{"id":"https://openalex.org/W628685110","doi":"https://doi.org/10.1109/tcomm.2016.2531719","title":"Success Probability and Area Spectral Efficiency in Multiuser MIMO HetNets","display_name":"Success Probability and Area Spectral Efficiency in Multiuser MIMO HetNets","publication_year":2016,"publication_date":"2016-02-18","ids":{"openalex":"https://openalex.org/W628685110","doi":"https://doi.org/10.1109/tcomm.2016.2531719","mag":"628685110"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2016.2531719","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2016.2531719","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","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/A5100429541","display_name":"Chang Li","orcid":"https://orcid.org/0000-0003-1341-2672"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Chang Li","raw_affiliation_strings":["Department of ECE, Hong Kong University of Science and Technology, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ECE, Hong Kong University of Science and Technology, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100433167","display_name":"Jun Zhang","orcid":"https://orcid.org/0000-0002-5222-1898"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jun Zhang","raw_affiliation_strings":["Department of ECE, Hong Kong University of Science and Technology, Kowloon, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ECE, Hong Kong University of Science and Technology, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042833857","display_name":"Jeffrey G. Andrews","orcid":"https://orcid.org/0000-0002-9115-5088"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeffrey G. Andrews","raw_affiliation_strings":["Wireless Networking and Communications Group (WNCG), University of Texas at Austin, Austin, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wireless Networking and Communications Group (WNCG), University of Texas at Austin, Austin, TX, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079052203","display_name":"Khaled B. Letaief","orcid":"https://orcid.org/0000-0003-2519-6401"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I4210144839","display_name":"Hamad bin Khalifa University","ror":"https://ror.org/03eyq4y97","country_code":"QA","type":"education","lineage":["https://openalex.org/I4210144839"]}],"countries":["HK","QA"],"is_corresponding":false,"raw_author_name":"Khaled B. Letaief","raw_affiliation_strings":["Department of ECE, Hong Kong University of Science and Technology, Kowloon, Hong Kong","Hamad bin Khalifa University, Qatar"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of ECE, Hong Kong University of Science and Technology, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Hamad bin Khalifa University, Qatar","institution_ids":["https://openalex.org/I4210144839"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.1573,"has_fulltext":false,"cited_by_count":97,"citation_normalized_percentile":{"value":0.98563358,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"64","issue":"4","first_page":"1544","last_page":"1556"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":1.0,"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":1.0,"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":0.9993000030517578,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9930999875068665,"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":0.7143531441688538},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.6541921496391296},{"id":"https://openalex.org/keywords/precoding","display_name":"Precoding","score":0.6328369379043579},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.593653678894043},{"id":"https://openalex.org/keywords/spectral-efficiency","display_name":"Spectral efficiency","score":0.5346516370773315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5270838141441345},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.4618353843688965},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.42754656076431274},{"id":"https://openalex.org/keywords/heterogeneous-network","display_name":"Heterogeneous network","score":0.4216667115688324},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.40140247344970703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3473414480686188},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3381548225879669},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.32416272163391113},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.2892887592315674},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.17422634363174438},{"id":"https://openalex.org/keywords/wireless-network","display_name":"Wireless network","score":0.16377511620521545},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.16038236021995544}],"concepts":[{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.7143531441688538},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.6541921496391296},{"id":"https://openalex.org/C160562895","wikidata":"https://www.wikidata.org/wiki/Q7239557","display_name":"Precoding","level":4,"score":0.6328369379043579},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.593653678894043},{"id":"https://openalex.org/C137246740","wikidata":"https://www.wikidata.org/wiki/Q583970","display_name":"Spectral efficiency","level":3,"score":0.5346516370773315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5270838141441345},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.4618353843688965},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.42754656076431274},{"id":"https://openalex.org/C158207573","wikidata":"https://www.wikidata.org/wiki/Q5747224","display_name":"Heterogeneous