295422269373890494225950452433917319810","date":"2025-03-30T04:20:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"54144781725724201221795096084824826122","date":"2025-03-30T02:39:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"64384321961314935012415572489126372979","date":"2025-03-30T01:42:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"19888099402405823131007883410122850211","date":"2025-03-29T21:27:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"18272397617364056775801526508257966062","date":"2025-03-29T20:48:12+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-29T20:42:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-14T12:43:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-03-14T12:39:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"The Journal of Supercomputing","date":"2025-03-13T06:48:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5d794638-3b05-4438-9fd2-6f7c98566f2b","owner":[],"postedDate":"April 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-06-26T15:23:32+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-18 07:44:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6217152","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6217152","identity":"rs-6217152","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}