{"id":"https://openalex.org/W2304298069","doi":"https://doi.org/10.1109/tmc.2016.2516981","title":"Chance Constrained Robust Downlink Beamforming in Multicell Networks","display_name":"Chance Constrained Robust Downlink Beamforming in Multicell Networks","publication_year":2016,"publication_date":"2016-01-12","ids":{"openalex":"https://openalex.org/W2304298069","doi":"https://doi.org/10.1109/tmc.2016.2516981","mag":"2304298069"},"language":"en","primary_location":{"id":"doi:10.1109/tmc.2016.2516981","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmc.2016.2516981","pdf_url":null,"source":{"id":"https://openalex.org/S69141925","display_name":"IEEE Transactions on Mobile Computing","issn_l":"1536-1233","issn":["1536-1233","1558-0660","2161-9875"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Mobile Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://kclpure.kcl.ac.uk/ws/files/45843243/paper.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089309345","display_name":"Saba Nasseri","orcid":null},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Saba Nasseri","raw_affiliation_strings":["Department of Informatics, Centre for Telecommunications Research, King's College London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Centre for Telecommunications Research, King's College London, London, UK","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041338005","display_name":"Mohammad Reza Nakhai","orcid":"https://orcid.org/0000-0001-6718-8448"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mohammad Reza Nakhai","raw_affiliation_strings":["Department of Informatics, Centre for Telecommunications Research, King's College London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Centre for Telecommunications Research, King's College London, London, UK","institution_ids":["https://openalex.org/I183935753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100458415","display_name":"Tuan Anh Le","orcid":"https://orcid.org/0000-0003-0612-3717"},"institutions":[{"id":"https://openalex.org/I60488453","display_name":"Middlesex University","ror":"https://ror.org/01rv4p989","country_code":"GB","type":"education","lineage":["https://openalex.org/I60488453"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tuan Anh Le","raw_affiliation_strings":["School of Science and Technology, Middlesex University, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science and Technology, Middlesex University, London, UK","institution_ids":["https://openalex.org/I60488453"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.891,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.76328947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"11","first_page":"2682","last_page":"2691"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9930999875068665,"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/T11946","display_name":"Antenna Design and Optimization","score":0.988099992275238,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.7467159032821655},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.720430314540863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7091281414031982},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6889785528182983},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6789981126785278},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.618787407875061},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.6046828031539917},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.5502309799194336},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5189782977104187},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.48976922035217285},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.4767250120639801},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.46257972717285156},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.459783136844635},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4266360402107239},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.41599684953689575},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.3255794048309326},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2508276700973511},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2236609160900116},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.19179478287696838},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.18905848264694214},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.13807189464569092}],"concepts":[{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.7467159032821655},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.720430314540863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7091281414031982},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6889785528182983},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6789981126785278},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.618787407875061},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.6046828031539917},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.5502309799194336},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5189782977104187},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.48976922035217285},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.4767250120639801},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.46257972717285156},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.459783136844635},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4266360402107239},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.41599684953689575},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3255794048309326},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2508276700973511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2236609160900116},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.19179478287696838},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.18905848264694214},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.13807189464569092},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tmc.2016.2516981","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmc.2016.2516981","pdf_url":null,"source":{"id":"https://openalex.org/S69141925","display_name":"IEEE