Wirtinger Flow Meets Constant Modulus Algorithm: Revisiting Signal Recovery for Grant-Free Access

In this work, we analyze the convergence of constant modulus algorithm (CMA) in blindly recovering multiple signals to facilitate grant-free wireless access. The CMA typically solves a non-convex problem by utilizing stochastic gradient descent. The iterative convergence of CMA can be affected by ad...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	IEEE transactions on signal processing Ročník 69; s. 6515 - 6529
Hlavní autori:	Feres, Carlos, Ding, Zhi
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Algorithms blind signal recovery Channel noise Constant-modulus algorithm Convergence Cost function Heuristic algorithms Internet of Things Iterative methods Minimization Optimization Phase retrieval Recovery Signal processing algorithms Signal reconstruction Wirtinger Flow
ISSN:	1053-587X, 1941-0476
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	In this work, we analyze the convergence of constant modulus algorithm (CMA) in blindly recovering multiple signals to facilitate grant-free wireless access. The CMA typically solves a non-convex problem by utilizing stochastic gradient descent. The iterative convergence of CMA can be affected by additive channel noise and finite number of samples, which is a problem not fully investigated previously. We point out the strong similarity between CMA and the Wirtinger Flow (WF) algorithm originally proposed for Phase Retrieval. In light of the convergence proof of WF under limited data samples, we adopt the WF algorithm to implement CMA-based blind signal recovery. We generalize the convergence analysis of WF in the context of CMA-based blind signal recovery. Numerical simulation results also corroborate the analysis.
AbstractList	In this work, we analyze the convergence of constant modulus algorithm (CMA) in blindly recovering multiple signals to facilitate grant-free wireless access. The CMA typically solves a non-convex problem by utilizing stochastic gradient descent. The iterative convergence of CMA can be affected by additive channel noise and finite number of samples, which is a problem not fully investigated previously. We point out the strong similarity between CMA and the Wirtinger Flow (WF) algorithm originally proposed for Phase Retrieval. In light of the convergence proof of WF under limited data samples, we adopt the WF algorithm to implement CMA-based blind signal recovery. We generalize the convergence analysis of WF in the context of CMA-based blind signal recovery. Numerical simulation results also corroborate the analysis.
Author	Feres, Carlos Ding, Zhi
Author_xml	– sequence: 1 givenname: Carlos orcidid: 0000-0002-3341-0378 surname: Feres fullname: Feres, Carlos email: cjferes@ucdavis.edu organization: Department of Electrical and Computer Engineering, University of California, Davis, Davis, CA, US – sequence: 2 givenname: Zhi orcidid: 0000-0002-2649-2125 surname: Ding fullname: Ding, Zhi email: zding@ucdavis.edu organization: Department of Electrical and Computer Engineering, University of California, Davis, Davis, CA, US
BookMark	eNp9kMFOAjEQQBuDiYDeTbw08bzY2Xa3u94IETSBaASjt00ps1iybLEtGP7eJRAPHjzNZGbezOR1SKu2NRJyDawHwPK72fSlF7MYehwYZzw7I23IBURMyLTV5CzhUZLJjwvS8X7FGAiRp22i3o0Lpl6io8PKftMJYvB0YGsfVB3oxC621dbTfrW0zoTP9T19xZ3x5sDQqVnWqmoq2u7Q7WlpHR25houGDpH2tUbvL8l5qSqPV6fYJW_Dh9ngMRo_j54G_XGk4xxCpHiupVQ8AQmJWHCOGao0gzJL87mQqunwOc6F1plmUrE4zkuQYq4RRJYqzrvk9rh34-zXFn0oVnbrmv98EafAQLIsSZopdpzSznrvsCw2zqyV2xfAioPIohFZHEQWJ5ENkv5BtAkqGFsHp0z1H3hzBA0i_t7JEwDgMf8BlE-B9w
CODEN	ITPRED
