{"id":"https://openalex.org/W2217718762","doi":"https://doi.org/10.1109/tit.2014.2308988","title":"Subspace Alignment Chains and the Degrees of Freedom of the Three-User MIMO Interference Channel","display_name":"Subspace Alignment Chains and the Degrees of Freedom of the Three-User MIMO Interference Channel","publication_year":2014,"publication_date":"2014-02-27","ids":{"openalex":"https://openalex.org/W2217718762","doi":"https://doi.org/10.1109/tit.2014.2308988","mag":"2217718762"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2308988","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2308988","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5100704324","display_name":"Chenwei Wang","orcid":"https://orcid.org/0000-0002-6283-8007"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chenwei Wang","raw_affiliation_strings":["Mobile Network Technology Group, Docomo Innovations Inc., Palo Alto, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mobile Network Technology Group, Docomo Innovations Inc., Palo Alto, CA, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077292579","display_name":"Tiangao Gou","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101778","display_name":"Samsung (United States)","ror":"https://ror.org/01bfbvm65","country_code":"US","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210101778"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tiangao Gou","raw_affiliation_strings":["Samsung Mobile Solutions Laboratory, San Diego, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Samsung Mobile Solutions Laboratory, San Diego, CA, USA","institution_ids":["https://openalex.org/I4210101778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049553679","display_name":"Syed A. Jafar","orcid":"https://orcid.org/0000-0003-2038-2977"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Syed Ali Jafar","raw_affiliation_strings":["Center for Pervasive Communications and Computing, University of California at Irvine, Irvine, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Pervasive Communications and Computing, University of California at Irvine, Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.1059,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.98631148,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"60","issue":"5","first_page":"2432","last_page":"2479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9990000128746033,"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/subspace-topology","display_name":"Subspace topology","score":0.4262096583843231},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3649490475654602},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3554344177246094},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28855812549591064}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4262096583843231},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3649490475654602},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3554344177246094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28855812549591064}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2014.2308988","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2308988","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W56381403","https://openalex.org/W1525037223","https://openalex.org/W1654459120","https://openalex.org/W1686467250","https://openalex.org/W1802395297","https://openalex.org/W1971328044","https://openalex.org/W1979408141","https://openalex.org/W2002469179","https://openalex.org/W2010645529","https://openalex.org/W2012454404","https://openalex.org/W2088404815","https://openalex.org/W2089318831","https://openalex.org/W2098363461","https://openalex.org/W2100842176","https://openalex.org/W2106549261","https://openalex.org/W2108850836","https://openalex.org/W2136180028","https://openalex.org/W2136608712","https://openalex.org/W2146214529","https://openalex.org/W2159159660","https://openalex.org/W2162370583","https://openalex.org/W2168095411","https://openalex.org/W2170023479","https://openalex.org/W2293033173","https://openalex.org/W2332213783","https://openalex.org/W2963697396","https://openalex.org/W3106263997","https://openalex.org/W4205417298","https://openalex.org/W6638211556"],"related_works":["https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506","https://openalex.org/W231025981","https://openalex.org/W2333698505","https://openalex.org/W2168402779","https://openalex.org/W2129083493","https://openalex.org/W2609315104","https://openalex.org/W2065107184"],"abstract_inverted_index":{"We":[0],"show":[1,98,444,487,543],"that":[2,99,445,484,488,503,522,544],"the":[3,52,65,85,88,106,130,136,145,169,181,207,214,226,239,247,250,274,281,294,348,383,399,402,413,428,446,473,476,508,527,549,566,579,583],"three-user":[4,107,429],"MT\u00d7":[5,430],"MRMultiple-Input":[6],"Multiple-Output":[7],"(MIMO)":[8],"interference":[9,112,153,183,252,419,432,448],"channel":[10,159,162],"where":[11,43],"each":[12,19,277],"transmitter":[13],"is":[14,21