{"id":"https://openalex.org/W2106820694","doi":"https://doi.org/10.1109/tsp.2011.2135347","title":"Multiuser Downlink Beamforming in Multicell Wireless Systems: A Game Theoretical Approach","display_name":"Multiuser Downlink Beamforming in Multicell Wireless Systems: A Game Theoretical Approach","publication_year":2011,"publication_date":"2011-04-06","ids":{"openalex":"https://openalex.org/W2106820694","doi":"https://doi.org/10.1109/tsp.2011.2135347","mag":"2106820694"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2135347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2135347","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/A5027364315","display_name":"Duy H. N. Nguyen","orcid":"https://orcid.org/0000-0002-1412-1175"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"D H N Nguyen","raw_affiliation_strings":["Department of Electrical Engineering, Department of Electrical and Computer Engineering, McGill University, Montreal, QUE, Canada","Dept. of Electr. Eng., McGill Univ., Montreal, QC, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Department of Electrical and Computer Engineering, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Dept. of Electr. Eng., McGill Univ., Montreal, QC, Canada#TAB#","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026464766","display_name":"Tho Le\u2010Ngoc","orcid":"https://orcid.org/0000-0002-9308-8894"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Tho Le-Ngoc","raw_affiliation_strings":["Department of Electrical Engineering, Department of Electrical and Computer Engineering, McGill University, Montreal, QUE, Canada","Dept. of Electr. Eng., McGill Univ., Montreal, QC, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Department of Electrical and Computer Engineering, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Dept. of Electr. Eng., McGill Univ., Montreal, QC, Canada#TAB#","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027364315"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":11.393,"has_fulltext":false,"cited_by_count":94,"citation_normalized_percentile":{"value":0.98763702,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"59","issue":"7","first_page":"3326","last_page":"3338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","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"}},"topics":[{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10575","display_name":"Wireless Communication Networks Research","score":0.9968000054359436,"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/telecommunications-link","display_name":"Telecommunications link","score":0.8071560859680176},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.7914983034133911},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.7553026080131531},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6815297603607178},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6610466837882996},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5405724048614502},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.5279233455657959},{"id":"https://openalex.org/keywords/non-cooperative-game","display_name":"Non-cooperative game","score":0.5161657929420471},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5060686469078064},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.49689796566963196},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.32301878929138184},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2646160423755646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18385934829711914},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.16395097970962524}],"concepts":[{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.8071560859680176},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.7914983034133911},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.7553026080131531},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6815297603607178},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6610466837882996},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5405724048614502},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.5279233455657959},{"id":"https://openalex.org/C47175762","wikidata":"https://www.wikidata.org/wiki/Q13422573","display_name":"Non-cooperative game","level":3,"score":0.5161657929420471},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5060686469078064},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.49689796566963196},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.32301878929138184},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2646160423755646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18385934829711914},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.16395097970962524},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2011.2135347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2135347","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1500921805","https://openalex.org/W1545861347","https://openalex.org/W1603765807","https://openalex.org/W1919846929","https://openalex.org/W1972255804","https://openalex.org/W1989873462","https://openalex.org/W2000151369","https://openalex.org/W2050967017","https://openalex.org/W2101727634","https://openalex.org/W2108077180","https://openalex.org/W2108680348","https://openalex.org/W2109005286","https://openalex.org/W2114798382","https://openalex.org/W2118809092","https://openalex.org/W2120445834","https://openalex.org/W2124409123","https://openalex.org/W2131350052","https://openalex.org/W2139306630","https://openalex.org/W2144778327","https://openalex.org/W2145075030","https://openalex.org/W2149803021","https://openalex.org/W2151960821","https://openalex.org/W2161473225","https://openalex.org/W2164271287","https://openalex.org/W2166977026","https://openalex.org/W2167144534","https://openalex.org/W2610857016","https://openalex.org/W2948315098","https://openalex.org/W3146387078"],"related_works":["https://openalex.org/W3087844490","https://openalex.org/W3090699061","https://openalex.org/W4387546583","https://openalex.org/W2169192185","https://openalex.org/W2103590590","https://openalex.org/W2013230419","https://openalex.org/W2055634632","https://openalex.org/W2051762234","https://openalex.org/W2131408743","https://openalex.org/W4372349176"],"abstract_inverted_index":{"This":[0],"paper":[1,56,121,185,235],"is":[2,89,231],"concerned":[3],"with":[4],"the":[5,11,19,23,44,48,55,81,84,96,104,127,136,143,148,154,158,161,175,178,181,184,213,222,227,241,246,252,256,261,265],"game":[6,61,85,93,190],"theoretical":[7],"approach":[8,251],"in":[9,15,47,73,113,131,163,171,180,205],"designing":[10],"multiuser":[12],"downlink":[13,70,133],"beamformers":[14,138,204],"multicell":[16,132,266],"systems.":[17],"Sharing":[18],"same":[20],"physical":[21],"resource,":[22],"base-station":[24,65,200],"of":[25,38,98,108,156,165,177,226,264],"each":[26,64,166],"cell":[27],"wishes":[28],"to":[29,35,95,126,173,201,216,250],"minimize":[30],"its":[31,68,203],"transmit":[32],"power":[33],"subject":[34],"a":[36,58,74,109,124,187,192,199,206,238],"set":[37],"target":[39],"signal-to-interference-plus-noise":[40],"ratios":[41],"(SINRs)":[42],"at":[43,53],"multiple":[45],"users":[46],"cell.":[49],"In":[50],"this":[51,92,114],"context,":[52],"first,":[54],"considers":[57,186],"strategic":[59],"noncooperative":[60],"(SNG)":[62],"where":[63,135],"greedily":[66],"determines":[67],"optimal":[69,137],"beamformer":[71],"strategy":[72],"distributed":[75,168,262],"manner,":[76,209],"without":[77],"any":[78],"coordination":[79],"between":[80,142,147],"cells.":[82,218],"Via":[83],"theory":[86],"framework,":[87],"it":[88],"shown":[90],"that":[91,244],"belongs":[94],"framework":[97],"standard":[99],"functions.":[100],"The":[101,120,195,219,234],"conditions":[102],"guaranteeing":[103],"existence":[105,223],"and":[106,150,224],"uniqueness":[107,225],"Nash":[110],"Equilibrium":[111],"(NE)":[112],"competitive":[115,149,182],"design":[116,130],"are":[117,139],"subsequently":[118],"examined.":[119],"then":[122,232],"makes":[123],"revisit":[125],"fully":[128],"coordinated":[129,151,257],"beamforming,":[134],"jointly":[140],"designed":[141],"base-stations.":[144],"A":[145],"comparison":[146],"designs":[152],"shows":[153],"benefits":[155],"applying":[157],"former":[159],"over":[160],"latter":[162],"terms":[164],"design's":[167],"implementation.":[169],"Finally,":[170],"order":[172],"improve":[174],"efficiency":[176],"NE":[179,230,248],"design,":[183,258],"more":[188,207],"cooperative":[189,208],"through":[191],"pricing":[193,196,242],"mechanism.":[194],"consideration":[197],"enables":[198],"steer":[202],"which":[210],"ultimately":[211],"limits":[212],"interference":[214],"induced":[215],"other":[217],"study":[220],"on":[221,240],"new":[228,247],"game's":[229],"given.":[233],"also":[236],"presents":[237],"condition":[239],"factors":[243],"allow":[245],"point":[249],"performance":[253],"established":[254],"by":[255],"while":[259],"retaining":[260],"nature":[263],"game.":[267]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":20},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":13}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
