Information Theoretic Bounds for Compound MIMO Gaussian Channels
In this paper, achievable rates for compound Gaussian multiple-input-multiple-output (MIMO) channels are derived. Two types of channels, modeled in the frequency domain, are considered when: 1) the channel frequency response matrix H belongs to a subset of H infin normed linear space, and 2) the pow...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on information theory 2009-04, Vol.55 (4), p.1603-1617 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1617 |
|---|---|
| container_issue | 4 |
| container_start_page | 1603 |
| container_title | IEEE transactions on information theory |
| container_volume | 55 |
| creator | Denic, S.Z. Charalambous, C.D. Djouadi, S.M. |
| description | In this paper, achievable rates for compound Gaussian multiple-input-multiple-output (MIMO) channels are derived. Two types of channels, modeled in the frequency domain, are considered when: 1) the channel frequency response matrix H belongs to a subset of H infin normed linear space, and 2) the power spectral density (PSD) matrix of the Gaussian noise belongs to a subset of L 1 space. The achievable rates of these two compound channels are related to the maximin of the mutual information rate. The minimum is with respect to the set of all possible H matrices or all possible PSD matrices of the noise. The maximum is with respect to all possible PSD matrices of the transmitted signal with bounded power. For the compound channel modeled by the set of H matrices, it is shown, under certain conditions, that the code for the worst case channel can be used for the whole class of channels. For the same model, the water-filling argument implies that the larger the set of matrices H , the smaller the bandwidth of the transmitted signal will be. For the second compound channel, the explicit relation between the maximizing PSD matrix of the transmitted signal and the minimizing PSD matrix of the noise is found. Two PSD matrices are related through a Riccati equation, which is always present in Kalman filtering and liner-quadratic Gaussian control problems. |
| doi_str_mv | 10.1109/TIT.2009.2013007 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_ieee_primary_4802319</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>4802319</ieee_id><sourcerecordid>919915750</sourcerecordid><originalsourceid>FETCH-LOGICAL-c383t-7e04e3b59dc102587dcfd03db1ab8b66ff023f1b9bb487a75a5545043eaff3023</originalsourceid><addsrcrecordid>eNp9kMFLwzAUxoMoOKd3wUsR1FNnXpMszU0dOgsbu8xzSNuEdbTJTNqD_70ZGzt4EB7v8fh-74P3IXQLeAKAxfO6WE8yjEVsQDDmZ2gEjPFUTBk9RyOMIU8FpfklugphG1fKIBuhl8Ia5zvVN84m6412XvdNlby5wdYhiVIyc91uvyXLYrlK5moIoVE2mW2UtboN1-jCqDbom-Mco6-P9_XsM12s5sXsdZFWJCd9yjWmmpRM1BXgjOW8rkyNSV2CKvNyOjUGZ8RAKcqS5lxxphijDFOilTEkamP0dPDdefc96NDLrgmVbltltRuCFCAEMM5wJB__JQmdEpZF6zG6_wNu3eBt_EKCYILE2kP4AFXeheC1kTvfdMr_SMByn7yMyct98vKYfDx5OPqqUKnWeGWrJpzuMqA88hC5uwPXaK1PMs3jtyDIL1f-iiU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>195935934</pqid></control><display><type>article</type><title>Information Theoretic Bounds for Compound MIMO Gaussian Channels</title><source>IEEE Electronic Library (IEL)</source><creator>Denic, S.Z. ; Charalambous, C.D. ; Djouadi, S.M.</creator><creatorcontrib>Denic, S.Z. ; Charalambous, C.D. ; Djouadi, S.M.</creatorcontrib><description>In this paper, achievable rates for compound Gaussian multiple-input-multiple-output (MIMO) channels are derived. Two types of channels, modeled in the frequency domain, are considered when: 1) the channel frequency response matrix H belongs to a subset of H infin normed linear space, and 2) the power spectral density (PSD) matrix of the Gaussian noise belongs to a subset of L 1 space. The achievable rates of these two compound channels are related to the maximin of the mutual information rate. The minimum is with respect to the set of all possible H matrices or all possible PSD matrices of the noise. The maximum is with respect to all possible PSD matrices of the transmitted signal with bounded power. For the compound channel modeled by the set of H matrices, it is shown, under certain conditions, that the code for the worst case channel can be used for the whole class of channels. For the same model, the water-filling argument implies that the larger the set of matrices H , the smaller the bandwidth of the transmitted signal will be. For the second compound channel, the explicit relation between the maximizing PSD matrix of the transmitted signal and the minimizing PSD matrix of the noise is found. Two PSD matrices are related through a Riccati equation, which is always present in Kalman filtering and liner-quadratic Gaussian control problems.