{"id":"https://openalex.org/W3212701158","doi":"https://doi.org/10.3390/e23111484","title":"Full-Duplex Relay with Delayed CSI Elevates the SDoF of the MIMO X Channel","display_name":"Full-Duplex Relay with Delayed CSI Elevates the SDoF of the MIMO X Channel","publication_year":2021,"publication_date":"2021-11-10","ids":{"openalex":"https://openalex.org/W3212701158","doi":"https://doi.org/10.3390/e23111484","mag":"3212701158","pmid":"https://pubmed.ncbi.nlm.nih.gov/34828182"},"language":"en","primary_location":{"id":"doi:10.3390/e23111484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23111484","pdf_url":"https://www.mdpi.com/1099-4300/23/11/1484/pdf?version=1636528961","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/11/1484/pdf?version=1636528961","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075254989","display_name":"Tong Zhang","orcid":"https://orcid.org/0000-0002-6770-0664"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tong Zhang","raw_affiliation_strings":["The Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China"],"raw_orcid":"https://orcid.org/0000-0002-6770-0664","affiliations":[{"raw_affiliation_string":"The Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012861792","display_name":"Gaojie Chen","orcid":"https://orcid.org/0000-0003-2978-0365"},"institutions":[{"id":"https://openalex.org/I28290843","display_name":"University of Surrey","ror":"https://ror.org/00ks66431","country_code":"GB","type":"education","lineage":["https://openalex.org/I28290843"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Gaojie Chen","raw_affiliation_strings":["5GIC & 6GIC, Institute for Communication Systems, University of Surrey, Guildford GU2 7XH, UK"],"raw_orcid":"https://orcid.org/0000-0003-2978-0365","affiliations":[{"raw_affiliation_string":"5GIC & 6GIC, Institute for Communication Systems, University of Surrey, Guildford GU2 7XH, UK","institution_ids":["https://openalex.org/I28290843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100328259","display_name":"Shuai Wang","orcid":"https://orcid.org/0000-0002-0288-4212"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuai Wang","raw_affiliation_strings":["The Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China"],"raw_orcid":"https://orcid.org/0000-0002-0288-4212","affiliations":[{"raw_affiliation_string":"The Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100431342","display_name":"Rui Wang","orcid":"https://orcid.org/0000-0003-0044-8932"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Rui Wang","raw_affiliation_strings":["The Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China"],"raw_orcid":"https://orcid.org/0000-0003-0044-8932","affiliations":[{"raw_affiliation_string":"The Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China","institution_ids":["https://openalex.org/I3045169105"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100431342"],"corresponding_institution_ids":["https://openalex.org/I3045169105"],"apc_list":{"value":1800,"currency":"CHF","value_usd":1944},"apc_paid":{"value":1800,"currency":"CHF","value_usd":1944},"fwci":0.1625,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46277166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":95},"biblio":{"volume":"23","issue":"11","first_page":"1484","last_page":"1484"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9994000196456909,"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":0.9696999788284302,"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/channel-state-information","display_name":"Channel state information","score":0.750394344329834},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.671574056148529},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.6669612526893616},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.6615040302276611},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.660969078540802},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5827224850654602},{"id":"https://openalex.org/keywords/antenna","display_name":"Antenna (radio)","score":0.4994475841522217},{"id":"https://openalex.org/keywords/jamming","display_name":"Jamming","score":0.4907110929489136},{"id":"https://openalex.org/keywords/relay-channel","display_name":"Relay channel","score":0.45116567611694336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44676318764686584},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.43403956294059753},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.42664793133735657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3688889145851135},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.33522671461105347},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33455950021743774},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.20615500211715698},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15571460127830505},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09404075145721436},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.061803460121154785}],"concepts":[{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.750394344329834},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.671574056148529},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.6669612526893616},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.6615040302276611},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.660969078540802},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5827224850654602},{"id":"https://openalex.org/C21822782","wikidata":"https://www.wikidata.org/wiki/Q131214","display_name":"Antenna (radio)","level":2,"score":0.4994475841522217},{"id":"https://openalex.org/C2779079576","wikidata":"https://www.wikidata.org/wiki/Q17092823","display_name":"Jamming","level":2,"score":0.4907110929489136},{"id":"https://openalex.org/C46257984","wikidata":"https://www.wikidata.org/wiki/Q7310895","display_name":"Relay