{"id":"https://openalex.org/W2139060658","doi":"https://doi.org/10.1109/tit.2009.2023717","title":"The Effect of Finite Rate Feedback on CDMA Signature Optimization and MIMO Beamforming Vector Selection","display_name":"The Effect of Finite Rate Feedback on CDMA Signature Optimization and MIMO Beamforming Vector Selection","publication_year":2009,"publication_date":"2009-07-18","ids":{"openalex":"https://openalex.org/W2139060658","doi":"https://doi.org/10.1109/tit.2009.2023717","mag":"2139060658"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2009.2023717","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2023717","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/A5100752236","display_name":"Wei Dai","orcid":"https://orcid.org/0000-0002-4781-3485"},"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":"Wei Dai","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL, USA","Dept. of Electr. & Comput. Eng., Univ. of Illinois, Urbana, IL, , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Univ. of Illinois, Urbana, IL, , USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084454849","display_name":"Youjian Liu","orcid":"https://orcid.org/0000-0003-4681-0546"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Youjian Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA","Department of Electrical and Computer Engineering, University of Colorado Boulder, CO"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Colorado Boulder, CO","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017012202","display_name":"Brian Rider","orcid":"https://orcid.org/0000-0002-0538-8441"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Rider","raw_affiliation_strings":["Mathematics Department, University of Colorado, Boulder, CO, USA","Mathematics Department, University of Colorado, Boulder, CO"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Mathematics Department, University of Colorado, Boulder, CO","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.831,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.865061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"55","issue":"8","first_page":"3651","last_page":"3669"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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/T10575","display_name":"Wireless Communication Networks Research","score":0.9995999932289124,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9976000189781189,"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/codebook","display_name":"Codebook","score":0.853922963142395},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.8291494846343994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5521475672721863},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.5269594788551331},{"id":"https://openalex.org/keywords/code-division-multiple-access","display_name":"Code division multiple access","score":0.5099567174911499},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48907095193862915},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.455101877450943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38028281927108765},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35593974590301514},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20871800184249878},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.14262431859970093},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07569938898086548}],"concepts":[{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.853922963142395},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.8291494846343994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5521475672721863},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.5269594788551331},{"id":"https://openalex.org/C47696715","wikidata":"https://www.wikidata.org/wiki/Q233394","display_name":"Code division multiple access","level":2,"score":0.5099567174911499},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48907095193862915},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.455101877450943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38028281927108765},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35593974590301514},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20871800184249878},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.14262431859970093},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07569938898086548},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2009.2023717","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2023717","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:CiteSeerX.psu:10.1.1.158.928","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ece.colorado.edu/~liue/publications/papers/Liu_IT06s_CDMA.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.4412","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.4412","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.colorado.edu/~brider/CDMA_journal7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.4419","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.4419","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0612078v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.7869","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.7869","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0612078v2.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":29,"referenced_works":["https://openalex.org/W174635644","https://openalex.org/W1969097180","https://openalex.org/W1974637548","https://openalex.org/W1974755392","https://openalex.org/W1981573335","https://openalex.org/W1997834106","https://openalex.org/W2001932083","https://openalex.org/W2009188663","https://openalex.org/W2027559193","https://openalex.org/W2034680120","https://openalex.org/W2038021890","https://openalex.org/W2060187788","https://openalex.org/W2081715952","https://openalex.org/W2089794108","https://openalex.org/W2120350343","https://openalex.org/W2129394611","https://openalex.org/W2129940604","https://openalex.org/W2134765312","https://openalex.org/W2136979582","https://openalex.org/W2142066418","https://openalex.org/W2151853371","https://openalex.org/W2159107945","https://openalex.org/W2912369344","https://openalex.org/W3099134300","https://openalex.org/W4293005804","https://openalex.org/W4301258660","https://openalex.org/W4362230038","https://openalex.org/W6607265895","https://openalex.org/W6679416389"],"related_works":["https://openalex.org/W3207918248","https://openalex.org/W2130785056","https://openalex.org/W2506626932","https://openalex.org/W2037755532","https://openalex.org/W2620095399","https://openalex.org/W1488668773","https://openalex.org/W2006021297","https://openalex.org/W4288602396","https://openalex.org/W2914555611","https://openalex.org/W4285192270"],"abstract_inverted_index":{"We":[0],"analyze":[1],"the":[2,29,48,53,61,73,80,84,115,131,134,137,143,155,159,172],"effect":[3],"of":[4,133,139,158],"finite":[5,103],"rate":[6,119,145],"feedback":[7,116,144],"on":[8,154,180],"code-division":[9],"multiple-access":[10],"(CDMA)":[11],"signature":[12,23,33],"optimization":[13],"and":[14,45,77,142],"multiple-input":[15],"multiple-output":[16],"(MIMO)":[17],"beamforming":[18,58,65],"vector":[19,34,59,66,100],"selection.":[20],"In":[21],"CDMA":[22],"optimization,":[24],"for":[25],"a":[26,32,36,64,68,97,102,108],"particular":[27],"user,":[28],"receiver":[30,62],"selects":[31],"from":[35,42,67,101,171],"codebook":[37,70,105],"to":[38,52,71,83,106],"best":[39],"avoid":[40],"interference":[41],"other":[43],"users,":[44],"then":[46],"feeds":[47,78],"corresponding":[49,81],"index":[50,82],"back":[51,79],"specified":[54],"user.":[55],"For":[56],"MIMO":[57],"selection,":[60],"chooses":[63],"given":[69],"maximize":[72],"instantaneous":[74],"information":[75],"rate,":[76],"transmitter.":[85],"These":[86],"two":[87],"problems":[88],"are":[89,175],"dual:":[90],"both":[91],"can":[92],"be":[93],"modeled":[94],"as":[95],"selecting":[96],"unit":[98],"norm":[99],"size":[104],"ldquomatchrdquo":[107],"randomly":[109],"generated":[110,170],"Gaussian":[111],"matrix.":[112],"Assuming":[113],"that":[114,167],"link":[117],"is":[118,124],"limited,":[120],"our":[121],"main":[122],"result":[123],"an":[125],"exact":[126],"asymptotic":[127],"performance":[128],"formula":[129],"where":[130],"length":[132],"signature/beamforming":[135],"vector,":[136],"dimensions":[138],"interference/channel":[140],"matrix,":[141],"approach":[146],"infinity":[147],"with":[148],"constant":[149],"ratios.":[150],"The":[151],"proof":[152],"rests":[153],"large":[156],"deviations":[157],"underlying":[160],"random":[161,168],"matrix":[162],"ensemble.":[163],"Further,":[164],"we":[165],"show":[166],"codebooks":[169],"isotropic":[173],"distribution":[174],"asymptotically":[176],"optimal":[177],"not":[178],"only":[179],"average,":[181],"but":[182],"also":[183],"in":[184],"probability.":[185]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}