{"id":"https://openalex.org/W4409762950","doi":"https://doi.org/10.1109/tsp.2025.3564126","title":"QoS-Based Beamforming and Compression Design for Cooperative Cellular Networks via Lagrangian Duality","display_name":"QoS-Based Beamforming and Compression Design for Cooperative Cellular Networks via Lagrangian Duality","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409762950","doi":"https://doi.org/10.1109/tsp.2025.3564126"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2025.3564126","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3564126","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/A5071100627","display_name":"Xilai Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xilai Fan","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0007-8396-7020","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020753840","display_name":"Ya\u2010Feng Liu","orcid":"https://orcid.org/0000-0002-9684-9150"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ya-Feng Liu","raw_affiliation_strings":["Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing, China","State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-9684-9150","affiliations":[{"raw_affiliation_string":"Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]},{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Liang Liu","orcid":"https://orcid.org/0000-0002-6509-9609"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liang Liu","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China","Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China"],"raw_orcid":"https://orcid.org/0000-0002-6509-9609","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064271996","display_name":"Tsung\u2010Hui Chang","orcid":"https://orcid.org/0000-0003-1349-2764"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tsung-Hui Chang","raw_affiliation_strings":["School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen, China","School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0003-1349-2764","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6534,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63862185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"73","issue":null,"first_page":"2070","last_page":"2086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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/T10069","display_name":"Antenna Design and Analysis","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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":0.9973999857902527,"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/beamforming","display_name":"Beamforming","score":0.5965169072151184},{"id":"https://openalex.org/keywords/quality-of-service","display_name":"Quality of service","score":0.5295974612236023},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5238333344459534},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5145087242126465},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.49707749485969543},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4581344425678253},{"id":"https://openalex.org/keywords/compression","display_name":"Compression (physics)","score":0.43643274903297424},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.41249918937683105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3197535276412964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.23525264859199524},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.22461387515068054},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.22016212344169617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1815546452999115},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1320900022983551}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.5965169072151184},{"id":"https://openalex.org/C5119721","wikidata":"https://www.wikidata.org/wiki/Q220501","display_name":"Quality of service","level":2,"score":0.5295974612236023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5238333344459534},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5145087242126465},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.49707749485969543},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4581344425678253},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.43643274903297424},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.41249918937683105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3197535276412964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.23525264859199524},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.22461387515068054},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.22016212344169617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1815546452999115},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1320900022983551},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2025.3564126","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2025.3564126","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/G3553588891","display_name":null,"funder_award_id":"12021001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8515280332","display_name":null,"funder_award_id":"12371314","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