A Comparative Explorative Analysis of Frequency offset design and Trailing-effects for Dot-shaped Beampatterns in Frequency Diverse Arrays

A Comparative Explorative Analysis of Frequency offset design and Trailing-effects for Dot-shaped Beampatterns in Frequency Diverse Arrays | 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 Article A Comparative Explorative Analysis of Frequency offset design and Trailing-effects for Dot-shaped Beampatterns in Frequency Diverse Arrays Zahid Ullah Khan, Hongyuan Gao, Abdul Qadir, Aman Muhammad, Javed Khan, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9550448/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Frequency diverse arrays (FDAs) permit range-angle-dependent beamforming, but the effective operation is limited by angle-distance coupling and periodicity of standard beampatterns. In this paper, we examined a dot-shaped emission beamforming technique using the concept of S-beam frequency offset to enhance spatial focusing in the angle distance plane. We analyze four nonlinear frequency offset growth strategies, i.e. (i) Logarithmic growth deviation, (ii) Square deviation, (iii) Incremental frequency deviation and (iv) Sine cubic partial frequency deviation. Their impacts on beampattern periodicity, beam localization, and trailing behavior are discussed in a systematic manner. The simulation results indicate that each of the four strategies is successful in suppressing the periodic repetition of the S-beam, and produce a beam that is approximately in the shape of a dot. However, in all cases, a noticeable beam trailing effect is present that decreases compactness and restricts optimum focusing performance. This research explains the effect of frequency offset growth laws on the synthesis of FDAs beam and gives a practical foundation to the future trailing suppression and high resolution dot beam design. Physical sciences/Engineering Physical sciences/Physics Frequency diverse array angle distance coupling Beampattern Synthesis Dot-shaped Beamforming S-beam Frequency Offset design Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 18 May, 2026 Reviewers agreed at journal 10 May, 2026 Reviewers invited by journal 08 May, 2026 Editor invited by journal 08 May, 2026 Editor assigned by journal 29 Apr, 2026 Submission checks completed at journal 29 Apr, 2026 First submitted to journal 28 Apr, 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-9550448","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":638658242,"identity":"c1113819-72dd-4c1e-9da5-620140f78d80","order_by":0,"name":"Zahid Ullah Khan","email":"","orcid":"","institution":"1.\tCollege of Information and Communication Engineering, Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Zahid","middleName":"Ullah","lastName":"Khan","suffix":""},{"id":638658243,"identity":"b0d45db1-4de6-43fe-9f5f-b13564812580","order_by":1,"name":"Hongyuan 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In this paper, we examined a dot-shaped emission beamforming technique using the concept of S-beam frequency offset to enhance spatial focusing in the angle distance plane. We analyze four nonlinear frequency offset growth strategies, i.e. (i) Logarithmic growth deviation, (ii) Square deviation, (iii) Incremental frequency deviation and (iv) Sine cubic partial frequency deviation. Their impacts on beampattern periodicity, beam localization, and trailing behavior are discussed in a systematic manner. The simulation results indicate that each of the four strategies is successful in suppressing the periodic repetition of the S-beam, and produce a beam that is approximately in the shape of a dot. However, in all cases, a noticeable beam trailing effect is present that decreases compactness and restricts optimum focusing performance. This research explains the effect of frequency offset growth laws on the synthesis of FDAs beam and gives a practical foundation to the future trailing suppression and high resolution dot beam design.\u003c/p\u003e","manuscriptTitle":"A Comparative Explorative Analysis of Frequency offset design and Trailing-effects for Dot-shaped Beampatterns in Frequency Diverse Arrays","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-18 11:34:27","doi":"10.21203/rs.3.rs-9550448/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-18T11:57:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"81211252752057241321408957476895359748","date":"2026-05-10T07:21:11+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-08T11:23:22+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-05-08T10:01:49+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-29T05:25:31+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-29T05:25:10+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-04-28T07:48:39+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8eeed536-ba81-47c0-9cfc-b90dd828004d","owner":[],"postedDate":"May 18th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-18T11:57:32+00:00","index":23,"fulltext":""},{"type":"reviewerAgreed","content":"81211252752057241321408957476895359748","date":"2026-05-10T07:21:11+00:00","index":21,"fulltext":""},{"type":"reviewersInvited","content":"5","date":"2026-05-08T11:23:22+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-05-08T10:01:49+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":67970623,"name":"Physical sciences/Engineering"},{"id":67970624,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-18T11:34:27+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-18 11:34:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9550448","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9550448","identity":"rs-9550448","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}