Analog Precoder and Equalizer Designs and their Geometry for Multichannel Communication
This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize th...
Uloženo v:
| Vydáno v: | IEEE transactions on wireless communications Ročník 7; číslo 8; s. 2957 - 2963 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Piscataway, NJ
IEEE
01.08.2008
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 1536-1276, 1558-2248 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L 2 (R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual two- channel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two-channel communication problem into what might be called the Shannon channel. |
|---|---|
| AbstractList | This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L super(2)(R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual two- channel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two-channel communication problem into what might be called the Shannon channel. This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency- selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L@@u2@(R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual two- channel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two- channel communication problem into what might be called the Shannon channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective additive Gaussian noise (AGN) channel. The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. We assume a continuous channel model with precoder transmissions for m subchannels that lie in an n-dimensional linear subspace of L 2 (R). m and n are design parameters. We first design the subspace according to the channel characteristics, and then design the precoders as functions in this subspace. After the design of the optimal precoder and equalizer, we explore the geometry of these designs. We show that all of these precoder and equalizer designs are, in fact, decompositions of a virtual two- channel problem into a system of canonical coordinates, wherein variables in the canonical message channel are correlated only pairwise with corresponding variables in the canonical measurement channel. This finding clarifies the geometry of precoder and equalizer designs and illustrates that they decompose the two-channel communication problem into what might be called the Shannon channel. |
| Author | Zhifei Fan Gubner, J.A. Scharf, L.L. |
| Author_xml | – sequence: 1 surname: Zhifei Fan fullname: Zhifei Fan organization: QualComm, San Diego, CA – sequence: 2 givenname: L.L. surname: Scharf fullname: Scharf, L.L. – sequence: 3 givenname: J.A. surname: Gubner fullname: Gubner, J.A. |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20581519$$DView record in Pascal Francis |
| BookMark | eNp9kU1v1DAQhi1UJNqFMwcuERKFS7bjzzjHaikFqQgORT1ajjNpXSV2ayeH8uvx7hYOlejJ49HzjK15j8hBiAEJeUthTSm0J5dXmzUD0GtQoJR6QQ6plLpmTOiDbc1VTVmjXpGjnG8BaKOkPCRXp8GO8br6mdDFHlNlQ1-d3S929L_L7TNmfx3yrjvfoE_VOcYJ5_RQDTFV35dx9u7GhoBjtYnTtATv7OxjeE1eDnbM-ObxXJFfX84uN1_rix_n3zanF7UTVMw1xR6U1bYTSBnDppOOtQy0ta7rsKdDL8E1XYt6EC3tiqS4ZFQ0HQzatj1fkY_7uXcp3i-YZzP57HAcbcC4ZNMCV1xJLgt5_CzJhRCqEbqAn54FqWro7hOqoO-foLdxSWWj2WjFBRfb11fkwyNks7PjkGxwPpu75CebHgwDqamkbeHknnMp5pxwMM7Pu2XOyfrRUDDboE0J2myDNvugi3fyxPs7-v_Gu73hEfEfLRQAg5b_AbLks-8 |
| CODEN | ITWCAX |
| CitedBy_id | crossref_primary_10_1109_TSP_2019_2926017 |
