{"id":"https://openalex.org/W4313291187","doi":"https://doi.org/10.1109/twc.2022.3231496","title":"On the Exact Sum PDF and CDF of <i>\u03b1-\u03bc</i> Variates","display_name":"On the Exact Sum PDF and CDF of <i>\u03b1-\u03bc</i> Variates","publication_year":2022,"publication_date":"2022-12-29","ids":{"openalex":"https://openalex.org/W4313291187","doi":"https://doi.org/10.1109/twc.2022.3231496"},"language":"en","primary_location":{"id":"doi:10.1109/twc.2022.3231496","is_oa":false,"landing_page_url":"https://doi.org/10.1109/twc.2022.3231496","pdf_url":null,"source":{"id":"https://openalex.org/S63459445","display_name":"IEEE Transactions on Wireless Communications","issn_l":"1536-1276","issn":["1536-1276","1558-2248"],"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 Wireless Communications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.03850","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087614736","display_name":"Fernando Dar\u00edo Almeida Garc\u00eda","orcid":"https://orcid.org/0000-0003-3747-1511"},"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":"Fernando Dar\u00edo Almeida Garc\u00eda","raw_affiliation_strings":["Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-3747-1511","affiliations":[{"raw_affiliation_string":"Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007378075","display_name":"Francisco Parente","orcid":"https://orcid.org/0000-0001-9827-6707"},"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":"Francisco Raimundo Albuquerque Parente","raw_affiliation_strings":["Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-9827-6707","affiliations":[{"raw_affiliation_string":"Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","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 Daoud Yacoub","raw_affiliation_strings":["Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-5866-5879","affiliations":[{"raw_affiliation_string":"Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040525043","display_name":"Jos\u00e9 C\u00e2ndido Silveira Santos Filho","orcid":"https://orcid.org/0000-0002-0106-1548"},"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":"Jos\u00e9 C\u00e2ndido Silveira Santos Filho","raw_affiliation_strings":["Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-0106-1548","affiliations":[{"raw_affiliation_string":"Department of Communications, School of Electrical and Computer Engineering, Wireless Technology Laboratory (WissTek), State University of Campinas (UNICAMP), Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I181391015"],"apc_list":null,"apc_paid":null,"fwci":0.9718,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.74336714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"8","first_page":"5084","last_page":"5095"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9997000098228455,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9997000098228455,"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/T10936","display_name":"Millimeter-Wave Propagation and Modeling","score":0.9993000030517578,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9991000294685364,"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":0.5102605819702148},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.49258166551589966},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.4498622715473175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43082213401794434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4123136103153229},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3848796486854553},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.35711681842803955},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35357773303985596},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2911412715911865},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11449471116065979}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5102605819702148},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.49258166551589966},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.4498622715473175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43082213401794434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4123136103153229},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3848796486854553},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.35711681842803955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35357773303985596},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2911412715911865},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11449471116065979}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/twc.2022.3231496","is_oa":false,"landing_page_url":"https://doi.org/10.1109/twc.2022.3231496","pdf_url":null,"source":{"id":"https://openalex.org/S63459445","display_name":"IEEE Transactions on Wireless Communications","issn_l":"1536-1276","issn":["1536-1276","1558-2248"],"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 