{"id":"https://openalex.org/W1654063178","doi":"https://doi.org/10.1109/tit.2013.2267721","title":"Statistical Beamforming on the Grassmann Manifold for the Two-User Broadcast Channel","display_name":"Statistical Beamforming on the Grassmann Manifold for the Two-User Broadcast Channel","publication_year":2013,"publication_date":"2013-06-11","ids":{"openalex":"https://openalex.org/W1654063178","doi":"https://doi.org/10.1109/tit.2013.2267721","mag":"1654063178"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2267721","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2267721","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1104.2116","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Vasanthan Raghavan","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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vasanthan Raghavan","raw_affiliation_strings":["Department of Mathematics, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Stephen V. Hanly","orcid":null},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Stephen V. Hanly","raw_affiliation_strings":["Macquarie University, Sydney, NSW, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Macquarie University, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"last","author":{"id":null,"display_name":"Venugopal V. Veeravalli","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Venugopal V. Veeravalli","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.6974,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.95084167,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"59","issue":"10","first_page":"6464","last_page":"6489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.8327999711036682,"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":0.8327999711036682,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.03909999877214432,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.020800000056624413,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.7556999921798706},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6370000243186951},{"id":"https://openalex.org/keywords/rayleigh-fading","display_name":"Rayleigh fading","score":0.5203999876976013},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5134000182151794},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.46389999985694885},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.46059998869895935},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4575999975204468},{"id":"https://openalex.org/keywords/generalized-eigenvector","display_name":"Generalized eigenvector","score":0.38609999418258667},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.3716999888420105},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.3691999912261963}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.7556999921798706},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6370000243186951},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6047000288963318},{"id":"https://openalex.org/C56985126","wikidata":"https://www.wikidata.org/wiki/Q854039","display_name":"Rayleigh fading","level":4,"score":0.5203999876976013},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.46389999985694885},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.46059998869895935},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4115999937057495},{"id":"https://openalex.org/C147925508","wikidata":"https://www.wikidata.org/wiki/Q970767","display_name":"Generalized eigenvector","level":5,"score":0.38609999418258667},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.3716999888420105},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3619000017642975},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36000001430511475},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3596999943256378},{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.35519999265670776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32260000705718994},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3124000132083893},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.29030001163482666},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.2784999907016754},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.27619999647140503},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.26930001378059387},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.26899999380111694},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.266400009393692},{"id":"https://openalex.org/C203234222","wikidata":"https://www.wikidata.org/wiki/Q2133519","display_name":"Noise