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2009.2013007</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Bandwidth ; Bandwidths ; Channel degrading ; Channels ; Communication channels ; compound channel ; Compound channels ; Data transmission ; Density ; Detection, estimation, filtering, equalization, prediction ; Exact sciences and technology ; Filtering ; Frequency domain analysis ; Frequency response ; Gaussian ; Gaussian channels ; Gaussian noise ; Information theory ; Information, signal and communications theory ; Input output ; Kalman filters ; Mathematical analysis ; Matrices ; Matrix methods ; MIMO ; multiple-input-multiple-output (MIMO) Gaussian channel ; Mutual information ; Noise ; Riccati equations ; Signal and communications theory ; Signal to noise ratio ; Signal, noise ; Systems, networks and services of telecommunications ; Telecommunications ; Telecommunications and information theory ; Transmission and modulation (techniques and equipments)</subject><ispartof>IEEE transactions on information theory, 2009-04, Vol.55 (4), p.1603-1617</ispartof><rights>2009 INIST-CNRS</rights><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Apr 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c383t-7e04e3b59dc102587dcfd03db1ab8b66ff023f1b9bb487a75a5545043eaff3023</citedby><cites>FETCH-LOGICAL-c383t-7e04e3b59dc102587dcfd03db1ab8b66ff023f1b9bb487a75a5545043eaff3023</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4802319$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4802319$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21472001$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Denic, S.Z.</creatorcontrib><creatorcontrib>Charalambous, C.D.</creatorcontrib><creatorcontrib>Djouadi, S.M.</creatorcontrib><title>Information Theoretic Bounds for Compound MIMO Gaussian Channels</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>In this paper, achievable rates for compound Gaussian multiple-input-multiple-output (MIMO) channels are derived. Two types of channels, modeled in the frequency domain, are considered when: 1) the channel frequency response matrix H belongs to a subset of H infin normed linear space, and 2) the power spectral density (PSD) matrix of the Gaussian noise belongs to a subset of L 1 space. The achievable rates of these two compound channels are related to the maximin of the mutual information rate. The minimum is with respect to the set of all possible H matrices or all possible PSD matrices of the noise. The maximum is with respect to all possible PSD matrices of the transmitted signal with bounded power. For the compound channel modeled by the set of H matrices, it is shown, under certain conditions, that the code for the worst case channel can be used for the whole class of channels. For the same model, the water-filling argument implies that the larger the set of matrices H , the smaller the bandwidth of the transmitted signal will be. For the second compound channel, the explicit relation between the maximizing PSD matrix of the transmitted signal and the minimizing PSD matrix of the noise is found. Two PSD matrices are related through a Riccati equation, which is always present in Kalman filtering and liner-quadratic Gaussian control problems.</description><subject>Applied sciences</subject><subject>Bandwidth</subject><subject>Bandwidths</subject><subject>Channel degrading</subject><subject>Channels</subject><subject>Communication channels</subject><subject>compound channel</subject><subject>Compound channels</subject><subject>Data transmission</subject><subject>Density</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Exact sciences and technology</subject><subject>Filtering</subject><subject>Frequency domain analysis</subject><subject>Frequency response</subject><subject>Gaussian</subject><subject>Gaussian channels</subject><subject>Gaussian noise</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>Input output</subject><subject>Kalman filters</subject><subject>Mathematical analysis</subject><subject>Matrices</subject><subject>Matrix methods</subject><subject>MIMO</subject><subject>multiple-input-multiple-output (MIMO) Gaussian channel</subject><subject>Mutual information</subject><subject>Noise</subject><subject>Riccati equations</subject><subject>Signal and communications theory</subject><subject>Signal to noise ratio</subject><subject>Signal, noise</subject><subject>Systems, networks and services of telecommunications</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Transmission and modulation (techniques and equipments)</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kMFLwzAUxoMoOKd3wUsR1FNnXpMszU0dOgsbu8xzSNuEdbTJTNqD_70ZGzt4EB7v8fh-74P3IXQLeAKAxfO6WE8yjEVsQDDmZ2gEjPFUTBk9RyOMIU8FpfklugphG1fKIBuhl8Ia5zvVN84m6412XvdNlby5wdYhiVIyc91uvyXLYrlK5moIoVE2mW2UtboN1-jCqDbom-Mco6-P9_XsM12s5sXsdZFWJCd9yjWmmpRM1BXgjOW8rkyNSV2CKvNyOjUGZ8RAKcqS5lxxphijDFOilTEkamP0dPDdefc96NDLrgmVbltltRuCFCAEMM5wJB__JQmdEpZF6zG6_wNu3eBt_EKCYILE2kP4AFXeheC1kTvfdMr_SMByn7yMyct98vKYfDx5OPqqUKnWeGWrJpzuMqA88hC5uwPXaK1PMs3jtyDIL1f-iiU</recordid><startdate>20090401</startdate><enddate>20090401</enddate><creator>Denic, S.Z.</creator><creator>Charalambous, C.D.</creator><creator>Djouadi, S.M.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20090401</creationdate><title>Information Theoretic Bounds for Compound MIMO Gaussian Channels</title><author>Denic, S.Z. ; Charalambous, C.D. ; Djouadi, S.