{"id":"https://openalex.org/W1977905728","doi":"https://doi.org/10.1109/glocom.2012.6503771","title":"Downlink coverage analysis in a heterogeneous cellular network","display_name":"Downlink coverage analysis in a heterogeneous cellular network","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W1977905728","doi":"https://doi.org/10.1109/glocom.2012.6503771","mag":"1977905728"},"language":"en","primary_location":{"id":"doi:10.1109/glocom.2012.6503771","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2012.6503771","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Global Communications Conference (GLOBECOM)","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1206.4723","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043656319","display_name":"Prasanna Madhusudhanan","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Prasanna Madhusudhanan","raw_affiliation_strings":["Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, 80309-0425 USA","Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, 80309-0425 USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041169962","display_name":"Juan G. Restrepo","orcid":"https://orcid.org/0000-0002-2665-2256"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Juan G. Restrepo","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado, Boulder, 80309-0425 USA","Department of Applied Mathematics, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado, Boulder, 80309-0425 USA","institution_ids":["https://openalex.org/I188538660","https://openalex.org/I2802236040"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084454849","display_name":"Youjian Liu","orcid":"https://orcid.org/0000-0003-4681-0546"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Youjian Liu","raw_affiliation_strings":["Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, 80309-0425 USA","Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, 80309-0425 USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109945443","display_name":"Timothy X Brown","orcid":null},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timothy X Brown","raw_affiliation_strings":["Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, 80309-0425 USA","Department of Electrical, Computer and Energy Engineering, Interdisciplinary Telecommunications Program, University of Colorado, Boulder, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, 80309-0425 USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Electrical, Computer and Energy Engineering, Interdisciplinary Telecommunications Program, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.1026,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.97845721,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"4170","last_page":"4175"},"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":0.9965000152587891,"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":0.9965000152587891,"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":0.8116979598999023},{"id":"https://openalex.org/keywords/poisson-point-process","display_name":"Poisson point process","score":0.7257902026176453},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.7220989465713501},{"id":"https://openalex.org/keywords/stochastic-geometry","display_name":"Stochastic geometry","score":0.6685345768928528},{"id":"https://openalex.org/keywords/cellular-network","display_name":"Cellular network","score":0.6466190814971924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6208807229995728},{"id":"https://openalex.org/keywords/path-loss","display_name":"Path loss","score":0.589532196521759},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.585636556148529},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.5561361312866211},{"id":"https://openalex.org/keywords/coverage-probability","display_name":"Coverage probability","score":0.5248389840126038},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.4689587652683258},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.4574929177761078},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.42541220784187317},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.42104238271713257},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3917276859283447},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.33979532122612},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28279852867126465},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2110694944858551},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.2083406150341034},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.15906694531440735}],"concepts":[{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.8116979598999023},{"id":"https://openalex.org/C16757284","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson point process","level":3,"score":0.7257902026176453},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.7220989465713501},{"id":"https://openalex.org/C31243852","wikidata":"https://www.wikidata.org/wiki/Q1666739","display_name":"Stochastic geometry","level":2,"score":0.6685345768928528},{"id":"https://openalex.org/C153646914","wikidata":"https://www.wikidata.org/wiki/Q535695","display_name":"Cellular network","level":2,"score":0.6466190814971924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6208807229995728},{"id":"https://openalex.org/C194273485","wikidata":"https://www.wikidata.org/wiki/Q1478845","display_name":"Path loss","level":3,"score":0.589532196521759},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.585636556148529},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.5561361312866211},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.5248389840126038},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.4689587652683258},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.4574929177761078},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.42541220784187317},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.42104238271713257},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3917276859283447},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.33979532122612},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28279852867126465},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2110694944858551},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2083406150341034},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.15906694531440735},{"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},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/glocom.2012.6503771","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2012.6503771","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Global Communications Conference (GLOBECOM)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1206.4723","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.4723","pdf_url":"https://arxiv.org/pdf/1206.4723","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.757.5412","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.757.5412","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1206.4723.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1206.4723","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1206.4723","pdf_url":"https://arxiv.org/pdf/1206.4723","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.550000011920929,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1563138358","https://openalex.org/W1972727027","https://openalex.org/W1995900307","https://openalex.org/W2043180800","https://openalex.org/W2059973889","https://openalex.org/W2061084757","https://openalex.org/W2122496159","https://openalex.org/W2138798774","https://openalex.org/W3101445254","https://openalex.org/W3103707284","https://openalex.org/W3105072513","https://openalex.org/W6633737566","https://openalex.org/W6785320466","https://openalex.org/W6785874605"],"related_works":["https://openalex.org/W2591746957","https://openalex.org/W4252323550","https://openalex.org/W2065735671","https://openalex.org/W2964313726","https://openalex.org/W2949860582","https://openalex.org/W3007555197","https://openalex.org/W3033996344","https://openalex.org/W2010129028","https://openalex.org/W2061819184","https://openalex.org/W4362659870"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,86],"consider":[4],"the":[5,57,64,68,75,92,96],"downlink":[6],"signal-to-interference-plus-noise":[7],"ratio":[8],"(SINR)":[9],"analysis":[10],"in":[11],"a":[12,24,30,52,83],"heterogeneous":[13],"cellular":[14],"network":[15],"with":[16,35,45,63],"K":[17],"tiers.":[18],"Each":[19],"tier":[20],"is":[21],"characterized":[22],"by":[23],"base-station":[25],"(BS)":[26],"arrangement":[27],"according":[28],"to":[29],"homogeneous":[31],"Poisson":[32],"point":[33],"process":[34],"certain":[36,53],"BS":[37,65],"density,":[38],"transmission":[39],"power,":[40],"random":[41],"shadow":[42],"fading":[43],"factors":[44],"arbitrary":[46,48],"distribution,":[47],"path-loss":[49],"exponent":[50],"and":[51],"bias":[54],"towards":[55],"admitting":[56],"mobile-station":[58],"(MS).":[59],"The":[60],"MS":[61],"associates":[62],"that":[66],"has":[67],"maximum":[69],"instantaneous":[70],"biased":[71],"received":[72],"power":[73],"under":[74],"open":[76],"access":[77],"cell":[78],"association":[79],"scheme.":[80],"For":[81],"such":[82],"general":[84],"setting,":[85],"provide":[87],"an":[88],"analytical":[89],"characterization":[90],"of":[91],"coverage":[93],"probability":[94],"at":[95],"MS.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}