{"id":"https://openalex.org/W4205221953","doi":"https://doi.org/10.1109/tvt.2022.3141232","title":"Bivariate Complex $\\alpha$-$\\mu$ Statistics","display_name":"Bivariate Complex $\\alpha$-$\\mu$ Statistics","publication_year":2022,"publication_date":"2022-01-07","ids":{"openalex":"https://openalex.org/W4205221953","doi":"https://doi.org/10.1109/tvt.2022.3141232"},"language":"en","primary_location":{"id":"doi:10.1109/tvt.2022.3141232","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2022.3141232","pdf_url":null,"source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"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 Vehicular Technology","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/A5031188652","display_name":"Thiago Bairros","orcid":"https://orcid.org/0000-0002-5123-2157"},"institutions":[{"id":"https://openalex.org/I71346753","display_name":"National Institute of Telecommunications","ror":"https://ror.org/0378w3a30","country_code":"BR","type":"facility","lineage":["https://openalex.org/I71346753"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Thiago de Bairros","raw_affiliation_strings":["National Institute of Telecommunications, Santa Rita do Sapuca&#x00ED;, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-5123-2157","affiliations":[{"raw_affiliation_string":"National Institute of Telecommunications, Santa Rita do Sapuca&#x00ED;, Brazil","institution_ids":["https://openalex.org/I71346753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059091167","display_name":"Pedro M. R. Pereira","orcid":"https://orcid.org/0000-0001-6946-2746"},"institutions":[{"id":"https://openalex.org/I71346753","display_name":"National Institute of Telecommunications","ror":"https://ror.org/0378w3a30","country_code":"BR","type":"facility","lineage":["https://openalex.org/I71346753"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Pedro Pereira","raw_affiliation_strings":["National Institute of Telecommunications, Santa Rita do Sapuca&#x00ED;, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-6946-2746","affiliations":[{"raw_affiliation_string":"National Institute of Telecommunications, Santa Rita do Sapuca&#x00ED;, Brazil","institution_ids":["https://openalex.org/I71346753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070641490","display_name":"Rausley A. A. de Souza","orcid":"https://orcid.org/0000-0002-6179-9894"},"institutions":[{"id":"https://openalex.org/I71346753","display_name":"National Institute of Telecommunications","ror":"https://ror.org/0378w3a30","country_code":"BR","type":"facility","lineage":["https://openalex.org/I71346753"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Rausley de Souza","raw_affiliation_strings":["National Institute of Telecommunications, Santa Rita do Sapuca&#x00ED;, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-6179-9894","affiliations":[{"raw_affiliation_string":"National Institute of Telecommunications, Santa Rita do Sapuca&#x00ED;, Brazil","institution_ids":["https://openalex.org/I71346753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084825347","display_name":"Michel Daoud Yacoub","orcid":"https://orcid.org/0000-0002-5866-5879"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Michel Yacoub","raw_affiliation_strings":["Wireless Technology Laboratory, Department of Communications, University of Campinas, Campinas, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-5866-5879","affiliations":[{"raw_affiliation_string":"Wireless Technology Laboratory, Department of Communications, University of Campinas, Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00757442,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"3","first_page":"3276","last_page":"3280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9954000115394592,"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/T12146","display_name":"Power Line Communications and Noise","score":0.989799976348877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5639040470123291},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.48793575167655945},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.46527099609375},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37206971645355225},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3566396236419678}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5639040470123291},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.48793575167655945},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.46527099609375},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37206971645355225},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3566396236419678}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvt.2022.3141232","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2022.3141232","pdf_url":null,"source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"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 Vehicular Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1981734827","https://openalex.org/W2086959462","https://openalex.org/W2097398761","https://openalex.org/W2114437869","https://openalex.org/W2134062427","https://openalex.org/W2804771868","https://openalex.org/W2995926107","https://openalex.org/W4212888567","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W1721599012","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W3099337062","https://openalex.org/W2513280345"],"abstract_inverted_index":{"In":[0],"this":[1],"correspondence,":[2],"new":[3],"fundamental":[4],"statistics":[5,56],"for":[6],"the":[7,54,95,125,135,163,169],"<inline-formula":[8,13,28,33,151,156],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,14,29,34,152,157],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[10,15,30,35,153,158],"notation=\"LaTeX\">$\\alpha$</tex-math></inline-formula>":[11,31,154],"-":[12,32,155],"notation=\"LaTeX\">$\\mu$</tex-math></inline-formula>":[16,36,159],"fading":[17,96,160],"model":[18],"are":[19,57],"derived.":[20],"Broadly":[21],"speaking,":[22],"these":[23],"involve":[24],"two":[25],"correlated":[26],"complex":[27],"variates":[37],"with":[38],"identical":[39],"clustering":[40],"parameters,":[41],"but":[42],"arbitrary":[43],"nonlinearity":[44],"and":[45,48,109,162],"power":[46,101],"parameters":[47],"nonuniform":[49],"phase":[50,79,83,88,100,106,112,127,184],"distribution.":[51],"More":[52],"specifically,":[53],"following":[55],"derived:":[58],"(i)":[59],"exact":[60,71,82,87,105],"joint":[61,72],"bivariate":[62,73,78],"probability":[63],"density":[64],"function":[65,93],"(PDF)":[66],"of":[67,94],"quadrature":[68],"processes;":[69],"(ii)":[70],"phase-envelope":[74],"PDF;":[75,80,108],"(iii)":[76],"approximate":[77,111,126],"(iv)":[81],"correlation":[84],"coefficient;":[85],"(v)":[86],"autocorrelation":[89],"coefficient":[90],"as":[91,131,168],"a":[92,116,118,132,145,149,182,187],"environment":[97],"parameters;":[98],"(vi)":[99],"spectrum":[102],"density;":[103],"(vii)":[104],"difference":[107,113,128],"(viii)":[110],"PDF.":[114,140],"As":[115],"by-product,":[117],"useful":[119],"mathematical":[120],"identity":[121],"is":[122,178],"obtained.":[123],"Strikingly,":[124],"PDF":[129],"encompasses,":[130],"particular":[133],"case,":[134],"von":[136],"Mises":[137],"or":[138],"Tikhonov":[139],"An":[141],"application":[142],"example":[143],"considers":[144],"signal":[146],"transmission":[147],"over":[148],"slow-flat":[150],"channel,":[161],"pilot":[164],"symbol":[165],"assisted":[166],"modulation":[167],"channel":[170,175],"estimation":[171],"technique,":[172],"assuming":[173],"imperfect":[174],"estimation.":[176],"It":[177],"clearly":[179],"seen":[180],"that":[181],"uniform":[183],"assumption":[185],"depicts":[186],"pessimistic":[188],"scenario.":[189]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-01-25T00:00:00"}