{"id":"https://openalex.org/W3188983320","doi":"https://doi.org/10.1109/iwcmc51323.2021.9498957","title":"Coverage Probability and Area Spectral Efficiency Analysis of Multi-Antenna Ultra-Dense Networks over Nakagami-$m$ Fading Channels","display_name":"Coverage Probability and Area Spectral Efficiency Analysis of Multi-Antenna Ultra-Dense Networks over Nakagami-$m$ Fading Channels","publication_year":2021,"publication_date":"2021-06-28","ids":{"openalex":"https://openalex.org/W3188983320","doi":"https://doi.org/10.1109/iwcmc51323.2021.9498957","mag":"3188983320"},"language":"en","primary_location":{"id":"doi:10.1109/iwcmc51323.2021.9498957","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iwcmc51323.2021.9498957","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 International Wireless Communications and Mobile Computing (IWCMC)","raw_type":"proceedings-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/A5112212992","display_name":"Donglai Zhao","orcid":"https://orcid.org/0000-0002-2307-6695"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Donglai Zhao","raw_affiliation_strings":["Communication Research Center, Harbin Institute of Technology, Harbin, China"],"affiliations":[{"raw_affiliation_string":"Communication Research Center, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100367467","display_name":"Gang Wang","orcid":"https://orcid.org/0000-0003-4088-0009"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Wang","raw_affiliation_strings":["Communication Research Center, Harbin Institute of Technology, Harbin, China"],"affiliations":[{"raw_affiliation_string":"Communication Research Center, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036421907","display_name":"Haoyang Liu","orcid":"https://orcid.org/0009-0009-6394-9348"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haoyang Liu","raw_affiliation_strings":["Communication Research Center, Harbin Institute of Technology, Harbin, China"],"affiliations":[{"raw_affiliation_string":"Communication Research Center, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100371683","display_name":"Ruoyu Zhang","orcid":"https://orcid.org/0000-0002-4105-5310"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruoyu Zhang","raw_affiliation_strings":["Ministerial Key Laboratory of JGMT, Nanjing University of Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Ministerial Key Laboratory of JGMT, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5112212992"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07829956,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1225","last_page":"1230"},"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":0.9998000264167786,"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/T10936","display_name":"Millimeter-Wave Propagation and Modeling","score":0.9994999766349792,"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/nakagami-distribution","display_name":"Nakagami distribution","score":0.8262995481491089},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.7605733871459961},{"id":"https://openalex.org/keywords/stochastic-geometry","display_name":"Stochastic geometry","score":0.7280358672142029},{"id":"https://openalex.org/keywords/rayleigh-fading","display_name":"Rayleigh fading","score":0.6204208135604858},{"id":"https://openalex.org/keywords/spectral-efficiency","display_name":"Spectral efficiency","score":0.591412365436554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5451844930648804},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.5312283635139465},{"id":"https://openalex.org/keywords/signal-to-interference-plus-noise-ratio","display_name":"Signal-to-interference-plus-noise ratio","score":0.5045634508132935},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.47783398628234863},{"id":"https://openalex.org/keywords/coverage-probability","display_name":"Coverage probability","score":0.46717745065689087},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4459362030029297},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.42498496174812317},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.42290979623794556},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.4184715449810028},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3698861598968506},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.32597821950912476},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2927241921424866},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.1829153299331665},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.1690630316734314},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13349738717079163},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.08963418006896973}],"concepts":[{"id":"https://openalex.org/C115098869","wikidata":"https://www.wikidata.org/wiki/Q3258347","display_name":"Nakagami distribution","level":4,"score":0.8262995481491089},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.7605733871459961},{"id":"https://openalex.org/C31243852","wikidata":"https://www.wikidata.org/wiki/Q1666739","display_name":"Stochastic