{"id":"https://openalex.org/W2023335474","doi":"https://doi.org/10.1109/icassp.2010.5496027","title":"On the complexity of optimal coordinated downlink beamforming","display_name":"On the complexity of optimal coordinated downlink beamforming","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2023335474","doi":"https://doi.org/10.1109/icassp.2010.5496027","mag":"2023335474"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2010.5496027","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2010.5496027","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Conference on Acoustics, Speech and Signal Processing","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/A5020753840","display_name":"Ya\u2010Feng Liu","orcid":"https://orcid.org/0000-0002-9684-9150"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4391767993","display_name":"State Key Laboratory of Scientific and Engineering Computing","ror":"https://ror.org/02fp7dp35","country_code":null,"type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4391767993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ya-Feng Liu","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Chinese Academy and Sciences, Beijing, China","State Key Lab. of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Chinese Academy and Sciences, Beijing, China","institution_ids":["https://openalex.org/I4391767993"]},{"raw_affiliation_string":"State Key Lab. of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109187979","display_name":"Yu\u2010Hong Dai","orcid":"https://orcid.org/0000-0002-6932-9512"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4391767993","display_name":"State Key Laboratory of Scientific and Engineering Computing","ror":"https://ror.org/02fp7dp35","country_code":null,"type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4391767993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Hong Dai","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Chinese Academy and Sciences, Beijing, China","State Key Lab. of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Chinese Academy and Sciences, Beijing, China","institution_ids":["https://openalex.org/I4391767993"]},{"raw_affiliation_string":"State Key Lab. of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101766226","display_name":"Zhi\u2010Quan Luo","orcid":"https://orcid.org/0000-0003-3995-914X"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhi-Quan Luo","raw_affiliation_strings":["Department of ECE, University of Minnesota, Minneapolis, MN, USA","Department of ECE, University of Minnesota, Minneapolis, 55455 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ECE, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Department of ECE, University of Minnesota, Minneapolis, 55455 USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":"2","issue":null,"first_page":"3274","last_page":"3277"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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/T10575","display_name":"Wireless Communication Networks Research","score":0.9980000257492065,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.996399998664856,"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/beamforming","display_name":"Beamforming","score":0.9046158790588379},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.8510205745697021},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.8394627571105957},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.718726634979248},{"id":"https://openalex.org/keywords/utility-maximization-problem","display_name":"Utility maximization problem","score":0.6561471819877625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.639419674873352},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6256250739097595},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.5344248414039612},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.5045148134231567},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4759135842323303},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.4758833944797516},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.473201721906662},{"id":"https://openalex.org/keywords/wsdma","display_name":"WSDMA","score":0.43513816595077515},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4311745762825012},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4279623031616211},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2776795029640198},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.24677348136901855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24173244833946228},{"id":"https://openalex.org/keywords/utility-maximization","display_name":"Utility maximization","score":0.23728930950164795},{"id":"https://openalex.org/keywords/precoding","display_name":"Precoding","score":0.201625257730484},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.19233423471450806}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.9046158790588379},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.8510205745697021},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.8394627571105957},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.718726634979248},{"id":"https://openalex.org/C2779044140","wikidata":"https://www.wikidata.org/wiki/Q3274096","display_name":"Utility maximization problem","level":3,"score":0.6561471819877625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.639419674873352},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6256250739097595},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.5344248414039612},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.5045148134231567},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4759135842323303},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.4758833944797516},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.473201721906662},{"id":"https://openalex.org/C57466844","wikidata":"https://www.wikidata.org/wiki/Q7955559","display_name":"WSDMA","level":5,"score":0.43513816595077515},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4311745762825012},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4279623031616211},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2776795029640198},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.24677348136901855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24173244833946228},{"id":"https://openalex.org/C2985793214","wikidata":"https://www.wikidata.org/wiki/Q3274096","display_name":"Utility maximization","level":2,"score":0.23728930950164795},{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.201625257730484},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.19233423471450806},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2010.5496027","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2010.5496027","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Conference on Acoustics, Speech and Signal Processing","raw_type":"proceedings-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/W1563919256","https://openalex.org/W2105147943","https://openalex.org/W2109005286","https://openalex.org/W2111717285","https://openalex.org/W2131350052","https://openalex.org/W2144000019","https://openalex.org/W2151896803","https://openalex.org/W4246287953","https://openalex.org/W6634018624"],"related_works":["https://openalex.org/W2780252087","https://openalex.org/W2890273742","https://openalex.org/W2121063273","https://openalex.org/W2337309234","https://openalex.org/W2130902301","https://openalex.org/W1981344466","https://openalex.org/W4390447722","https://openalex.org/W2923631784","https://openalex.org/W2092456355","https://openalex.org/W2036968796"],"abstract_inverted_index":{"In":[0,15],"a":[1,20,43,62],"cellular":[2],"wireless":[3],"system,":[4],"users":[5],"located":[6],"at":[7,79,97,102],"cell":[8,47],"edges":[9],"often":[10],"suffer":[11],"significant":[12],"out-of-cell":[13],"interference.":[14],"this":[16,56],"paper":[17],"we":[18,54,131],"consider":[19],"coordinated":[21,107],"beamforming":[22,32,108],"approach":[23],"whereby":[24],"multiple":[25],"base":[26,81,99],"stations":[27],"jointly":[28],"optimize":[29],"their":[30],"downlink":[31],"vectors":[33],"in":[34,138],"order":[35],"to":[36,75],"simultaneously":[37],"improve":[38],"the":[39,59,87,93,105,115,121,127,134],"data":[40],"rates":[41],"of":[42,46,61,95],"given":[44],"group":[45],"edge":[48],"users.":[49],"Assuming":[50],"perfect":[51],"channel":[52],"knowledge,":[53],"formulate":[55],"problem":[57,109,135],"as":[58],"maximization":[60],"system":[63],"utility":[64,118,124,129],"function":[65,119],"(which":[66],"balances":[67],"user":[68,72],"fairness":[69,123],"and":[70,91,120],"average":[71],"rates),":[73],"subject":[74],"individual":[76],"power":[77],"constraints":[78],"each":[80,98],"station.":[82],"We":[83],"show":[84,132],"that,":[85],"for":[86,113],"single":[88],"carrier":[89],"case":[90],"when":[92],"number":[94],"antennas":[96],"station":[100],"is":[101,110,136],"least":[103],"two,":[104],"optimal":[106],"strongly":[111],"NP-hard":[112],"both":[114],"harmonic":[116],"mean":[117],"proportional":[122],"function.":[125],"For":[126],"min-rate":[128],"function,":[130],"that":[133],"solvable":[137],"polynomial":[139],"time.":[140]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
