{"id":"https://openalex.org/W2075870768","doi":"https://doi.org/10.1109/tsp.2011.2173334","title":"Polite Water-Filling for Weighted Sum-Rate Maximization in MIMO B-MAC Networks Under Multiple Linear Constraints","display_name":"Polite Water-Filling for Weighted Sum-Rate Maximization in MIMO B-MAC Networks Under Multiple Linear Constraints","publication_year":2011,"publication_date":"2011-10-25","ids":{"openalex":"https://openalex.org/W2075870768","doi":"https://doi.org/10.1109/tsp.2011.2173334","mag":"2075870768"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2173334","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2173334","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/A5100340369","display_name":"An Liu","orcid":"https://orcid.org/0000-0002-3943-5234"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"An Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China","State Key Laboratory of Advanced Optical Communication Systems and Networks, School of EECS, Peking University, China","State Key Laboratory of Advanced Optical Communication Systems and Networks, School of EECS Peking University China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems and Networks, School of EECS, Peking University, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems and Networks, School of EECS Peking University China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084454849","display_name":"Youjian Liu","orcid":"https://orcid.org/0000-0003-4681-0546"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Youjian Liu","raw_affiliation_strings":["Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, Boulder, USA","Dept. of Electrical and Computer Engineering, University of Colorado at Boulder, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, Boulder, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, University of Colorado at Boulder, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101824600","display_name":"Haige Xiang","orcid":"https://orcid.org/0000-0001-7620-5326"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Haige Xiang","raw_affiliation_strings":["State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electrical Engineering and Computer Science, Peking University, Beijing, China","Department of Electronic and Computer Eng., Hong Kong Univ. of Science and Technology, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electrical Engineering and Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"Department of Electronic and Computer Eng., Hong Kong Univ. of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108200040","display_name":"Wu Luo","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wu Luo","raw_affiliation_strings":["State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electrical Engineering and Computer Science, Peking University, Beijing, China","State Key Laboratory of Advanced Optical Communication Systems and Networks, School of EECS Peking University China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electrical Engineering and Computer Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems and Networks, School of EECS Peking University China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9733,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.91557617,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"60","issue":"2","first_page":"834","last_page":"847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"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":1.0,"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/T11392","display_name":"Energy Harvesting in Wireless Networks","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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9995999932289124,"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/mimo","display_name":"MIMO","score":0.7690783739089966},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5826396942138672},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5751324892044067},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5739531517028809},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.5739085674285889},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5535712838172913},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4854443669319153},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.46622326970100403},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.4336867928504944},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.4314134120941162},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.42941394448280334},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4111140966415405},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.29073774814605713},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.20471647381782532}],"concepts":[{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.7690783739089966},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5826396942138672},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5751324892044067},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5739531517028809},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.5739085674285889},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5535712838172913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4854443669319153},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.46622326970100403},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.4336867928504944},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.4314134120941162},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.42941394448280334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4111140966415405},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.29073774814605713},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.20471647381782532},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2011.2173334","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2173334","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.2524","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.2524","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ecee.colorado.edu/~liue/publications/papers/Liu_11ISIT_WSR_iTree_MLC.pdf","raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-52708","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-52708","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Clean water and sanitation","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/6"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1583497301","https://openalex.org/W1822442307","https://openalex.org/W1974891392","https://openalex.org/W1976109068","https://openalex.org/W1979408141","https://openalex.org/W2034771294","https://openalex.org/W2037869274","https://openalex.org/W2039388525","https://openalex.org/W2100928329","https://openalex.org/W2101727634","https://openalex.org/W2112151127","https://openalex.org/W2124409123","https://openalex.org/W2127886694","https://openalex.org/W2129562390","https://openalex.org/W2130509920","https://openalex.org/W2136608712","https://openalex.org/W2143046241","https://openalex.org/W2150726040","https://openalex.org/W2163844889","https://openalex.org/W2167249094","https://openalex.org/W2167357515","https://openalex.org/W2168448439","https://openalex.org/W2296319761","https://openalex.org/W2798766386","https://openalex.org/W3111166378","https://openalex.org/W3142581169","https://openalex.org/W4210923851","https://openalex.org/W4250589301","https://openalex.org/W6638772164","https://openalex.org/W6660442709","https://openalex.org/W6675356473"],"related_works":["https://openalex.org/W59120657","https://openalex.org/W3091795725","https://openalex.org/W1531121096","https://openalex.org/W2384509413","https://openalex.org/W3193940080","https://openalex.org/W2325128397","https://openalex.org/W2995861515","https://openalex.org/W2512536427","https://openalex.org/W2121601714","https://openalex.org/W2139615693"],"abstract_inverted_index":{"Optimization":[0],"under":[1],"multiple":[2,131],"linear":[3,128,132],"constraints":[4,19,133],"is":[5,42,48,70],"important":[6],"for":[7,25,51,74,86,157,164],"practical":[8,110],"systems":[9],"with":[10],"individual":[11],"power":[12,15],"constraints,":[13,16],"per-antenna":[14],"and/or":[17],"interference":[18,64,95,104],"as":[20,113,139],"in":[21],"cognitive":[22],"radios.":[23],"While":[24],"single-user":[26],"multiple-input":[27],"multiple-output":[28],"(MIMO)":[29],"channel":[30],"transmitter":[31],"optimization,":[32],"no":[33],"one":[34],"uses":[35],"general":[36,93],"purpose":[37],"convex":[38,158],"programming":[39],"because":[40,66],"water-filling":[41,69,123],"optimal":[43,73,155,162],"and":[44,59,108,134,149,160,172],"much":[45],"simpler,":[46],"it":[47],"not":[49],"true":[50],"MIMO":[52,94],"multiaccess":[53],"channels":[54,57],"(MAC),":[55],"broadcast":[56],"(BC),":[58],"the":[60,67,79,92,121,179],"nonconvex":[61,165],"optimization":[62],"of":[63,82,91,174],"networks":[65,112],"traditional":[68],"far":[71],"from":[72,125],"networks.":[75],"We":[76],"recently":[77],"found":[78],"right":[80],"form":[81],"water-filling,":[83,85],"polite":[84,122],"capacity":[87],"or":[88],"achievable":[89],"regions":[90],"networks,":[96,99,107],"named":[97],"B-MAC":[98],"which":[100,153],"include":[101],"BC,":[102],"MAC,":[103],"channels,":[105],"X":[106],"most":[109],"wireless":[111],"special":[114],"cases.":[115,166],"In":[116],"this":[117],"paper,":[118],"we":[119],"extend":[120],"results":[124],"a":[126],"single":[127],"constraint":[129],"to":[130,142,145],"use":[135],"weighted":[136],"sum-rate":[137],"maximization":[138],"an":[140],"example":[141],"show":[143],"how":[144],"design":[146],"high":[147],"efficiency":[148],"low":[150],"complexity":[151],"algorithms,":[152],"find":[154],"solution":[156,163],"cases":[159],"locally":[161],"Several":[167],"times":[168],"faster":[169],"convergence":[170],"speed":[171],"orders":[173],"magnitude":[175],"higher":[176],"accuracy":[177],"than":[178],"state-of-the-art":[180],"are":[181],"demonstrated":[182],"by":[183],"numerical":[184],"examples.":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
