{"id":"https://openalex.org/W2107520399","doi":"https://doi.org/10.1109/icassp.2011.5946309","title":"Probabilistic SINR constrained robust transmit beamforming: A Bernstein-type inequality based conservative approach","display_name":"Probabilistic SINR constrained robust transmit beamforming: A Bernstein-type inequality based conservative approach","publication_year":2011,"publication_date":"2011-05-01","ids":{"openalex":"https://openalex.org/W2107520399","doi":"https://doi.org/10.1109/icassp.2011.5946309","mag":"2107520399"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2011.5946309","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2011.5946309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-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":null,"display_name":"Kun-Yu Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Kun-Yu Wang","raw_affiliation_strings":["Institute of Communication Engineering, National Tsing Hua University, Hsinchu, Taiwan","Institute of Commun. Eng., National Tsing Hua University, Hsinchu, Taiwan 30013"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Communication Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Institute of Commun. Eng., National Tsing Hua University, Hsinchu, Taiwan 30013","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064271996","display_name":"Tsung\u2010Hui Chang","orcid":"https://orcid.org/0000-0003-1349-2764"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Tsung-Hui Chang","raw_affiliation_strings":["Institute of Communication Engineering, National Tsing Hua University, Hsinchu, Taiwan","Institute of Commun. Eng., National Tsing Hua University, Hsinchu, Taiwan 30013"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Communication Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Institute of Commun. Eng., National Tsing Hua University, Hsinchu, Taiwan 30013","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016986549","display_name":"Wing\u2010Kin Ma","orcid":"https://orcid.org/0000-0001-7314-3537"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wing-Kin Ma","raw_affiliation_strings":["Department of Electronic Engineering, Chinese University of Hong Kong, Sha Tin, Hong Kong, China","Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, Hong Kong,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Chinese University of Hong Kong, Sha Tin, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, Hong Kong,#TAB#","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105881332","display_name":"Anthony Man\u2013Cho So","orcid":"https://orcid.org/0000-0003-2588-7851"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Anthony Man-Cho So","raw_affiliation_strings":["Department of System Engineering & Engineering Mgmt., Chinese University of Hong Kong, Sha Tin, Hong Kong, China","Dept. of Sys. Eng. & Eng. Mgmt., Chinese Univ. of Hong Kong, Shatin, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of System Engineering & Engineering Mgmt., Chinese University of Hong Kong, Sha Tin, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Dept. of Sys. Eng. & Eng. Mgmt., Chinese Univ. of Hong Kong, Shatin, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061813280","display_name":"Chong\u2010Yung Chi","orcid":"https://orcid.org/0000-0001-5004-7155"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chong-Yung Chi","raw_affiliation_strings":["Institute of Communication Engineering, National Tsing Hua University, Hsinchu, Taiwan","Institute of Commun. Eng., National Tsing Hua University, Hsinchu, Taiwan 30013"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Communication Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Institute of Commun. Eng., National Tsing Hua University, Hsinchu, Taiwan 30013","institution_ids":["https://openalex.org/I25846049"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.5418,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.98574551,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"3080","last_page":"3083"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9991999864578247,"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":0.9986000061035156,"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/beamforming","display_name":"Beamforming","score":0.7283129692077637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6039505004882812},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5828034281730652},{"id":"https://openalex.org/keywords/signal-to-interference-plus-noise-ratio","display_name":"Signal-to-interference-plus-noise ratio","score":0.5761468410491943},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5467381477355957},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.4700784981250763},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.43573760986328125},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4266745448112488},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.41010114550590515},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39681869745254517},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3869713544845581},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3526379466056824},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.30761510133743286},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.19380992650985718},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.14641648530960083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07107073068618774}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.7283129692077637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6039505004882812},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5828034281730652},{"id":"https://openalex.org/C98824394","wikidata":"https://www.wikidata.org/wiki/Q4035626","display_name":"Signal-to-interference-plus-noise ratio","level":3,"score":0.5761468410491943},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5467381477355957},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.4700784981250763},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.43573760986328125},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4266745448112488},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.41010114550590515},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39681869745254517},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3869713544845581},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3526379466056824},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.30761510133743286},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.19380992650985718},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.14641648530960083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07107073068618774},{"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2011.5946309","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2011.5946309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1545861347","https://openalex.org/W1577408952","https://openalex.org/W1996215314","https://openalex.org/W2000034396","https://openalex.org/W2103670141","https://openalex.org/W2112417096","https://openalex.org/W2121233130","https://openalex.org/W2140288088","https://openalex.org/W2145486800","https://openalex.org/W2151851437","https://openalex.org/W6675715838","https://openalex.org/W6682510097","https://openalex.org/W7014245034"],"related_works":["https://openalex.org/W2963170046","https://openalex.org/W2376244802","https://openalex.org/W2088352174","https://openalex.org/W4286695888","https://openalex.org/W3084132786","https://openalex.org/W4327661444","https://openalex.org/W2034991012","https://openalex.org/W1985427746","https://openalex.org/W2012739423","https://openalex.org/W1935013425"],"abstract_inverted_index":{"Recently,":[0],"robust":[1,34,85],"transmit":[2],"beamforming":[3,35,87],"has":[4],"drawn":[5],"considerable":[6],"attention":[7],"because":[8],"it":[9],"can":[10,94],"provide":[11],"guaranteed":[12],"receiver":[13],"performance":[14],"in":[15,54,108],"the":[16,33,40,84,100,113],"presence":[17],"of":[18,73],"channel":[19],"state":[20],"information":[21],"(CSI)":[22],"errors.":[23],"Assuming":[24],"complex":[25,74],"Gaussian":[26,75],"distributed":[27],"CSI":[28],"errors,":[29],"this":[30],"paper":[31],"investigates":[32],"design":[36,88],"problem":[37],"that":[38],"minimizes":[39],"transmission":[41],"power":[42,118],"subject":[43],"to":[44,63,83,97,123],"probabilistic":[45,51],"signal-to-interference-plus-noise":[46],"ratio":[47],"(SINR)":[48],"constraints.":[49],"The":[50,90],"SINR":[52,127],"constraints":[53],"general":[55],"have":[56],"no":[57],"closed-form":[58],"expression":[59],"and":[60,120],"are":[61],"difficult":[62],"handle.":[64],"Based":[65],"on":[66],"a":[67,80],"Bernstein-type":[68],"inequality":[69],"for":[70,129],"quadratic":[71],"forms":[72],"random":[76],"variables,":[77],"we":[78],"propose":[79],"conservative":[81,102],"formulation":[82],"single-cell":[86],"problem.":[89],"semidefinite":[91],"relaxation":[92],"technique":[93],"be":[95],"applied":[96],"efficiently":[98],"handle":[99],"proposed":[101,114],"formulation.":[103],"Simulation":[104],"results":[105],"show":[106],"that,":[107],"comparison":[109],"with":[110],"existing":[111],"methods,":[112],"method":[115],"is":[116,121],"more":[117],"efficient":[119],"able":[122],"support":[124],"higher":[125],"target":[126],"values":[128],"receivers.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}