{"id":"https://openalex.org/W3013288433","doi":"https://doi.org/10.1109/tsipn.2020.2981990","title":"Proof of the Equivalency of MSE-Constrained and Rate-Constrained Power Optimization Approaches to Distributed Bi-Directional Beamforming","display_name":"Proof of the Equivalency of MSE-Constrained and Rate-Constrained Power Optimization Approaches to Distributed Bi-Directional Beamforming","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3013288433","doi":"https://doi.org/10.1109/tsipn.2020.2981990","mag":"3013288433"},"language":"en","primary_location":{"id":"doi:10.1109/tsipn.2020.2981990","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsipn.2020.2981990","pdf_url":"https://ieeexplore.ieee.org/ielx7/6884276/8949869/09048131.pdf","source":{"id":"https://openalex.org/S4306422866","display_name":"IEEE Transactions on Signal and Information Processing over Networks","issn_l":"2373-776X","issn":["2373-776X","2373-7778"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal and Information Processing over Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/6884276/8949869/09048131.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087204899","display_name":"Razgar Rahimi","orcid":"https://orcid.org/0000-0001-8574-7063"},"institutions":[{"id":"https://openalex.org/I39470171","display_name":"University of Ontario Institute of Technology","ror":"https://ror.org/016zre027","country_code":"CA","type":"education","lineage":["https://openalex.org/I39470171"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Razgar Rahimi","raw_affiliation_strings":["Department of Electrical, Software, and Computer Engineering, University of Ontario Institute of Technology, Oshawa, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Electrical, Software, and Computer Engineering, University of Ontario Institute of Technology, Oshawa, Canada","institution_ids":["https://openalex.org/I39470171"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049043069","display_name":"Shahram Shahbazpanahi","orcid":"https://orcid.org/0000-0001-8914-5481"},"institutions":[{"id":"https://openalex.org/I39470171","display_name":"University of Ontario Institute of Technology","ror":"https://ror.org/016zre027","country_code":"CA","type":"education","lineage":["https://openalex.org/I39470171"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shahram ShahbazPanahi","raw_affiliation_strings":["Department of Electrical, Software, and Computer Engineering, University of Ontario Institute of Technology, Oshawa, Canada","SnT Centre, Luxembourg City, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Department of Electrical, Software, and Computer Engineering, University of Ontario Institute of Technology, Oshawa, Canada","institution_ids":["https://openalex.org/I39470171"]},{"raw_affiliation_string":"SnT Centre, Luxembourg City, Luxembourg","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080037825","display_name":"Bj\u00f6rn Ottersten","orcid":"https://orcid.org/0000-0003-2298-6774"},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]}],"countries":["LU"],"is_corresponding":false,"raw_author_name":"Bjorn Ottersten","raw_affiliation_strings":["Reliability and Trust (SnT), Interdisciplinary Centre for Security, University of Luxembourg, Luxembourg City, Luxembourg"],"affiliations":[{"raw_affiliation_string":"Reliability and Trust (SnT), Interdisciplinary Centre for Security, University of Luxembourg, Luxembourg City, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087204899"],"corresponding_institution_ids":["https://openalex.org/I39470171"],"apc_list":null,"apc_paid":null,"fwci":0.1612,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50894076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"6","issue":null,"first_page":"460","last_page":"478"},"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/T10148","display_name":"Advanced MIMO Systems Optimization","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/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9990000128746033,"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/transceiver","display_name":"Transceiver","score":0.7464015483856201},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.7030662894248962},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.6307904124259949},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.619581401348114},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5265942811965942},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.46317416429519653},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4627535343170166},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4254944920539856},{"id":"https://openalex.org/keywords/multipath-propagation","display_name":"Multipath propagation","score":0.4237714409828186},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.41694897413253784},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4021589159965515},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.25936153531074524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2231871783733368},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.13401880860328674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11022308468818665}],"concepts":[{"id":"https://openalex.org/C7720470","wikidata":"https://www.wikidata.org/wiki/Q954187","display_name":"Transceiver","level":3,"score":0.7464015483856201},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.7030662894248962},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.6307904124259949},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.619581401348114},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5265942811965942},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.46317416429519653},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4627535343170166},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4254944920539856},{"id":"https://openalex.org/C161218011","wikidata":"https://www.wikidata.org/wiki/Q11827794","display_name":"Multipath