{"id":"https://openalex.org/W2107151467","doi":"https://doi.org/10.1109/vetecs.2009.5073356","title":"Accurate Approximations and Asymptotic Results for the Sum-Rate of Random Beamforming for Multi-Antenna Gaussian Broadcast Channels","display_name":"Accurate Approximations and Asymptotic Results for the Sum-Rate of Random Beamforming for Multi-Antenna Gaussian Broadcast Channels","publication_year":2009,"publication_date":"2009-04-01","ids":{"openalex":"https://openalex.org/W2107151467","doi":"https://doi.org/10.1109/vetecs.2009.5073356","mag":"2107151467"},"language":"en","primary_location":{"id":"doi:10.1109/vetecs.2009.5073356","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vetecs.2009.5073356","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VTC Spring 2009 - IEEE 69th Vehicular Technology Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5100766772","display_name":"Ki\u2010Hong Park","orcid":"https://orcid.org/0000-0002-6867-4277"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Ki-Hong Park","raw_affiliation_strings":["School of Electrical Engineering, Korea University, Seoul, South Korea","Sch. of Electr. Eng., Korea Univ., Seoul"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Korea University, Seoul, South Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Sch. of Electr. Eng., Korea Univ., Seoul","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087836855","display_name":"Young\u2010Chai Ko","orcid":"https://orcid.org/0000-0003-1043-9028"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Young-Chai Ko","raw_affiliation_strings":["School of Electrical Engineering, Korea University, Seoul, South Korea","Sch. of Electr. Eng., Korea Univ., Seoul"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Korea University, Seoul, South Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Sch. of Electr. Eng., Korea Univ., Seoul","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083193286","display_name":"Mohamed\u2010Slim Alouini","orcid":"https://orcid.org/0000-0003-4827-1793"},"institutions":[{"id":"https://openalex.org/I58152225","display_name":"Texas A&M University at Qatar","ror":"https://ror.org/03vb4dm14","country_code":"QA","type":"education","lineage":["https://openalex.org/I58152225","https://openalex.org/I91045830"]}],"countries":["QA"],"is_corresponding":false,"raw_author_name":"Mohamed-Slim Alouini","raw_affiliation_strings":["Electrical and Computer Engineering Program, Texas A and M University, Qatar, Doha, Qatar","Texas A&M University at Qatar, Doha, Qatar"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Program, Texas A and M University, Qatar, Doha, Qatar","institution_ids":["https://openalex.org/I58152225"]},{"raw_affiliation_string":"Texas A&M University at Qatar, Doha, Qatar","institution_ids":["https://openalex.org/I58152225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10069","display_name":"Antenna Design and Analysis","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9991000294685364,"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/beamforming","display_name":"Beamforming","score":0.773977518081665},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.541437029838562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.512722373008728},{"id":"https://openalex.org/keywords/antenna","display_name":"Antenna (radio)","score":0.493436723947525},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4744725823402405},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.4206525683403015},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41117367148399353},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33050352334976196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30701786279678345},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.20517143607139587},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13721352815628052},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13096883893013}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.773977518081665},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.541437029838562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.512722373008728},{"id":"https://openalex.org/C21822782","wikidata":"https://www.wikidata.org/wiki/Q131214","display_name":"Antenna (radio)","level":2,"score":0.493436723947525},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4744725823402405},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.4206525683403015},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41117367148399353},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33050352334976196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30701786279678345},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.20517143607139587},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13721352815628052},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13096883893013},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/vetecs.2009.5073356","is_oa":false,"landing_page_url":"https://doi.org/10.1109/vetecs.2009.5073356","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"VTC Spring 2009 - IEEE 69th Vehicular Technology Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1976109068","https://openalex.org/W2083962008","https://openalex.org/W2098583876","https://openalex.org/W2101493165","https://openalex.org/W2130509920","https://openalex.org/W2136875719","https://openalex.org/W2142134616","https://openalex.org/W2143927285","https://openalex.org/W2151795416","https://openalex.org/W2157005274","https://openalex.org/W3008609509"],"related_works":["https://openalex.org/W2963170046","https://openalex.org/W2376244802","https://openalex.org/W1585007175","https://openalex.org/W1971477554","https://openalex.org/W2382521049","https://openalex.org/W2158075901","https://openalex.org/W818226659","https://openalex.org/W2144385241","https://openalex.org/W2923631784","https://openalex.org/W4311414679"],"abstract_inverted_index":{"In":[0],"this":[1,26],"paper,":[2],"we":[3],"first":[4],"present":[5],"a":[6],"new":[7],"closed":[8],"form":[9],"approximation":[10,27,63],"for":[11,29,48],"the":[12,72,82,86,89],"sum-rate":[13,74],"of":[14,36,54,91],"random":[15],"beamforming.":[16],"A":[17],"generic":[18],"curve":[19],"fitting":[20],"procedure":[21],"is":[22],"developed":[23],"to":[24,44,65,71,81,94],"make":[25],"accurate":[28],"arbitrary":[30],"signal-to-noise":[31],"ratios":[32],"(SNRs)":[33],"and":[34,75],"number":[35,53,90],"transmit":[37],"antennas.":[38,55],"Our":[39],"analytical":[40],"approach":[41],"leads":[42,64],"also":[43],"simple":[45],"asymptotic":[46,78],"formulas":[47,79],"high":[49,95],"SNR":[50,87],"or":[51,88],"large":[52],"Selected":[56],"numerical":[57],"results":[58,66],"show":[59],"that":[60,67,76],"our":[61,77],"proposed":[62],"come":[68],"very":[69],"close":[70],"exact":[73,83],"converge":[80],"values":[84],"when":[85],"antennas":[92],"tend":[93],"values.":[96]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}