{"id":"https://openalex.org/W2944780132","doi":"https://doi.org/10.1109/tvt.2019.2915005","title":"Spectral Efficiency of Multipair Massive MIMO Two-Way Relaying With Imperfect CSI","display_name":"Spectral Efficiency of Multipair Massive MIMO Two-Way Relaying With Imperfect CSI","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2944780132","doi":"https://doi.org/10.1109/tvt.2019.2915005","mag":"2944780132"},"language":"en","primary_location":{"id":"doi:10.1109/tvt.2019.2915005","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2019.2915005","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":true,"oa_status":"green","oa_url":"https://pureadmin.qub.ac.uk/ws/files/168578867/final.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101529499","display_name":"Chuili Kong","orcid":null},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuili Kong","raw_affiliation_strings":["State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an, China","State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0003-4255-6894","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024046434","display_name":"Caijun Zhong","orcid":"https://orcid.org/0000-0002-9960-7800"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Caijun Zhong","raw_affiliation_strings":["State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an, China","State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-9960-7800","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035876091","display_name":"Michail Matthaiou","orcid":"https://orcid.org/0000-0001-9235-7741"},"institutions":[{"id":"https://openalex.org/I126231945","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62","country_code":"GB","type":"education","lineage":["https://openalex.org/I126231945"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michail Matthaiou","raw_affiliation_strings":["Institute of Electronics, Communications and Information Technology, Queen's University Belfast, Belfast, U.K"],"raw_orcid":"https://orcid.org/0000-0001-9235-7741","affiliations":[{"raw_affiliation_string":"Institute of Electronics, Communications and Information Technology, Queen's University Belfast, Belfast, U.K","institution_ids":["https://openalex.org/I126231945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062293532","display_name":"Emil Bj\u00f6rnson","orcid":"https://orcid.org/0000-0002-5954-434X"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Emil Bjornson","raw_affiliation_strings":["Department of Electrical Engineering, Link\u00f6ping University, Link\u00f6ping, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-5954-434X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Link\u00f6ping University, Link\u00f6ping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100751311","display_name":"Zhaoyang Zhang","orcid":"https://orcid.org/0000-0003-2346-6228"},"institutions":[{"id":"https://openalex.org/I4210141176","display_name":"Communication University of Zhejiang","ror":"https://ror.org/04t7gxr16","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210141176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaoyang Zhang","raw_affiliation_strings":["Zhejiang Provincial Key Laboratory of Information Processing, Communication and Networking, Institute of Information and Communication Engineering, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-2346-6228","affiliations":[{"raw_affiliation_string":"Zhejiang Provincial Key Laboratory of Information Processing, Communication and Networking, Institute of Information and Communication Engineering, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I4210141176"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3102,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.89270453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"68","issue":"7","first_page":"6593","last_page":"6607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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":0.9995999932289124,"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/T10148","display_name":"Advanced MIMO Systems Optimization","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"}}],"keywords":[{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.7709228992462158},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.5999182462692261},{"id":"https://openalex.org/keywords/spectral-efficiency","display_name":"Spectral efficiency","score":0.5138728618621826},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5133184790611267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5123716592788696},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.47586697340011597},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.4514637291431427},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4195232391357422},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3398815393447876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31496304273605347},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.23139330744743347},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20419850945472717},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2002839744091034}],"concepts":[{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.7709228992462158},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.5999182462692261},{"id":"https://openalex.org/C137246740","wikidata":"https://www.wikidata.org/wiki/Q583970","display_name":"Spectral efficiency","level":3,"score":0.5138728618621826},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5133184790611267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5123716592788696},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.47586697340011597},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.4514637291431427},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4195232391357422},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3398815393447876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31496304273605347},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.23139330744743347},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20419850945472717},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2002839744091034},{"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/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tvt.2019.2915005","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2019.2915005","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"},{"id":"pmh:oai:pure.qub.ac.uk/portal:openaire/5b08bf9c-06b7-43ff-b416-cb0518677668","is_oa":true,"landing_page_url":"https://pure.qub.ac.uk/en/publications/5b08bf9c-06b7-43ff-b416-cb0518677668","pdf_url":"https://pureadmin.qub.ac.uk/ws/files/168578867/final.pdf","source":{"id":"https://openalex.org/S4306402319","display_name":"Research Portal (Queen's University