An Enhanced Jacobi Precoder for Downlink Massive MIMO Systems

Linear precoding methods such as zero-forcing (ZF) are near optimal for downlink massive multi-user multiple input multiple output (MIMO) systems due to their asymptotic channel property. However, as the number of users increases, the computational complexity of obtaining the inverse matrix of the g...

Full description

Saved in:

Bibliographic Details
Published in:	Computers, materials & continua Vol. 68; no. 1; pp. 137 - 148
Main Authors:	Chan-Yeob, Park, Jae, Hyun-Ro, Jang, Jun-Yong, Hyoung-Kyu, Song
Format:	Journal Article
Language:	English
Published:	Henderson Tech Science Press 01.01.2021
Subjects:	Algorithms Asymptotic properties Complexity Downlinking Errors Iterative methods Linear equations Mathematical analysis Matrix methods MIMO (control systems) Polynomials Preconditioning
ISSN:	1546-2226, 1546-2218, 1546-2226
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Linear precoding methods such as zero-forcing (ZF) are near optimal for downlink massive multi-user multiple input multiple output (MIMO) systems due to their asymptotic channel property. However, as the number of users increases, the computational complexity of obtaining the inverse matrix of the gram matrix increases. For solving the computational complexity problem, this paper proposes an improved Jacobi (JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems. The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel implementation. However, the conventional JC has poor error performance when the number of users increases, which means that the diagonal dominance component of the gram matrix is reduced. In this paper, the preconditioning method is proposed to improve the error performance. Before executing the JC, the condition number of the linear equation and spectrum radius of the iteration matrix are reduced by multiplying the preconditioning matrix of the linear equation. To further reduce the condition number of the linear equation, this paper proposes a polynomial expansion precondition matrix that supplements diagonal components. The results show that the proposed method provides better performance than other iterative methods and has similar performance to the ZF.
AbstractList	Linear precoding methods such as zero-forcing (ZF) are near optimal for downlink massive multi-user multiple input multiple output (MIMO) systems due to their asymptotic channel property. However, as the number of users increases, the computational complexity of obtaining the inverse matrix of the gram matrix increases. For solving the computational complexity problem, this paper proposes an improved Jacobi (JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems. The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel implementation. However, the conventional JC has poor error performance when the number of users increases, which means that the diagonal dominance component of the gram matrix is reduced. In this paper, the preconditioning method is proposed to improve the error performance. Before executing the JC, the condition number of the linear equation and spectrum radius of the iteration matrix are reduced by multiplying the preconditioning matrix of the linear equation. To further reduce the condition number of the linear equation, this paper proposes a polynomial expansion precondition matrix that supplements diagonal components. The results show that the proposed method provides better performance than other iterative methods and has similar performance to the ZF.
Author	Jae, Hyun-Ro Jang, Jun-Yong Hyoung-Kyu, Song Chan-Yeob, Park
Author_xml	– sequence: 1 givenname: Park surname: Chan-Yeob fullname: Chan-Yeob, Park – sequence: 2 givenname: Hyun-Ro surname: Jae fullname: Jae, Hyun-Ro – sequence: 3 givenname: Jun-Yong surname: Jang fullname: Jang, Jun-Yong – sequence: 4 givenname: Song surname: Hyoung-Kyu fullname: Hyoung-Kyu, Song
