{"id":"https://openalex.org/W2012454404","doi":"https://doi.org/10.1109/tit.2010.2080830","title":"Degrees of Freedom of the $K$ User $M \\times N$ MIMO Interference Channel","display_name":"Degrees of Freedom of the $K$ User $M \\times N$ MIMO Interference Channel","publication_year":2010,"publication_date":"2010-11-30","ids":{"openalex":"https://openalex.org/W2012454404","doi":"https://doi.org/10.1109/tit.2010.2080830","mag":"2012454404"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2080830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2080830","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/A5077292579","display_name":"Tiangao Gou","orcid":null},"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"]},{"id":"https://openalex.org/I4210140791","display_name":"Irvine University","ror":"https://ror.org/04ysmca02","country_code":"US","type":"education","lineage":["https://openalex.org/I4210140791"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tiangao Gou","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Irvine, CA, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of California Irvine, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of California Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578","https://openalex.org/I4210140791"]}]},{"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"]},{"id":"https://openalex.org/I4210140791","display_name":"Irvine University","ror":"https://ror.org/04ysmca02","country_code":"US","type":"education","lineage":["https://openalex.org/I4210140791"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Syed A. Jafar","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Irvine, CA, USA","Dept. of Electr. Eng. & Comput. Sci., Univ. of California Irvine, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"Dept. of Electr. Eng. & Comput. Sci., Univ. of California Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578","https://openalex.org/I4210140791"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":54.7158,"has_fulltext":false,"cited_by_count":458,"citation_normalized_percentile":{"value":0.99925955,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"56","issue":"12","first_page":"6040","last_page":"6057"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","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/T10964","display_name":"Wireless Communication Security Techniques","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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9994000196456909,"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":0.9991000294685364,"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/algorithm","display_name":"Algorithm","score":0.4103507995605469},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39956268668174744}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4103507995605469},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39956268668174744}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2010.2080830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2080830","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1654459120","https://openalex.org/W1979408141","https://openalex.org/W1990208988","https://openalex.org/W2029558701","https://openalex.org/W2029920391","https://openalex.org/W2052530379","https://openalex.org/W2068118751","https://openalex.org/W2088831296","https://openalex.org/W2089318831","https://openalex.org/W2100842176","https://openalex.org/W2105147943","https://openalex.org/W2106549261","https://openalex.org/W2116406049","https://openalex.org/W2120365147","https://openalex.org/W2140076291","https://openalex.org/W2145129885","https://openalex.org/W2147775941","https://openalex.org/W2157989362","https://openalex.org/W2167047009","https://openalex.org/W2167357515","https://openalex.org/W2168448439","https://openalex.org/W2168957483","https://openalex.org/W2538583446","https://openalex.org/W2964250559"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2317200988","https://openalex.org/W2376932109","https://openalex.org/W2382290278","https://openalex.org/W2386767533"],"abstract_inverted_index":{"We":[0,79],"provide":[1,81],"inner":[2],"bound":[3,6],"and":[4,37],"outer":[5],"for":[7,101],"the":[8,32,48,61],"total":[9,62],"number":[10,63],"of":[11,13,15,64,66,95],"degrees":[12,65,94],"freedom":[14,67,96],"theKuser":[16],"multiple-input":[17],"multiple-output":[18],"(MIMO)":[19],"Gaussian":[20],"interference":[21,77,85,104],"channel":[22,33,108],"withMantennas":[23],"at":[24,28],"each":[25,29],"transmitter":[26],"andNantennas":[27],"receiver":[30],"if":[31],"coefficients":[34],"are":[35,45],"time-varying":[36],"drawn":[38],"from":[39],"a":[40],"continuous":[41],"distribution.":[42],"The":[43],"bounds":[44],"tight":[46],"when":[47],"ratio":[49],"[(max(M,N))/(min(M,N))]=Ris":[50],"equal":[51,69],"to":[52,70],"an":[53],"integer.":[54],"For":[55],"this":[56],"case,":[57],"we":[58],"show":[59],"that":[60],"is":[68,74],"min(M,N)KifK\u2264Rand":[71],"min(M,N)[(R)/(R+1)]KifK>R.":[72],"Achievability":[73],"based":[75],"on":[76],"alignment.":[78],"also":[80],"examples":[82],"where":[83],"using":[84],"alignment":[86],"combined":[87],"with":[88,106],"zero":[89,99],"forcing":[90,100],"can":[91],"achieve":[92],"more":[93],"than":[97],"merely":[98],"some":[102],"MIMO":[103],"channels":[105],"constant":[107],"coefficients.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":39},{"year":2015,"cited_by_count":43},{"year":2014,"cited_by_count":73},{"year":2013,"cited_by_count":70},{"year":2012,"cited_by_count":69}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}