Preferred Z-Complementary Pairs and Their Application in Doppler Resilient Waveform Design

Preferred Z-Complementary Pairs and Their Application in Doppler Resilient Waveform Design | 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 Preferred Z-Complementary Pairs and Their Application in Doppler Resilient Waveform Design Bingsheng Shen, Yang Yang, Pingzhi Fan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2145057/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Feb, 2023 Read the published version in Cryptography and Communications → Version 1 posted 7 You are reading this latest preprint version Abstract Z-complementary pairs (ZCPs) are well-known, but few work has dedicated to their aperiodic cross-correlation. One objective of this paper is to propose a novel class of sequence pairs, called ``preferred Z-complementary pairs (PZCPs)'', where each sequence pair has Z-complementary property, and the aperiodic cross-correlation between the two sequences in each pair are zeros within a certain region. Some constructions of PZCPs from Golay complementary pairs (GCPs) are presented. Another objective of this paper is to apply PZCPs to design Doppler resilient waveforms combined with equal sums of powers (ESPs). Simulation results show that the proposed waveform has good Doppler tolerance. Mathematics Subject Classification (2000) 06E30 · 11T71 · 94A60 Preferred Z-complementary pair Golay complementary pair Doppler resilient waveform equal sums of power Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Feb, 2023 Read the published version in Cryptography and Communications → Version 1 posted Editorial decision: Major revision 18 Dec, 2022 Reviews received at journal 29 Oct, 2022 Reviewers agreed at journal 13 Oct, 2022 Reviewers invited by journal 12 Oct, 2022 Editor assigned by journal 10 Oct, 2022 Submission checks completed at journal 10 Oct, 2022 First submitted to journal 08 Oct, 2022 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-2145057","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":142991523,"identity":"394b11d9-6850-4476-ae13-10dc8aaa4aa1","order_by":0,"name":"Bingsheng Shen","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Bingsheng","middleName":"","lastName":"Shen","suffix":""},{"id":142991524,"identity":"a53780ff-0487-4ea1-b444-60f026337ad0","order_by":1,"name":"Yang Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYNACNiBmbyBRiwQDzwGStUgkEKnY4PjZwy8Yyuzq+Gc+3niDocYmmrCWM3lpFgznkiUkbqcVWzAcS8ttIKjlQI6ZAWMbswTD7RwzCcaGw0RoOf8GpKVeQv7mGWK13MgxfsDYdljC4AYPkVokb7wxY2A4d1xy4xmgXxKI8Qvf+RzjDwxl1fxyxw9vvPGhxoawFoUDDGzSf6COJC5q5BsYmD8wwLQQo2MUjIJRMApGHgAA6+U+FT8JBT8AAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Yang","middleName":"","lastName":"Yang","suffix":""},{"id":142991525,"identity":"957b6364-85cf-4d87-8c5e-ff95c1054be0","order_by":2,"name":"Pingzhi Fan","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Pingzhi","middleName":"","lastName":"Fan","suffix":""}],"badges":[],"createdAt":"2022-10-08 11:29:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2145057/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2145057/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s12095-023-00636-4","type":"published","date":"2023-02-22T18:59:21+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":27681084,"identity":"2355da3a-385d-4129-a195-95df69e6598e","added_by":"auto","created_at":"2022-10-12 15:07:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2778062,"visible":true,"origin":"","legend":"","description":"","filename":"PZCPCCDS20221008.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2145057/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Preferred Z-Complementary Pairs and Their Application in Doppler Resilient Waveform Design","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-2145057/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"cryptography-and-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ccds","sideBox":"Learn more about [Cryptography and Communications](http://link.springer.com/journal/12095)","snPcode":"12095","submissionUrl":"https://submission.nature.com/new-submission/12095/3","title":"Cryptography and Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Preferred Z-complementary pair, Golay complementary pair, Doppler resilient waveform, equal sums of power","lastPublishedDoi":"10.21203/rs.3.rs-2145057/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2145057/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eZ-complementary pairs (ZCPs) are well-known, but few work has dedicated to their aperiodic cross-correlation. One objective of this paper is to propose a novel class of sequence pairs, called ``preferred Z-complementary pairs (PZCPs)'', where each sequence pair has Z-complementary property, and the aperiodic cross-correlation between the two sequences in each pair are zeros within a certain region. Some constructions of PZCPs from Golay complementary pairs (GCPs) are presented. Another objective of this paper is to apply PZCPs to design Doppler resilient waveforms combined with equal sums of powers (ESPs). Simulation results show that the proposed waveform has good Doppler tolerance.\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification (2000) 06E30 · 11T71 · 94A60\u003c/p\u003e","manuscriptTitle":"Preferred Z-Complementary Pairs and Their Application in Doppler Resilient Waveform Design","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-10-12 15:06:59","doi":"10.21203/rs.3.rs-2145057/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2022-12-18T07:54:26+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-10-29T16:26:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"9fc399a0-9b22-431f-9d4b-3f5c7ba6b091","date":"2022-10-13T09:14:26+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-10-13T02:44:11+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-10-11T03:01:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-10-10T07:03:04+00:00","index":"","fulltext":""},{"type":"submitted","content":"Cryptography and Communications","date":"2022-10-08T11:20:04+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"cryptography-and-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ccds","sideBox":"Learn more about [Cryptography and Communications](http://link.springer.com/journal/12095)","snPcode":"12095","submissionUrl":"https://submission.nature.com/new-submission/12095/3","title":"Cryptography and Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"3fa45261-abfb-4b28-8f71-8054a6559fb3","owner":[],"postedDate":"October 12th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T19:07:46+00:00","versionOfRecord":{"articleIdentity":"rs-2145057","link":"https://doi.org/10.1007/s12095-023-00636-4","journal":{"identity":"cryptography-and-communications","isVorOnly":false,"title":"Cryptography and Communications"},"publishedOn":"2023-02-22 18:59:21","publishedOnDateReadable":"February 22nd, 2023"},"versionCreatedAt":"2022-10-12 15:06:59","video":"","vorDoi":"10.1007/s12095-023-00636-4","vorDoiUrl":"https://doi.org/10.1007/s12095-023-00636-4","workflowStages":[]},"version":"v1","identity":"rs-2145057","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2145057","identity":"rs-2145057","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}