BookMark	eNp1kM9LwzAYhoNMcJvePQY8d-ZHmyYHD2NOnWxMUM8hTVLMbJOZdMr-e6vzIIKn9zu8z_fCMwIDH7wF4ByjCSUM5Ze61ROCCJ4gzDDiR2CIi5xlhBA2-HWfgFFKG4QoowINwdXUw7l_UV5bA--VDpWDD9HqYGyEdYjwOnz4xvlXuFIpuXcLV4vVGj7uU2fbdAqOa9Uke_aTY_B8M3-a3WXL9e1iNl1mmmLaZZYTW2mBSU5IWRqiqGFlZQUSjJuy1Kampq6IqHKljRKF0Jobgw1XtLCFqukYXBz-bmN429nUyU3YRd9PSlKgkqOcF7hvsUNLx5BStLXUrlOdC76LyjUSI_mtSvaq5JcqeVDVg-gPuI2uVXH_P_IJ7lJtCg
CitedBy_id	crossref_primary_10_1049_2023_8887060 crossref_primary_10_32604_cmc_2022_020777
Cites_doi	10.1109/LCOMM.2016.2525807 10.1109/JSYST.2017.2776401 10.1109/MCOM.2014.6736761 10.4218/etrij.17.0116.0732 10.1109/JSTSP.2014.2317671 10.1109/LCOMM.2019.2897798 10.1109/LCOMM.2015.2504506 10.1109/MCOM.2016.7402270 10.1109/ACCESS.2019.2934090 10.1109/MSP.2011.2178495 10.15325/BLTJ.2015.2407793 10.1109/COMST.2019.2935810 10.1049/el.2017.3329
ContentType	Journal Article
Copyright	2021. This work is licensed under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml	– notice: 2021. This work is licensed under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID	AAYXX CITATION 7SC 7SR 8BQ 8FD ABUWG AFKRA AZQEC BENPR CCPQU DWQXO JG9 JQ2 L7M L~C L~D PHGZM PHGZT PIMPY PKEHL PQEST PQQKQ PQUKI PRINS
DOI	10.32604/cmc.2021.016108
DatabaseName	CrossRef Computer and Information Systems Abstracts Engineered Materials Abstracts METADEX Technology Research Database ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest One Community College ProQuest Central Korea Materials Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China
DatabaseTitle	CrossRef Publicly Available Content Database Materials Research Database Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Central China METADEX Computer and Information Systems Abstracts Professional ProQuest Central Engineered Materials Abstracts ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic Advanced Technologies Database with Aerospace ProQuest One Academic (New)
DatabaseTitleList	Publicly Available Content Database
Database_xml	– sequence: 1 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1546-2226
EndPage	148
ExternalDocumentID	10_32604_cmc_2021_016108
GroupedDBID	AAFWJ AAYXX ACIWK ADMLS AFFHD AFKRA ALMA_UNASSIGNED_HOLDINGS BENPR CCPQU CITATION EBS EJD J9A OK1 P2P PHGZM PHGZT PIMPY RTS TUS 7SC 7SR 8BQ 8FD ABUWG AZQEC DWQXO JG9 JQ2 L7M L~C L~D PKEHL PQEST PQQKQ PQUKI PRINS
ID	FETCH-LOGICAL-c313t-e82ebc91242277d2a3d67be90968d77cdf3dfb29b4acda959cc8dd1d8a35e5af3
IEDL.DBID	BENPR
ISICitedReferencesCount	2
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000632822900008&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1546-2226 1546-2218
IngestDate	Sun Nov 09 07:42:41 EST 2025 Tue Nov 18 21:19:36 EST 2025 Sat Nov 29 03:13:16 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c313t-e82ebc91242277d2a3d67be90968d77cdf3dfb29b4acda959cc8dd1d8a35e5af3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
OpenAccessLink	https://www.proquest.com/docview/2507804851?pq-origsite=%requestingapplication%
PQID	2507804851
PQPubID	2048737
PageCount	12
ParticipantIDs	proquest_journals_2507804851 crossref_citationtrail_10_32604_cmc_2021_016108 crossref_primary_10_32604_cmc_2021_016108
PublicationCentury	2000
PublicationDate	2021-01-01
PublicationDateYYYYMMDD	2021-01-01
PublicationDate_xml	– month: 01 year: 2021 text: 2021-01-01 day: 01
PublicationDecade	2020
PublicationPlace	Henderson
PublicationPlace_xml	– name: Henderson
PublicationTitle	Computers, materials & continua
PublicationYear	2021
Publisher	Tech Science Press
Publisher_xml	– name: Tech Science Press
References	Kang (ref14) 2017; 39 Rusek (ref1) 2013; 30 Pyzara (ref20) 2011 Gustafsson (ref9) 2017 Lu (ref3) 2014; 8 Larsson (ref2) 2014; 52 Zhu (ref10) 2015 Jin (ref21) 2019; 23 Ruperee (ref22) 2019; 13 Xie (ref13) 2016; 20 Albreem (ref6) 2019; 21 Lee (ref15) 2017; 53 Gao (ref12) 2014 Ro (ref19) 2019; 7 Björnson (ref5) 2016; 54 Zhang (ref7) 2016 Fatema (ref8) 2018; 12 Zhang (ref18) 2018 Marzetta (ref4) 2015; 20 Gao (ref11) 2015 Qin (ref17) 2016; 20 Song (ref16) 2016