Wireless Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2510.03850","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.03850","pdf_url":"https://arxiv.org/pdf/2510.03850","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.03850","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.03850","pdf_url":"https://arxiv.org/pdf/2510.03850","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6268612666","display_name":null,"funder_award_id":"2021/03923-9","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G8249799024","display_name":null,"funder_award_id":"2018/25009-4","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W1576718945","https://openalex.org/W1578842116","https://openalex.org/W1918686272","https://openalex.org/W1995691340","https://openalex.org/W2004689163","https://openalex.org/W2027458993","https://openalex.org/W2046169013","https://openalex.org/W2097398761","https://openalex.org/W2102431479","https://openalex.org/W2102591969","https://openalex.org/W2108165364","https://openalex.org/W2114126054","https://openalex.org/W2116840238","https://openalex.org/W2118958706","https://openalex.org/W2123937856","https://openalex.org/W2130934944","https://openalex.org/W2131642205","https://openalex.org/W2140997379","https://openalex.org/W2144180392","https://openalex.org/W2146739710","https://openalex.org/W2150386840","https://openalex.org/W2163099106","https://openalex.org/W2165403303","https://openalex.org/W2165598324","https://openalex.org/W2166203438","https://openalex.org/W2168990175","https://openalex.org/W2172015024","https://openalex.org/W2276496321","https://openalex.org/W2486175508","https://openalex.org/W2493309683","https://openalex.org/W2549295457","https://openalex.org/W2588775896","https://openalex.org/W2678223665","https://openalex.org/W2775698417","https://openalex.org/W2801292740","https://openalex.org/W2906569673","https://openalex.org/W2908827479","https://openalex.org/W2921228459","https://openalex.org/W2942228371","https://openalex.org/W2963386232","https://openalex.org/W2974678512","https://openalex.org/W2978971398","https://openalex.org/W3096572777","https://openalex.org/W3120042657","https://openalex.org/W3138267861","https://openalex.org/W3142517368","https://openalex.org/W3147919432","https://openalex.org/W3157621235","https://openalex.org/W3186667102","https://openalex.org/W3199336768","https://openalex.org/W3207464738","https://openalex.org/W4205390942","https://openalex.org/W4226019069","https://openalex.org/W4248676392","https://openalex.org/W6635044782"],"related_works":["https://openalex.org/W4213267843","https://openalex.org/W1980528650","https://openalex.org/W3102213005","https://openalex.org/W2168519368","https://openalex.org/W2036854414","https://openalex.org/W2392327107","https://openalex.org/W192702211","https://openalex.org/W2753355162","https://openalex.org/W3129080429","https://openalex.org/W2791034190"],"abstract_inverted_index":{"The":[0,24,80,255],"sum":[1,30,49,72,126,132,162],"of":[2,21,27,37,68,87,115,122,130,160,163,197,203,206,222,260],"random":[3],"variables":[4],"(RVs)":[5],"appears":[6],"extensively":[7],"in":[8,85,124,215],"wireless":[9],"communications,":[10],"at":[11],"large,":[12],"both":[13,264],"conventional":[14],"and":[15,17,56,74,134,158,171,217,233,257,268,290],"advanced,":[16],"has":[18],"been":[19,44],"subject":[20,137],"longstanding":[22],"research.":[23],"statistical":[25],"characterization":[26],"the":[28,35,70,89,94,120,125,128,131,156,161,191,194,204,220,261,275,287],"referred":[29],"is":[31,136,201],"crucial":[32],"to":[33,46,78,111,138],"determine":[34],"performance":[36,221],"such":[38],"communications":[39],"systems.":[40],"Although":[41],"efforts":[42],"have":[43],"undertaken":[45],"unveil":[47],"these":[48,105],"statistics,":[50],"e.g.,":[51],"probability":[52],"density":[53],"function":[54,59],"(PDF)":[55],"cumulative":[57],"distribution":[58],"(CDF),":[60],"no":[61],"general":[62],"efficient":[63,289],"nor":[64],"manageable":[65,291],"solutions":[66],"capable":[67],"evaluating":[69],"exact":[71,153,216],"PDF":[73,133,157],"CDF":[75,135,159],"are":[76,83,107,266,285],"available":[77,192],"date.":[79],"only":[81,108],"formulations":[82,154,292],"given":[84],"terms":[86],"either":[88],"multi-fold":[90],"Brennan\u2019s":[91],"integral":[92],"or":[93,143],"multivariate":[95],"Fox":[96],"<inline-formula":[97,164,174,182,223,238,246],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[98,165,175,183,224,239,247],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[99,166,176,184,225,240,248],"<tex-math":[100,167,177,185,226,241,249],"notation=\"LaTeX\">$H$":[101],"</tex-math></inline-formula>":[102,169,180,188,228,244,252],"-function.":[103],"Unfortunately,":[104],"methods":[106],"feasible":[109],"up":[110],"a":[112],"certain":[113],"number":[114,121,205],"RVs,":[116],"meaning":[117],"that":[118,274],"when":[119,280],"RVs":[123],"increases,":[127],"computation":[129,276],"stability":[139],"problems,":[140],"convergence":[141],"issues,":[142],"inaccurate":[144],"results.":[145],"In":[146],"this":[147],"paper,":[148],"we":[149,213],"derive":[150],"new,":[151],"simple,":[152],"for":[155,263],"notation=\"LaTeX\">$L$":[168,227],"independent":[170,202],"identically":[172],"distributed":[173],"notation=\"LaTeX\">$\\alpha":[178,242],"$":[179,187,243,251],"-":[181,245],"notation=\"LaTeX\">$\\mu":[186,250],"RVs.":[189],"Unlike":[190],"solutions,":[193],"computational":[195],"complexity":[196],"our":[198,210,282],"analytical":[199],"expressions":[200],"summands.":[207],"Capitalizing":[208],"on":[209],"unprecedented":[211],"findings,":[212],"analyze,":[214],"asymptotic":[218],"manners,":[219],"-branch":[229],"pre-detection":[230],"equal-gain":[231],"combining":[232,235],"maximal-ratio":[234],"receivers":[236,265],"over":[237],"fading":[253],"environments.":[254],"coding":[256],"diversity":[258],"gains":[259],"system":[262],"analyzed":[267],"quantified.":[269],"Moreover,":[270],"numerical":[271],"simulations":[272],"show":[273],"time":[277],"reduces":[278],"drastically":[279],"using":[281],"expressions,":[283],"which":[284],"arguably":[286],"most":[288],"derived":[293],"so":[294],"far.":[295]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2023-01-06T00:00:00"}