{"id":"https://openalex.org/W1606337839","doi":"https://doi.org/10.1109/tit.2012.2184909","title":"Linear Transceiver Design for Interference Alignment: Complexity and Computation","display_name":"Linear Transceiver Design for Interference Alignment: Complexity and Computation","publication_year":2012,"publication_date":"2012-01-31","ids":{"openalex":"https://openalex.org/W1606337839","doi":"https://doi.org/10.1109/tit.2012.2184909","mag":"1606337839"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2184909","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2184909","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/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/A5046195860","display_name":"Maziar Sanjabi","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":"Maziar Sanjabi","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":"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":19.6423,"has_fulltext":false,"cited_by_count":143,"citation_normalized_percentile":{"value":0.99567061,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"58","issue":"5","first_page":"2896","last_page":"2910"},"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":0.9998000264167786,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.7256970405578613},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.624803364276886},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5994670391082764},{"id":"https://openalex.org/keywords/transceiver","display_name":"Transceiver","score":0.5771499872207642},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.5768799781799316},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5596870183944702},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.5112905502319336},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5108949542045593},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4784667193889618},{"id":"https://openalex.org/keywords/interference-alignment","display_name":"Interference alignment","score":0.4595685303211212},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4440816044807434},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.383966326713562},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.21343785524368286},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.19644761085510254}],"concepts":[{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.7256970405578613},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.624803364276886},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5994670391082764},{"id":"https://openalex.org/C7720470","wikidata":"https://www.wikidata.org/wiki/Q954187","display_name":"Transceiver","level":3,"score":0.5771499872207642},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.5768799781799316},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5596870183944702},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.5112905502319336},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5108949542045593},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4784667193889618},{"id":"https://openalex.org/C2982854036","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference alignment","level":4,"score":0.4595685303211212},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4440816044807434},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.383966326713562},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.21343785524368286},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.19644761085510254},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2012.2184909","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2184909","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","score":0.8199999928474426,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1504840802","https://openalex.org/W1537960262","https://openalex.org/W1563919256","https://openalex.org/W1603634784","https://openalex.org/W1979408141","https://openalex.org/W1989873462","https://openalex.org/W1991331367","https://openalex.org/W1991706575","https://openalex.org/W1994887634","https://openalex.org/W2008754806","https://openalex.org/W2029920391","https://openalex.org/W2030546921","https://openalex.org/W2046980951","https://openalex.org/W2052530379","https://openalex.org/W2062610219","https://openalex.org/W2068118751","https://openalex.org/W2071707134","https://openalex.org/W2074078878","https://openalex.org/W2087258384","https://openalex.org/W2093763487","https://openalex.org/W2096212850","https://openalex.org/W2098363461","https://openalex.org/W2101727634","https://openalex.org/W2101792326","https://openalex.org/W2103579292","https://openalex.org/W2103749601","https://openalex.org/W2110391887","https://openalex.org/W2111933819","https://openalex.org/W2119393839","https://openalex.org/W2120365147","https://openalex.org/W2123531758","https://openalex.org/W2124409123","https://openalex.org/W2125113829","https://openalex.org/W2129821947","https://openalex.org/W2139960897","https://openalex.org/W2144000019","https://openalex.org/W2145203050","https://openalex.org/W2147055067","https://openalex.org/W2149258241","https://openalex.org/W2155174176","https://openalex.org/W2157242700","https://openalex.org/W2157989362","https://openalex.org/W2163762663","https://openalex.org/W2164275514","https://openalex.org/W2168034909","https://openalex.org/W2168095411","https://openalex.org/W2172008677","https://openalex.org/W2293033173","https://openalex.org/W6634018624","https://openalex.org/W6640667000","https://openalex.org/W6652823068","https://openalex.org/W6677733858","https://openalex.org/W6681297494"],"related_works":["https://openalex.org/W4249165909","https://openalex.org/W2117255793","https://openalex.org/W2113805088","https://openalex.org/W3188388194","https://openalex.org/W4244023365","https://openalex.org/W4390195751","https://openalex.org/W4311591647","https://openalex.org/W1995409306","https://openalex.org/W2963438473","https://openalex.org/W2037307649"],"abstract_inverted_index":{"Consider":[0],"a":[1,108,124,169,192],"multiple":[2,16],"input-multiple":[3],"output":[4],"(MIMO)":[5],"interference":[6,72,88,111,211],"channel":[7,92,112],"where":[8],"each":[9,137,155,189],"transmitter":[10],"and":[11,49,70,94],"receiver":[12,138,190],"are":[13],"equipped":[14,140,159],"with":[15,141,160],"antennas.":[17,145,165],"An":[18],"effective":[19],"approach":[20],"to":[21,28],"practically":[22],"achieving":[23],"high":[24,76],"system":[25,217],"throughput":[26],"is":[27,113,134,139,158],"deploy":[29],"linear":[30,193],"transceivers":[31],"(or":[32],"beamformers)":[33],"that":[34,60,96,118,177,188,204],"can":[35],"optimally":[36],"exploit":[37],"the":[38,42,65,75,87,97,101,121,147,181,186,205,209],"spatial":[39],"characteristics":[40],"of":[41,47,68,99,105,123,127,129,216],"channel.":[43],"The":[44,200],"recent":[45],"work":[46],"Cadambe":[48],"Jafar":[50],"(IEEE":[51],"Trans.":[52],"Inf.":[53],"Theory,":[54],"vol.":[55],"54,":[56],"no.":[57],"8)":[58],"suggests":[59],"optimal":[61],"beamformers":[62],"should":[63],"maximize":[64],"total":[66,102],"degrees":[67,104,128],"freedom":[69,106,130],"achieve":[71],"alignment":[73,89,212],"in":[74,214],"signal-to-noise":[77],"ratio":[78],"(SNR)":[79],"regime.":[80],"In":[81],"this":[82],"paper":[83],"we":[84,116],"first":[85],"consider":[86],"problem":[90,98,149],"without":[91],"extension":[93],"prove":[95],"maximizing":[100],"achieved":[103],"for":[107,131,172],"given":[109,125],"MIMO":[110],"NP-hard.":[114],"Furthermore,":[115],"show":[117,203],"even":[119],"checking":[120],"achievability":[122],"tuple":[126,183],"all":[132],"receivers":[133],"NP-hard":[135],"when":[136,154],"at":[142],"least":[143],"three":[144],"Interestingly,":[146],"same":[148],"becomes":[150],"polynomial":[151],"time":[152],"solvable":[153],"transmit/receive":[156],"node":[157],"no":[161],"more":[162],"than":[163],"two":[164],"We":[166],"also":[167],"propose":[168],"distributed":[170],"algorithm":[171,207],"transmit":[173],"covariance":[174],"matrix":[175],"design":[176],"does":[178],"not":[179],"require":[180],"DoF":[182],"preassignment,":[184],"under":[185],"assumption":[187],"uses":[191],"minimum":[194],"mean":[195],"square":[196],"error":[197],"(MMSE)":[198],"beamformer.":[199],"simulation":[201],"results":[202],"proposed":[206],"outperforms":[208],"existing":[210],"algorithms":[213],"terms":[215],"throughput.":[218]},"counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":28},{"year":2013,"cited_by_count":23},{"year":2012,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}