{"id":"https://openalex.org/W1662081346","doi":"https://doi.org/10.1109/tsp.2015.2460223","title":"Linear Beamformer Design for Interference Alignment via Rank Minimization","display_name":"Linear Beamformer Design for Interference Alignment via Rank Minimization","publication_year":2015,"publication_date":"2015-07-23","ids":{"openalex":"https://openalex.org/W1662081346","doi":"https://doi.org/10.1109/tsp.2015.2460223","mag":"1662081346"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.2460223","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2460223","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":["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/A5102878359","display_name":"Gokul Sridharan","orcid":"https://orcid.org/0000-0003-1753-8782"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Gokul Sridharan","raw_affiliation_strings":["The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada","The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto , Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto , Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004681822","display_name":"Wei Yu","orcid":"https://orcid.org/0000-0002-7453-422X"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wei Yu","raw_affiliation_strings":["The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada","The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto , Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto , Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102878359"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":2.4054,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"63","issue":"22","first_page":"5910","last_page":"5923"},"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":0.9994000196456909,"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/T11946","display_name":"Antenna Design and Optimization","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/matrix-norm","display_name":"Matrix norm","score":0.6461021900177002},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.6392114162445068},{"id":"https://openalex.org/keywords/interference-alignment","display_name":"Interference alignment","score":0.6188470125198364},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5837176442146301},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5722153186798096},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5565991401672363},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.5153202414512634},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.474370539188385},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47295066714286804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4613795876502991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4574446380138397},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.437760591506958},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41201162338256836},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.22065487504005432},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.17382892966270447},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.14557641744613647},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14414486289024353}],"concepts":[{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.6461021900177002},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.6392114162445068},{"id":"https://openalex.org/C2982854036","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference alignment","level":4,"score":0.6188470125198364},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5837176442146301},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5722153186798096},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5565991401672363},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.5153202414512634},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.474370539188385},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47295066714286804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4613795876502991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4574446380138397},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.437760591506958},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41201162338256836},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.22065487504005432},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.17382892966270447},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.14557641744613647},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14414486289024353},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2015.2460223","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2460223","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:CiteSeerX.psu:10.1.1.727.3931","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.727.3931","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.comm.utoronto.ca/%7Eweiyu/2015_TSP_Gokul.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1916337001","https://openalex.org/W1966096622","https://openalex.org/W1971328044","https://openalex.org/W1979408141","https://openalex.org/W1999913571","https://openalex.org/W2017140917","https://openalex.org/W2033147302","https://openalex.org/W2037253724","https://openalex.org/W2048309032","https://openalex.org/W2055294446","https://openalex.org/W2059283452","https://openalex.org/W2066021549","https://openalex.org/W2066459185","https://openalex.org/W2074471762","https://openalex.org/W2075132089","https://openalex.org/W2078483498","https://openalex.org/W2087799952","https://openalex.org/W2096154138","https://openalex.org/W2096212850","https://openalex.org/W2098363461","https://openalex.org/W2106005123","https://openalex.org/W2107861471","https://openalex.org/W2113642685","https://openalex.org/W2118550318","https://openalex.org/W2136912397","https://openalex.org/W2139960897","https://openalex.org/W2143075842","https://openalex.org/W2149863017","https://openalex.org/W2154415981","https://openalex.org/W2161374719","https://openalex.org/W2167391223","https://openalex.org/W2168095411","https://openalex.org/W2210514616","https://openalex.org/W2217718762","https://openalex.org/W2258392231","https://openalex.org/W2539999335","https://openalex.org/W2550766755","https://openalex.org/W2912522929","https://openalex.org/W3102105495","https://openalex.org/W3103720502","https://openalex.org/W6672173587","https://openalex.org/W6680391196","https://openalex.org/W6684217156"],"related_works":["https://openalex.org/W2952489973","https://openalex.org/W4300776969","https://openalex.org/W2883042798","https://openalex.org/W1880408471","https://openalex.org/W2952101572","https://openalex.org/W1976707736","https://openalex.org/W2811302639","https://openalex.org/W4301291886","https://openalex.org/W2949959192","https://openalex.org/W2949412345"],"abstract_inverted_index":{"This":[0],"paper":[1,123,136,184],"proposes":[2],"a":[3,29,94,146,199,217,221,244,248],"new":[4],"framework":[5,51],"for":[6,14,58,129,141,230,254],"the":[7,56,68,74,77,81,89,97,101,107,111,151,179,192],"design":[8],"of":[9,63,70,87,113,127,134,150,156,182,201,220,247],"transmit":[10,78],"and":[11,43,73,106,240],"receive":[12],"beamformers":[13,79,229],"interference":[15,71,84,114,152,194],"alignment":[16,117],"(IA)":[17],"without":[18,235],"symbol":[19],"extensions":[20],"in":[21,28,80,100,226],"multi-antenna":[22],"cellular":[23],"networks.":[24],"We":[25],"consider":[26],"IA":[27,59,142],"G":[30],"cell":[31],"network":[32],"with":[33,173,233,256],"K":[34],"users/cell,":[35],"N":[36],"antennas":[37,45],"at":[38,46,93],"each":[39,47],"base":[40],"station":[41],"(BS)":[42],"M":[44],"user.":[48],"The":[49,83,131],"proposed":[50],"is":[52,224],"developed":[53],"by":[54,143],"recasting":[55],"conditions":[57,105],"as":[60,198],"two":[61,125,202],"sets":[62,126],"rank":[64,69,112,138],"constraints,":[65],"one":[66],"on":[67,76],"matrices,":[72],"other":[75],"uplink.":[82,102],"matrix":[85,148,157],"consists":[86],"all":[88],"interfering":[90],"vectors":[91],"received":[92],"BS":[95],"from":[96],"out-of-cell":[98],"users":[99],"Using":[103],"these":[104],"crucial":[108],"observation":[109],"that":[110,205,213],"matrices":[115,195,204],"under":[116],"can":[118],"be":[119],"determined":[120],"beforehand,":[121],"this":[122,135,183],"develops":[124,137],"algorithms":[128,140,172],"IA.":[130],"first":[132],"part":[133,181],"minimization":[139,164,170,188],"iteratively":[144],"minimizing":[145],"weighted":[147],"norm":[149,163,169],"matrix.":[153],"Different":[154],"choices":[155],"norms":[158],"lead":[159],"to":[160],"reweighted":[161,167],"nuclear":[162],"(RNNM)":[165],"or":[166,234],"Frobenius":[168],"(RFNM)":[171],"significantly":[174],"different":[175],"per-iteration":[176,218,245],"complexities.":[177],"Alternately,":[178],"second":[180],"devises":[185],"an":[186],"alternating":[187],"(AM)":[189],"algorithm":[190],"where":[191],"rank-deficient":[193],"are":[196,206,251],"expressed":[197],"product":[200],"lower-dimensional":[203],"then":[207],"alternately":[208],"optimized.":[209],"Simulation":[210],"results":[211],"indicate":[212],"RNNM,":[214],"which":[215,242],"has":[216],"complexity":[219,246],"semidefinite":[222],"program,":[223,250],"effective":[225],"designing":[227],"aligned":[228],"proper-feasible":[231],"systems":[232,255],"redundant":[236,257],"antennas,":[237],"while":[238],"RFNM":[239],"AM,":[241],"have":[243],"quadratic":[249],"better":[252],"suited":[253],"antennas.":[258]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}