CitedBy_id	crossref_primary_10_1109_LWC_2024_3376724 crossref_primary_10_1109_TVT_2024_3407718 crossref_primary_10_1109_TSP_2022_3159988 crossref_primary_10_1109_LCOMM_2024_3417473 crossref_primary_10_1109_TSP_2023_3310895
Cites_doi	10.1002/cpa.21638 10.1016/j.sigpro.2019.02.007 10.1109/GLOCOM.2016.7841970 10.1109/ACSSC.1991.186537 10.1109/TCOM.1980.1094608 10.1109/GLOCOM.2017.8255054 10.1109/TSP.2016.2523459 10.1109/78.796434 10.1109/TIT.2003.811903 10.1109/78.502327 10.1109/TSP.2018.2864660 10.1109/TIT.2010.2046205 10.1109/ACSSC.1994.471567 10.1109/COMST.2015.2444095 10.1016/S0165-1684(98)00186-8 10.1109/97.623042 10.1109/TIT.2015.2399924 10.1109/18.737518 10.1109/TWC.2019.2962113 10.1109/TSP.2002.808112 10.1109/TCOMM.2008.050484 10.1109/MILCOM.1994.474026 10.1109/TAC.1974.1100705 10.2140/pjm.1966.16.1 10.1109/ACSSC.1995.540639 10.1109/ISIT.2017.8007083 10.1109/TASSP.1985.1164557 10.1109/ICC.2018.8422890 10.1109/78.651224 10.1017/CBO9780511794308.006 10.1109/ICASSP.2001.940427 10.1109/ICIP.2018.8451437 10.1109/MSP.2010.936019 10.1109/TSP.2014.2376886
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021
DBID	97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D
DOI	10.1109/TSP.2021.3103038
DatabaseName	IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Technology Research Database
Database_xml	– sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	1941-0476
EndPage	6529
ExternalDocumentID	10_1109_TSP_2021_3103038 9511132
Genre	orig-research
GrantInformation_xml	– fundername: National Science Foundation grantid: 2009001; 1711823; 1824553 funderid: 10.13039/501100008982 – fundername: National Agency for Research and Development grantid: 72170648
GroupedDBID	-~X .DC 0R~ 29I 3EH 4.4 53G 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACIWK ACKIV ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AJQPL AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 E.L EBS EJD F5P HZ~ H~9 ICLAB IFIPE IFJZH IPLJI JAVBF LAI MS~ O9- OCL P2P RIA RIE RNS TAE TN5 VH1 AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c291t-a39c77a3517154d33e8ea681f869b47aa353beb4cc8c07a0229f174bce1486a33
IEDL.DBID	RIE
ISICitedReferencesCount	8
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000730475800010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1053-587X
IngestDate	Mon Jun 30 10:17:47 EDT 2025 Sat Nov 29 04:10:54 EST 2025 Tue Nov 18 21:32:40 EST 2025 Wed Aug 27 02:38:52 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c291t-a39c77a3517154d33e8ea681f869b47aa353beb4cc8c07a0229f174bce1486a33
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-3341-0378 0000-0002-2649-2125
PQID	2610170855
PQPubID	85478
PageCount	15
ParticipantIDs	crossref_primary_10_1109_TSP_2021_3103038 crossref_citationtrail_10_1109_TSP_2021_3103038 ieee_primary_9511132 proquest_journals_2610170855
PublicationCentury	2000
PublicationDate	20210000 2021-00-00 20210101
PublicationDateYYYYMMDD	2021-01-01
PublicationDate_xml	– year: 2021 text: 20210000
PublicationDecade	2020
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	IEEE transactions on signal processing
PublicationTitleAbbrev	TSP
PublicationYear	2021
Publisher	IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml	– name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References	ref12 ref37 ref36 ref14 vershynin (ref47) 2018 ref31 wang (ref15) 2018 ref30 ref33 kreutz-delgado (ref35) 2009 ref11 mariere (ref13) 2003; 51 veen (ref19) 0; 4 ref2 ref1 ref39 ref17 ref38 ref16 ref18 feres (ref48) 0 ref46 candès (ref24) 2013 ref23 dong (ref34) 2018 ref26 ref25 ref20 ref42 ding (ref6) 2000 li (ref8) 0; 1 ref41 ref22 ref44 ref21 ref43 zhang (ref32) 2017; 18 (ref28) 2016 ref27 ref29 ref7 ref9 ref4 ref3 ref5 ref40 gao (ref45) 2019 chung (ref10) 0; 6