| Cites_doi | 10.1109/49.768200 10.1109/79.841722 10.1109/TCOMM.2003.815080 10.1109/TCOM.1971.1090705 10.1023/A:1008859809455 10.1007/978-1-4612-0003-1 10.1007/978-1-4615-3136-4 10.1109/26.339844 10.1109/18.761338 10.1109/ICC.1999.768001 10.1109/GLOCOM.1999.831760 10.1109/ICASSP.2002.5744004 10.1109/TCOM.1967.1089674 10.1109/5.387096 10.1109/78.824676 10.1109/78.905856 10.1002/j.1538-7305.1961.tb03976.x 10.1109/TCOM.1963.1088793 10.1109/78.995062 10.1137/0522035 10.1109/TSP.2003.815393 10.1109/TSP.2002.803324 10.1109/78.661332 10.1109/78.771047 10.1002/j.1538-7305.1966.tb02435.x 10.1109/TSP.2003.815387 |
| ContentType | Journal Article |
| Copyright | 2008 INIST-CNRS Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008 |
| Copyright_xml | – notice: 2008 INIST-CNRS – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008 |
| DBID | 97E RIA RIE AAYXX CITATION IQODW 7SC 7SP 8FD JQ2 L7M L~C L~D F28 FR3 |
| DOI | 10.1109/TWC.2008.060666 |
| DatabaseName | IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Pascal-Francis 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 ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
| 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 Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database Technology Research Database Technology Research Database 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 Applied Sciences |
| EISSN | 1558-2248 |
| EndPage | 2963 |
| ExternalDocumentID | 2329642341 20581519 10_1109_TWC_2008_060666 4600209 |
| Genre | orig-research |
| GroupedDBID | -~X 0R~ 29I 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACGFS ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AIBXA AKJIK AKQYR ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD HZ~ H~9 IES IFIPE IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RNS AAYXX CITATION IQODW RIG 7SC 7SP 8FD JQ2 L7M L~C L~D F28 FR3 |
| ID | FETCH-LOGICAL-c414t-1ed06a8ab4e122e7b5c29208aacbbed1fd50c7b9e8f491bc416352147b0f8a9d3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000259367000020&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1536-1276 |
| IngestDate | Sun Sep 28 09:26:27 EDT 2025 Sat Sep 27 21:01:51 EDT 2025 Sun Sep 28 08:31:09 EDT 2025 Mon Jun 30 10:18:29 EDT 2025 Mon Jul 21 09:16:18 EDT 2025 Sat Nov 29 02:54:55 EST 2025 Tue Nov 18 21:45:01 EST 2025 Wed Aug 27 02:52:40 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Keywords | Additive noise Design criterion Parameter estimation Multichannel transmission Bit error rate Gaussian channel Two channel system Transmission channel Information rate Subspace method Data transmission Equalizer Information transmission Mean square error Frequency selection Gaussian noise Channel estimation Modulation multichannel communication Analog precoder geometry canonical coordinates Multiple channel Mutual information |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c414t-1ed06a8ab4e122e7b5c29208aacbbed1fd50c7b9e8f491bc416352147b0f8a9d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 |
| PQID | 863434036 |
| PQPubID | 23500 |
| PageCount | 7 |
| ParticipantIDs | proquest_miscellaneous_903636535 crossref_citationtrail_10_1109_TWC_2008_060666 ieee_primary_4600209 proquest_journals_863434036 proquest_miscellaneous_1671352146 proquest_miscellaneous_34446748 crossref_primary_10_1109_TWC_2008_060666 pascalfrancis_primary_20581519 |
| PublicationCentury | 2000 |
| PublicationDate | 2008-08-01 |
| PublicationDateYYYYMMDD | 2008-08-01 |