channel","level":4,"score":0.45116567611694336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44676318764686584},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.43403956294059753},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.42664793133735657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3688889145851135},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.33522671461105347},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33455950021743774},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.20615500211715698},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15571460127830505},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09404075145721436},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.061803460121154785},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e23111484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23111484","pdf_url":"https://www.mdpi.com/1099-4300/23/11/1484/pdf?version=1636528961","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:34828182","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34828182","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":"Journal Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:8621486","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8621486","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:fa81cf9389c943b39a14469284f71341","is_oa":true,"landing_page_url":"https://doaj.org/article/fa81cf9389c943b39a14469284f71341","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 11, p 1484 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e23111484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23111484","pdf_url":"https://www.mdpi.com/1099-4300/23/11/1484/pdf?version=1636528961","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8399999737739563,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3714742385","display_name":"\u9002\u7528\u4e8e\u591a\u79cd\u5927\u89c4\u6a21\u591a\u5929\u7ebf\u7f51\u7edc\u7684\u8de8\u5c42\u968f\u673a\u4f18\u5316\u6280\u672f\u7814\u7a76","funder_award_id":"61771232","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5353349450","display_name":null,"funder_award_id":"2021M691453","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6243945240","display_name":null,"funder_award_id":"62001203","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/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3212701158.pdf","grobid_xml":"https://content.openalex.org/works/W3212701158.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1796621330","https://openalex.org/W1994125924","https://openalex.org/W2021846802","https://openalex.org/W2033481961","https://openalex.org/W2056418000","https://openalex.org/W2089665343","https://openalex.org/W2106543408","https://openalex.org/W2108438541","https://openalex.org/W2118269164","https://openalex.org/W2130509920","https://openalex.org/W2136928846","https://openalex.org/W2167443349","https://openalex.org/W2288226817","https://openalex.org/W2320115123","https://openalex.org/W2330749234","https://openalex.org/W2337906902","https://openalex.org/W2475797641","https://openalex.org/W2597947158","https://openalex.org/W2758759047","https://openalex.org/W2803921113","https://openalex.org/W2921122044","https://openalex.org/W2939154461","https://openalex.org/W2963815111","https://openalex.org/W2964182504","https://openalex.org/W3005539399","https://openalex.org/W3034852212","https://openalex.org/W3125378177","https://openalex.org/W3134290885","https://openalex.org/W3138423112","https://openalex.org/W3141610964","https://openalex.org/W6702313851"],"related_works":["https://openalex.org/W2608897767","https://openalex.org/W2153829573","https://openalex.org/W2099376255","https://openalex.org/W2963768675","https://openalex.org/W2004047158","https://openalex.org/W2119153672","https://openalex.org/W2993015344","https://openalex.org/W1559320887","https://openalex.org/W2374704553","https://openalex.org/W2006290459"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"the":[3,9,51,58,69,73,82,99,117,136,142,151,156,183,186,193,196,205,208],"sum":[4],"secure":[5],"degrees-of-freedom":[6],"(SDoF)":[7],"of":[8,95,103,116,121,185,207],"multiple-input":[10],"multiple-output":[11],"(MIMO)":[12],"X":[13],"channel":[14,29,125,132],"with":[15,126,178,211],"confidential":[16,127],"messages":[17,128],"(XCCM)":[18],"and":[19,36,44,54,76,81,85,101,130,145,150,214],"arbitrary":[20],"antenna":[21,96],"configurations":[22],"is":[23,27,112,153,190],"studied,":[24],"where":[25],"there":[26],"no":[28,165],"state":[30,133],"information":[31,134],"(CSI)":[32],"at":[33,40,49,135,167],"two":[34,168],"transmitters":[35],"only":[37],"delayed":[38,131,179,215],"CSI":[39,166,180],"a":[41,140,174],"multiple-antenna,":[42],"full-duplex,":[43],"decode-and-forward":[45],"relay.":[46],"We":[47],"aim":[48],"establishing":[50],"sum-SDoF":[52,59,109,143,152,184,198,206],"lower":[53,60,144,199],"upper":[55,110,146],"bounds.":[56],"For":[57],"bound,":[61],"we":[62],"design":[63],"three":[64],"relay-aided":[65,70,74,83],"transmission":[66],"schemes,":[67],"namely,":[68],"jamming":[71,75,84],"scheme,":[72,80,89],"one-receiver":[77],"interference":[78,87],"alignment":[79,88],"two-receiver":[86],"each":[90,104],"corresponding":[91],"to":[92],"one":[93],"case":[94],"configurations.":[97],"Moreover,":[98],"security":[100],"decoding":[102],"scheme":[105],"are":[106,148],"analyzed.":[107],"The":[108],"bound":[111,200],"proposed":[113],"by":[114,192],"means":[115],"existing":[118],"SDoF":[119],"region":[120],"two-user":[122],"MIMO":[123,187,209],"broadcast":[124],"(BCCM)":[129],"transmitter":[137],"(CSIT).":[138],"As":[139],"result,":[141],"bounds":[147],"derived,":[149],"characterized":[154],"when":[155],"relay":[157,177],"has":[158],"sufficiently":[159],"large":[160],"antennas.":[161],"Furthermore,":[162],"even":[163],"assuming":[164],"transmitters,":[169],"our":[170],"results":[171],"show":[172],"that":[173,195],"multiple-antenna":[175],"full-duplex":[176],"can":[181,201],"elevate":[182],"XCCM.":[188],"This":[189],"corroborated":[191],"fact":[194],"derived":[197],"be":[202],"greater":[203],"than":[204],"XCCM":[210],"output":[212],"feedback":[213],"CSIT.":[216]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
