{"id":"https://openalex.org/W2151538365","doi":"https://doi.org/10.1109/glocom.2009.5426306","title":"On the Rate Duality of MIMO Interference Channel and Its Application to Sum Rate Maximization","display_name":"On the Rate Duality of MIMO Interference Channel and Its Application to Sum Rate Maximization","publication_year":2009,"publication_date":"2009-11-01","ids":{"openalex":"https://openalex.org/W2151538365","doi":"https://doi.org/10.1109/glocom.2009.5426306","mag":"2151538365"},"language":"en","primary_location":{"id":"doi:10.1109/glocom.2009.5426306","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2009.5426306","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference","raw_type":"proceedings-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/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":"An Liu","raw_affiliation_strings":["State Key Laboratory of Advanced Optical Communication Systems & Networks, School of EECS, Peking University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems & 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 and Computer Engineering, University of Colorado Boulder, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Colorado 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/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":"Haige Xiang","raw_affiliation_strings":["State Key Laboratory of Advanced Optical Communication Systems & Networks, School of EECS, Peking University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems & Networks, School of EECS, Peking University, China","institution_ids":["https://openalex.org/I20231570"]}]},{"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 & Networks, School of EECS, Peking University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Advanced Optical Communication Systems & Networks, School of EECS, Peking University, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6005,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73429249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9994000196456909,"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/T10069","display_name":"Antenna Design and Analysis","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.6523532271385193},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.6274009346961975},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.6230219006538391},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5882704257965088},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5351707935333252},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5265054106712341},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5238007307052612},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.47844958305358887},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4369460344314575},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.43616700172424316},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.422727108001709},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41290000081062317},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3802882134914398},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3740394711494446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3555065393447876},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.22614192962646484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.0829857885837555},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0791437029838562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07086798548698425}],"concepts":[{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.6523532271385193},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.6274009346961975},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.6230219006538391},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5882704257965088},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5351707935333252},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5265054106712341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5238007307052612},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.47844958305358887},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4369460344314575},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.43616700172424316},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.422727108001709},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41290000081062317},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3802882134914398},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3740394711494446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3555065393447876},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.22614192962646484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0829857885837555},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0791437029838562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07086798548698425},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/glocom.2009.5426306","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2009.5426306","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.3220","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.3220","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_Globecom09_Duality_Interference.pdf","raw_type":"text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-67437","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-67437","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":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1537514565","https://openalex.org/W1979408141","https://openalex.org/W2099111195","https://openalex.org/W2108687047","https://openalex.org/W2112820013","https://openalex.org/W2112996088","https://openalex.org/W2127886694","https://openalex.org/W2130509920","https://openalex.org/W2136717506","https://openalex.org/W2142134616","https://openalex.org/W2151505406","https://openalex.org/W2161410889","https://openalex.org/W2161473225","https://openalex.org/W2167249094","https://openalex.org/W2167357515","https://openalex.org/W2555143980","https://openalex.org/W3100696645"],"related_works":["https://openalex.org/W2545343974","https://openalex.org/W4291895924","https://openalex.org/W1783583321","https://openalex.org/W2038397443","https://openalex.org/W2807251790","https://openalex.org/W2941374357","https://openalex.org/W2026727497","https://openalex.org/W4388520214","https://openalex.org/W2164866798","https://openalex.org/W1976502299"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,59],"establish":[4],"a":[5,114],"rate":[6,71,125],"duality":[7,115],"between":[8,99],"the":[9,19,26,33,37,45,50,62,68,87,97,100,104,108,123,137],"forward":[10,34,46,63],"and":[11,30,36,64,103],"reverse":[12,20,65],"links":[13,21,66],"of":[14,28,44,86,126],"MIMO":[15,127],"interference":[16,55,75,128],"channel,":[17],"where":[18],"are":[22,41,146],"obtained":[23],"by":[24,73,151],"exchanging":[25],"roles":[27],"transmitters":[29],"receivers":[31],"in":[32,107],"links,":[35],"corresponding":[38,88],"channel":[39,47,56,129],"matrices":[40],"conjugate":[42],"transpose":[43],"matrices.":[48],"Since":[49],"capacity":[51],"region":[52,72],"for":[53],"general":[54],"is":[57,93,119],"unknown,":[58],"show":[60],"that":[61],"have":[67],"same":[69],"achievable":[70],"treating":[74],"as":[76],"noise":[77],"under":[78,130],"some":[79],"sum":[80,124,131],"power":[81,132,141],"constraint.":[82,133,142],"The":[83,143],"explicit":[84],"expression":[85],"input":[89],"covariance":[90],"matrix":[91],"transformation":[92,102],"provided.":[94],"We":[95,134],"discuss":[96],"connection":[98],"proposed":[101,120,144],"MAC-BC":[105],"transformations":[106],"previous":[109],"works.":[110],"As":[111],"an":[112],"application,":[113],"based":[116],"iterative":[117],"algorithm":[118,138],"to":[121,139,148],"maximize":[122],"also":[135],"extend":[136],"individual":[140],"algorithms":[145],"shown":[147],"be":[149],"effective":[150],"simulation.":[152]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}