References_xml	– volume: 20 start-page: 744 year: 2016 ident: ref13 article-title: Low-complexity SSOR-based precoding for massive MIMO systems publication-title: IEEE Communications Letters doi: 10.1109/LCOMM.2016.2525807 – volume: 12 start-page: 3920 year: 2018 ident: ref8 article-title: Massive MIMO linear precoding: A survey publication-title: IEEE Systems Journal doi: 10.1109/JSYST.2017.2776401 – volume: 52 start-page: 186 year: 2014 ident: ref2 article-title: Massive MIMO for next generation wireless systems publication-title: IEEE Communications Magazine doi: 10.1109/MCOM.2014.6736761 – volume: 39 start-page: 326 year: 2017 ident: ref14 article-title: Low-complexity massive MIMO detectors based on Richardson method publication-title: Etri Journal doi: 10.4218/etrij.17.0116.0732 – volume: 8 start-page: 742 year: 2014 ident: ref3 article-title: An overview of massive MIMO: Benefits and challenges publication-title: IEEE Journal of Selected Topics in Signal Processing doi: 10.1109/JSTSP.2014.2317671 – start-page: 203 year: 2018 ident: ref18 article-title: Adaptive damped Jacobi detector and architecture for massive MIMO uplink – volume: 23 start-page: 748 year: 2019 ident: ref21 article-title: A low complexity signal detection scheme based on improved newton iteration for massive MIMO systems publication-title: IEEE Communications Letters doi: 10.1109/LCOMM.2019.2897798 – volume: 20 start-page: 276 year: 2016 ident: ref17 article-title: A near-optimal detection scheme based on joint steepest descent and Jacobi method for uplink massive MIMO systems publication-title: IEEE Communications Letters doi: 10.1109/LCOMM.2015.2504506 – start-page: 1763 year: 2015 ident: ref10 article-title: On the matrix inversion approximation based on Neumann series in massive MIMO systems – start-page: 62 year: 2017 ident: ref9 article-title: Approximate Neumann series or exact matrix inversion for massive MIMO? – volume: 54 start-page: 114 year: 2016 ident: ref5 article-title: Massive MIMO: Ten myths and one critical question publication-title: IEEE Communications Magazine doi: 10.1109/MCOM.2016.7402270 – volume: 7 start-page: 112318 year: 2019 ident: ref19 article-title: An efficient precoding method for improved downlink massive MIMO system publication-title: IEEE Access doi: 10.1109/ACCESS.2019.2934090 – start-page: 1 year: 2016 ident: ref16 article-title: Joint conjugate gradient and Jacobi iteration based low complexity precoding for massive MIMO systems – start-page: 1577 year: 2015 ident: ref11 article-title: Capacity-approaching linear precoding with low-complexity for large-scale MIMO systems – start-page: 459 year: 2011 ident: ref20 article-title: The influence of a matrix condition number on iterative methods’ convergence – volume: 30 start-page: 40 year: 2013 ident: ref1 article-title: Scaling up MIMO: Opportunities and challenges with very large arrays publication-title: IEEE Signal Processing Magazine doi: 10.1109/MSP.2011.2178495 – volume: 20 start-page: 11 year: 2015 ident: ref4 article-title: Massive MIMO: An introduction publication-title: Bell Labs Technical Journal doi: 10.15325/BLTJ.2015.2407793 – volume: 21 start-page: 3109 year: 2019 ident: ref6 article-title: Massive MIMO detection techniques: A survey publication-title: IEEE Communications Surveys & Tutorials doi: 10.1109/COMST.2019.2935810 – start-page: 3291 year: 2014 ident: ref12 article-title: Matrix inversion-less signal detection using SOR method for uplink large-scale MIMO systems – volume: 53 start-page: 1552 year: 2017 ident: ref15 article-title: Decision-aided Jacobi iteration for signal detection in massive MIMO systems publication-title: Electronics Letters doi: 10.1049/el.2017.3329 – volume: 13 start-page: 4390 year: 2019 ident: ref22 article-title: Time shifted pilot signal transmission with pilot hopping to improve the uplink performance of massive MIMO systems for next generation network publication-title: KSII Transactions on Internet and Information Systems – start-page: 1 year: 2016 ident: ref7 article-title: Reviews of recent progress on low-complexity linear detection via iterative algorithms for massive MIMO systems
SSID	ssj0036390
Score	2.2032943
Snippet	Linear precoding methods such as zero-forcing (ZF) are near optimal for downlink massive multi-user multiple input multiple output (MIMO) systems due to their...
