{"id":"https://openalex.org/W2970663993","doi":"https://doi.org/10.1109/tvt.2019.2937575","title":"Generalized Benders Decomposition to Secure Energy-Efficient Resource Allocation for Multiuser Full-Duplex Relay Cooperative Networks","display_name":"Generalized Benders Decomposition to Secure Energy-Efficient Resource Allocation for Multiuser Full-Duplex Relay Cooperative Networks","publication_year":2019,"publication_date":"2019-08-26","ids":{"openalex":"https://openalex.org/W2970663993","doi":"https://doi.org/10.1109/tvt.2019.2937575","mag":"2970663993"},"language":"en","primary_location":{"id":"doi:10.1109/tvt.2019.2937575","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2019.2937575","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/A5081396120","display_name":"Ruoguang Li","orcid":"https://orcid.org/0000-0001-6834-4916"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruoguang Li","raw_affiliation_strings":["School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-6834-4916","affiliations":[{"raw_affiliation_string":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100335940","display_name":"Li Wang","orcid":"https://orcid.org/0000-0002-0973-1614"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Wang","raw_affiliation_strings":["Key Laboratory of the Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China","School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-0973-1614","affiliations":[{"raw_affiliation_string":"Key Laboratory of the Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101459082","display_name":"Xiaoming Tao","orcid":"https://orcid.org/0000-0002-8763-9338"},"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":"Xiaoming Tao","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-8763-9338","affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101792370","display_name":"Mei Song","orcid":"https://orcid.org/0000-0003-4476-729X"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mei Song","raw_affiliation_strings":["School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063667378","display_name":"Zhu Han","orcid":"https://orcid.org/0000-0002-6606-5822"},"institutions":[{"id":"https://openalex.org/I35928602","display_name":"Kyung Hee University","ror":"https://ror.org/01zqcg218","country_code":"KR","type":"education","lineage":["https://openalex.org/I35928602"]},{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["KR","US"],"is_corresponding":false,"raw_author_name":"Zhu Han","raw_affiliation_strings":["Department of Computer Science and Engineering, Kyung Hee University, Seoul, South Korea","Department of Electrical and Computer Engineering, University of Houston, USA"],"raw_orcid":"https://orcid.org/0000-0002-6606-5822","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Kyung Hee University, Seoul, South Korea","institution_ids":["https://openalex.org/I35928602"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Houston, USA","institution_ids":["https://openalex.org/I44461941"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3503,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.60140163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"68","issue":"11","first_page":"10728","last_page":"10741"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12791","display_name":"Full-Duplex Wireless Communications","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/T12791","display_name":"Full-Duplex Wireless Communications","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/T10964","display_name":"Wireless Communication Security Techniques","score":0.998199999332428,"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":0.9884999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6820753216743469},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5506460666656494},{"id":"https://openalex.org/keywords/orthogonal-frequency-division-multiplexing","display_name":"Orthogonal frequency-division multiplexing","score":0.5390723347663879},{"id":"https://openalex.org/keywords/subcarrier","display_name":"Subcarrier","score":0.520918071269989},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.5018179416656494},{"id":"https://openalex.org/keywords/resource-allocation","display_name":"Resource allocation","score":0.4844191372394562},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4787822961807251},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.46120375394821167},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.46083834767341614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2766517996788025},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.1891716718673706},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18071147799491882},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.10638511180877686}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6820753216743469},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5506460666656494},{"id":"https://openalex.org/C40409654","wikidata":"https://www.wikidata.org/wiki/Q375889","display_name":"Orthogonal frequency-division multiplexing","level":3,"score":0.5390723347663879},{"id":"https://openalex.org/C198329298","wikidata":"https://www.wikidata.org/wiki/Q586358","display_name":"Subcarrier","level":4,"score":0.520918071269989},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.5018179416656494},{"id":"https://openalex.org/C29202148","wikidata":"https://www.wikidata.org/wiki/Q287260","display_name":"Resource