References_xml	– ident: ref31 doi: 10.1002/cpa.21638 – ident: ref16 doi: 10.1016/j.sigpro.2019.02.007 – ident: ref26 doi: 10.1109/GLOCOM.2016.7841970 – ident: ref30 doi: 10.1109/ACSSC.1991.186537 – ident: ref7 doi: 10.1109/TCOM.1980.1094608 – ident: ref2 doi: 10.1109/GLOCOM.2017.8255054 – volume: 4 year: 0 ident: ref19 article-title: An adaptive version of the algebraic constant modulus algorithm publication-title: Proc IEEE Intl Conf Acoust Speech Signal Process – ident: ref4 doi: 10.1109/TSP.2016.2523459 – ident: ref11 doi: 10.1109/78.796434 – ident: ref12 doi: 10.1109/TIT.2003.811903 – ident: ref18 doi: 10.1109/78.502327 – ident: ref27 doi: 10.1109/TSP.2018.2864660 – ident: ref25 doi: 10.1109/TIT.2010.2046205 – year: 2019 ident: ref45 article-title: Phase retrieval for sub-gaussian measurements – ident: ref17 doi: 10.1109/ACSSC.1994.471567 – ident: ref1 doi: 10.1109/COMST.2015.2444095 – year: 2009 ident: ref35 article-title: The complex gradient operator and the CR-calculus – ident: ref22 doi: 10.1016/S0165-1684(98)00186-8 – ident: ref38 doi: 10.1109/97.623042 – ident: ref23 doi: 10.1109/TIT.2015.2399924 – volume: 1 start-page: 617 year: 0 ident: ref8 article-title: Global convergence of fractionally spaced godard equalizers publication-title: Proc 28th Asilomar Conf Signals Syst Comput – ident: ref41 doi: 10.1109/18.737518 – ident: ref29 doi: 10.1109/TWC.2019.2962113 – volume: 51 start-page: 805 year: 2003 ident: ref13 article-title: Blind constant modulus equalization via convex optimization publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2002.808112 – ident: ref20 doi: 10.1109/TCOMM.2008.050484 – year: 2000 ident: ref6 publication-title: Blind Equalization and Identification – ident: ref21 doi: 10.1109/MILCOM.1994.474026 – ident: ref42 doi: 10.1109/78.796434 – ident: ref43 doi: 10.1109/TAC.1974.1100705 – year: 2018 ident: ref34 article-title: Blind over-the-air computation and data fusion via provable wirtinger flow – year: 0 ident: ref48 article-title: Wirtinger flow meets constant modulus algorithm: revisiting signal recovery for grant-free access (supplemental material and code) – ident: ref36 doi: 10.2140/pjm.1966.16.1 – volume: 6 start-page: 3345 year: 0 ident: ref10 article-title: The local minima of fractionally-spaced CMA blind equalizer cost function in the presence of channel noise publication-title: Proc IEEE Int Conf Acoust Speech Signal Process – ident: ref37 doi: 10.1109/ACSSC.1995.540639 – ident: ref40 doi: 10.1109/ISIT.2017.8007083 – ident: ref44 doi: 10.1109/TASSP.1985.1164557 – ident: ref5 doi: 10.1109/ICC.2018.8422890 – ident: ref9 doi: 10.1109/78.651224 – ident: ref46 doi: 10.1017/CBO9780511794308.006 – ident: ref39 doi: 10.1109/ICASSP.2001.940427 – year: 2018 ident: ref15 article-title: Semidefinite relaxation based blind equalization using constant modulus criterion – year: 2016 ident: ref28 publication-title: Evolved Universal Terrestrial Radio Access (E-UTRAN) Multiplexing and Channel Coding – year: 2013 ident: ref24 article-title: Phase retrieval from masked fourier transforms – ident: ref33 doi: 10.1109/ICIP.2018.8451437 – year: 2018 ident: ref47 publication-title: High-Dimensional Probability An Introduction with Applications in Data Science – volume: 18 start-page: 1 year: 2017 ident: ref32 article-title: A nonconvex approach for phase retrieval: Reshaped wirtinger flow and incremental algorithms publication-title: J Mach Learn Res – ident: ref14 doi: 10.1109/MSP.2010.936019 – ident: ref3 doi: 10.1109/TSP.2014.2376886
SSID	ssj0014496
Score	2.4023576
Snippet	In this work, we analyze the convergence of constant modulus algorithm (CMA) in blindly recovering multiple signals to facilitate grant-free wireless access....
