{"id":"https://openalex.org/W1584905095","doi":"https://doi.org/10.1109/jsac.2015.2435471","title":"Heterogeneous Cellular Network Models With Dependence","display_name":"Heterogeneous Cellular Network Models With Dependence","publication_year":2015,"publication_date":"2015-05-20","ids":{"openalex":"https://openalex.org/W1584905095","doi":"https://doi.org/10.1109/jsac.2015.2435471","mag":"1584905095"},"language":"en","primary_location":{"id":"doi:10.1109/jsac.2015.2435471","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsac.2015.2435471","pdf_url":null,"source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"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 Journal on Selected Areas in 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/A5010826342","display_name":"Na Deng","orcid":"https://orcid.org/0000-0002-9565-559X"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Na Deng","raw_affiliation_strings":["Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China","Dept. of Electronic Engineering & Information Science, University of Science and Technology of China, Hefei, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"Dept. of Electronic Engineering & Information Science, University of Science and Technology of China, Hefei, China#TAB#","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065141875","display_name":"Wuyang Zhou","orcid":"https://orcid.org/0000-0003-2229-2852"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wuyang Zhou","raw_affiliation_strings":["Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China","Dept. of Electronic Engineering & Information Science, University of Science and Technology of China, Hefei, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"Dept. of Electronic Engineering & Information Science, University of Science and Technology of China, Hefei, China#TAB#","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","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","Dept. of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Dept. of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.6333,"has_fulltext":false,"cited_by_count":108,"citation_normalized_percentile":{"value":0.98980565,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"33","issue":"10","first_page":"2167","last_page":"2181"},"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/T10936","display_name":"Millimeter-Wave Propagation and Modeling","score":0.9952999949455261,"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":0.9940000176429749,"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/poisson-point-process","display_name":"Poisson point process","score":0.7926169633865356},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.7792155742645264},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7591535449028015},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.7325443625450134},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.7111722230911255},{"id":"https://openalex.org/keywords/cellular-network","display_name":"Cellular network","score":0.6306738257408142},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.5630192160606384},{"id":"https://openalex.org/keywords/stochastic-geometry","display_name":"Stochastic geometry","score":0.534518301486969},{"id":"https://openalex.org/keywords/macro","display_name":"Macro","score":0.5005102157592773},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.38629329204559326},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.38033878803253174},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1735074818134308},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.15922993421554565},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09061327576637268}],"concepts":[{"id":"https://openalex.org/C16757284","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson point process","level":3,"score":0.7926169633865356},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.7792155742645264},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7591535449028015},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.7325443625450134},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.7111722230911255},{"id":"https://openalex.org/C153646914","wikidata":"https://www.wikidata.org/wiki/Q535695","display_name":"Cellular network","level":2,"score":0.6306738257408142},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.5630192160606384},{"id":"https://openalex.org/C31243852","wikidata":"https://www.wikidata.org/wiki/Q1666739","display_name":"Stochastic geometry","level":2,"score":0.534518301486969},{"id":"https://openalex.org/C166955791","wikidata":"https://www.wikidata.org/wiki/Q629579","display_name":"Macro","level":2,"score":0.5005102157592773},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38629329204559326},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.38033878803253174},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1735074818134308},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15922993421554565},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09061327576637268},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/jsac.2015.2435471","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsac.2015.2435471","pdf_url":null,"source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"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 