{"id":"https://openalex.org/W1987131910","doi":"https://doi.org/10.1109/tsp.2011.2169250","title":"Bit Allocation Laws for Multiantenna Channel Feedback Quantization: Multiuser Case","display_name":"Bit Allocation Laws for Multiantenna Channel Feedback Quantization: Multiuser Case","publication_year":2011,"publication_date":"2011-09-28","ids":{"openalex":"https://openalex.org/W1987131910","doi":"https://doi.org/10.1109/tsp.2011.2169250","mag":"1987131910"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2169250","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2169250","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/A5004659384","display_name":"Behrouz Khoshnevis","orcid":null},"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":"Behrouz Khoshnevis","raw_affiliation_strings":["Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","Edward S. Rogers Sr.Dept. of Electr. & Comput. Eng., Univ. of Toronto, Toronto, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Edward S. Rogers Sr.Dept. of Electr. & Comput. Eng., Univ. of Toronto, Toronto, ON, 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":["Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","Edward S. Rogers Sr.Dept. of Electr. & Comput. Eng., Univ. of Toronto, Toronto, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Edward S. Rogers Sr.Dept. of Electr. & Comput. Eng., Univ. of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":3.7278,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.93285405,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"1","first_page":"367","last_page":"382"},"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9997000098228455,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9962000250816345,"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/telecommunications-link","display_name":"Telecommunications link","score":0.7384803295135498},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.6691427230834961},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6310955286026001},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.6174076795578003},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5154843926429749},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.4726860821247101},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4615834355354309},{"id":"https://openalex.org/keywords/multiplexing","display_name":"Multiplexing","score":0.43607693910598755},{"id":"https://openalex.org/keywords/quality-of-service","display_name":"Quality of service","score":0.4175119698047638},{"id":"https://openalex.org/keywords/antenna-array","display_name":"Antenna array","score":0.41313236951828003},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34446024894714355},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.29283618927001953},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.267905592918396},{"id":"https://openalex.org/keywords/antenna","display_name":"Antenna (radio)","score":0.17484450340270996},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.16273951530456543}],"concepts":[{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.7384803295135498},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.6691427230834961},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6310955286026001},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.6174076795578003},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5154843926429749},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.4726860821247101},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4615834355354309},{"id":"https://openalex.org/C19275194","wikidata":"https://www.wikidata.org/wiki/Q222903","display_name":"Multiplexing","level":2,"score":0.43607693910598755},{"id":"https://openalex.org/C5119721","wikidata":"https://www.wikidata.org/wiki/Q220501","display_name":"Quality of service","level":2,"score":0.4175119698047638},{"id":"https://openalex.org/C62191587","wikidata":"https://www.wikidata.org/wiki/Q4771249","display_name":"Antenna array","level":3,"score":0.41313236951828003},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34446024894714355},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.29283618927001953},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.267905592918396},{"id":"https://openalex.org/C21822782","wikidata":"https://www.wikidata.org/wiki/Q131214","display_name":"Antenna (radio)","level":2,"score":0.17484450340270996},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.16273951530456543},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2011.2169250","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2169250","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W103210042","https://openalex.org/W1522995151","https://openalex.org/W1577636146","https://openalex.org/W1634005169","https://openalex.org/W1981791056","https://openalex.org/W1983750859","https://openalex.org/W1997260775","https://openalex.org/W2054244643","https://openalex.org/W2073345302","https://openalex.org/W2074120933","https://openalex.org/W2074863717","https://openalex.org/W2083962008","https://openalex.org/W2091497247","https://openalex.org/W2095936794","https://openalex.org/W2098660254","https://openalex.org/W2101067739","https://openalex.org/W2106872716","https://openalex.org/W2106993652","https://openalex.org/W2109005286","https://openalex.org/W2110851539","https://openalex.org/W2111673250","https://openalex.org/W2113588842","https://openalex.org/W2116141601","https://openalex.org/W2121297044","https://openalex.org/W2124858630","https://openalex.org/W2127441946","https://openalex.org/W2128296785","https://openalex.org/W2130785056","https://openalex.org/W2142905341","https://openalex.org/W2143432773","https://openalex.org/W2143927285","https://openalex.org/W2144778327","https://openalex.org/W2151444885","https://openalex.org/W2161473225","https://openalex.org/W2162876202","https://openalex.org/W2168679175","https://openalex.org/W2172085187","https://openalex.org/W2296319761","https://openalex.org/W2545271035","https://openalex.org/W3098178686","https://openalex.org/W3112681748","https://openalex.org/W3141468348","https://openalex.org/W4210801094","https://openalex.org/W4250589301","https://openalex.org/W4297970755","https://openalex.org/W6674625002","https://openalex.org/W6685120885"],"related_works":["https://openalex.org/W4365807906","https://openalex.org/W2157864637","https://openalex.org/W4223416141","https://openalex.org/W2546639359","https://openalex.org/W1922070205","https://openalex.org/W2106711889","https://openalex.org/W4226210192","https://openalex.org/W2032430904","https://openalex.org/W2101042359","https://openalex.org/W2011751543"],"abstract_inverted_index":{"This":[0],"paper":[1,97,251],"addresses":[2],"the":[3,45,49,54,72,77,80,107,124,127,142,154,185,194,201,209,213,218,222,229,239,245,250,255,265,268,272],"optimal":[4],"design":[5],"of":[6,47,109,129,144,156,184,212,221,258,267],"limited-feedback":[7,269],"downlink":[8,174],"multiuser":[9],"spatial":[10],"multiplexing":[11],"systems.":[12],"A":[13],"multiple-antenna":[14],"base-station":[15,55,157],"is":[16,42,69,111,153,189,234],"assumed":[17],"to":[18,57,70,198,236],"serve":[19],"multiple":[20],"single-antenna":[21],"users,":[22],"who":[23],"quantize":[24],"and":[25,63,79,84,171,217],"feed":[26],"back":[27],"their":[28],"channel":[29,82,130,145],"state":[30],"information":[31],"(CSI)":[32],"through":[33],"a":[34,89],"shared":[35],"rate-limited":[36],"feedback":[37,73,186,203,232,259],"channel.":[38],"The":[39,67,117],"optimization":[40,100],"problem":[41],"cast":[43],"in":[44,88,123],"form":[46],"minimizing":[48],"average":[50],"transmission":[51],"power":[52],"at":[53],"subject":[56],"users'":[58,240],"target":[59,168,178,195,214,224,241],"signal-to-interference-plus-noise":[60],"ratios":[61],"(SINR)":[62],"outage":[64,169,225],"probability":[65],"constraints.":[66],"goal":[68],"derive":[71],"bit":[74],"allocations":[75],"among":[76],"users":[78,160],"corresponding":[81,246],"magnitude":[83,146],"direction":[85,131],"quantization":[86,91,132,147],"codebooks":[87],"high-resolution":[90],"regime.":[92],"Toward":[93],"this":[94,96],"end,":[95],"develops":[98],"an":[99],"framework":[101],"using":[102],"approximate":[103],"analytical":[104],"closed-form":[105],"solutions,":[106],"accuracy":[108],"which":[110],"then":[112],"verified":[113],"by":[114],"numerical":[115],"results.":[116],"results":[118],"show":[119],"that,":[120,192,253],"for":[121,193],"channels":[122],"real":[125],"space,":[126],"number":[128,143,155,257],"bits":[133,260],"should":[134,180,205],"be":[135,199],"(":[136],"<i":[137,150,261,280,284],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[138,151,262,278,281,285,288],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">M</i>":[139,152,286],"-1)":[140],"times":[141],"bits,":[148],"where":[149],"antennas.":[158],"Moreover,":[159],"with":[161,208],"higher":[162,172,177],"requested":[163,173],"quality-of-service":[164],"(QoS),":[165],"i.e.,":[166,176],"lower":[167],"probabilities,":[170],"rates,":[175],"SINR's,":[179],"use":[181],"larger":[182],"shares":[183],"rate.":[187],"It":[188],"also":[190],"shown":[191,235],"QoS":[196],"parameters":[197,242],"feasible,":[200],"total":[202,256],"bandwidth":[204],"scale":[206],"logarithmically":[207],"geometric":[210,219,247],"mean":[211,220],"SINR":[215],"values":[216],"inverse":[223],"probabilities.":[226],"In":[227],"particular,":[228],"minimum":[230],"required":[231],"rate":[233],"increase":[237],"if":[238],"deviate":[243],"from":[244],"means.":[248],"Finally,":[249],"shows":[252],"as":[254,275],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">B</i>":[263,282],"increases,":[264],"performance":[266],"system":[270,274],"approaches":[271],"perfect-CSI":[273],"2":[276],"<sup":[277,287],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-</sup>":[279],"/":[283],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[289],".":[290]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}