allocation","level":2,"score":0.4844191372394562},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4787822961807251},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.46120375394821167},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.46083834767341614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2766517996788025},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.1891716718673706},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18071147799491882},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.10638511180877686},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvt.2019.2937575","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2019.2937575","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":[{"score":0.6499999761581421,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G3098713759","display_name":null,"funder_award_id":"L172010","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G5001818044","display_name":"\u57fa\u4e8e\u7528\u6237\u793e\u7fa4\u548c\u8de8\u57df\u534f\u4f5c\u7684\u591a\u76ee\u6807\u5bfc\u5411\u65e0\u7ebf\u8d44\u6e90\u7ba1\u7406\u7814\u7a76","funder_award_id":"61571056","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7295829493","display_name":null,"funder_award_id":"2018XKJC03","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7437350951","display_name":"\u9762\u5411\u6570\u636e\u589e\u5f3a\u7684\u7269\u8054\u7f51\u65e0\u7ebf\u4f20\u8f93\u4e0e\u667a\u80fd\u670d\u52a1\u5173\u952e\u6280\u672f\u7814\u7a76","funder_award_id":"61871046","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8202390991","display_name":null,"funder_award_id":"61871416","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null},{"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":35,"referenced_works":["https://openalex.org/W40343472","https://openalex.org/W1607470944","https://openalex.org/W1964590153","https://openalex.org/W1967956032","https://openalex.org/W1973977831","https://openalex.org/W1999218360","https://openalex.org/W2039065876","https://openalex.org/W2083058703","https://openalex.org/W2086842720","https://openalex.org/W2132305759","https://openalex.org/W2153639779","https://openalex.org/W2247171314","https://openalex.org/W2472065965","https://openalex.org/W2484634279","https://openalex.org/W2511751301","https://openalex.org/W2520092822","https://openalex.org/W2524617287","https://openalex.org/W2555963685","https://openalex.org/W2557661876","https://openalex.org/W2559636962","https://openalex.org/W2564566221","https://openalex.org/W2566769952","https://openalex.org/W2587576275","https://openalex.org/W2597004530","https://openalex.org/W2751232734","https://openalex.org/W2769717388","https://openalex.org/W2770025135","https://openalex.org/W2808112695","https://openalex.org/W2963136492","https://openalex.org/W2964113506","https://openalex.org/W2972771729","https://openalex.org/W3101887446","https://openalex.org/W4234997161","https://openalex.org/W4250589301","https://openalex.org/W6730999400"],"related_works":["https://openalex.org/W2547202878","https://openalex.org/W1964989099","https://openalex.org/W2917559461","https://openalex.org/W2096856057","https://openalex.org/W2100607072","https://openalex.org/W2083000360","https://openalex.org/W1983237045","https://openalex.org/W1735229475","https://openalex.org/W2090622761","https://openalex.org/W1995464007"],"abstract_inverted_index":{"In":[0,65],"this":[1],"paper,":[2],"we":[3,114,160],"investigate":[4],"the":[5,29,49,57,66,108,117,122,133,154,157,190,196,199],"issue":[6],"of":[7,31,68,110,156,179,198],"resource":[8,73],"allocation":[9,74,87],"for":[10,140,148],"secure":[11,51],"energy":[12,52,60],"efficient":[13],"communication":[14],"in":[15,28],"a":[16,32,72,96,112,137,145],"multiuser":[17,69],"orthogonal":[18],"frequency":[19],"division":[20],"multiplexing":[21],"(OFDM)":[22],"based":[23],"full-duplex":[24],"(FD)":[25],"relaying":[26],"network":[27],"presence":[30],"passive":[33],"eavesdropper":[34],"whose":[35],"channel":[36],"state":[37],"information":[38],"(CSI)":[39],"is":[40,46,93,103],"not":[41],"perfectly":[42],"known.":[43],"Our":[44],"goal":[45],"to":[47,120,131,188,194],"maximize":[48],"overall":[50],"efficiency":[53],"(SEE),":[54],"which":[55,102],"presents":[56],"relationship":[58],"between":[59],"consumption":[61],"and":[62,125,144,177,193],"secrecy":[63],"performance.":[64],"context":[67],"communications,":[70],"such":[71,111],"strategy":[75],"jointly":[76],"combines":[77],"subcarrier":[78,80],"permutation,":[79],"pair":[81],"allocation,":[82],"as":[83,85,95],"well":[84],"power":[86],"altogether.":[88],"The":[89,183],"considered":[90],"optimization":[91],"problem":[92,135,139,147,169],"formulated":[94],"mixed":[97],"integer":[98,142],"nonconvex":[99],"programming":[100,143],"problem,":[101,113,159],"generally":[104],"NP":[105],"hard.":[106],"Analyzing":[107],"property":[109],"first":[115],"use":[116],"Dinkelbach's":[118],"method":[119],"eliminate":[121],"fractional":[123],"form":[124],"then":[126],"exploit":[127],"Generalized":[128],"Benders":[129],"decomposition":[130],"decouple":[132],"original":[134],"into":[136,164],"master":[138],"pure":[141],"primal":[146,158],"nonlinear":[149],"programming.":[150,182],"More":[151],"specific,":[152],"given":[153],"nonconvexity":[155],"accordingly":[161],"transform":[162],"it":[163],"an":[165],"equivalent":[166],"relaxed":[167],"convex":[168,175,180],"by":[170],"applying":[171],"dual":[172],"decomposition,":[173],"alternative":[174],"search,":[176],"difference":[178],"function":[181],"numerical":[184],"results":[185],"are":[186],"provided":[187],"validate":[189],"theoretical":[191],"analysis":[192],"demonstrate":[195],"effectiveness":[197],"proposed":[200],"algorithm.":[201]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
