{"id":"https://openalex.org/W1976922185","doi":"https://doi.org/10.1186/1687-1499-2012-243","title":"Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?","display_name":"Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?","publication_year":2012,"publication_date":"2012-08-06","ids":{"openalex":"https://openalex.org/W1976922185","doi":"https://doi.org/10.1186/1687-1499-2012-243","mag":"1976922185"},"language":"en","primary_location":{"id":"doi:10.1186/1687-1499-2012-243","is_oa":true,"landing_page_url":"https://doi.org/10.1186/1687-1499-2012-243","pdf_url":"https://jwcn-eurasipjournals.springeropen.com/counter/pdf/10.1186/1687-1499-2012-243","source":{"id":"https://openalex.org/S82675988","display_name":"EURASIP Journal on Wireless Communications and Networking","issn_l":"1687-1472","issn":["1687-1472","1687-1499"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Wireless Communications and Networking","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://jwcn-eurasipjournals.springeropen.com/counter/pdf/10.1186/1687-1499-2012-243","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091631370","display_name":"Enbin Song","orcid":"https://orcid.org/0000-0003-2100-5313"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Enbin Song","raw_affiliation_strings":["Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China","Department of Mathematics, Sichuan University, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059252324","display_name":"Qingjiang Shi","orcid":"https://orcid.org/0000-0003-0507-9080"},"institutions":[{"id":"https://openalex.org/I1328775524","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55","country_code":"CN","type":"education","lineage":["https://openalex.org/I1328775524"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingjiang Shi","raw_affiliation_strings":["School of Information and Science Technology, Zhejiang Sci-Tech University, Hangzhou, 310018, China","School of Information and Science Technology, Zhejiang Sci-Tech University, Hangzhou, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Science Technology, Zhejiang Sci-Tech University, Hangzhou, 310018, China","institution_ids":["https://openalex.org/I1328775524"]},{"raw_affiliation_string":"School of Information and Science Technology, Zhejiang Sci-Tech University, Hangzhou, China#TAB#","institution_ids":["https://openalex.org/I1328775524"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046195860","display_name":"Maziar Sanjabi","orcid":null},"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":"Maziar Sanjabi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN, 55455, USA","Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, USA#TAB#","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028963874","display_name":"Ruoyu Sun","orcid":"https://orcid.org/0000-0003-2487-5322"},"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":"Ruo-Yu Sun","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN, 55455, USA","Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, USA#TAB#","institution_ids":["https://openalex.org/I130238516"]}]},{"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 Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN, 55455, USA","Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, USA#TAB#","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091631370"],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":{"value":1665,"currency":"USD","value_usd":1665},"apc_paid":{"value":1665,"currency":"USD","value_usd":1665},"fwci":7.0263,"has_fulltext":true,"cited_by_count":70,"citation_normalized_percentile":{"value":0.97197593,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"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/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.8887338042259216},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7421551942825317},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7374778985977173},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.6979721188545227},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.6737455725669861},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6556556224822998},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6171269416809082},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.568189799785614},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5198891162872314},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.510529637336731},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.5104860067367554},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.4343539774417877},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.42765089869499207},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.42292237281799316},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.29540497064590454},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27341124415397644},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.24658581614494324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21133890748023987}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.8887338042259216},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7421551942825317},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7374778985977173},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.6979721188545227},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.6737455725669861},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6556556224822998},