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c383t-7e04e3b59dc102587dcfd03db1ab8b66ff023f1b9bb487a75a5545043eaff3023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Applied sciences</topic><topic>Bandwidth</topic><topic>Bandwidths</topic><topic>Channel degrading</topic><topic>Channels</topic><topic>Communication channels</topic><topic>compound channel</topic><topic>Compound channels</topic><topic>Data transmission</topic><topic>Density</topic><topic>Detection, estimation, filtering, equalization, prediction</topic><topic>Exact sciences and technology</topic><topic>Filtering</topic><topic>Frequency domain analysis</topic><topic>Frequency response</topic><topic>Gaussian</topic><topic>Gaussian channels</topic><topic>Gaussian noise</topic><topic>Information theory</topic><topic>Information, signal and communications theory</topic><topic>Input output</topic><topic>Kalman filters</topic><topic>Mathematical analysis</topic><topic>Matrices</topic><topic>Matrix methods</topic><topic>MIMO</topic><topic>multiple-input-multiple-output (MIMO) Gaussian channel</topic><topic>Mutual information</topic><topic>Noise</topic><topic>Riccati equations</topic><topic>Signal and communications theory</topic><topic>Signal to noise ratio</topic><topic>Signal, noise</topic><topic>Systems, networks and services of telecommunications</topic><topic>Telecommunications</topic><topic>Telecommunications and information theory</topic><topic>Transmission and modulation (techniques and equipments)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Denic, S.Z.</creatorcontrib><creatorcontrib>Charalambous, C.D.</creatorcontrib><creatorcontrib>Djouadi, S.M.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Denic, S.Z.</au><au>Charalambous, C.D.</au><au>Djouadi, S.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Information Theoretic Bounds for Compound MIMO Gaussian Channels</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2009-04-01</date><risdate>2009</risdate><volume>55</volume><issue>4</issue><spage>1603</spage><epage>1617</epage><pages>1603-1617</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>In this paper, achievable rates for compound Gaussian multiple-input-multiple-output (MIMO) channels are derived. Two types of channels, modeled in the frequency domain, are considered when: 1) the channel frequency response matrix H belongs to a subset of H infin normed linear space, and 2) the power spectral density (PSD) matrix of the Gaussian noise belongs to a subset of L 1 space. The achievable rates of these two compound channels are related to the maximin of the mutual information rate. The minimum is with respect to the set of all possible H matrices or all possible PSD matrices of the noise. The maximum is with respect to all possible PSD matrices of the transmitted signal with bounded power. For the compound channel modeled by the set of H matrices, it is shown, under certain conditions, that the code for the worst case channel can be used for the whole class of channels. For the same model, the water-filling argument implies that the larger the set of matrices H , the smaller the bandwidth of the transmitted signal will be. For the second compound channel, the explicit relation between the maximizing PSD matrix of the transmitted signal and the minimizing PSD matrix of the noise is found. Two PSD matrices are related through a Riccati equation, which is always present in Kalman filtering and liner-quadratic Gaussian control problems.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TIT.2009.2013007</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9448 |
| ispartof | IEEE transactions on information theory, 2009-04, Vol.55 (4), p.1603-1617 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_ieee_primary_4802319 |
| source | IEEE Electronic Library (IEL) |
| subjects | Applied sciences Bandwidth Bandwidths Channel degrading Channels Communication channels compound channel Compound channels Data transmission Density Detection, estimation, filtering, equalization, prediction Exact sciences and technology Filtering Frequency domain analysis Frequency response Gaussian Gaussian channels Gaussian noise Information theory Information, signal and communications theory Input output Kalman filters Mathematical analysis Matrices Matrix methods MIMO multiple-input-multiple-output (MIMO) Gaussian channel Mutual information Noise Riccati equations Signal and communications theory Signal to noise ratio Signal, noise Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) |
| title | Information Theoretic Bounds for Compound MIMO Gaussian Channels |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-25T01%3A10%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Information%20Theoretic%20Bounds%20for%20Compound%20MIMO%20Gaussian%20Channels&rft.jtitle=IEEE%20transactions%20on%20information%20theory&rft.au=Denic,%20S.Z.&rft.date=2009-04-01&rft.volume=55&rft.issue=4&rft.spage=1603&rft.epage=1617&rft.pages=1603-1617&rft.issn=0018-9448&rft.eissn=1557-9654&rft.coden=IETTAW&rft_id=info:doi/10.1109/TIT.2009.2013007&rft_dat=%3Cproquest_RIE%3E919915750%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=195935934&rft_id=info:pmid/&rft_ieee_id=4802319&rfr_iscdi=true |