{"id":"https://openalex.org/W2294403625","doi":"https://doi.org/10.1109/tsp.2017.2649488","title":"Unraveling the Rank-One Solution Mystery of Robust MISO Downlink Transmit Optimization: A Verifiable Sufficient Condition via a New Duality Result","display_name":"Unraveling the Rank-One Solution Mystery of Robust MISO Downlink Transmit Optimization: A Verifiable Sufficient Condition via a New Duality Result","publication_year":2017,"publication_date":"2017-01-09","ids":{"openalex":"https://openalex.org/W2294403625","doi":"https://doi.org/10.1109/tsp.2017.2649488","mag":"2294403625"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2017.2649488","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2649488","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1602.01569","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wing-Kin Ma","raw_affiliation_strings":["Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046500541","display_name":"Jiaxian Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210148979","display_name":"MediaTek (Taiwan)","ror":"https://ror.org/05g9jck81","country_code":"TW","type":"company","lineage":["https://openalex.org/I4210148979"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jiaxian Pan","raw_affiliation_strings":["MediaTek, Inc., Hsinchu, Taiwan"],"affiliations":[{"raw_affiliation_string":"MediaTek, Inc., Hsinchu, Taiwan","institution_ids":["https://openalex.org/I4210148979"]}]},{"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":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Anthony Man-Cho So","raw_affiliation_strings":["Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064271996","display_name":"Tsung\u2010Hui Chang","orcid":"https://orcid.org/0000-0003-1349-2764"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tsung-Hui Chang","raw_affiliation_strings":["School of Science and Engineering, Shenzhen Research Institute of Big Data, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"School of Science and Engineering, Shenzhen Research Institute of Big Data, Shenzhen, China","institution_ids":["https://openalex.org/I4210099586"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016986549"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":1.4565,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.82692212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"65","issue":"7","first_page":"1909","last_page":"1924"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"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":1.0,"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":0.9991000294685364,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9988999962806702,"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/rank","display_name":"Rank (graph theory)","score":0.7052685022354126},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.6770012378692627},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6019484996795654},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.5735223293304443},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5671470761299133},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5207707285881042},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5132865309715271},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.4977412521839142},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45230698585510254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.448886513710022},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.44797131419181824},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.2013740837574005},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09267568588256836},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07080858945846558}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7052685022354126},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.6770012378692627},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6019484996795654},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.5735223293304443},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5671470761299133},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5207707285881042},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5132865309715271},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.4977412521839142},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45230698585510254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.448886513710022},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.44797131419181824},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.2013740837574005},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09267568588256836},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07080858945846558},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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":2,"locations":[{"id":"doi:10.1109/tsp.2017.2649488","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2649488","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"},{"id":"pmh:oai:arXiv.org:1602.01569","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.01569","pdf_url":"https://arxiv.org/pdf/1602.01569","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1602.01569","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.01569","pdf_url":"https://arxiv.org/pdf/1602.01569","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5152845964","display_name":null,"funder_award_id":"4055009","funder_id":"https://openalex.org/F4320322942","funder_display_name":"Chinese