{"id":"https://openalex.org/W2095114822","doi":"https://doi.org/10.1109/tvt.2012.2230657","title":"Secure Relay Beamforming With Imperfect Channel Side Information","display_name":"Secure Relay Beamforming With Imperfect Channel Side Information","publication_year":2012,"publication_date":"2012-11-30","ids":{"openalex":"https://openalex.org/W2095114822","doi":"https://doi.org/10.1109/tvt.2012.2230657","mag":"2095114822"},"language":"en","primary_location":{"id":"doi:10.1109/tvt.2012.2230657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2012.2230657","pdf_url":null,"source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"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 Vehicular Technology","raw_type":"journal-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":"https://openalex.org/A5016442564","display_name":"Xiyuan Wang","orcid":"https://orcid.org/0009-0006-0245-071X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiyuan Wang","raw_affiliation_strings":["Department of Automation and Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China","Department of Automation, Tsinghua University, Beijing (China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation and Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing (China)","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100366692","display_name":"Kun Wang","orcid":"https://orcid.org/0000-0002-9099-2781"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kun Wang","raw_affiliation_strings":["Department of Automation and Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China","Department of Automation, Tsinghua University, Beijing (China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation and Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing (China)","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063336422","display_name":"Xian\u2010Da Zhang","orcid":"https://orcid.org/0009-0005-3705-7769"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xian-Da Zhang","raw_affiliation_strings":["Department of Automation and Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China","Department of Automation, Tsinghua University, Beijing (China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation and Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing (China)","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":7.9035,"has_fulltext":false,"cited_by_count":110,"citation_normalized_percentile":{"value":0.97744449,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"62","issue":"5","first_page":"2140","last_page":"2155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","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/T10964","display_name":"Wireless Communication Security Techniques","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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9995999932289124,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9944000244140625,"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":0.761982798576355},{"id":"https://openalex.org/keywords/rician-fading","display_name":"Rician fading","score":0.7268801927566528},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.6647177934646606},{"id":"https://openalex.org/keywords/relay-channel","display_name":"Relay channel","score":0.6424683928489685},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.600226104259491},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5577982664108276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5221624374389648},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.41331803798675537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38085925579071045},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3036789894104004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29547661542892456},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2572658658027649},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.23883408308029175}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.761982798576355},{"id":"https://openalex.org/C60472773","wikidata":"https://www.wikidata.org/wiki/Q7331156","display_name":"Rician fading","level":4,"score":0.7268801927566528},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.6647177934646606},{"id":"https://openalex.org/C46257984","wikidata":"https://www.wikidata.org/wiki/Q7310895","display_name":"Relay channel","level":4,"score":0.6424683928489685},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.600226104259491},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5577982664108276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5221624374389648},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.41331803798675537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38085925579071045},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3036789894104004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29547661542892456},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2572658658027649},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.23883408308029175},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvt.2012.2230657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2012.2230657","pdf_url":null,"source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"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 Vehicular Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1568096262","https://openalex.org/W1989840033","https://openalex.org/W1991614769","https://openalex.org/W2025488327","https://openalex.org/W2030621674","https://openalex.org/W2043769961","https://openalex.org/W2066922259","https://openalex.org/W2072231838","https://openalex.org/W2077563768","https://openalex.org/W2096151870","https://openalex.org/W2097555694","https://openalex.org/W2109394932","https://openalex.org/W2118257351","https://openalex.org/W2121494080","https://openalex.org/W2121881701","https://openalex.org/W2124071994","https://openalex.org/W2124193021","https://openalex.org/W2130324471","https://openalex.org/W2135137654","https://openalex.org/W2142102521","https://openalex.org/W2145514111","https://openalex.org/W2152121970","https://openalex.org/W2159547908","https://openalex.org/W2159687282","https://openalex.org/W2162678712","https://openalex.org/W2165589418","https://openalex.org/W2168792413","https://openalex.org/W2171006634","https://openalex.org/W2171468377","https://openalex.org/W2542429611","https://openalex.org/W4250589301","https://openalex.org/W4299687603","https://openalex.org/W6678148518","https://openalex.org/W6729286676"],"related_works":["https://openalex.org/W4206664053","https://openalex.org/W2951851781","https://openalex.org/W3140554627","https://openalex.org/W4289865786","https://openalex.org/W2952612796","https://openalex.org/W2071484753","https://openalex.org/W2124642768","https://openalex.org/W2171685396","https://openalex.org/W2171099224","https://openalex.org/W2379485241"],"abstract_inverted_index":{"In":[0,22],"this":[1,23],"paper,":[2],"we":[3,44,102],"study":[4],"the":[5,12,19,25,35,46,54,58,68,74,79,84,88,99,107,112,117,122,129,141,144,149,157,165,180,186,190,203,206],"robust":[6],"relay":[7,27,47,208],"beamformer":[8,147,152,168,193],"design":[9],"problem":[10,49],"in":[11],"relay-eavesdropper":[13],"network":[14],"with":[15,30],"imperfect":[16],"knowledge":[17],"of":[18,67,87,106,143,205],"eavesdropper's":[20,55,69,89],"channel.":[21],"network,":[24],"half-duplexing":[26],"is":[28,71,92,153,162],"equipped":[29],"multiple":[31],"antennas":[32],"and":[33,77,116,134,140,148],"employs":[34],"amplify-and-forward":[36],"(AF)":[37],"relaying":[38],"protocol.":[39],"Assuming":[40],"static":[41],"legitimate":[42,75],"links,":[43],"consider":[45],"beamforming":[48],"under":[50,111,121,185],"two":[51],"models":[52],"for":[53,98],"channel:":[56],"1)":[57],"Rician":[59,113,158],"fading":[60,114,159],"channel":[61,70,90],"model,":[62,82,160,189],"where":[63,83],"only":[64],"statistical":[65],"information":[66],"known":[72],"by":[73],"nodes;":[76],"2)":[78],"deterministic":[80,123,187],"uncertainty":[81,85,124,188],"region":[86],"vector":[91],"modeled":[93],"as":[94],"a":[95,171],"sphere.":[96],"As":[97],"optimization":[100],"criteria,":[101],"use":[103],"an":[104],"approximation":[105],"ergodic":[108],"secrecy":[109,119],"rate":[110,120],"model":[115],"worst-case":[118],"model.":[125],"Under":[126,156],"both":[127],"models,":[128],"optimal":[130,145,150,166,181,191],"rank-1,":[131],"match-and-forward":[132],"(MF),":[133],"zero-forcing":[135],"(ZF)":[136],"beamformers":[137],"are":[138,199],"developed,":[139],"equivalence":[142],"rank-1":[146],"MF":[151,182],"also":[154],"established.":[155],"it":[161],"shown":[163],"that":[164],"ZF":[167,192],"may":[169],"have":[170],"rank":[172],"greater":[173],"than":[174],"1":[175],"and,":[176],"therefore,":[177],"could":[178],"outperform":[179],"beamformer,":[183],"whereas":[184],"must":[194],"be":[195],"rank-1.":[196],"Numerical":[197],"results":[198],"presented":[200],"to":[201],"verify":[202],"effectiveness":[204],"proposed":[207],"beamformers.":[209]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":30},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":18},{"year":2013,"cited_by_count":3}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
