{"id":"https://openalex.org/W2042559773","doi":"https://doi.org/10.1109/twc.2014.2318050","title":"Achievable Degrees of Freedom for &lt;inline-formula&gt; &lt;tex-math notation=\"TeX\"&gt;$K$&lt;/tex-math&gt;&lt;/inline-formula&gt;-User MIMO Y Channels Using Signal Group Based Alignment","display_name":"Achievable Degrees of Freedom for &lt;inline-formula&gt; &lt;tex-math notation=\"TeX\"&gt;$K$&lt;/tex-math&gt;&lt;/inline-formula&gt;-User MIMO Y Channels Using Signal Group Based Alignment","publication_year":2014,"publication_date":"2014-04-17","ids":{"openalex":"https://openalex.org/W2042559773","doi":"https://doi.org/10.1109/twc.2014.2318050","mag":"2042559773"},"language":"en","primary_location":{"id":"doi:10.1109/twc.2014.2318050","is_oa":false,"landing_page_url":"https://doi.org/10.1109/twc.2014.2318050","pdf_url":null,"source":{"id":"https://openalex.org/S63459445","display_name":"IEEE Transactions on Wireless Communications","issn_l":"1536-1276","issn":["1536-1276","1558-2248"],"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 Wireless Communications","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/A5103168223","display_name":"Hua Mu","orcid":"https://orcid.org/0000-0002-5001-9928"},"institutions":[{"id":"https://openalex.org/I106959904","display_name":"Florida Institute of Technology","ror":"https://ror.org/04atsbb87","country_code":"US","type":"education","lineage":["https://openalex.org/I106959904"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hua Mu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Florida Institute of Technology, Melbourne, FL, USA","Department of Electrical and Computer Engineering, Florida Institute of Technology, Melbourne, Fl, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Florida Institute of Technology, Melbourne, FL, USA","institution_ids":["https://openalex.org/I106959904"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Florida Institute of Technology, Melbourne, Fl, USA","institution_ids":["https://openalex.org/I106959904"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034880586","display_name":"J.K. Tugnait","orcid":"https://orcid.org/0000-0002-0220-2453"},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jitendra K. Tugnait","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, USA","Department of Electrical and Computer Engineering, Auburn University, Auburn, AL , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, USA","institution_ids":["https://openalex.org/I82497590"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Auburn University, Auburn, AL , USA","institution_ids":["https://openalex.org/I82497590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5721,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.96133302,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"13","issue":"8","first_page":"4520","last_page":"4533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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":0.9987000226974487,"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":0.9972000122070312,"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/mimo","display_name":"MIMO","score":0.5842903852462769},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.4970124065876007},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44502073526382446},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.44275251030921936},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.439948707818985},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4287145137786865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3750971257686615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3730941414833069},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.373055100440979},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2715960741043091},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.2642233371734619},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19446206092834473},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1724570393562317}],"concepts":[{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.5842903852462769},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.4970124065876007},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44502073526382446},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.44275251030921936},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.439948707818985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4287145137786865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3750971257686615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3730941414833069},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.373055100440979},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2715960741043091},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.2642233371734619},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19446206092834473},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1724570393562317},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/twc.2014.2318050","is_oa":false,"landing_page_url":"https://doi.org/10.1109/twc.2014.2318050","pdf_url":null,"source":{"id":"https://openalex.org/S63459445","display_name":"IEEE