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6171269416809082},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.568189799785614},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5198891162872314},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.510529637336731},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.5104860067367554},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.4343539774417877},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.42765089869499207},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.42292237281799316},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.29540497064590454},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27341124415397644},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.24658581614494324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21133890748023987},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1186/1687-1499-2012-243","is_oa":true,"landing_page_url":"https://doi.org/10.1186/1687-1499-2012-243","pdf_url":"https://jwcn-eurasipjournals.springeropen.com/counter/pdf/10.1186/1687-1499-2012-243","source":{"id":"https://openalex.org/S82675988","display_name":"EURASIP Journal on Wireless Communications and Networking","issn_l":"1687-1472","issn":["1687-1472","1687-1499"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Wireless Communications and Networking","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1186/1687-1499-2012-243","is_oa":true,"landing_page_url":"https://doi.org/10.1186/1687-1499-2012-243","pdf_url":"https://jwcn-eurasipjournals.springeropen.com/counter/pdf/10.1186/1687-1499-2012-243","source":{"id":"https://openalex.org/S82675988","display_name":"EURASIP Journal on Wireless Communications and Networking","issn_l":"1687-1472","issn":["1687-1472","1687-1499"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EURASIP Journal on Wireless Communications and Networking","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8899999856948853,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1515455231","display_name":"Semidefinite Programming Relaxation: Approximation Algorithms, Performance Analysis and Applications","funder_award_id":"1015346","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7282849541","display_name":null,"funder_award_id":"60901037","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1976922185.pdf","grobid_xml":"https://content.openalex.org/works/W1976922185.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1168406117","https://openalex.org/W1972546746","https://openalex.org/W1996215314","https://openalex.org/W2011961109","https://openalex.org/W2012325084","https://openalex.org/W2023409468","https://openalex.org/W2045021643","https://openalex.org/W2072603128","https://openalex.org/W2092575814","https://openalex.org/W2106929598","https://openalex.org/W2106993652","https://openalex.org/W2109005286","https://openalex.org/W2110323470","https://openalex.org/W2111135554","https://openalex.org/W2112277368","https://openalex.org/W2113168978","https://openalex.org/W2134791097","https://openalex.org/W2135352374","https://openalex.org/W2145486800","https://openalex.org/W2150244542","https://openalex.org/W2151851437","https://openalex.org/W2167826503","https://openalex.org/W2541530951","https://openalex.org/W3210839039","https://openalex.org/W4206478473","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W3087844490","https://openalex.org/W4220680272","https://openalex.org/W2088352174","https://openalex.org/W3090699061","https://openalex.org/W4387546583","https://openalex.org/W2005678164","https://openalex.org/W3084132786","https://openalex.org/W4327661444","https://openalex.org/W2055634632","https://openalex.org/W2034991012"],"abstract_inverted_index":{"We":[0],"consider":[1,78],"the":[2,16,19,24,30,45,50,91,96,106,115,128,134,140,146],"multiuser":[3,85],"beamforming":[4,86,98],"problem":[5,39,99],"for":[6,83],"a":[7,70,79],"multi-input":[8],"single-output":[9],"downlink":[10],"channel":[11,20,107],"that":[12,90,127],"takes":[13],"into":[14],"account":[15],"errors":[17,32],"in":[18,137],"state":[21],"information":[22],"at":[23,120,145],"transmitter":[25,116],"side":[26],"(CSIT).":[27],"By":[28],"modeling":[29],"CSIT":[31],"as":[33,43,103,105],"elliptically":[34],"bounded":[35],"uncertainty":[36,108],"regions,":[37],"this":[38,62,75,84],"can":[40,68],"be":[41],"formulated":[42],"minimizing":[44],"transmission":[46],"power":[47,143],"subject":[48],"to":[49,60,100],"worst-case":[51],"signal-to-interference-plus-noise":[52],"ratio":[53],"constraints.":[54],"Several":[55],"methods":[56,136],"have":[57],"been":[58],"proposed":[59,129],"solve":[61],"nonconvex":[63],"optimization":[64],"problem,":[65,87],"but":[66],"none":[67],"guarantee":[69],"global":[71,101],"optimal":[72],"solution.":[73],"In":[74],"article,":[76],"we":[77],"semidefinite":[80],"relaxation":[81],"(SDR)":[82],"and":[88],"prove":[89],"SDR":[92,130],"method":[93],"actually":[94],"solves":[95],"robust":[97],"optimality":[102],"long":[104],"bound":[109],"is":[110,117],"sufficiently":[111],"small":[112],"or":[113],"when":[114],"equipped":[118],"with":[119],"most":[121],"two":[122],"antennas.":[123],"Numerical":[124],"examples":[125],"show":[126],"approach":[131],"significantly":[132],"outperforms":[133],"existing":[135],"terms":[138],"of":[139],"average":[141],"required":[142],"consumption":[144],"transmitter.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