University of Hong Kong"}],"funders":[{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W591794949","https://openalex.org/W1491719355","https://openalex.org/W1545861347","https://openalex.org/W1568307856","https://openalex.org/W1577245107","https://openalex.org/W1954775620","https://openalex.org/W1964250489","https://openalex.org/W1967073510","https://openalex.org/W1976922185","https://openalex.org/W1985077192","https://openalex.org/W1996215314","https://openalex.org/W1997834106","https://openalex.org/W2004516181","https://openalex.org/W2005102197","https://openalex.org/W2012325084","https://openalex.org/W2014410019","https://openalex.org/W2027650277","https://openalex.org/W2042599231","https://openalex.org/W2061626026","https://openalex.org/W2063185045","https://openalex.org/W2072599023","https://openalex.org/W2074166063","https://openalex.org/W2076694117","https://openalex.org/W2095887113","https://openalex.org/W2098126478","https://openalex.org/W2106993652","https://openalex.org/W2107151067","https://openalex.org/W2108927308","https://openalex.org/W2109005286","https://openalex.org/W2111135554","https://openalex.org/W2113271807","https://openalex.org/W2119741793","https://openalex.org/W2122744491","https://openalex.org/W2124250240","https://openalex.org/W2125884950","https://openalex.org/W2128757878","https://openalex.org/W2129434754","https://openalex.org/W2130302745","https://openalex.org/W2130532371","https://openalex.org/W2132900674","https://openalex.org/W2140214428","https://openalex.org/W2145486800","https://openalex.org/W2149655188","https://openalex.org/W2151268585","https://openalex.org/W2151851437","https://openalex.org/W2152587757","https://openalex.org/W2160086716","https://openalex.org/W2164536085","https://openalex.org/W2164664877","https://openalex.org/W2275443578","https://openalex.org/W2342398231","https://openalex.org/W2492151844","https://openalex.org/W2504806216","https://openalex.org/W2962727887","https://openalex.org/W4296926842","https://openalex.org/W6668830590","https://openalex.org/W6682510097","https://openalex.org/W7014245034"],"related_works":["https://openalex.org/W4313028534","https://openalex.org/W3149055374","https://openalex.org/W2053131036","https://openalex.org/W2216231335","https://openalex.org/W3195104199","https://openalex.org/W4386254288","https://openalex.org/W4292572523","https://openalex.org/W2809352861","https://openalex.org/W2056349093","https://openalex.org/W2952007803"],"abstract_inverted_index":{"This":[0,24,83],"paper":[1],"concentrates":[2],"on":[3],"a":[4,29,36,65,87,104,127,154,168,178],"robust":[5,25,54,101,121,165],"transmit":[6,31,59,81],"optimization":[7],"problem":[8,26,55,102,122,166,171],"for":[9],"the":[10,53,100,120,131,139,149,164,184,202],"multiuser":[11,140,185],"multi-input":[12],"single-output":[13],"(MISO)":[14],"downlink":[15],"scenario":[16],"and":[17,34,138,167,187],"under":[18,40,98],"inaccurate":[19],"channel":[20,141,186],"state":[21],"information":[22],"(CSI).":[23],"deals":[27],"with":[28,72,181],"general-rank":[30],"covariance":[32],"design":[33],"follows":[35],"safe":[37],"rate-constrained":[38],"formulation":[39],"spherically":[41],"bounded":[42],"CSI":[43,132,216],"uncertainties.":[44],"Curiously,":[45],"simulation":[46],"results":[47],"in":[48,61,201],"previous":[49],"works":[50],"suggested":[51],"that":[52,119,198],"admits":[56,103],"rank-one":[57,73,105,128,196],"optimal":[58],"covariances":[60,74],"most":[62],"cases.":[63],"Such":[64],"numerical":[66],"finding":[67],"is":[68,123,142,172,205,219],"appealing":[69],"because":[70],"transmission":[71],"can":[75,94],"be":[76],"easily":[77],"realized":[78],"by":[79],"single-stream":[80],"beamforming.":[82],"gives":[84],"rise":[85],"to":[86,125,183,213],"fundamentally":[88],"important":[89],"question,":[90],"namely,":[91],"whether":[92],"we":[93,110,117,152],"theoretically":[95],"identify":[96,111],"conditions":[97,197],"which":[99,159],"solution.":[106],"In":[107,191],"this":[108],"paper,":[109],"one":[112],"such":[113],"condition.":[114],"Simply":[115],"speaking,":[116],"show":[118],"guaranteed":[124],"admit":[126],"solution":[129],"if":[130],"uncertainties":[133],"are":[134],"not":[135,143],"too":[136,144],"large":[137],"poorly":[145],"conditioned.":[146],"To":[147],"establish":[148],"aforementioned":[150],"condition,":[151],"develop":[153],"novel":[155],"duality":[156],"framework,":[157],"through":[158],"an":[160],"intimate":[161],"relationship":[162],"between":[163],"related":[169],"maximin":[170],"revealed.":[173],"Our":[174],"condition":[175],"involves":[176],"only":[177],"simple":[179],"expression":[180],"respect":[182],"other":[188,194,215],"system":[189],"parameters.":[190],"particular,":[192],"unlike":[193],"sufficient":[195],"have":[199],"appeared":[200],"literature,":[203],"ours":[204],"verifiable.":[206],"The":[207],"application":[208],"of":[209],"our":[210],"analysis":[211],"framework":[212],"several":[214],"uncertainty":[217],"models":[218],"also":[220],"discussed.":[221]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}