SourceID	proquest crossref
SourceType	Aggregation Database Enrichment Source Index Database
StartPage	137
SubjectTerms	Algorithms Asymptotic properties Complexity Downlinking Errors Iterative methods Linear equations Mathematical analysis Matrix methods MIMO (control systems) Polynomials Preconditioning
Title	An Enhanced Jacobi Precoder for Downlink Massive MIMO Systems
URI	https://www.proquest.com/docview/2507804851
Volume	68
WOSCitedRecordID	wos000632822900008&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: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1546-2226 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0036390 issn: 1546-2226 databaseCode: BENPR dateStart: 20040101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 1546-2226 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0036390 issn: 1546-2226 databaseCode: PIMPY dateStart: 20040101 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELagZWChPEWhIA8sDKHETmN7QjxaUURKhACVKYofEZUgLW3h93NOHB5LF6YMcaLo7nz33fnyHUJHxpc6FTL0AE1AghJI7Uke2E6ATAotA-0XdAxPt2ww4MOhiF3BbebaKiufWDhqPVa2Rt6GUG25cgAgnE3ePTs1yp6uuhEay6humcrAzusX3UF8X_liCvG3-CWyE4QegWhWHlQCZDkN2urNUhgS_8SiHjte8ndg-uuXi2DTa_z3M9fRmoOZ-Ly0iw20ZPJN1KhGOGC3o7cQpP-4m78UbQD4BryjHOHYJskaVgGexVeWTB_yVRwBygbPiKN-dIcdz_k2eux1Hy6vPTdRwVPUp3PPcGKkEhDTCWFMk5TqkEkjII_hmjGlM6ozSYQMUgUq7AiluNa-5intmE6a0R1Uy8e52UVYEipSRiQNTRYoyUUWkoyp0PILUp7yJmpX4kyUoxu3Uy9eE0g7CgUkoIDEKiApFdBEx99PTEqqjQVrW5X4E7fpZsmP7PcW395Hq_ZdZSWlhWrz6Yc5QCvqcz6aTQ-dDcE17kfx8xeFk8_H
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3JTsMwEB2VggQXdkRZfYADh1Bip4l9QAhREIWm9AAITiFeIipBCrSA-Cm-kXEWlgs3DpzjWHLeaN4bx54HsGFcqWMhfQfVBBYontSO5J49CZBIoaWn3awdw2U76HT41ZXoVuC9vAtjj1WWOTFL1Lqv7B55Hana9spBgbD38OhY1yj7d7W00MjD4tS8vWLJNthtNRHfTUqPDs8Pjp3CVcBRzGVDx3BqpBLIa5QGgaYx034gjUAtz3UQKJ0wnUgqpBcrXEZDKMW1djWPWcM04oThvCMw6tlgr8JotxV2r8vcz5DvsyuYDc93KLJn_mMUJdKOV1f3tmUidbetyrJ2lt-J8CcPZOR2NPXfPss0TBYymuzncT8DFZPOwlRpUUGKjDUHu_spOUxvs2MO5ASzv-yRrt0E0DgK9TppWrMArMdJiFUEZn4StsIzUvRxn4eLP1nEAlTTfmoWgUjKRBxQyXyTeEpykfg0CZRv-ycyHvMa1Ev4IlW0U7euHncRllUZ4BECHlnAoxzwGmx9vvGQtxL5ZexKCXdUJJVB9IX10u-P12H8-DxsR-1W53QZJuy8-a7RClSHT89mFcbUy7A3eFor4pfAzV_HxgfhpC6A
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=An+Enhanced+Jacobi+Precoder+for+Downlink+Massive+MIMO+Systems&rft.jtitle=Computers%2C+materials+%26+continua&rft.au=Chan-Yeob%2C+Park&rft.au=Hyun-Ro+Jae&rft.au=Jun-Yong%2C+Jang&rft.au=Song+Hyoung-Kyu&rft.date=2021-01-01&rft.pub=Tech+Science+Press&rft.issn=1546-2218&rft.eissn=1546-2226&rft.volume=68&rft.issue=1&rft.spage=137&rft_id=info:doi/10.32604%2Fcmc.2021.016108
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1546-2226&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1546-2226&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1546-2226&client=summon