{"id":"https://openalex.org/W2962926283","doi":"https://doi.org/10.1109/tcomm.2018.2890247","title":"SIR Meta Distribution of $K$ -Tier Downlink Heterogeneous Cellular Networks With Cell Range Expansion","display_name":"SIR Meta Distribution of $K$ -Tier Downlink Heterogeneous Cellular Networks With Cell Range Expansion","publication_year":2018,"publication_date":"2018-12-28","ids":{"openalex":"https://openalex.org/W2962926283","doi":"https://doi.org/10.1109/tcomm.2018.2890247","mag":"2962926283"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2018.2890247","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2018.2890247","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/A5040081419","display_name":"Yuanjie Wang","orcid":"https://orcid.org/0000-0003-3601-4079"},"institutions":[{"id":"https://openalex.org/I4210087772","display_name":"National Computer Network Emergency Response Technical Team/Coordination Center of Chinar","ror":"https://ror.org/00247dh76","country_code":"CN","type":"nonprofit","lineage":["https://openalex.org/I4210087772"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanjie Wang","raw_affiliation_strings":["National Computer Network Emergency Response Technical Team/Coordination Center of China (CNCERT/CC), Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-3601-4079","affiliations":[{"raw_affiliation_string":"National Computer Network Emergency Response Technical Team/Coordination Center of China (CNCERT/CC), Beijing, China","institution_ids":["https://openalex.org/I4210087772"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003896287","display_name":"Martin Haenggi","orcid":"https://orcid.org/0000-0001-8547-0607"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin Haenggi","raw_affiliation_strings":["Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA"],"raw_orcid":"https://orcid.org/0000-0001-8547-0607","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100615716","display_name":"Zhenhui Tan","orcid":"https://orcid.org/0000-0002-7862-1910"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenhui Tan","raw_affiliation_strings":["State Key Laboratory of Railway Traffic Control and Safety, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-7862-1910","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Railway Traffic Control and Safety, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1664,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.9474834,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"67","issue":"4","first_page":"3069","last_page":"3081"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9945999979972839,"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":0.9817000031471252,"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/cellular-network","display_name":"Cellular network","score":0.6878179907798767},{"id":"https://openalex.org/keywords/coverage-probability","display_name":"Coverage probability","score":0.598783552646637},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5931407809257507},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.5619429349899292},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4775967597961426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4767623543739319},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.4764564335346222},{"id":"https://openalex.org/keywords/conditional-probability","display_name":"Conditional probability","score":0.4652586579322815},{"id":"https://openalex.org/keywords/poisson-point-process","display_name":"Poisson point process","score":0.4581751525402069},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4502904415130615},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.43604105710983276},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34696558117866516},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3462895154953003},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.17639335989952087},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1020556092262268},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09733226895332336}],"concepts":[{"id":"https://openalex.org/C153646914","wikidata":"https://www.wikidata.org/wiki/Q535695","display_name":"Cellular network","level":2,"score":0.6878179907798767},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.598783552646637},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5931407809257507},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5619429349899292},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4775967597961426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4767623543739319},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.4764564335346222},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.4652586579322815},{"id":"https://openalex.org/C16757284","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson point process","level":3,"score":0.4581751525402069},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4502904415130615},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.43604105710983276},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34696558117866516},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3462895154953003},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.17639335989952087},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1020556092262268},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09733226895332336},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcomm.2018.2890247","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2018.2890247","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3419934950","display_name":null,"funder_award_id":"61601018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5055946434","display_name":null,"funder_award_id":"Z181100003218010","funder_id":"https://openalex.org/F4320325902","funder_display_name":"Beijing Municipal Science and Technology Commission"},{"id":"https://openalex.org/G5262524897","display_name":"\u57fa\u4e8eLTE\u7684\u516c\u7f51\u548c\u4e13\u7f51\u5171\u5b58\u9ad8\u94c1\u901a\u4fe1\u7cfb\u7edf\u63a5\u5165\u67b6\u6784\u53ca\u5176\u5173\u952e\u6280\u672f\u7814\u7a76","funder_award_id":"61471030","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G692438369","display_name":null,"funder_award_id":"CCF 1525904","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7006046862","display_name":null,"funder_award_id":"2019D01","funder_id":"https://openalex.org/F4320324856","funder_display_name":"Southeast University"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324856","display_name":"Southeast University","ror":"https://ror.org/04ct4d772"},{"id":"https://openalex.org/F4320325902","display_name":"Beijing Municipal Science and Technology Commission","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W631335369","https://openalex.org/W922358034","https://openalex.org/W1584905095","https://openalex.org/W1640283668","https://openalex.org/W2034420299","https://openalex.org/W2049496443","https://openalex.org/W2058477717","https://openalex.org/W2059973889","https://openalex.org/W2094040025","https://openalex.org/W2101121986","https://openalex.org/W2114207517","https://openalex.org/W2149170915","https://openalex.org/W2150166076","https://openalex.org/W2332082792","https://openalex.org/W2479774998","https://openalex.org/W2570805543","https://openalex.org/W2605261135","https://openalex.org/W2736208033","https://openalex.org/W2755230429","https://openalex.org/W2769047447","https://openalex.org/W2799837476","https://openalex.org/W2963262497","https://openalex.org/W2963320716","https://openalex.org/W2963552745","https://openalex.org/W2963749079","https://openalex.org/W2964168570","https://openalex.org/W3101445254","https://openalex.org/W3105072513","https://openalex.org/W3124447267"],"related_works":["https://openalex.org/W2225046392","https://openalex.org/W1939724041","https://openalex.org/W1542638718","https://openalex.org/W2581319931","https://openalex.org/W2006738180","https://openalex.org/W1524411820","https://openalex.org/W2017282549","https://openalex.org/W2787833841","https://openalex.org/W4210295422","https://openalex.org/W3196246556"],"abstract_inverted_index":{"Heterogeneous":[0],"cellular":[1,12,38],"networks":[2,39],"(HCNs)":[3],"constitute":[4],"a":[5,27],"necessary":[6],"step":[7],"in":[8,56],"the":[9,19,42,61,65,71,82,87,98,102,105,109,114,127,132,138,143,148,160,165,170,180,183,187,192],"evolution":[10],"of":[11,32,64,104,118,137,147,152,164,169,182,186,196],"networks.":[13],"In":[14],"this":[15],"paper,":[16],"we":[17],"apply":[18],"signal-to-interference":[20],"ratio":[21],"(SIR)":[22],"meta":[23,84],"distribution":[24],"framework":[25],"for":[26,60,69,179],"refined":[28],"SIR":[29,116],"performance":[30,95],"analysis":[31],"HCNs,":[33],"focusing":[34],"on":[35,41,80],"K-tier":[36],"heterogeneous":[37],"based":[40,79],"homogeneous":[43],"independent":[44],"Poisson":[45],"point":[46],"process":[47],"(PPP)":[48],"model,":[49],"with":[50],"range":[51],"expansion":[52],"bias":[53],"(offloading":[54],"bias)":[55],"each":[57,75,119,153,197],"tier.":[58],"Expressions":[59],"b-th":[62,144],"moment":[63,145,167],"conditional":[66,106,149],"success":[67,100,107,135,150],"probability":[68,136,151],"both":[70],"entire":[72],"network":[73,140],"and":[74,86,92,113,141],"tier":[76,120,154,198],"are":[77,90,121,129],"derived,":[78],"which":[81],"exact":[83],"distributions":[85],"beta":[88],"approximations":[89],"evaluated":[91],"compared.":[93],"Key":[94],"metrics,":[96],"including":[97],"mean":[99,110,134,193],"probability,":[101,108],"variance":[103],"local":[111,194],"delay,":[112],"asymptotic":[115],"gains":[117],"obtained.":[122],"The":[123],"results":[124],"show":[125],"that":[126,142],"biases":[128],"detrimental":[130],"to":[131,190],"overall":[133],"whole":[139],"curve":[146,168],"can":[155],"be":[156],"tightly":[157],"approximated":[158],"by":[159],"horizontal":[161],"shifted":[162],"versions":[163],"first":[166],"single-tier":[171],"PPP":[172],"network.":[173],"We":[174],"also":[175],"provide":[176],"lower":[177],"bounds":[178],"region":[181],"active":[184],"probabilities":[185],"base":[188],"stations":[189],"keep":[191],"delay":[195],"finite.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