network","level":4,"score":0.4216667115688324},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40140247344970703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3473414480686188},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3381548225879669},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.32416272163391113},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.2892887592315674},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.17422634363174438},{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"score":0.16377511620521545},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.16038236021995544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcomm.2016.2531719","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2016.2531719","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-76593","is_oa":false,"landing_page_url":"http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=LinksAMR&SrcApp=PARTNER_APP&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000375032400015","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W631335369","https://openalex.org/W1516699597","https://openalex.org/W1938738734","https://openalex.org/W1967956032","https://openalex.org/W1985614579","https://openalex.org/W1990810841","https://openalex.org/W1999509241","https://openalex.org/W2005108639","https://openalex.org/W2031116206","https://openalex.org/W2032712938","https://openalex.org/W2034420299","https://openalex.org/W2038397443","https://openalex.org/W2039688938","https://openalex.org/W2044593797","https://openalex.org/W2044701388","https://openalex.org/W2054692642","https://openalex.org/W2056916045","https://openalex.org/W2057540419","https://openalex.org/W2081450055","https://openalex.org/W2094629654","https://openalex.org/W2095796369","https://openalex.org/W2101121986","https://openalex.org/W2102473388","https://openalex.org/W2109830484","https://openalex.org/W2112170521","https://openalex.org/W2114731473","https://openalex.org/W2128513990","https://openalex.org/W2132475944","https://openalex.org/W2132987440","https://openalex.org/W2134686390","https://openalex.org/W2137079066","https://openalex.org/W2139794367","https://openalex.org/W2149170915","https://openalex.org/W2150166076","https://openalex.org/W2150415860","https://openalex.org/W2150450717","https://openalex.org/W2155860576","https://openalex.org/W2329563144","https://openalex.org/W2545053579","https://openalex.org/W2572140128","https://openalex.org/W2963023977","https://openalex.org/W2963533254","https://openalex.org/W2963847582","https://openalex.org/W3098676606","https://openalex.org/W3101445254","https://openalex.org/W3103727043","https://openalex.org/W3104311449","https://openalex.org/W3105072513","https://openalex.org/W3106282754","https://openalex.org/W4205864033","https://openalex.org/W4250589301","https://openalex.org/W4254169510","https://openalex.org/W6679968120"],"related_works":["https://openalex.org/W3141240674","https://openalex.org/W2116541631","https://openalex.org/W2167568384","https://openalex.org/W2514205366","https://openalex.org/W3173074004","https://openalex.org/W1976511355","https://openalex.org/W2962922943","https://openalex.org/W2544668827","https://openalex.org/W2613807087","https://openalex.org/W4313028534"],"abstract_inverted_index":{"We":[0,111],"derive":[1],"a":[2,20,70,143,163],"general":[3],"and":[4,41,57,149,189],"closed-form":[5],"result":[6,68],"for":[7,44,97],"the":[8,31,88,101,107,114,128,139,147,158,173,182],"success":[9,102,116],"probability":[10,103,117],"in":[11,152],"downlink":[12],"multiple-antenna":[13],"(MIMO)":[14],"heterogeneous":[15],"cellular":[16],"networks":[17],"(HetNets),":[18],"utilizing":[19],"novel":[21],"Toeplitz":[22],"matrix":[23],"representation.":[24],"This":[25,141],"main":[26],"result,":[27],"which":[28],"is":[29,75,118,134,178],"equivalently":[30],"signal-to-interference":[32],"ratio":[33],"(SIR)":[34],"distribution,":[35],"includes":[36],"multiuser":[37,153],"MIMO,":[38],"single-user":[39],"MIMO":[40,98,154],"per-tier":[42],"biasing":[43],"K":[45],"different":[46],"tiers":[47,191],"of":[48,66,91,125],"randomly":[49],"placed":[50],"base":[51],"stations":[52],"(BSs),":[53],"assuming":[54],"zero-forcing":[55],"precoding":[56],"perfect":[58],"channel":[59],"state":[60],"information.":[61],"The":[62],"large":[63],"SIR":[64],"limit":[65],"this":[67],"admits":[69],"simple":[71],"closed":[72],"form":[73],"that":[74,87,113,180],"accurate":[76],"at":[77],"moderate":[78],"SIRs,":[79],"e.g.,":[80],"above":[81],"5":[82],"dB.":[83],"These":[84],"results":[85],"reveal":[86],"SIR-invariance":[89],"property":[90],"SISO":[92],"HetNets":[93],"does":[94],"not":[95],"hold":[96],"HetNets;":[99],"instead":[100],"may":[104],"decrease":[105],"as":[106,181],"network":[108],"density":[109],"increases.":[110],"prove":[112],"maximum":[115,129,159],"achieved":[119,135],"by":[120,136],"activating":[121,137],"only":[122],"one":[123],"tier":[124],"BSs,":[126],"while":[127,161],"area":[130],"spectral":[131],"efficiency":[132],"(ASE)":[133],"all":[138],"BSs.":[140],"reveals":[142],"unique":[144],"tradeoff":[145],"between":[146],"ASE":[148,160],"link":[150,165,183],"reliability":[151,184],"HetNets.":[155],"To":[156],"achieve":[157],"guaranteeing":[162],"certain":[164],"reliability,":[166],"we":[167],"develop":[168],"efficient":[169],"algorithms":[170],"to":[171],"find":[172],"optimal":[174],"BS":[175],"densities.":[176],"It":[177],"shown":[179],"requirement":[185],"increases,":[186],"more":[187,190],"BSs":[188],"should":[192],"be":[193],"deactivated.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":9}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}