Transactions on Mobile Computing","issn_l":"1536-1233","issn":["1536-1233","1558-0660","2161-9875"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Mobile Computing","raw_type":"journal-article"},{"id":"pmh:oai:eprints.mdx.ac.uk:19051","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400025","display_name":"Middlesex University Research Repository (Middlesex University Of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60488453","host_organization_name":"Middlesex University","host_organization_lineage":["https://openalex.org/I60488453"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/eb4932d3-edef-4cb2-9947-ac190b91c196","is_oa":true,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/eb4932d3-edef-4cb2-9947-ac190b91c196","pdf_url":"https://kclpure.kcl.ac.uk/ws/files/45843243/paper.pdf","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Nasseri , S , Nakhai , M R & Le , T A 2016 , ' Chance Constrained Robust Downlink Beamforming in Multicell Networks ' , IEEE Transactions on Mobile Computing , vol. 15 , no. 11 , pp. 2682-2691 . https://doi.org/10.1109/TMC.2016.2516981","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/eb4932d3-edef-4cb2-9947-ac190b91c196","is_oa":true,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/eb4932d3-edef-4cb2-9947-ac190b91c196","pdf_url":"https://kclpure.kcl.ac.uk/ws/files/45843243/paper.pdf","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Nasseri , S , Nakhai , M R & Le , T A 2016 , ' Chance Constrained Robust Downlink Beamforming in Multicell Networks ' , IEEE Transactions on Mobile Computing , vol. 15 , no. 11 , pp. 2682-2691 . https://doi.org/10.1109/TMC.2016.2516981","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2304298069.pdf"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1508642566","https://openalex.org/W1545861347","https://openalex.org/W1954775620","https://openalex.org/W1969482887","https://openalex.org/W1970580725","https://openalex.org/W1972104586","https://openalex.org/W1991331367","https://openalex.org/W1996215314","https://openalex.org/W1997025702","https://openalex.org/W2003073695","https://openalex.org/W2008367269","https://openalex.org/W2014020284","https://openalex.org/W2027650277","https://openalex.org/W2032770722","https://openalex.org/W2042599231","https://openalex.org/W2050967017","https://openalex.org/W2065548151","https://openalex.org/W2074120933","https://openalex.org/W2078424873","https://openalex.org/W2079032052","https://openalex.org/W2086609228","https://openalex.org/W2107520399","https://openalex.org/W2112417096","https://openalex.org/W2124822039","https://openalex.org/W2126972880","https://openalex.org/W2129533376","https://openalex.org/W2135352374","https://openalex.org/W2139683558","https://openalex.org/W2140960275","https://openalex.org/W2155174176","https://openalex.org/W2159773000","https://openalex.org/W2166544578","https://openalex.org/W2168233017","https://openalex.org/W2189437279","https://openalex.org/W2296319761","https://openalex.org/W4250589301","https://openalex.org/W6643325419","https://openalex.org/W7014245034"],"related_works":["https://openalex.org/W3087844490","https://openalex.org/W3090699061","https://openalex.org/W4387546583","https://openalex.org/W2005678164","https://openalex.org/W2051762234","https://openalex.org/W2055634632","https://openalex.org/W2389198916","https://openalex.org/W2787827467","https://openalex.org/W2131408743","https://openalex.org/W4367031485"],"abstract_inverted_index":{"We":[0,98,159],"introduce":[1],"a":[2,9,16,23,47,81,111,134],"downlink":[3,121],"robust":[4,120,168],"optimization":[5,41],"approach":[6,114,126,164,193],"that":[7,46,70],"minimizes":[8],"combination":[10],"of":[11,36,49,76,94,118,190],"total":[12],"transmit":[13],"power":[14,32,182],"by":[15],"multiple":[17],"antenna":[18],"base":[19],"station":[20],"(BS)":[21],"within":[22],"cell":[24],"and":[25,83,109,151,184],"the":[26,34,37,68,74,91,95,116,128,155,161,174,191],"resulting":[27,146],"aggregate":[28],"inter-cell":[29],"interference":[30],"(ICI)":[31],"on":[33],"users":[35,87,93],"other":[38,92,96],"cells.":[39,97],"This":[40],"is":[42,149],"constrained":[43],"to":[44,67,115],"assure":[45],"set":[48],"signal-to-interference-plus-noise":[50],"ratio":[51],"(SINR)":[52],"targets":[53],"are":[54,65],"met":[55],"at":[56],"user":[57],"terminals":[58],"with":[59,139],"certain":[60],"outage":[61],"probabilities.":[62],"The":[63,124,145,177],"outages":[64],"due":[66],"uncertainties":[69,101,189],"naturally":[71],"emerge":[72],"in":[73,133,194],"estimation":[75],"channel":[77,188],"covariance":[78],"matrices":[79],"between":[80],"BS":[82],"its":[84],"intra-cell":[85],"local":[86],"as":[88,90,171,173],"well":[89,172],"model":[99],"these":[100],"using":[102],"random":[103],"matrices,":[104],"analyze":[105],"their":[106],"statistical":[107],"behavior,":[108],"formulate":[110],"tractable":[112,153],"probabilistic":[113],"design":[117,169],"optimal":[119],"beamforming":[122],"vectors.":[123],"proposed":[125,162,192],"reformulates":[127],"original":[129],"intractable":[130],"non-convex":[131],"problem":[132],"semidefinite":[135],"programming":[136],"(SDP)":[137],"form":[138],"linear":[140],"matrix":[141],"inequality":[142],"(LMI)":[143],"constraints.":[144],"SDP":[147],"formulation":[148],"convex":[150],"numerically":[152],"under":[154],"standard":[156],"rank":[157],"relaxation.":[158],"compare":[160],"chance-constrained":[163],"against":[165,187],"two":[166],"different":[167],"schemes":[170],"worst-case":[175],"robustness.":[176],"simulation":[178],"results":[179],"confirm":[180],"better":[181],"efficiency":[183],"higher":[185],"resilience":[186],"realistic":[195],"scenarios.":[196]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}