Journal on Selected Areas in Communications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3730135242","display_name":null,"funder_award_id":"61461136002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4595550637","display_name":null,"funder_award_id":"CNS 1016742","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7608988406","display_name":null,"funder_award_id":"CCF 1216407","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W631335369","https://openalex.org/W1979888558","https://openalex.org/W2006763061","https://openalex.org/W2039688938","https://openalex.org/W2045521465","https://openalex.org/W2058477717","https://openalex.org/W2059973889","https://openalex.org/W2069051426","https://openalex.org/W2076773434","https://openalex.org/W2101121986","https://openalex.org/W2117059442","https://openalex.org/W2127337238","https://openalex.org/W2143252188","https://openalex.org/W2145873277","https://openalex.org/W2149170915","https://openalex.org/W2150166076","https://openalex.org/W2156356530","https://openalex.org/W2942228371","https://openalex.org/W2963121780","https://openalex.org/W2963320716","https://openalex.org/W3008609509","https://openalex.org/W3103087912","https://openalex.org/W3105072513","https://openalex.org/W3113221786","https://openalex.org/W4301253858"],"related_works":["https://openalex.org/W2591746957","https://openalex.org/W4252323550","https://openalex.org/W2065735671","https://openalex.org/W2964313726","https://openalex.org/W1871594675","https://openalex.org/W2624272231","https://openalex.org/W2944404691","https://openalex.org/W2952796263","https://openalex.org/W87902424","https://openalex.org/W2883651331"],"abstract_inverted_index":{"Due":[0],"to":[1,129,136,253],"its":[2,104],"tractability,":[3,266],"a":[4,77,83,95,101,124,138,156,214,221,249],"multitier":[5,228],"model":[6,212,219,231],"of":[7,30,115,141,167,251],"mutually":[8],"independent":[9,160,229],"Poisson":[10,78,84,126],"point":[11,79],"processes":[12],"(PPPs)":[13],"for":[14,177,201,220],"heterogeneous":[15],"cellular":[16],"networks":[17],"(HCNs)":[18],"has":[19],"recently":[20],"been":[21],"attracting":[22],"much":[23],"attention.":[24],"However,":[25],"in":[26,44],"reality,":[27],"the":[28,31,66,71,112,131,142,150,153,168,171,189,192,196,208,227,233,242,246,256,264],"locations":[29],"BSs,":[32],"within":[33],"each":[34],"tier":[35],"and":[36,57,70,82,92,103,118,144,152,158,170,181,186,195,217,245,267],"across":[37],"tiers,":[38],"are":[39,174],"not":[40],"fully":[41],"independent.":[42],"Accordingly,":[43],"this":[45,90],"paper,":[46],"we":[47,108,187],"propose":[48],"two":[49,257],"HCN":[50,222],"models":[51,258],"with":[52,183,223],"inter-tier":[53],"dependence":[54,59],"(Case":[55,60],"1)":[56],"intra-tier":[58],"2),":[61],"respectively.":[62,88,164],"In":[63,147],"Case":[64,148,210],"1,":[65],"macro-base":[67],"station":[68,73],"(MBS)":[69],"pico-base":[72],"(PBS)":[74],"deployments":[75],"follow":[76,155],"process":[80,86,128],"(PPP)":[81],"hole":[85],"(PHP),":[87],"Under":[89],"setup":[91],"conditioning":[93],"on":[94,111],"fixed":[96,178],"serving":[97,106,179],"distance":[98,180],"(distance":[99],"between":[100,263],"user":[102],"nearest":[105],"BS),":[107],"derive":[109,188],"bounds":[110],"outage":[113,145,172,190],"probabilities":[114],"both":[116,202],"macro":[117],"pico":[119],"users.":[120],"We":[121],"also":[122],"use":[123],"fitted":[125],"cluster":[127,162],"approximate":[130],"PHP,":[132],"which":[133],"is":[134,213],"shown":[135],"provide":[137,260],"good":[139,261],"approximation":[140],"interference":[143,169],"statistics.":[146],"2,":[149],"MBSs":[151],"PBSs":[154],"PPP":[157,230],"an":[159],"Matern":[161],"process,":[163],"Explicit":[165],"expressions":[166],"probability":[173],"derived":[175],"first":[176],"second":[182],"random":[184],"distance,":[185],"performance,":[191],"per-user":[193,243],"capacity,":[194],"area":[197],"spectral":[198],"efficiency":[199],"(ASE)":[200],"cases.":[203],"It":[204],"turns":[205],"out":[206],"that":[207],"proposed":[209,259],"2":[211],"more":[215],"appropriate":[216],"accurate":[218],"hotspot":[224],"regions":[225],"than":[226],"since":[232],"latter":[234],"underestimates":[235],"some":[236],"key":[237],"performance":[238],"metrics,":[239],"such":[240],"as":[241],"capacity":[244],"ASE,":[247],"by":[248],"factor":[250],"1.5":[252],"2.":[254],"Overall,":[255],"tradeoffs":[262],"accuracy,":[265],"practicability.":[268]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":8},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}