geometry","level":2,"score":0.7280358672142029},{"id":"https://openalex.org/C56985126","wikidata":"https://www.wikidata.org/wiki/Q854039","display_name":"Rayleigh fading","level":4,"score":0.6204208135604858},{"id":"https://openalex.org/C137246740","wikidata":"https://www.wikidata.org/wiki/Q583970","display_name":"Spectral efficiency","level":3,"score":0.591412365436554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5451844930648804},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.5312283635139465},{"id":"https://openalex.org/C98824394","wikidata":"https://www.wikidata.org/wiki/Q4035626","display_name":"Signal-to-interference-plus-noise ratio","level":3,"score":0.5045634508132935},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.47783398628234863},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.46717745065689087},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4459362030029297},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.42498496174812317},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.42290979623794556},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.4184715449810028},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3698861598968506},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.32597821950912476},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2927241921424866},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.1829153299331665},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.1690630316734314},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13349738717079163},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.08963418006896973},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"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/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iwcmc51323.2021.9498957","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iwcmc51323.2021.9498957","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 International Wireless Communications and Mobile Computing (IWCMC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4398009636","display_name":null,"funder_award_id":"61671184","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1938738734","https://openalex.org/W2034420299","https://openalex.org/W2061084757","https://openalex.org/W2149170915","https://openalex.org/W2150166076","https://openalex.org/W2398409936","https://openalex.org/W2545053579","https://openalex.org/W2887019724","https://openalex.org/W3006695592","https://openalex.org/W3008609509","https://openalex.org/W3028842957","https://openalex.org/W3101445254"],"related_works":["https://openalex.org/W4229001419","https://openalex.org/W2059270103","https://openalex.org/W2794570086","https://openalex.org/W2558244751","https://openalex.org/W2963123640","https://openalex.org/W2736564488","https://openalex.org/W4299643046","https://openalex.org/W2952424632","https://openalex.org/W2031858701","https://openalex.org/W2944103099"],"abstract_inverted_index":{"Ultra-dense":[0],"network":[1],"(UDN)":[2],"is":[3,132,142,149],"emerging":[4],"as":[5],"a":[6,33],"promising":[7],"solution":[8],"to":[9,23,65,104,124,151],"meet":[10],"the":[11,46,71,81,107,115,129,153,159],"1000-fold":[12],"wireless":[13,18],"traffic":[14],"volume":[15],"increment":[16],"in":[17,44,94],"communication":[19],"systems.":[20],"In":[21,102],"order":[22,103],"inspire":[24],"system":[25,110],"design":[26,152],"and":[27,60],"evaluate":[28],"performance,":[29],"this":[30],"paper":[31],"develops":[32],"tractable":[34],"analysis":[35],"framework":[36],"of":[37,50,62,74,87,98,109,164],"multi-antenna":[38],"UDNs":[39,88],"over":[40],"Nakagami-m":[41,99],"fading":[42,91,100],"channels,":[43],"which":[45,121],"base":[47],"stations":[48],"(BSs)":[49],"each":[51],"tier":[52],"are":[53,118,122],"distinguished":[54],"by":[55],"spatial":[56],"densities,":[57,157],"transmit":[58],"powers":[59],"numbers":[61],"antennas.":[63],"Resorting":[64],"stochastic":[66],"geometry":[67],"model,":[68],"we":[69],"derive":[70],"closed-form":[72],"expression":[73,79],"coverage":[75,113,165],"probability.":[76,166],"The":[77,137],"analytical":[78],"reveals":[80],"signal-to-interference-plus-noise":[82],"ratio":[83],"(SINR)":[84],"invariance":[85],"property":[86],"with":[89,161],"Rayleigh":[90],"only":[92],"holds":[93],"some":[95],"special":[96],"case":[97],"scenario.":[101],"observe":[105],"intuitively":[106],"effects":[108],"parameters":[111],"on":[112],"probability,":[114],"asymptotic":[116],"results":[117],"also":[119,143],"given,":[120],"verified":[123],"be":[125],"almost":[126],"accurate":[127],"when":[128],"SINR":[130],"threshold":[131],"greater":[133],"than":[134],"6":[135],"dB.":[136],"area":[138],"spectral":[139],"efficiency":[140],"(ASE)":[141],"provided.":[144],"Furthermore,":[145],"an":[146],"effective":[147],"algorithm":[148],"proposed":[150],"optimal":[154],"active":[155],"BSs":[156],"maximizing":[158],"ASE":[160],"appropriate":[162],"requirements":[163]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}