| PublicationDate_xml | – month: 08 year: 2008 text: 2008-08-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | Piscataway, NJ |
| PublicationPlace_xml | – name: Piscataway, NJ – name: New York |
| PublicationTitle | IEEE transactions on wireless communications |
| PublicationTitleAbbrev | TWC |
| PublicationYear | 2008 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref35 ref13 ref34 ref15 ref14 ref31 ref30 ref33 ref32 ref2 ref1 ref18 marshall (ref17) 1979 fan (ref7) 2004 gubner (ref12) 2003 ref24 ref23 ref26 ref20 ref22 gallager (ref10) 1968 ref21 loeve (ref16) 1977 ref28 ref27 grochenig (ref11) 2001 ref29 ref9 fan (ref8) 2004 ref3 john (ref19) 2000 ref5 fan (ref6) 2006 scharf (ref25) 1990 daubechies (ref4) 1991; 22 |
| References_xml | – ident: ref20 doi: 10.1109/49.768200 – ident: ref30 doi: 10.1109/79.841722 – ident: ref34 doi: 10.1109/TCOMM.2003.815080 – ident: ref31 doi: 10.1109/TCOM.1971.1090705 – ident: ref13 doi: 10.1023/A:1008859809455 – year: 1977 ident: ref16 publication-title: Probability Theory II – year: 2000 ident: ref19 publication-title: Proakis DIGITAL COMMUNICATIONS – year: 2001 ident: ref11 publication-title: Foundations of Time-Frequency Analysis doi: 10.1007/978-1-4612-0003-1 – ident: ref15 doi: 10.1007/978-1-4615-3136-4 – ident: ref32 doi: 10.1109/26.339844 – year: 2004 ident: ref7 article-title: Analog precoder and equalizer design for multichannel communication publication-title: Proc SPAWC – year: 2006 ident: ref6 publication-title: Signal design diversity and capacity in multi-access communication systems – year: 2004 ident: ref8 article-title: Canonical coordinate geometry of precoder and equalizer designs for multichannel communications publication-title: Proc SPAWC – year: 1968 ident: ref10 publication-title: Information Theory and Reliable Communcation – year: 1979 ident: ref17 publication-title: Inequalities Theory of Majorization and Its Applications – ident: ref23 doi: 10.1109/18.761338 – ident: ref2 doi: 10.1109/ICC.1999.768001 – ident: ref33 doi: 10.1109/GLOCOM.1999.831760 – ident: ref28 doi: 10.1109/ICASSP.2002.5744004 – ident: ref21 doi: 10.1109/TCOM.1967.1089674 – ident: ref9 doi: 10.1109/5.387096 – ident: ref26 doi: 10.1109/78.824676 – ident: ref14 doi: 10.1109/78.905856 – ident: ref29 doi: 10.1002/j.1538-7305.1961.tb03976.x – ident: ref1 doi: 10.1109/TCOM.1963.1088793 – ident: ref24 doi: 10.1109/78.995062 – year: 1990 ident: ref25 publication-title: Statistical Signal Processing – volume: 22 start-page: 554 year: 1991 ident: ref4 article-title: A simple Wilson orthonormal basis with exponential decay publication-title: SIAM J Math Anal doi: 10.1137/0522035 – ident: ref18 doi: 10.1109/TSP.2003.815393 – ident: ref35 doi: 10.1109/TSP.2002.803324 – year: 2003 ident: ref12 publication-title: Maximum mutual information signaling waveforms – ident: ref27 doi: 10.1109/78.661332 – ident: ref22 doi: 10.1109/78.771047 – ident: ref3 doi: 10.1002/j.1538-7305.1966.tb02435.x – ident: ref5 doi: 10.1109/TSP.2003.815387 |
| SSID | ssj0017655 |
| Score | 1.8879895 |
| Snippet | This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency-selective... The design goal is to maximize mutual information rate, minimize the mean square error, or minimize the bit error rate subject to a transmit power constraint. This is a paper on modulation theory that addresses joint analog precoder and equalizer design for multichannel data transmission over the frequency- selective... |