Transactions on Wireless Communications","issn_l":"1536-1276","issn":["1536-1276","1558-2248"],"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 Wireless Communications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.699999988079071,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W146084268","https://openalex.org/W1480597717","https://openalex.org/W1506498270","https://openalex.org/W1594585343","https://openalex.org/W1949836348","https://openalex.org/W1969434902","https://openalex.org/W1979408141","https://openalex.org/W1982109272","https://openalex.org/W1997834106","https://openalex.org/W1998482279","https://openalex.org/W1998836217","https://openalex.org/W2025808533","https://openalex.org/W2027186206","https://openalex.org/W2057929374","https://openalex.org/W2063534993","https://openalex.org/W2074601385","https://openalex.org/W2081934635","https://openalex.org/W2092253947","https://openalex.org/W2098596014","https://openalex.org/W2099111195","https://openalex.org/W2099561974","https://openalex.org/W2101413543","https://openalex.org/W2105831729","https://openalex.org/W2117718985","https://openalex.org/W2118696754","https://openalex.org/W2131264346","https://openalex.org/W2132107720","https://openalex.org/W2136608712","https://openalex.org/W2145386092","https://openalex.org/W2147355810","https://openalex.org/W2151382549","https://openalex.org/W2152496949","https://openalex.org/W2171159059","https://openalex.org/W2213107608","https://openalex.org/W4213311856","https://openalex.org/W4294338998","https://openalex.org/W6630520024","https://openalex.org/W6640924813","https://openalex.org/W6650135795"],"related_works":["https://openalex.org/W2539674285","https://openalex.org/W1998322187","https://openalex.org/W1038122923","https://openalex.org/W2952514781","https://openalex.org/W3019210376","https://openalex.org/W1980381208","https://openalex.org/W2391145594","https://openalex.org/W2326572623","https://openalex.org/W1559320887","https://openalex.org/W2284606164"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,17,55,59,83,115,196,265,294,317],"K-user":[3,189,309],"multiple":[4,6,73],"input":[5],"output":[7],"(MIMO)":[8],"Y":[9,191,310],"channel":[10,192,311],"consisting":[11],"of":[12,32,35,50,187,203,261,268,274,298,333],"K(\u2265":[13],"3)":[14],"users":[15,269,302,315],"and":[16,76,133,149,170,212,221,231,238,271,303,320],"relay.":[18,120,305],"Each":[19],"user":[20,124],"has":[21,324],"K-1":[22,29,220,237],"independent":[23],"messages":[24],"for":[25,54,67,146,167,180,228,242,264,307],"all":[26,94,142,313],"the":[27,48,72,77,107,119,122,134,183,200,205,252,259,304,308,321,331],"other":[28,288],"users.":[30],"Degrees":[31],"freedom":[33],"(DoF)":[34],"such":[36],"channels":[37],"is":[38,45,52,90,125,136,193,328,338],"not":[39],"known":[40,46],"in":[41,58,109],"general":[42],"but":[43],"it":[44,327],"that":[47,153,330],"DoF":[49,186,202,273,332],"K(K-1)/2":[51],"achievable":[53,272],"network":[56,68],"operating":[57],"half-duplex":[60],"mode":[61],"by":[62],"using":[63],"signal":[64,85,282,289],"space":[65],"alignment":[66,88,284],"coding":[69],"during":[70],"both":[71,147],"access":[74],"phase":[75],"broadcast":[78],"phase.":[79],"In":[80,245],"this":[81,188],"paper,":[82],"novel":[84],"group":[86,111,283],"based":[87],"scheme":[89],"proposed,":[91],"which":[92,292],"divides":[93],"K(K-1)":[95],"signals":[96,108],"into":[97,114],"l":[98,101],"groups":[99],"where":[100,141,312],"=":[102,159,162,175,178],"K":[103,169,270],"or":[104],"K-1.":[105],"Then,":[106],"each":[110],"are":[112,144,214],"aligned":[113],"smaller":[116],"subspace":[117],"at":[118,258,300],"If":[121],"i-th":[123],"equipped":[126,137],"with":[127,138],"M":[128,155,171,208,215,232,254],"<sub":[129,156,172,209,216,233,255],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[130,157,165,173,210,217,226,234,256],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[131,158,174,211,218,235,257],"antennas":[132,140,143,299],"relay":[135,322],"N":[139,161,177,213,222,239,263,325],"used":[145],"transmitting":[148],"receiving,":[150],"we":[151,249],"prove":[152],"when":[154],"K-1,":[160,176],"(K-1)":[163,224],"<sup":[164,225],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[166,227],"even":[168,229],"K(K-2)":[179,241],"odd":[181,243],"K,":[182,230],"optimal":[184],"total":[185,201],"MIMO":[190],"K(K-1)/2.":[194],"As":[195],"consequence,":[197],"to":[198,277],"achieve":[199],"K(K-1)/2,":[204,275],"requirements":[206],"on":[207],"\u2265":[219,223,236,240],"K.":[244],"our":[246],"proposed":[247],"approach,":[248],"significantly":[250],"decrease":[251],"minimum":[253],"expense":[260],"higher":[262],"given":[266],"number":[267,297],"compared":[276],"an":[278],"existing":[279],"approach.":[280],"This":[281],"concept":[285],"also":[286],"motivates":[287],"grouping":[290],"methods,":[291],"provide":[293],"tradeoff":[295],"between":[296],"end":[301,314],"Also,":[306],"have":[316],"single":[318],"antenna":[319],"node":[323],"antennas,":[326],"shown":[329],"min{K/2,":[334],"(N":[335],"+":[336],"1)/2}":[337],"achievable.":[339]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}