W1470390566","https://openalex.org/W1542938076","https://openalex.org/W1919846929","https://openalex.org/W1928152501","https://openalex.org/W1978842364","https://openalex.org/W1996215314","https://openalex.org/W2003581350","https://openalex.org/W2004101329","https://openalex.org/W2019905317","https://openalex.org/W2050815608","https://openalex.org/W2076988592","https://openalex.org/W2083739017","https://openalex.org/W2099003693","https://openalex.org/W2101029251","https://openalex.org/W2101727634","https://openalex.org/W2103749601","https://openalex.org/W2109005286","https://openalex.org/W2110323470","https://openalex.org/W2121233130","https://openalex.org/W2122337065","https://openalex.org/W2123531758","https://openalex.org/W2131350052","https://openalex.org/W2144778327","https://openalex.org/W2145977952","https://openalex.org/W2156949195","https://openalex.org/W2161410889","https://openalex.org/W2161473225","https://openalex.org/W2162636480","https://openalex.org/W2164271287","https://openalex.org/W2167249094","https://openalex.org/W2286275639","https://openalex.org/W2338770003","https://openalex.org/W2431771009","https://openalex.org/W2489815411","https://openalex.org/W2508393166","https://openalex.org/W2518981030","https://openalex.org/W2607982032","https://openalex.org/W2788350651","https://openalex.org/W2916737933","https://openalex.org/W2922110652","https://openalex.org/W2925232796","https://openalex.org/W2962750265","https://openalex.org/W2962899344","https://openalex.org/W2963694619","https://openalex.org/W2965123227","https://openalex.org/W3000471502","https://openalex.org/W3158832185","https://openalex.org/W3188358066","https://openalex.org/W3194645875","https://openalex.org/W3206890201","https://openalex.org/W3209298344","https://openalex.org/W4205204500","https://openalex.org/W4210260972","https://openalex.org/W4226208746","https://openalex.org/W4250589301","https://openalex.org/W4280558628","https://openalex.org/W4290996296","https://openalex.org/W4296079431","https://openalex.org/W4300840296","https://openalex.org/W4312922447","https://openalex.org/W4387587696","https://openalex.org/W4392903944","https://openalex.org/W4401567372","https://openalex.org/W4402979687"],"related_works":["https://openalex.org/W2002102264","https://openalex.org/W4237964977","https://openalex.org/W2155100848","https://openalex.org/W2075228635","https://openalex.org/W3097196196","https://openalex.org/W3183857959","https://openalex.org/W2195430740","https://openalex.org/W3149469165","https://openalex.org/W4313484281","https://openalex.org/W2616198151"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,13,26,37,46,49,54,83,94,109,115,123,133,138,142,155,166,191,196,206,216,222],"quality-of-service":[4],"(QoS)-based":[5],"joint":[6,85],"beamforming":[7],"and":[8,64,88,136,173,202,219],"compression":[9],"design":[10],"problem":[11,40,87,135,168],"in":[12,195,205],"downlink":[14],"cooperative":[15],"cellular":[16],"network,":[17],"where":[18],"multiple":[19],"relay-like":[20],"base":[21],"stations":[22],"(BSs),":[23],"connected":[24],"to":[25,36,57,163],"central":[27],"processor":[28],"via":[29,146],"ratelimited":[30],"fronthaul":[31,67],"links,":[32],"cooperatively":[33],"transmit":[34,51],"messages":[35],"users.":[38],"The":[39,118],"of":[41,48,53,96,126,132,154,190,221],"interest":[42],"is":[43,78,161,169,181,185],"formulated":[44],"as":[45],"minimization":[47],"total":[50],"power":[52],"BSs,":[55],"subject":[56],"all":[58,65],"users\u2019":[59],"signal-to-interference-plus-noise":[60],"ratio":[61],"(SINR)":[62],"constraints":[63],"BSs\u2019":[66],"rate":[68],"constraints.":[69],"In":[70],"this":[71],"paper,":[72],"we":[73,102],"first":[74],"show":[75,215],"that":[76,140],"there":[77],"no":[79],"duality":[80,111],"gap":[81],"between":[82],"considered":[84,116,134,167],"optimization":[86],"its":[89,97,175],"Lagrangian":[90],"dual":[91],"by":[92],"showing":[93],"tightness":[95],"semidefinite":[98],"relaxation":[99],"(SDR).":[100],"Then,":[101],"propose":[103],"an":[104,127],"efficient":[105,187],"algorithm":[106,120,157,198],"based":[107],"on":[108],"above":[110],"result":[112],"for":[113],"solving":[114],"problem.":[117],"proposed":[119,156,197,223],"judiciously":[121],"exploits":[122],"special":[124],"structure":[125],"enhanced":[128,143],"Karush-Kuhn-Tucker":[129],"(KKT)":[130],"conditions":[131,145],"approaches":[137],"solution":[139,178],"satisfies":[141],"KKT":[144],"two":[147],"fixed":[148,192,207],"point":[149,193,208],"iterations.":[150],"Two":[151],"key":[152],"features":[153],"are:":[158],"(1)":[159],"it":[160,180,184],"able":[162],"detect":[164],"whether":[165],"feasible":[170],"or":[171],"not":[172],"find":[174],"globally":[176],"optimal":[177],"when":[179],"feasible;":[182],"(2)":[183],"highly":[186],"because":[188],"both":[189],"iterations":[194,209],"are":[199,210],"linearly":[200],"convergent":[201],"function":[203],"evaluations":[204],"computationally":[211],"cheap.":[212],"Numerical":[213],"results":[214],"global":[217],"optimality":[218],"efficiency":[220],"algorithm.":[224]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
