{"id":"https://openalex.org/W2165312451","doi":"https://doi.org/10.1109/tit.2008.2006401","title":"Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems","display_name":"Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2165312451","doi":"https://doi.org/10.1109/tit.2008.2006401","mag":"2165312451"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2008.2006401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2008.2006401","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027131891","display_name":"Jes\u00fas Guti\u00e9rrez-Guti\u00e9rrez","orcid":"https://orcid.org/0000-0001-7423-5505"},"institutions":[{"id":"https://openalex.org/I88155538","display_name":"Universidad de Navarra","ror":"https://ror.org/02rxc7m23","country_code":"ES","type":"education","lineage":["https://openalex.org/I88155538"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jes\u00das Gutierrez-Gutierrez","raw_affiliation_strings":["University of Navarra, San Sabastian, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Navarra, San Sabastian, Spain","institution_ids":["https://openalex.org/I88155538"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077285752","display_name":"Pedro M. Crespo","orcid":"https://orcid.org/0000-0001-8259-3353"},"institutions":[{"id":"https://openalex.org/I88155538","display_name":"Universidad de Navarra","ror":"https://ror.org/02rxc7m23","country_code":"ES","type":"education","lineage":["https://openalex.org/I88155538"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Pedro M. Crespo","raw_affiliation_strings":["University of Navarra, San Sabastian, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Navarra, San Sabastian, Spain","institution_ids":["https://openalex.org/I88155538"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I88155538"],"apc_list":null,"apc_paid":null,"fwci":4.0305,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.93890335,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"54","issue":"12","first_page":"5671","last_page":"5680"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10575","display_name":"Wireless Communication Networks Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9125009775161743},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.8361588716506958},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7470738887786865},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5967737436294556},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.5748185515403748},{"id":"https://openalex.org/keywords/intersymbol-interference","display_name":"Intersymbol interference","score":0.5213764309883118},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3802064061164856},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35374078154563904},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3227950930595398},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25970935821533203},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1884734332561493},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10523441433906555},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.09499400854110718}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9125009775161743},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.8361588716506958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7470738887786865},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5967737436294556},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.5748185515403748},{"id":"https://openalex.org/C97812054","wikidata":"https://www.wikidata.org/wiki/Q2166055","display_name":"Intersymbol interference","level":3,"score":0.5213764309883118},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3802064061164856},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35374078154563904},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3227950930595398},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25970935821533203},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1884734332561493},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10523441433906555},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.09499400854110718},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2008.2006401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2008.2006401","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.329.7184","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.7184","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.comonsens.org/documents/journals/5_guti_crespo_ieee_it_08.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W292716351","https://openalex.org/W1488435683","https://openalex.org/W1492221128","https://openalex.org/W1550150926","https://openalex.org/W1980058119","https://openalex.org/W1982482853","https://openalex.org/W1999585957","https://openalex.org/W2000267193","https://openalex.org/W2014870838","https://openalex.org/W2016119814","https://openalex.org/W2019204386","https://openalex.org/W2041181660","https://openalex.org/W2045463928","https://openalex.org/W2047809378","https://openalex.org/W2058478885","https://openalex.org/W2071089334","https://openalex.org/W2097415784","https://openalex.org/W2099111195","https://openalex.org/W2106292563","https://openalex.org/W2120768147","https://openalex.org/W2128978199","https://openalex.org/W2132105090","https://openalex.org/W2141262522","https://openalex.org/W2167619382","https://openalex.org/W2291948167","https://openalex.org/W2312497442","https://openalex.org/W2478708596","https://openalex.org/W2595897327","https://openalex.org/W2610857016","https://openalex.org/W2798707604","https://openalex.org/W4206196235","https://openalex.org/W4240892741","https://openalex.org/W4255277669","https://openalex.org/W4255333822"],"related_works":["https://openalex.org/W3177828492","https://openalex.org/W2034415022","https://openalex.org/W2149698301","https://openalex.org/W4388372565","https://openalex.org/W2286689764","https://openalex.org/W63525287","https://openalex.org/W4388372654","https://openalex.org/W2026406497","https://openalex.org/W2105266774","https://openalex.org/W1444802581"],"abstract_inverted_index":{"For":[0],"the":[1,16,21,31,36,48,69,100,109],"engineering":[2],"community,":[3],"Gray's":[4],"tutorial":[5],"monograph":[6,38],"on":[7,24],"Toeplitz":[8,26,43],"and":[9,14,83,122],"circulant":[10],"matrices":[11,45],"has":[12],"been,":[13],"remains,":[15],"best":[17],"elementary":[18],"introduction":[19],"to":[20,41],"Szego":[22],"theory":[23],"large":[25],"matrices.":[27,63],"In":[28],"this":[29],"paper,":[30],"most":[32],"important":[33],"results":[34],"of":[35,62,66,99,108,112],"cited":[37],"are":[39,94],"generalized":[40],"block":[42],"(BT)":[44],"by":[46,53,57],"maintaining":[47],"same":[49],"mathematical":[50],"tools":[51],"used":[52],"Gray,":[54],"that":[55],"is,":[56],"using":[58],"asymptotically":[59],"equivalent":[60],"sequences":[61],"As":[64],"applications":[65],"these":[67],"results,":[68],"geometric":[70],"minimum":[71],"mean":[72],"square":[73],"error":[74],"(MMSE)":[75],"for":[76,90],"both":[77],"an":[78,84],"infinite-length":[79,85],"multivariate":[80],"linear":[81],"predictor":[82],"decision":[86],"feedback":[87],"equalizer":[88],"(DFE)":[89],"multiple-input-multiple-output":[91],"(MIMO)":[92],"channels,":[93],"obtained":[95],"as":[96],"a":[97,105,113],"limit":[98],"corresponding":[101],"finite-length":[102],"cases.":[103],"Similarly,":[104],"short":[106],"derivation":[107],"well-known":[110],"capacity":[111],"time-invariant":[114],"MIMO":[115],"Gaussian":[116],"channel":[117],"with":[118],"intersymbol":[119],"interference":[120],"(ISI)":[121],"fixed":[123],"input":[124],"covariance":[125],"matrix":[126],"is":[127],"also":[128],"presented.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}