power","level":3,"score":0.2624000012874603},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.2612000107765198},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.2558000087738037},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.25369998812675476},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2013.2267721","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2267721","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"},{"id":"pmh:oai:arXiv.org:1104.2116","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1104.2116","pdf_url":"https://arxiv.org/pdf/1104.2116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1104.2116","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1104.2116","pdf_url":"https://arxiv.org/pdf/1104.2116","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1976109068","https://openalex.org/W2030546921","https://openalex.org/W2045512849","https://openalex.org/W2048805039","https://openalex.org/W2097578209","https://openalex.org/W2098126478","https://openalex.org/W2099440786","https://openalex.org/W2101792326","https://openalex.org/W2103749601","https://openalex.org/W2105147296","https://openalex.org/W2109005286","https://openalex.org/W2115407331","https://openalex.org/W2116141601","https://openalex.org/W2120988089","https://openalex.org/W2121485091","https://openalex.org/W2124250240","https://openalex.org/W2130521103","https://openalex.org/W2133475491","https://openalex.org/W2135122024","https://openalex.org/W2136907755","https://openalex.org/W2139706615","https://openalex.org/W2143927285","https://openalex.org/W2145403270","https://openalex.org/W2146761479","https://openalex.org/W2146872403","https://openalex.org/W2147918068","https://openalex.org/W2148089951","https://openalex.org/W2150166380","https://openalex.org/W2150764210","https://openalex.org/W2151795416","https://openalex.org/W2153298783","https://openalex.org/W2154433856","https://openalex.org/W2155847893","https://openalex.org/W2159312879","https://openalex.org/W2161410889","https://openalex.org/W2161473225","https://openalex.org/W2162675362","https://openalex.org/W2163278024","https://openalex.org/W2164664877","https://openalex.org/W2165943096","https://openalex.org/W2167870633","https://openalex.org/W2171703142","https://openalex.org/W2484659212","https://openalex.org/W3147239237","https://openalex.org/W4242722506","https://openalex.org/W6682797351"],"related_works":[],"abstract_inverted_index":{"A":[0,59],"Rayleigh":[1],"fading":[2],"spatially":[3],"correlated":[4],"broadcast":[5,256],"setting":[6,257],"with":[7,23,258,278],"<formula":[8,259,270],"formulatype=\"inline\"":[9,260,271],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10,261,272],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[11,273],"Notation=\"TeX\">$M":[12],"=":[13],"2$</tex></formula>":[14],"antennas":[15,265],"at":[16,77,96,266],"the":[17,33,43,56,78,83,97,101,106,112,125,131,135,142,147,158,168,171,174,192,203,207,211,215,237,241,246,250,254,267,287,291,294],"transmitter":[18,44,98,268],"and":[19,68,118,182,214,269,293],"two":[20,107],"users":[21,34],"(each":[22,277],"a":[24,119,197,231,279],"single":[25,280],"antenna)":[26,281],"is":[27,30,75,122,139,152,164,191,206,217,230,282],"considered.":[28],"It":[29],"assumed":[31],"that":[32,64,86,146],"have":[35],"perfect":[36],"channel":[37],"information":[38,48,91],"about":[39],"their":[40],"links,":[41],"whereas":[42],"has":[45],"only":[46,88],"statistical":[47,90],"of":[49,55,130,134,176,196,199,210,233,240,286,290],"each":[50,73,187],"user's":[51],"link":[52,213],"(covariance":[53],"matrix":[54,205,209,244],"vector":[57],"channel).":[58],"low-complexity":[60],"linear":[61],"beamforming":[62,113,143,295],"strategy":[63],"allocates":[65],"equal":[66],"power":[67],"one":[69],"spatial":[70],"eigenmode":[71,239],"to":[72,93,99,105,161,166,173],"user":[74],"employed":[76],"transmitter.":[79],"Beamforming":[80],"vectors":[81,114,144],"on":[82,89],"Grassmann":[84],"manifold":[85],"depend":[87],"are":[92,115],"be":[94,167],"designed":[95,220],"maximize":[100],"ergodic":[102,126,251],"sum-rate":[103,127,252],"delivered":[104],"users.":[108],"Toward":[109],"this":[110,156,162,226],"goal,":[111],"first":[116,204],"fixed":[117],"closed-form":[120],"expression":[121,138],"obtained":[123,283],"for":[124,186,253],"in":[128,141,245,284],"terms":[129,285],"covariance":[132,208,223,243,288],"matrices":[133,201,289],"links.":[136],"This":[137,189],"nonconvex":[140],"ensuring":[145],"classical":[148],"Lagrange":[149],"multiplier":[150],"technique":[151],"not":[153],"applicable.":[154],"Despite":[155],"difficulty,":[157],"optimal":[159,234],"solution":[160,172,190],"problem":[163],"shown":[165],"same":[169],"as":[170],"maximization":[175],"an":[177,218],"appropriately":[178,219],"defined":[179],"average":[180],"signal-to-interference":[181],"noise":[183],"ratio":[184],"metric":[185],"user.":[188],"dominant":[193,238],"generalized":[194],"eigenvector":[195],"pair":[198],"positive-definite":[200],"where":[202],"forward":[212],"second":[216],"\u201ceffective\u201d":[221],"interference":[222],"matrix.":[224],"In":[225],"sense,":[227],"our":[228],"work":[229],"generalization":[232],"signalling":[235],"along":[236],"transmit":[242],"single-user":[247],"case.":[248],"Finally,":[249],"general":[255],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[262],"<tex":[263],"Notation=\"TeX\">$M$</tex></formula>":[264],"Notation=\"TeX\">$M$</tex>":[274],"</formula>":[275],"-users":[276],"links":[292],"vectors.":[296]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":33},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}