SourceID	proquest crossref ieee
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	6515
SubjectTerms	Algorithms blind signal recovery Channel noise Constant-modulus algorithm Convergence Cost function Heuristic algorithms Internet of Things Iterative methods Minimization Optimization Phase retrieval Recovery Signal processing algorithms Signal reconstruction Wirtinger Flow
Title	Wirtinger Flow Meets Constant Modulus Algorithm: Revisiting Signal Recovery for Grant-Free Access
URI	https://ieeexplore.ieee.org/document/9511132 https://www.proquest.com/docview/2610170855
Volume	69
WOSCitedRecordID	wos000730475800010&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1941-0476 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014496 issn: 1053-587X databaseCode: RIE dateStart: 19910101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEB5UPOjBt7i-yMGLYN1t020Sb4u4elARH7i30ibTdWHdSrer-O-dpN1FUARvLU1CyZd2vslk5gM4MsZIH4W2p6daXqhl5ikM6Ba5IntlVChcovC1uL2VvZ66m4OTWS4MIrrDZ3hqL10s3-R6YrfKmsQGrDD6PMwLEVW5WrOIQRg6LS6iC9xrS9GbhiRbqvn4cEeOYOCfOk0tm4nyzQQ5TZUfP2JnXbqr_3uvNVipWSTrVLCvwxyONmD5W23BTUieB7ZAQB8L1h3mH-wGsRyz84oOluwmN5PhZMw6w35eDMqX1zN27xLNbR_2MOjb8a1vSkv9kxGzZZdk1UqvWyCyjlNZ3IKn7sXj-ZVX6yl4OlB-6SVcaSES3vYFESfDOUpMIulnMlJpKBJ6wlNMQ62lbomErLvKyGFJNZLPFCWcb8PCKB_hDjCToCIgkQiGIUgzpXQU-FEahSlmmQka0JxOcazrYuNW82IYO6ejpWICJbagxDUoDTie9XirCm380XbTgjBrV89_A_anKMb1lziOyUO0JYJku737e689WLJjV9sq-7BQFhM8gEX9Xg7GxaFbZF_NL88i
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3fT9swED5BmbTxANsAUX7ND3uZtNAmTmObtwpRQGsrNIrWtyixL6VS16A0Zdp_z9lNKyQQEm-JYieRPyf3nc93H8B3Y4z0UWi7e6rphVpmnsKATpErsldGhcIlCndFvy-HQ3WzBj9XuTCI6Daf4ak9dLF8k-u5XSprEBuwwujrsGGVs6psrVXMIAydGhcRBu61pBgug5JN1Rjc3pArGPinTlXL5qI8M0JOVeXFr9jZl872-97sM2xVPJK1F8B_gTWcfoXNZ9UFdyD5M7YlAkZYsM4k_8d6iOWMnS8IYcl6uZlP5jPWnozyYlze_z1jv12que3Dbscje3_rndJk_8-I27JLsmul1ykQWdvpLO7CXedicH7lVYoKng6UX3oJV1qIhLd8QdTJcI4Sk0j6mYxUGoqErvAU01BrqZsiIfuuMnJZUo3kNUUJ53tQm-ZT3AdmElQEJRLFMARqppSOAj9KozDFLDNBHRrLIY51VW7cql5MYud2NFVMoMQWlLgCpQ4_Vj0eFqU23mi7Y0FYtavGvw5HSxTj6lucxeQj2iJBstU6eL3XN_h4Neh14-51_9chfLLPWSyyHEGtLOZ4DB_0YzmeFSduwj0BwZ7Saw
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Wirtinger+Flow+Meets+Constant+Modulus+Algorithm%3A+Revisiting+Signal+Recovery+for+Grant-Free+Access&rft.jtitle=IEEE+transactions+on+signal+processing&rft.au=Feres%2C+Carlos&rft.au=Ding%2C+Zhi&rft.date=2021&rft.issn=1053-587X&rft.eissn=1941-0476&rft.volume=69&rft.spage=6515&rft.epage=6529&rft_id=info:doi/10.1109%2FTSP.2021.3103038&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TSP_2021_3103038
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1053-587X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1053-587X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1053-587X&client=summon