Belfast)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126231945","host_organization_name":"Queen's University Belfast","host_organization_lineage":["https://openalex.org/I126231945"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kong, C, Zhong, C, Matthaiou, M, Bj\u00f6rnson, E & Zhang, Z 2019, 'Spectral efficiency of multipair massive MIMO two-way relaying with imperfect CSI', IEEE Transactions on Vehicular Technology. https://doi.org/10.1109/TVT.2019.2915005","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.qub.ac.uk/portal:openaire/5b08bf9c-06b7-43ff-b416-cb0518677668","is_oa":true,"landing_page_url":"https://pure.qub.ac.uk/en/publications/5b08bf9c-06b7-43ff-b416-cb0518677668","pdf_url":"https://pureadmin.qub.ac.uk/ws/files/168578867/final.pdf","source":{"id":"https://openalex.org/S4306402319","display_name":"Research Portal (Queen's University Belfast)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126231945","host_organization_name":"Queen's University Belfast","host_organization_lineage":["https://openalex.org/I126231945"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kong, C, Zhong, C, Matthaiou, M, Bj\u00f6rnson, E & Zhang, Z 2019, 'Spectral efficiency of multipair massive MIMO two-way relaying with imperfect CSI', IEEE Transactions on Vehicular Technology. https://doi.org/10.1109/TVT.2019.2915005","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7300000190734863,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1561785553","display_name":null,"funder_award_id":"61725104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7659387309","display_name":null,"funder_award_id":"LTSRF1718\\","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G8233345629","display_name":null,"funder_award_id":"LTSRF1718\\14\\2","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G8501632715","display_name":null,"funder_award_id":"U1709219","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G872349006","display_name":"\u65e0\u7ebf\u4f9b\u7535\u901a\u4fe1\u7cfb\u7edf\u7406\u8bba\u4e0e\u5173\u952e\u6280\u672f\u7814\u7a76","funder_award_id":"61671406","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320357","display_name":"Queen's University Belfast","ror":"https://ror.org/00hswnk62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321832","display_name":"Queen's University","ror":"https://ror.org/02y72wh86"},{"id":"https://openalex.org/F4320330485","display_name":"State Key Laboratory of Integrated Services Networks","ror":null},{"id":"https://openalex.org/F4320334064","display_name":"National Natural Science Foundation of China-Zhejiang Joint Fund for the Integration of Industrialization and Informatization","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2944780132.pdf","grobid_xml":"https://content.openalex.org/works/W2944780132.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1632601927","https://openalex.org/W1917415483","https://openalex.org/W1969648546","https://openalex.org/W1970904871","https://openalex.org/W1971443733","https://openalex.org/W1986468408","https://openalex.org/W1989151864","https://openalex.org/W1994185913","https://openalex.org/W2040566300","https://openalex.org/W2049483782","https://openalex.org/W2059245681","https://openalex.org/W2075509780","https://openalex.org/W2084304524","https://openalex.org/W2085768129","https://openalex.org/W2089375829","https://openalex.org/W2098567664","https://openalex.org/W2119523314","https://openalex.org/W2142699079","https://openalex.org/W2143365251","https://openalex.org/W2144295065","https://openalex.org/W2147601077","https://openalex.org/W2149912746","https://openalex.org/W2156960709","https://openalex.org/W2160466112","https://openalex.org/W2170431793","https://openalex.org/W2171048418","https://openalex.org/W2296319761","https://openalex.org/W2323227907","https://openalex.org/W2397897286","https://openalex.org/W2615605084","https://openalex.org/W2616323954","https://openalex.org/W2679131546","https://openalex.org/W2780578259","https://openalex.org/W2792717300","https://openalex.org/W2962798347","https://openalex.org/W2970034914","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W2766549347","https://openalex.org/W2381322962","https://openalex.org/W2802679222","https://openalex.org/W2090040424","https://openalex.org/W2872561304","https://openalex.org/W2735408343","https://openalex.org/W2104772677","https://openalex.org/W2783724799","https://openalex.org/W2971828277","https://openalex.org/W3111130483"],"abstract_inverted_index":{"We":[0,50],"consider":[1],"a":[2,17,52,64,94,103,155],"two-way":[3],"half-duplex":[4],"relaying":[5],"system":[6,61],"where":[7],"multiple":[8],"pairs":[9],"of":[10,26,38,74,106,112,143,162],"single-antenna":[11],"users":[12],"exchange":[13],"information":[14],"assisted":[15],"by":[16,101],"multiple-antenna":[18],"relay.":[19],"Taking":[20],"into":[21],"account":[22],"the":[23,32,39,44,56,68,72,86,109,113,159,163,171,175,187],"practical":[24],"constraint":[25],"imperfect":[27],"channel":[28],"knowledge,":[29],"we":[30,83],"study":[31,84],"achievable":[33],"sum":[34,57,69,176,188],"spectral":[35],"efficiency":[36],"(SE)":[37],"amplify-and-forward":[40],"protocol,":[41],"assuming":[42],"that":[43,100],"relay":[45,75,107],"employs":[46],"maximum":[47],"ratio":[48],"processing.":[49],"derive":[51],"closed-form":[53],"expression":[54],"for":[55,59,67,140,174],"SE":[58,70],"arbitrary":[60],"parameters":[62],"and":[63,116,135,146,165],"large-scale":[65],"approximation":[66],"when":[71],"number":[73,105],"antennas":[76],"M":[77,91],"becomes":[78],"sufficiently":[79],"large.":[80],"In":[81],"addition,":[82],"how":[85],"transmit":[87,110,160],"power":[88,151,179],"reduces":[89],"with":[90],"to":[92,124,184],"maintain":[93],"desired":[95],"SE.":[96,189],"Our":[97],"results":[98],"show":[99],"using":[102],"large":[104],"antennas,":[108],"powers":[111,161],"user,":[114],"relay,":[115],"pilot":[117,166],"symbol":[118],"can":[119],"be":[120],"scaled":[121],"down":[122],"proportionally":[123],"1/M":[125,130,136],"<sup":[126,131,137],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[127,132,138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b1</sup>":[128],",":[129,134],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b2</sup>":[133],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b3</sup>":[139],"certain":[141],"combinations":[142],"\u03b1,":[144],"\u03b2,":[145],"\u03b3,":[147],"respectively.":[148],"This":[149],"elegant":[150],"scaling":[152],"law":[153],"reveals":[154],"fundamental":[156],"tradeoff":[157],"between":[158],"user/relay":[164],"symbol.":[167],"Finally,":[168],"capitalizing":[169],"on":[170],"new":[172],"expressions":[173],"SE,":[177],"novel":[178],"allocation":[180],"schemes":[181],"are":[182],"designed":[183],"further":[185],"improve":[186]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}