{"id":"https://openalex.org/W2261552527","doi":"https://doi.org/10.1109/tsp.2015.2500879","title":"Secure Beamforming for Multiple-Antenna Amplify-and-Forward Relay Networks","display_name":"Secure Beamforming for Multiple-Antenna Amplify-and-Forward Relay Networks","publication_year":2015,"publication_date":"2015-11-13","ids":{"openalex":"https://openalex.org/W2261552527","doi":"https://doi.org/10.1109/tsp.2015.2500879","mag":"2261552527"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.2500879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2500879","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":["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/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiyuan Wang","raw_affiliation_strings":["Engineering and Technology Research Center for Convergence Networks, University of Science and Technology Beijing, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering and Technology Research Center for Convergence Networks, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101673576","display_name":"Zhongshan Zhang","orcid":"https://orcid.org/0000-0003-2924-8926"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongshan Zhang","raw_affiliation_strings":["Engineering and Technology Research Center for Convergence Networks, University of Science and Technology Beijing, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering and Technology Research Center for Convergence Networks, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029384171","display_name":"Keping Long","orcid":"https://orcid.org/0000-0001-6678-6075"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Keping Long","raw_affiliation_strings":["Engineering and Technology Research Center for Convergence Networks, University of Science and Technology Beijing, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering and Technology Research Center for Convergence Networks, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I92403157"],"apc_list":null,"apc_paid":null,"fwci":3.4985,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.93269244,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"64","issue":"6","first_page":"1477","last_page":"1492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","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/T10964","display_name":"Wireless Communication Security Techniques","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":0.9994000196456909,"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/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9965999722480774,"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/relay","display_name":"Relay","score":0.842811107635498},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.8166173696517944},{"id":"https://openalex.org/keywords/relay-channel","display_name":"Relay channel","score":0.6256632804870605},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.5623753070831299},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5592745542526245},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4917202293872833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44895139336586},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43745946884155273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4296955466270447},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.4210345149040222},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.3946889042854309},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.29766589403152466},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.2321712076663971}],"concepts":[{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.842811107635498},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.8166173696517944},{"id":"https://openalex.org/C46257984","wikidata":"https://www.wikidata.org/wiki/Q7310895","display_name":"Relay channel","level":4,"score":0.6256632804870605},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.5623753070831299},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5592745542526245},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4917202293872833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44895139336586},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43745946884155273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4296955466270447},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.4210345149040222},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3946889042854309},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.29766589403152466},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.2321712076663971},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2015.2500879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2500879","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3189940716","display_name":"\u65f6\u7a7a\u4e00\u81f4\u6027\u7684\u65e0\u7ebf\u63a5\u5165\u7f51\u7edc\u67b6\u6784\u4e0e\u5173\u952e\u6280\u672f\u7814\u7a76","funder_award_id":"61431001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6644042195","display_name":null,"funder_award_id":"NECT-12-0774","funder_id":"https://openalex.org/F4320334924","funder_display_name":"Program