propagation","level":3,"score":0.4237714409828186},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.41694897413253784},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4021589159965515},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.25936153531074524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2231871783733368},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.13401880860328674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11022308468818665},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsipn.2020.2981990","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsipn.2020.2981990","pdf_url":"https://ieeexplore.ieee.org/ielx7/6884276/8949869/09048131.pdf","source":{"id":"https://openalex.org/S4306422866","display_name":"IEEE Transactions on Signal and Information Processing over Networks","issn_l":"2373-776X","issn":["2373-776X","2373-7778"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal and Information Processing over Networks","raw_type":"journal-article"},{"id":"pmh:oai:orbilu.uni.lu:10993/44252","is_oa":true,"landing_page_url":"https://orbilu.uni.lu/handle/10993/44252","pdf_url":null,"source":{"id":"https://openalex.org/S4306401815","display_name":"Open Repository and Bibliography (University of Luxembourg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I186903577","host_organization_name":"University of Luxembourg","host_organization_lineage":["https://openalex.org/I186903577"],"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":"IEEE Transactions on Signal and Information Processing over Networks, 6 (2020-03-26)","raw_type":"peer reviewed"}],"best_oa_location":{"id":"doi:10.1109/tsipn.2020.2981990","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsipn.2020.2981990","pdf_url":"https://ieeexplore.ieee.org/ielx7/6884276/8949869/09048131.pdf","source":{"id":"https://openalex.org/S4306422866","display_name":"IEEE Transactions on Signal and Information Processing over Networks","issn_l":"2373-776X","issn":["2373-776X","2373-7778"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal and Information Processing over Networks","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8284766523","display_name":null,"funder_award_id":"(NSERC)","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3013288433.pdf","grobid_xml":"https://content.openalex.org/works/W3013288433.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1979596673","https://openalex.org/W1982754822","https://openalex.org/W1994585180","https://openalex.org/W2005089581","https://openalex.org/W2015157017","https://openalex.org/W2048057186","https://openalex.org/W2049532134","https://openalex.org/W2051762234","https://openalex.org/W2057026167","https://openalex.org/W2061008968","https://openalex.org/W2079350152","https://openalex.org/W2097888543","https://openalex.org/W2100211118","https://openalex.org/W2110092159","https://openalex.org/W2129477191","https://openalex.org/W2158058646","https://openalex.org/W2158155408","https://openalex.org/W2165383266","https://openalex.org/W2169729505","https://openalex.org/W2343690297","https://openalex.org/W2600366014","https://openalex.org/W2621310776","https://openalex.org/W2804753977","https://openalex.org/W2903118498","https://openalex.org/W2907860850","https://openalex.org/W2920292360","https://openalex.org/W2942477735"],"related_works":["https://openalex.org/W4249165909","https://openalex.org/W2783437851","https://openalex.org/W1672137312","https://openalex.org/W2539674285","https://openalex.org/W1998322187","https://openalex.org/W1038122923","https://openalex.org/W2952514781","https://openalex.org/W3019210376","https://openalex.org/W1650483958","https://openalex.org/W2391145594"],"abstract_inverted_index":{"Considered":[0],"in":[1,30,73,138,172,176,219,227],"this":[2,66,81,133,143,160,173,180,184],"article":[3,181],"is":[4,28,89,120],"an":[5,192],"<italic":[6],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">asynchronous</i>":[8],"single-carrier":[9],"two-way":[10],"relay":[11],"network,":[12,80],"where":[13],"two":[14,41,84,107,128,157,238],"transceivers":[15,42,108],"aim":[16],"to":[17,188,205],"communicate":[18],"through":[19,47],"a":[20,58,79,110,199],"set":[21],"of":[22,39,93,96,101,126,132,150,153,236,246,262],"amplify-and-forward":[23],"(AF)":[24],"relays.":[25],"This":[26],"network":[27,248,264],"asynchronous":[29],"the":[31,34,40,44,74,90,94,97,102,106,123,127,139,148,156,165,169,177,216,220,224,228,242,247,253,258,263,269],"sense":[32],"that":[33,141,191,241],"signal":[35],"transmitted":[36],"by":[37],"any":[38],"arrives":[43],"other":[45],"transceiver":[46,207],"different":[48,53],"relaying":[49],"paths,":[50],"with":[51],"possibly":[52],"propagation":[54],"delays,":[55],"thereby":[56],"materializing":[57],"multipath":[59],"channel.":[60],"At":[61],"sufficiently":[62],"high":[63],"data":[64],"rates,":[65],"multi-path":[67],"end-to-end":[68],"channel":[69],"causes":[70],"inter-symbol-interference":[71],"(ISI)":[72],"received":[75],"signals.":[76],"Considering":[77],"such":[78],"paper":[82],"presents":[83],"contributions.":[85],"The":[86,130,234],"first":[87],"contribution":[88,171],"rigorous":[91],"characterization":[92,136,147,163,187],"region":[95,135,144,149,162,186],"mean-squared":[98],"errors":[99],"(MSEs)":[100],"symbol":[103],"estimates":[104],"at":[105,122,155],"under":[109],"total":[111,194,201,271],"power":[112,195,202,208,272],"budget,":[113],"and":[114,198,210,223,256],"when":[115],"linear":[116],"block":[117],"post-channel":[118],"equalization":[119],"used":[121],"receiver":[124],"front-end":[125],"transceivers.":[129,158],"importance":[131],"MSE":[134,161,185,217,244],"resides":[137],"fact":[140],"knowing":[142],"allows":[145],"for":[146],"un-coded":[151,243],"probabilities":[152],"error":[154],"Also,":[159],"paves":[164],"way":[166],"towards":[167],"presenting":[168],"second":[170,178],"paper.":[174],"Indeed,":[175],"contribution,":[179],"relies":[182],"on":[183],"rigorously":[189],"prove":[190],"MSE-constrained":[193,270],"minimization":[196,203,273],"approach":[197,204,222,230],"rate-constrained":[200,254],"design":[206],"allocation":[209],"distributed":[211],"beamforming":[212],"are":[213,231],"equivalent,":[214],"if":[215],"thresholds":[218,226],"former":[221],"rate":[225,260],"latter":[229],"properly":[232],"chosen.":[233],"equivalence":[235],"these":[237],"approaches":[239],"implies":[240],"performance":[245,261],"can":[249,265],"be":[250,266],"inferred":[251,267],"from":[252,268],"problem,":[255],"conversely,":[257],"coded":[259],"problem.":[274]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}