{"id":"https://openalex.org/W1971328044","doi":"https://doi.org/10.1109/tsp.2011.2173683","title":"On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel","display_name":"On the Degrees of Freedom Achievable Through Interference Alignment in a MIMO Interference Channel","publication_year":2011,"publication_date":"2011-10-26","ids":{"openalex":"https://openalex.org/W1971328044","doi":"https://doi.org/10.1109/tsp.2011.2173683","mag":"1971328044"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2173683","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2173683","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1104.0992","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041237539","display_name":"Meisam Razaviyayn","orcid":"https://orcid.org/0000-0003-4342-6661"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meisam Razaviyayn","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018875079","display_name":"Gennady Lyubeznik","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gennady Lyubeznik","raw_affiliation_strings":["Department of Mathematics, University of Minnesota, Minneapolis, MN, USA","Dept. of Math., Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101766226","display_name":"Zhi\u2010Quan Luo","orcid":"https://orcid.org/0000-0003-3995-914X"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhi-Quan Luo","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":29.5178,"has_fulltext":false,"cited_by_count":264,"citation_normalized_percentile":{"value":0.9976539,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"60","issue":"2","first_page":"812","last_page":"821"},"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/T11392","display_name":"Energy Harvesting in Wireless Networks","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/interference","display_name":"Interference (communication)","score":0.5323643684387207},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.46847644448280334},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.43567174673080444},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4215222895145416},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4128211736679077},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3823031485080719},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3573092818260193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3438771367073059},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3215600848197937},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.21048566699028015},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14949998259544373}],"concepts":[{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.5323643684387207},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.46847644448280334},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.43567174673080444},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4215222895145416},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4128211736679077},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3823031485080719},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3573092818260193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3438771367073059},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3215600848197937},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.21048566699028015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14949998259544373}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2011.2173683","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2173683","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:arXiv.org:1104.0992","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1104.0992","pdf_url":"https://arxiv.org/pdf/1104.0992","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1104.0992","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1104.0992","pdf_url":"https://arxiv.org/pdf/1104.0992","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"score":0.75,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W142693673","https://openalex.org/W640442761","https://openalex.org/W1479863711","https://openalex.org/W1525037223","https://openalex.org/W1979408141","https://openalex.org/W2028676993","https://openalex.org/W2049707341","https://openalex.org/W2100755644","https://openalex.org/W2106549261","https://openalex.org/W2123051422","https://openalex.org/W2136608712","https://openalex.org/W2139386760","https://openalex.org/W2139960897","https://openalex.org/W2144000019","https://openalex.org/W2159159660","https://openalex.org/W2162370583","https://openalex.org/W2168095411","https://openalex.org/W2949300787","https://openalex.org/W3141776272","https://openalex.org/W6681297494"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W4386900933","https://openalex.org/W2545343974","https://openalex.org/W4297797135","https://openalex.org/W3125672081","https://openalex.org/W1673581201","https://openalex.org/W4385301946","https://openalex.org/W2006389905"],"abstract_inverted_index":{"Consider":[0],"a":[1,58,86,107],"K-user":[2],"flat":[3],"fading":[4],"MIMO":[5],"interference":[6,54,104],"channel":[7,28,80],"where":[8,78],"the":[9,43,76,124,154,165],"kth":[10],"transmitter":[11],"(or":[12],"receiver)":[13],"is":[14,82,134,151,161],"equipped":[15],"with":[16,64,110,131],"Mk(respectively":[17],"Nk)":[18],"antennas.":[19],"If":[20],"an":[21],"exponential":[22],"(in":[23],"K)":[24],"number":[25,155,166],"of":[26,47,96,156,167],"generic":[27],"extensions":[29],"are":[30],"used":[31],"either":[32],"across":[33],"time":[34],"or":[35],"frequency,":[36],"Cadambe":[37],"and":[38,84,133],"Jafar":[39],"[1]":[40],"showed":[41],"that":[42,61,89,123,148],"total":[44,59,125],"achievable":[45,101,126],"degrees":[46,95],"freedom":[48,97],"(DoF)":[49],"can":[50],"be":[51,91],"maximized":[52],"via":[53],"alignment,":[55],"resulting":[56],"in":[57,135],"DoF":[60,127],"grows":[62],"linearly":[63,130],"A":[65],"even":[66],"if":[67],"Mkand":[68],"Nkare":[69],"bounded.":[70],"In":[71],"this":[72,120,149],"work":[73],"we":[74],"consider":[75],"case":[77],"no":[79,137],"extension":[81],"allowed,":[83],"establish":[85],"general":[87],"condition":[88,121],"must":[90],"satisfied":[92],"by":[93,163],"any":[94],"tuple":[98],"(d1.":[99],"d2....dK)":[100],"through":[102],"linear":[103],"alignment.":[105],"For":[106],"symmetric":[108],"system":[109],"Mk=":[111],"M,":[112],"Nk=":[113],"N,":[114],"dk=":[115],"d":[116],"for":[117],"all":[118],"k,":[119],"implies":[122],"cannot":[128],"grow":[129],"K,":[132],"fact":[136],"more":[138],"than":[139],"K(M":[140],"+":[141,143],"N)/(K":[142],"1).":[144],"We":[145],"also":[146],"show":[147],"bound":[150],"tight":[152],"when":[153],"antennas":[157],"at":[158],"each":[159],"transceiver":[160],"divisible":[162],"d,":[164],"data":[168],"streams":[169],"per":[170],"user.":[171]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":33},{"year":2015,"cited_by_count":33},{"year":2014,"cited_by_count":64},{"year":2013,"cited_by_count":41},{"year":2012,"cited_by_count":17}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}