,59,71,129,175,206,260,334,368,462,555],"equipped":[15,22],"with":[16,23,79,268,391,483],"MTantennas":[17],"and":[18,40,156,325,339,359,387,393,406,465,481,538],"receiver":[20,237],"MRantennas":[24],"has":[25],"(M)":[26],"d(M,":[27,57,68,258,470],"N)":[28,58,69,101,139,259],"=\u0394min":[29],"(M/2-1/\u03ba,":[30],"N/2+1/\u03ba)":[31],"degrees":[32],"of":[33,56,67,87,90,171,209,249,265,299,323,329,357,363,415,417,438,475,515,529,559,578],"freedom":[34],"(DoF)":[35],"normalized":[36],"by":[37,232,423,458,499],"time,":[38],"frequency,":[39],"space":[41],"dimensions,":[42],"=\u0394min(MT,":[44],"MR),":[45,48],"N":[46,272],"=\u0394max(MT,":[47],"\u03ba":[49],"=\u0394\u2308M/N-M\u2309.":[50],"While":[51],"DoF":[53,70,102,215,240,256,403,557],"outer":[54,241,404],"bound":[55],"established":[60,72],"for":[61,105,114,238,331,365,401,427,435,489,552],"every":[62,490],"MT,":[63,439],"MRvalue,":[64],"achievability":[66,146],"in":[73,164,224,246,336,371,455,511,526,582],"general":[74],"subject":[75],"to":[76,81,134,201,229,235,305],"a":[77,124,233,236,261,534,576],"normalization":[78],"respect":[80],"spatial":[82,125,143,172],"extensions,":[83,144,173],"i.e.,":[84,287,341,376],"scaling":[86,131],"number":[89],"antennas":[91,564],"at":[92,565],"all":[93,320,354,436,512],"nodes.":[94],"In":[95,168,441],"particular,":[96,442],"we":[97,443,486],"qd(M,":[100,138],"are":[103,221,398,494,504,523,548],"achievable":[104],"qMT":[108],"\u00d7":[109],"qMR":[110],"MIMO":[111],"channel,":[113,433],"some":[115,285],"positive":[116],"integer":[117],"q,":[118],"which":[119,332,366,553],"may":[120,186,571],"be":[121,187,230,290,344,379,573],"seen":[122,574],"as":[123,213,243,245,519,575],"extension":[126],"factor.":[127],"q":[128],"factor":[132],"needed":[133],"make":[135],"value":[137,257,283,492],"an":[140],"integer.":[141],"Given":[142],"relies":[147],"only":[148,326,360,466,482,550],"on":[149],"linear":[150,263,278,302,418,447],"beamforming":[151],"based":[152],"alignment":[154,184,211,219,253,449],"schemes":[155],"requires":[157],"neither":[158,377],"extensions":[160],"nor":[161],"variations":[163],"time":[165],"or":[166,194,271,374,568],"frequency.":[167],"absence":[170],"it":[174,288],"shown":[176],"through":[177],"examples":[178],"how":[179],"essentially":[180,396],"same":[182],"scheme":[185],"applied":[188],"over":[189,191],"time-extensions":[190],"either":[192,269,342,372],"constant":[193],"time-varying":[195],"channels.":[196],"The":[197,217,255,296,316,350],"central":[198],"new":[199],"insight":[200],"emerge":[202],"from":[203],"this":[204],"paper":[205,457],"notion":[208],"subspace":[210,218],"chains":[212,220],"bottlenecks.":[216],"instrumental":[222],"both":[223,337],"identifying":[225],"extra":[227],"dimensions":[228],"provided":[231],"genie":[234],"bound,":[242],"well":[244],"construction":[248],"optimal":[251],"schemes.":[254],"piecewise":[262,301],"function":[264],"M,":[266],"N,":[267,340,375],"M":[270,338,373],"being":[273],"bottleneck":[275],"within":[276],"segment,":[279],"whereas":[280],"other":[282,513],"contains":[284,319,353],"redundancy,":[286,395],"can":[289,343,378],"reduced":[291,345,380],"without":[292,346,381],"reducing":[293,347,382],"DoF.":[295,349,384],"corner":[297],"points":[298],"these":[300],"segments":[303],"correspond":[304],"two":[306],"sets,":[307],"A={1/2,":[308],"2/3,":[309],"3/4,":[310],"...}and":[311],"B={1/3,":[312],"3/5,":[313],"5/7,":[314],"...}.":[315],"set":[317,351],"A":[318,386,547,586],"those":[321,327,355,361],"values":[322,328,356,362,437,477,514,551],"M/N":[324,330,358,364,478,491,516,545,584],"there":[333,367,493,554],"redundancy":[335,370,509,581],"B":[352,388],"no":[369,556],"Because":[385],"represent":[389],"settings":[390],"maximum":[392,580],"minimum":[394],"they":[397],"basis":[400],"bounds":[405],"inner":[407],"bounds,":[408],"respectively.":[409],"Our":[410,541],"results":[411,542],"settle":[412],"question":[414],"feasibility":[416],"alignment,":[420],"introduced":[421],"previously":[422],"Cenk":[424,459,500],"et":[425,460,501],"al.,":[426],"MRMIMO":[431],"completely":[434],"MR.":[440],"problem":[450],"(MT\u00d7":[451],"MR,":[452],"d)3(as":[453],"defined":[454,498],"previous":[456],"al.)":[461,502],"feasible":[463,539],"if":[464,467],"d":[468],"\u2264":[469],"N).":[471],"With":[472],"exception":[474],"\u2208":[479,546,585],"B,":[480],"exception,":[485],"proper":[495,530,537],"systems":[496],"(as":[497],"not":[505,524],"feasible.":[506],"Evidently":[507],"contained":[510],"manifests":[517],"itself":[518],"superfluous":[520],"variables":[521],"discounted":[525],"definition":[528],"systems,":[531],"thus":[532],"creating":[533],"discrepancy":[535],"between":[536],"systems.":[540],"benefit":[558],"joint":[560],"processing":[561],"among":[562],"co-located":[563],"transmitters":[567],"receivers.":[569],"This":[570],"also":[572],"consequence":[577],"settings.":[587]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":23},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
