{"id":"https://openalex.org/W7124437204","doi":"https://doi.org/10.1109/tsp.2025.3648327","title":"On Stochastic Beamforming for Ergodic Sum-Rate Maximization in Cooperative Transmission Systems","display_name":"On Stochastic Beamforming for Ergodic Sum-Rate Maximization in Cooperative Transmission Systems","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7124437204","doi":"https://doi.org/10.1109/tsp.2025.3648327"},"language":null,"primary_location":{"id":"doi:10.1109/tsp.2025.3648327","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3648327","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":null,"display_name":"Xi Wang","orcid":"https://orcid.org/0009-0005-9897-2282"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xi Wang","raw_affiliation_strings":["School of Computer Science and Technology, Tongji University, Shanghai, China"],"raw_orcid":"https://orcid.org/0009-0005-9897-2282","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123196214","display_name":"Yang Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["School of Information and Communication Engineering, Dalian University of Technology, Dalian, China"],"raw_orcid":"https://orcid.org/0000-0002-1917-783X","affiliations":[{"raw_affiliation_string":"School of Information and Communication Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058559599","display_name":"Xiaotong Zhao","orcid":"https://orcid.org/0000-0003-4870-8588"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Xiaotong Zhao","raw_affiliation_strings":["Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong, SAR, China"],"raw_orcid":"https://orcid.org/0000-0003-4870-8588","affiliations":[{"raw_affiliation_string":"Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong, SAR, China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123207777","display_name":"Qingjiang Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingjiang Shi","raw_affiliation_strings":["School of Computer Science and Technology, Tongji University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-0507-9080","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ye Yang","orcid":"https://orcid.org/0000-0002-7661-0396"},"institutions":[{"id":"https://openalex.org/I4210159102","display_name":"Huawei Technologies (Sweden)","ror":"https://ror.org/0500fyd17","country_code":"SE","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210159102"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Ye Yang","raw_affiliation_strings":["Stockholm Research Center, Huawei Technologies Sweden AB, Solna, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-7661-0396","affiliations":[{"raw_affiliation_string":"Stockholm Research Center, Huawei Technologies Sweden AB, Solna, Sweden","institution_ids":["https://openalex.org/I4210159102"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05771702,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"74","issue":null,"first_page":"781","last_page":"797"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.871399998664856,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.871399998664856,"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":0.06880000233650208,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.012799999676644802,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/ergodic-theory","display_name":"Ergodic theory","score":0.6834999918937683},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5577999949455261},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.5291000008583069},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5127000212669373},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.4555000066757202},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.44369998574256897},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.40070000290870667},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.3727000057697296}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6834999918937683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6158000230789185},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5577999949455261},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5199000239372253},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5127000212669373},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49219998717308044},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.44369998574256897},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.40070000290870667},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.3727000057697296},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.3643999993801117},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3287999927997589},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.31619998812675476},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