for New Century Excellent Talents in University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334924","display_name":"Program for New Century Excellent Talents in University","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1482298744","https://openalex.org/W1972604748","https://openalex.org/W1972785130","https://openalex.org/W1974165189","https://openalex.org/W1984540590","https://openalex.org/W1989840033","https://openalex.org/W2008011453","https://openalex.org/W2011670293","https://openalex.org/W2025488327","https://openalex.org/W2040317577","https://openalex.org/W2043769961","https://openalex.org/W2055037018","https://openalex.org/W2067386499","https://openalex.org/W2073216863","https://openalex.org/W2075147842","https://openalex.org/W2077563768","https://openalex.org/W2095114822","https://openalex.org/W2096151870","https://openalex.org/W2097555694","https://openalex.org/W2104478100","https://openalex.org/W2109394932","https://openalex.org/W2115525320","https://openalex.org/W2121881701","https://openalex.org/W2124193021","https://openalex.org/W2125327035","https://openalex.org/W2128757878","https://openalex.org/W2135137654","https://openalex.org/W2135244448","https://openalex.org/W2138836120","https://openalex.org/W2139683558","https://openalex.org/W2140960275","https://openalex.org/W2151324163","https://openalex.org/W2171006634","https://openalex.org/W2171468377","https://openalex.org/W2261552527","https://openalex.org/W4300053452"],"related_works":["https://openalex.org/W2608897767","https://openalex.org/W2963768675","https://openalex.org/W2153829573","https://openalex.org/W2099376255","https://openalex.org/W2004047158","https://openalex.org/W2993015344","https://openalex.org/W2119153672","https://openalex.org/W1965566556","https://openalex.org/W2787091472","https://openalex.org/W2006290459"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,97,155,216],"investigate":[4],"the":[5,11,17,20,23,26,33,41,48,100,108,120,129,134,145,151,161,166,181,185,189,193,210,219,234,240,258,261],"secure":[6],"relay":[7,14,31,58,70,168,195,237,242],"beamforming":[8,71],"problems":[9],"for":[10,184],"amplify-and-forward":[12],"(AF)":[13],"network,":[15],"where":[16,107],"transmitter":[18],"sends":[19],"information":[21,54],"to":[22,92,99,256],"receiver":[24],"with":[25,72,197],"help":[27],"of":[28,35,50,102,110,160,188,233],"a":[29,115,176,198],"multiple-antenna":[30],"in":[32,47,64,68,138,170,239,260],"presence":[34],"an":[36,157,171],"eavesdropper.":[37],"We":[38,164],"first":[39],"study":[40,119],"secrecy":[42,122],"rate":[43,123],"maximization":[44,124],"(SRM)":[45],"problem":[46],"case":[49,101],"complete":[51],"channel":[52,74,146],"state":[53],"(CSI).":[55],"The":[56,230],"rank-1":[57,167,190],"beamformer,":[59],"which":[60],"has":[61],"been":[62],"solved":[63,225],"our":[65,139],"previous":[66],"work":[67],"\u201cSecure":[69],"imperfect":[73],"side":[75],"information,\u201d":[76],"IEEE":[77],"Trans.":[78],"Veh.":[79],"Technol.,":[80],"vol.":[81],"62,":[82],"no.":[83],"5,":[84],"pp.":[85],"2140-2155,":[86],"June":[87],"2013,":[88],"is":[89,112,205,245],"rigorously":[90],"proved":[91,247],"be":[93,224],"globally":[94],"optimal.":[95],"Then,":[96],"turn":[98],"partial":[103],"eavesdropper's":[104],"CSI":[105],"(ECSI),":[106],"uncertainty":[109,132,135,153],"ECSI":[111],"characterized":[113],"as":[114],"bounded":[116],"region,":[117,133,154],"and":[118,148,174],"worst-case":[121],"(WCSRM)":[125],"problem.":[126,163],"Different":[127],"from":[128],"common":[130],"spherical":[131],"region":[136,244],"adopted":[137],"paper":[140],"imposes":[141],"independent":[142],"constraints":[143],"on":[144],"gain":[147],"direction.":[149],"With":[150],"proposed":[152,220,235],"give":[156],"in-depth":[158],"analysis":[159,259],"WCSRM":[162],"solve":[165],"beamformer":[169,196,238],"explicit":[172],"form":[173],"move":[175],"step":[177],"further":[178],"by":[179,226],"establishing":[180],"sufficient":[182],"conditions":[183],"global":[186],"optimality":[187,232],"solution.":[191],"Besides,":[192],"rank-2":[194,221,236],"special":[199],"singular":[200],"value":[201],"decomposition":[202],"(SVD)":[203],"structure":[204],"also":[206,246],"considered.":[207],"By":[208],"reducing":[209],"optimization":[211],"variables":[212],"into":[213],"single":[214],"variable,":[215],"show":[217],"that":[218],"solution":[222],"can":[223],"simple":[227],"line":[228],"search.":[229],"asymptotic":[231],"high":[241],"power":[243],"under":[248],"mild":[249],"conditions.":[250],"Finally,":[251],"numerical":[252],"results":[253],"are":[254],"presented":[255],"verify":[257],"paper.":[262]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}