| SourceID | proquest pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 2957 |
| SubjectTerms | Additive noise Analog precoder Applied sciences Bit error rate canonical coordinates Channels Communication channels Coordinate measuring machines Data communication Data transmission Decomposition Design engineering Detection, estimation, filtering, equalization, prediction equalizer Equalizers Exact sciences and technology Frequency Gaussian noise Geometry Information, signal and communications theory Mathematical models Mean square error methods Mean square errors Modulation, demodulation multichannel communication Mutual information Signal and communications theory Signal, noise Subspaces Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Wireless communication |
| Title | Analog Precoder and Equalizer Designs and their Geometry for Multichannel Communication |
| URI | https://ieeexplore.ieee.org/document/4600209 https://www.proquest.com/docview/863434036 https://www.proquest.com/docview/1671352146 https://www.proquest.com/docview/34446748 https://www.proquest.com/docview/903636535 |
| Volume | 7 |
| WOSCitedRecordID | wos000259367000020&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: 1558-2248 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0017655 issn: 1536-1276 databaseCode: RIE dateStart: 20020101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwEB6VigMceBVEKBQjceBA2nhjO_YRlRZOVQ9F7S3yY4yQ2gRtdpHg1-Nx0ogV7IFbEk8ka8bOjDPfzAfwVgeupIuSYIO-FN6r0i1sOriiqzB5cO4bn8kmmrMzfXVlznfg_VwLg4gZfIaHdJlz-aH3a_pVdiQoiUTVeneaRo21WnPGoFGZ4TRtYOKVadTUxodX5uji8ngCTeZofcMDZUoVAkTaIekkjmQWf32Xs7M5ffh_03wED6agkn0YV8Fj2MHuCdz_o9XgHlxS95H-KzunE3DAJbNdYCe5pPJXuvuYgRxDfppzB-wT9je4Wv5kKapluUyXaoQ7vGYbNSVP4cvpycXx53IiVSi94GJVcgyVsto6gXyxwMZJT4RV2lrvHAYeg6x84wzqKAx3ngI2SWRGroramlA_g92u7_A5sGjr6L2xKch0Ipqg0cdKRq59bKwNuoDDW0W3fuo4TsQX120-eVSmTZaZeDCzZQp4N7_wfWy2sV10jxQ_i006L-Bgw5Lz-KKSOgU3SWD_1rTttFuHVqta1CL58gLezKNpm1HuxHbYr4eWK-IyJBb0Al5vkamFyNwtBbAtEobS5krW8sW_p78P90Y8CgEMX8LuarnGV3DX_1h9G5YHecH_BmFQAGY |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwEB5VBQk48CqIUGiNxIEDaePETpwjKi1FlFUPi9pb5Me4QioJ2uwiwa_H46QRK9gDtySeSNaMnRlnvpkP4LVyvJTGS4IN2lRYW6Ym1-HgiibD4MG5rWwkm6hmM3V5WZ9vwdupFgYRI_gMD-gy5vJdZ1f0q-xQUBKJqvVuSSHybKjWmnIGVRk5TsMWJmaZqhwb-fCsPpxfHI2wyRivr_mgSKpCkEjdB634gc7iry9zdDcnD_5vog_h_hhWsnfDOngEW9g-hnt_NBvcgQvqP9JdsXM6AztcMN06dhyLKn-Fu_cRytHHpzF7wD5g9w2Xi58sxLUsFupSlXCL12ytquQJfDk5nh-dpiOtQmoFF8uUo8tKrbQRyPMcKyMtUVYpra0x6Lh3MrOVqVF5UXNjKWSTRGdkMq907YqnsN12LT4D5nXhra11CDON8LVTaH0mPVfWV1o7lcDBjaIbO_YcJ-qL6yaePbK6CZYZmTCjZRJ4M73wfWi3sVl0hxQ_iY06T2BvzZLTeJ5JFcKbILB7Y9pm3K99o8pCFCJ48wReTaNho1H2RLfYrfqGl8RmSDzoCexvkCmEiOwtCbANEjUlzktZyOf_nv4-3Dmdfz5rzj7OPu3C3QGdQnDDF7C9XKzwJdy2P5Zf-8VeXPy_AdHQA60 |
| 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=Analog+Precoder+and+Equalizer+Designs+and+their+Geometry+for+Multichannel+Communication&rft.jtitle=IEEE+transactions+on+wireless+communications&rft.au=Zhifei+Fan&rft.au=Scharf%2C+L.L.&rft.au=Gubner%2C+J.A.&rft.date=2008-08-01&rft.issn=1536-1276&rft.volume=7&rft.issue=8&rft.spage=2957&rft.epage=2963&rft_id=info:doi/10.1109%2FTWC.2008.060666&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TWC_2008_060666 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1536-1276&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1536-1276&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1536-1276&client=summon |