{"id":"https://openalex.org/W2134637906","doi":"https://doi.org/10.1109/tsp.2011.2113177","title":"Asymptotics of Multifold Vandermonde Matrices With Random Entries","display_name":"Asymptotics of Multifold Vandermonde Matrices With Random Entries","publication_year":2011,"publication_date":"2011-02-11","ids":{"openalex":"https://openalex.org/W2134637906","doi":"https://doi.org/10.1109/tsp.2011.2113177","mag":"2134637906"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2113177","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2113177","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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/A5072774127","display_name":"Alessandro Nordio","orcid":"https://orcid.org/0000-0001-8258-051X"},"institutions":[{"id":"https://openalex.org/I4210155236","display_name":"National Research Council","ror":"https://ror.org/04zaypm56","country_code":"IT","type":"funder","lineage":["https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I4210100607","display_name":"Institute of Electronics, Computer and Telecommunication Engineering","ror":"https://ror.org/00n4jbh84","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210100607","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessandro Nordio","raw_affiliation_strings":["Institute of Electronics, Telecommunications and Information Engineering, IEIIT-National Research Council, Torino, Italy"],"affiliations":[{"raw_affiliation_string":"Institute of Electronics, Telecommunications and Information Engineering, IEIIT-National Research Council, Torino, Italy","institution_ids":["https://openalex.org/I4210100607","https://openalex.org/I4210155236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079559885","display_name":"G. Alfano","orcid":"https://orcid.org/0000-0001-9016-9835"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppa Alfano","raw_affiliation_strings":["Dipartimento di Elettronica, Politecnico di Turino, Torino, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Politecnico di Turino, Torino, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021780258","display_name":"Carla Fabiana Chiasserini","orcid":"https://orcid.org/0000-0003-1410-660X"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carla-Fabiana Chiasserini","raw_affiliation_strings":["Dipartimento di Elettronica, Politecnico di Turino, Torino, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica, Politecnico di Turino, Torino, Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066992345","display_name":"Antonia M. Tulino","orcid":"https://orcid.org/0000-0002-6050-4150"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonia M. Tulino","raw_affiliation_strings":["Department of Electrical and Telecommunications Engineering, Universit\u00e0 degli Studi di Napoli Federico II, Naples, Italy","Department of Wireless Communications, Bell Laboratories, Alcatel-Lucent, Holmdel, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Telecommunications Engineering, Universit\u00e0 degli Studi di Napoli Federico II, Naples, Italy","institution_ids":["https://openalex.org/I71267560"]},{"raw_affiliation_string":"Department of Wireless Communications, Bell Laboratories, Alcatel-Lucent, Holmdel, NJ, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072774127"],"corresponding_institution_ids":["https://openalex.org/I4210100607","https://openalex.org/I4210155236"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15995157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"6","first_page":"2760","last_page":"2772"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.993399977684021,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.9678915143013},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.6641955971717834},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.6637521982192993},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.6220338344573975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5945567488670349},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.5395355224609375},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.503527820110321},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.49131718277931213},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47075608372688293},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44712504744529724},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43521082401275635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4007663130760193},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33675992488861084},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2890086770057678},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.20144051313400269},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18383687734603882},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10227194428443909}],"concepts":[{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.9678915143013},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.6641955971717834},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.6637521982192993},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.6220338344573975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5945567488670349},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.5395355224609375},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.503527820110321},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.49131718277931213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47075608372688293},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44712504744529724},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43521082401275635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4007663130760193},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33675992488861084},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2890086770057678},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.20144051313400269},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18383687734603882},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10227194428443909},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"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/tsp.2011.2113177","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2113177","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:porto.polito.it:2381035","is_oa":false,"landing_page_url":"http://porto.polito.it/2381035/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1053-587X","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W591099569","https://openalex.org/W1557486844","https://openalex.org/W1586554030","https://openalex.org/W1974169366","https://openalex.org/W1978999584","https://openalex.org/W1986316936","https://openalex.org/W2007550391","https://openalex.org/W2021798854","https://openalex.org/W2045463928","https://openalex.org/W2053559899","https://openalex.org/W2060581589","https://openalex.org/W2067161429","https://openalex.org/W2072184935","https://openalex.org/W2117617716","https://openalex.org/W2120849543","https://openalex.org/W2122101931","https://openalex.org/W2135355720","https://openalex.org/W2142398916","https://openalex.org/W2148664799","https://openalex.org/W2149305338","https://openalex.org/W2154625249","https://openalex.org/W2159479457","https://openalex.org/W2163059027","https://openalex.org/W2170022658","https://openalex.org/W2288509490","https://openalex.org/W2312497442","https://openalex.org/W2330078975","https://openalex.org/W2912369344","https://openalex.org/W3104192529","https://openalex.org/W6635108411","https://openalex.org/W7026971381","https://openalex.org/W7048899662"],"related_works":["https://openalex.org/W2134745771","https://openalex.org/W1554357707","https://openalex.org/W2121163938","https://openalex.org/W4200057011","https://openalex.org/W1963507207","https://openalex.org/W2075897667","https://openalex.org/W4221163639","https://openalex.org/W4324367781","https://openalex.org/W2907746047","https://openalex.org/W3125536267"],"abstract_inverted_index":{"We":[0,39,92],"study":[1,102],"the":[2,14,41,65,72,78,89,101,109,113,121],"performance":[3],"of":[4,48,77,103,128],"systems":[5],"for":[6,100,125],"signal":[7,80],"parameters":[8],"estimation,":[9],"which":[10],"are":[11],"based":[12],"on":[13,64],"linear":[15],"minimum":[16],"mean":[17,73],"square":[18,74],"error":[19,75],"(LMMSE)":[20],"filtering.":[21],"Such":[22],"an":[23],"estimation":[24,42],"technique":[25],"is":[26],"widely":[27],"used":[28],"in":[29],"practical":[30,104],"scenarios,":[31],"specifically":[32],"wireless":[33],"sensor":[34],"networks":[35],"and":[36,46,86,106,120],"MIMO":[37],"communications.":[38],"model":[40],"system":[43],"through":[44,117],"sums":[45],"products":[47],"random":[49],"matrices,":[50],"involving":[51],"a":[52],"d":[53],"-fold":[54],"Vandermonde":[55],"matrix":[56],"(d":[57],"\u2265":[58],"1)":[59],"with":[60],"entries":[61],"uniformly":[62],"distributed":[63],"complex":[66],"unit":[67],"circle.":[68],"Then,":[69],"we":[70,107],"derive":[71],"(MSE)":[76],"estimated":[79],"by":[81,87],"resorting":[82],"to":[83],"asymptotic":[84,114],"analysis":[85,119],"applying":[88],"\u03b7-transform":[90],"operator.":[91],"describe":[93],"how":[94],"our":[95,118],"results":[96,115,123],"can":[97],"be":[98],"exploited":[99],"systems,":[105],"show":[108],"agreement":[110],"existing":[111],"between":[112],"derived":[116],"simulation":[122],"obtained":[124],"small":[126],"values":[127],"d.":[129]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