.273499995470047},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2025.3648327","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3648327","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":[{"id":"https://openalex.org/G3990962312","display_name":null,"funder_award_id":"62231019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5047231983","display_name":null,"funder_award_id":"U25A20394","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W595252221","https://openalex.org/W615589970","https://openalex.org/W1491719355","https://openalex.org/W1577245107","https://openalex.org/W1970830346","https://openalex.org/W1976817824","https://openalex.org/W1997834106","https://openalex.org/W2015301486","https://openalex.org/W2022939180","https://openalex.org/W2050968963","https://openalex.org/W2060695112","https://openalex.org/W2086323639","https://openalex.org/W2093903644","https://openalex.org/W2096171043","https://openalex.org/W2106553657","https://openalex.org/W2116133516","https://openalex.org/W2118640817","https://openalex.org/W2119163179","https://openalex.org/W2121390976","https://openalex.org/W2144497295","https://openalex.org/W2155174176","https://openalex.org/W2163762663","https://openalex.org/W2164497732","https://openalex.org/W2175446003","https://openalex.org/W2293606211","https://openalex.org/W2395300968","https://openalex.org/W2508393166","https://openalex.org/W2585273943","https://openalex.org/W2612881001","https://openalex.org/W2784709112","https://openalex.org/W2895677730","https://openalex.org/W2916737933","https://openalex.org/W2962882009","https://openalex.org/W2962980630","https://openalex.org/W2963328334","https://openalex.org/W2963796235","https://openalex.org/W2963812263","https://openalex.org/W3030700743","https://openalex.org/W3133299745","https://openalex.org/W3171989079","https://openalex.org/W3187807001","https://openalex.org/W3195410378","https://openalex.org/W4226006816","https://openalex.org/W4226113210","https://openalex.org/W4252698487","https://openalex.org/W4312392183","https://openalex.org/W4386869656","https://openalex.org/W4390496060","https://openalex.org/W4391877812","https://openalex.org/W4394744084","https://openalex.org/W4414221763"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,27],"paper,":[2],"we":[3,49,113],"investigate":[4],"stochastic":[5,43,53],"beamforming":[6],"approaches":[7],"to":[8,85,158],"maximize":[9],"the":[10,31,42,59,79,99,103,123,135,145,148,169,178,189],"ergodic":[11],"sum-rate":[12],"(ESR)":[13],"for":[14,137,185,196],"cooperative":[15],"transmission":[16],"systems,":[17],"including":[18],"both":[19],"coherent":[20,23],"and":[21,40,82,125,133,171,194],"non":[22],"joint":[24],"transmission.":[25],"To":[26],"end,":[28],"by":[29,97],"utilizing":[30],"seminal":[32],"weighted":[33],"minimum":[34],"mean":[35],"square":[36],"error":[37],"(WMMSE)":[38],"transform":[39],"adopting":[41],"successive":[44],"upper-bound":[45],"minimization":[46],"(SSUM)":[47],"framework,":[48],"first":[50],"propose":[51],"a":[52,116],"WMMSE":[54],"(SWMMSE)":[55],"algorithm":[56,71,154,180,191],"that":[57],"maximizes":[58],"network\u2019s":[60],"ESR":[61],"via":[62],"analytically":[63],"updating":[64],"beamformers":[65],"in":[66,147],"an":[67],"online":[68],"manner.":[69],"This":[70,119],"can":[72,155],"operate":[73],"without":[74],"any":[75],"prior":[76],"knowledge":[77],"on":[78,95],"channel":[80,88,129,161],"statistics":[81,127],"is":[83,181,192],"applicable":[84],"very":[86],"generic":[87,160],"models":[89,162],"with":[90,102],"arbitrary":[91],"probability":[92],"distributions.":[93],"Based":[94],"that,":[96],"substituting":[98],"SWMMSE":[100,179],"update":[101],"determinant":[104],"equivalents":[105],"(DEs)":[106],"derived":[107],"from":[108],"large-dimensional":[109],"random":[110],"matrix":[111],"theory,":[112],"further":[114],"develop":[115],"DE-WMMSE":[117,153,190],"algorithm.":[118],"method":[120],"requires":[121],"only":[122],"first-":[124],"second-order":[126],"of":[128,173],"state":[130],"information":[131],"(CSI)":[132],"obviates":[134],"need":[136],"sampling":[138],"channel.":[139],"As":[140],"will":[141],"be":[142,156],"proved,":[143],"unlike":[144],"restrictions":[146],"existing":[149],"literature,":[150],"our":[151,174],"proposed":[152,175],"applied":[157],"rather":[159],"beyond":[163],"Rayleigh.":[164],"Extensive":[165],"numerical":[166],"results":[167],"verify":[168],"effectiveness":[170],"benefit":[172],"algorithms.":[176],"Especially,":[177],"highly":[182],"computationally":[183],"efficient":[184],"large-scale":[186],"networks,":[187],"while":[188],"fast":[193],"convenient":[195],"modest-scale":[197],"networks.":[198]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-01-17T00:00:00"}