{"id":"https://openalex.org/W3111472228","doi":"https://doi.org/10.1109/tit.2016.2620180","title":"Linear Degrees of Freedom of the MIMO X-Channel With Delayed CSIT","display_name":"Linear Degrees of Freedom of the MIMO X-Channel With Delayed CSIT","publication_year":2016,"publication_date":"2016-10-21","ids":{"openalex":"https://openalex.org/W3111472228","doi":"https://doi.org/10.1109/tit.2016.2620180","mag":"3111472228"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2620180","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2620180","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/A5014395205","display_name":"David Kao","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David T. H. Kao","raw_affiliation_strings":["Google Inc., Mountain View, CA, USA","University of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Google Inc., Mountain View, CA, USA","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047191296","display_name":"A. Salman Avestimehr","orcid":"https://orcid.org/0000-0003-3102-0867"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Salman Avestimehr","raw_affiliation_strings":["Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014395205"],"corresponding_institution_ids":["https://openalex.org/I1174212","https://openalex.org/I1291425158"],"apc_list":null,"apc_paid":null,"fwci":1.1154,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.81668163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"63","issue":"1","first_page":"297","last_page":"319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9994999766349792,"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":0.9994999766349792,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9993000030517578,"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":0.9951000213623047,"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":0.8201738595962524},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.659965455532074},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.6530061364173889},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5445296168327332},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5217189192771912},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5134595036506653},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.49696019291877747},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.43352261185646057},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4334486126899719},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.42127859592437744},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.33233433961868286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30396056175231934},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22767719626426697},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.1990227997303009},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11806750297546387}],"concepts":[{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.8201738595962524},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.659965455532074},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.6530061364173889},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5445296168327332},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5217189192771912},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5134595036506653},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.49696019291877747},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.43352261185646057},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4334486126899719},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.42127859592437744},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.33233433961868286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30396056175231934},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22767719626426697},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.1990227997303009},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11806750297546387},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/tit.2016.2620180","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2620180","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8299999833106995}],"awards":[{"id":"https://openalex.org/G1057863689","display_name":null,"funder_award_id":"EARS-1411244","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2098038213","display_name":null,"funder_award_id":"CAREER CCF 1408639","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1990118566","https://openalex.org/W2002469179","https://openalex.org/W2030357686","https://openalex.org/W2041616144","https://openalex.org/W2106549261","https://openalex.org/W2106641685","https://openalex.org/W2106697356","https://openalex.org/W2113817460","https://openalex.org/W2124982134","https://openalex.org/W2136608712","https://openalex.org/W2161443611","https://openalex.org/W2200991597","https://openalex.org/W2210514616","https://openalex.org/W2570151474","https://openalex.org/W2763552505","https://openalex.org/W3103053992","https://openalex.org/W3125864775","https://openalex.org/W4250958385","https://openalex.org/W4293163450"],"related_works":["https://openalex.org/W2059045613","https://openalex.org/W4250215096","https://openalex.org/W2119209917","https://openalex.org/W2145047504","https://openalex.org/W2147127144","https://openalex.org/W2159179523","https://openalex.org/W2344350961","https://openalex.org/W2950791861","https://openalex.org/W4250958385","https://openalex.org/W2165992111"],"abstract_inverted_index":{"We":[0,31,166],"study":[1],"the":[2,8,20,29,36,49,74,78,85,92,105,110,122,128,132,175,182,186,191,199],"degrees":[3],"of":[4,7,80,91,124,144,154],"freedom":[5],"(DoFs)":[6],"multiple-input":[9],"multiple-output":[10],"X-channel":[11],"(MIMO":[12],"XC)":[13],"with":[14,43,56,112],"delayed":[15,116,138],"channel":[16],"state":[17],"information":[18],"at":[19,28,84,127],"transmitters":[21,136],"(delayed":[22],"CSITs),":[23],"assuming":[24],"linear":[25,37,50,82,93,142,170,200],"coding":[26],"strategies":[27],"transmitters.":[30],"present":[32],"two":[33,86,107],"results:":[34],"1)":[35],"sum":[38,94,187],"DoF":[39,51,95,171,188,201],"for":[40,53,61,174,203],"MIMO":[41,54,176],"XC":[42,55,177],"general":[44],"antenna":[45,205],"configurations":[46],"and":[47,158,190],"2)":[48],"region":[52,202],"symmetric":[57,204],"antennas.":[58],"The":[59,89],"converse":[60,189],"each":[62,149],"result":[63],"is":[64,96],"based":[65,97],"on":[66,98],"developing":[67],"a":[68,99,152],"novel":[69],"rank-ratio":[70],"inequality":[71],"that":[72,148],"characterizes":[73],"maximum":[75],"ratio":[76],"between":[77],"dimensions":[79],"received":[81],"subspaces":[83],"multiple-antenna":[87],"receivers.":[88,165],"achievability":[90],"three-phase":[100],"strategy,":[101,194],"in":[102,118,179],"which":[103],"during":[104],"first":[106],"phases":[108],"only":[109],"transmitter":[111],"fewer":[113],"antennas":[114],"exploits":[115],"CSIT":[117,139],"order":[119],"to":[120,140,181,197],"minimize":[121],"dimension":[123],"its":[125],"signal":[126],"unintended":[129],"receiver.":[130],"During":[131],"third":[133],"phase,":[134],"both":[135,164],"use":[137],"send":[141],"combinations":[143],"past":[145],"transmissions,":[146],"such":[147],"receiver":[150],"receives":[151],"superposition":[153],"desired":[155],"message":[156],"data":[157],"known":[159],"interference,":[160],"thus":[161],"simultaneously":[162],"serving":[163],"also":[167],"derive":[168],"other":[169],"outer":[172,183],"bounds":[173,184],"that,":[178],"addition":[180],"from":[185],"proposed":[192],"transmission":[193],"allow":[195],"us":[196],"characterize":[198],"configurations.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}