{"id":"https://openalex.org/W2124201613","doi":"https://doi.org/10.1109/tsp.2011.2177830","title":"A Semi-Closed-Form Solution to Optimal Distributed Beamforming for Two-Way Relay Networks","display_name":"A Semi-Closed-Form Solution to Optimal Distributed Beamforming for Two-Way Relay Networks","publication_year":2011,"publication_date":"2011-12-03","ids":{"openalex":"https://openalex.org/W2124201613","doi":"https://doi.org/10.1109/tsp.2011.2177830","mag":"2124201613"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2177830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2177830","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/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":true,"raw_author_name":"Shahram Shahbazpanahi","raw_affiliation_strings":["Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, ON, Canada","Fac. of Eng. & Appl. Sci., Univ. of Ontario Inst. of Technol., Oshawa, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, ON, Canada","institution_ids":["https://openalex.org/I39470171"]},{"raw_affiliation_string":"Fac. of Eng. & Appl. Sci., Univ. of Ontario Inst. of Technol., Oshawa, ON, Canada","institution_ids":["https://openalex.org/I39470171"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035819120","display_name":"Min Dong","orcid":"https://orcid.org/0000-0002-7223-8865"},"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":"Min Dong","raw_affiliation_strings":["Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, ON, Canada","Fac. of Eng. & Appl. Sci., Univ. of Ontario Inst. of Technol., Oshawa, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, Oshawa, ON, Canada","institution_ids":["https://openalex.org/I39470171"]},{"raw_affiliation_string":"Fac. of Eng. & Appl. Sci., Univ. of Ontario Inst. of Technol., Oshawa, ON, Canada","institution_ids":["https://openalex.org/I39470171"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049043069"],"corresponding_institution_ids":["https://openalex.org/I39470171"],"apc_list":null,"apc_paid":null,"fwci":7.2872,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.97299512,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"60","issue":"3","first_page":"1511","last_page":"1516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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":1.0,"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":0.998199999332428,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9962000250816345,"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":0.9202522039413452},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.9126899242401123},{"id":"https://openalex.org/keywords/transceiver","display_name":"Transceiver","score":0.7545790672302246},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.6494765281677246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6260683536529541},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.516149640083313},{"id":"https://openalex.org/keywords/relay-channel","display_name":"Relay channel","score":0.4893054664134979},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.47433987259864807},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4431694746017456},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4401543438434601},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42649421095848083},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.39275139570236206},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36250144243240356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33166301250457764},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.22139015793800354},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.21590203046798706},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20665737986564636},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.16990360617637634},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06496894359588623}],"concepts":[{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.9202522039413452},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.9126899242401123},{"id":"https://openalex.org/C7720470","wikidata":"https://www.wikidata.org/wiki/Q954187","display_name":"Transceiver","level":3,"score":0.7545790672302246},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.6494765281677246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6260683536529541},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.516149640083313},{"id":"https://openalex.org/C46257984","wikidata":"https://www.wikidata.org/wiki/Q7310895","display_name":"Relay channel","level":4,"score":0.4893054664134979},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.47433987259864807},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4431694746017456},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4401543438434601},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42649421095848083},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.39275139570236206},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36250144243240356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33166301250457764},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.22139015793800354},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.21590203046798706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20665737986564636},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.16990360617637634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06496894359588623},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2011.2177830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2177830","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1629323560","https://openalex.org/W1967393606","https://openalex.org/W2012049708","https://openalex.org/W2096333425","https://openalex.org/W2097888543","https://openalex.org/W2101597841","https://openalex.org/W2119523314","https://openalex.org/W2127292376","https://openalex.org/W2131559343","https://openalex.org/W2145386092","https://openalex.org/W2149800807","https://openalex.org/W2149847268","https://openalex.org/W2158776959","https://openalex.org/W2169742169","https://openalex.org/W2171847598","https://openalex.org/W6641973308"],"related_works":["https://openalex.org/W2099376255","https://openalex.org/W2608897767","https://openalex.org/W2963768675","https://openalex.org/W2153829573","https://openalex.org/W2004047158","https://openalex.org/W2119153672","https://openalex.org/W2993015344","https://openalex.org/W1559320887","https://openalex.org/W2374704553","https://openalex.org/W2082611414"],"abstract_inverted_index":{"In":[0,22],"this":[1,100,147],"correspondence,":[2],"we":[3,149],"present":[4],"a":[5,24,40,45,114,161,194,205,227],"computationally":[6],"simple":[7,206],"semi-closed-form":[8,210],"solution":[9,192,211],"to":[10,33,50,80,105,128,189,193,226],"the":[11,26,53,58,67,70,76,84,93,106,109,119,123,129,132,136,140,152,170,174,177,191,215,218,232,238,242,254,258],"problem":[12,102],"of":[13,69,108,122,131,135,173,217,231,234,247,260],"designing":[14],"distributed":[15],"beamformer":[16],"for":[17,113],"two-way":[18,142],"(bi-directional)":[19],"multi-relay":[20],"networks.":[21],"such":[23],"network,":[25,78,181],"relay":[27,54,94,116,143,153,180],"nodes":[28],"use":[29],"amplify-and-forward":[30],"relaying":[31],"protocol":[32],"help":[34],"two":[35,85,137],"transceivers":[36,138],"exchange":[37],"information":[38],"in":[39,75,139,160,176],"bidirectional":[41],"manner.":[42],"We":[43,87],"consider":[44],"total":[46,71,110],"power":[47,112,172],"minimization":[48,68,101,107],"approach":[49,63],"optimally":[51],"find":[52],"beamforming":[55,95,154,220],"weights":[56],"and":[57,198],"transceiver":[59,125],"transmit":[60,72,111,171],"powers.":[61],"This":[62,184,236],"is":[64,98,103,126,182,187],"based":[65,244],"on":[66,146],"power,":[73],"consumed":[74],"whole":[77],"subject":[79],"SNR":[81,121],"constraints":[82],"at":[83],"transceivers.":[86],"show":[88,150],"that":[89,151,165],"as":[90,92],"far":[91],"weight":[96,155,221],"vector":[97,156],"concerned,":[99],"equivalent":[104,178],"one-way":[115,179],"network":[117],"where":[118,253],"target":[120,133],"receiving":[124],"equal":[127],"sum":[130],"SNRs":[134],"original":[141],"network.":[144],"Based":[145],"observation,":[148],"can":[157,201],"be":[158,190,202],"obtained":[159,203],"closed":[162],"from":[163],"given":[164],"an":[166],"intermediate":[167,185],"parameter,":[168],"namely":[169],"transmitter":[175],"available.":[183],"parameter":[186],"shown":[188],"one-dimensional":[195,228],"optimization":[196],"problem,":[197],"thus,":[199],"it":[200],"using":[204],"bisection":[207],"method.":[208],"Our":[209],"not":[212],"only":[213],"reveals":[214],"structure":[216],"optimal":[219],"vector,":[222],"but":[223],"also":[224],"leads":[225],"search":[229],"regardless":[230],"number":[233,259],"relays.":[235,261],"provides":[237],"computational":[239],"advantage":[240],"over":[241],"gradient":[243,255],"numerical":[245],"method":[246],"Havary-Nassab":[248],"<etal":[249],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[250],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"/>":[251],",":[252],"dimension":[256],"reflects":[257]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}