{"id":"https://openalex.org/W2548918789","doi":"https://doi.org/10.3390/s16111854","title":"Analytical Study on Multi-Tier 5G Heterogeneous Small Cell Networks: Coverage Performance and Energy Efficiency","display_name":"Analytical Study on Multi-Tier 5G Heterogeneous Small Cell Networks: Coverage Performance and Energy Efficiency","publication_year":2016,"publication_date":"2016-11-04","ids":{"openalex":"https://openalex.org/W2548918789","doi":"https://doi.org/10.3390/s16111854","mag":"2548918789","pmid":"https://pubmed.ncbi.nlm.nih.gov/27827917"},"language":"en","primary_location":{"id":"doi:10.3390/s16111854","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s16111854","pdf_url":"https://www.mdpi.com/1424-8220/16/11/1854/pdf?version=1478250646","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/16/11/1854/pdf?version=1478250646","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001435169","display_name":"Zhu Xiao","orcid":"https://orcid.org/0000-0001-5645-160X"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]},{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhu Xiao","raw_affiliation_strings":["College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China","State Key Laboratory of Integrated Service Networks, Xidian University, Xi\u2019an 710071, China","State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China"],"raw_orcid":"https://orcid.org/0000-0001-5645-160X","affiliations":[{"raw_affiliation_string":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Service Networks, Xidian University, Xi\u2019an 710071, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115833478","display_name":"Hongjing Liu","orcid":"https://orcid.org/0000-0003-1997-0632"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongjing Liu","raw_affiliation_strings":["College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114585123","display_name":"Vincent Havyarimana","orcid":"https://orcid.org/0000-0002-3545-7639"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Vincent Havyarimana","raw_affiliation_strings":["College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"],"raw_orcid":"https://orcid.org/0000-0002-3545-7639","affiliations":[{"raw_affiliation_string":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359025","display_name":"Tong Li","orcid":"https://orcid.org/0000-0002-4343-703X"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tong Li","raw_affiliation_strings":["College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006089504","display_name":"Dong Wang","orcid":"https://orcid.org/0000-0002-2210-640X"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dong Wang","raw_affiliation_strings":["College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5006089504"],"corresponding_institution_ids":["https://openalex.org/I16609230"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2598},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2598},"fwci":2.2319,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.8909257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"16","issue":"11","first_page":"1854","last_page":"1854"},"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/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.9979000091552734,"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/efficient-energy-use","display_name":"Efficient energy use","score":0.5844659805297852},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5359889268875122},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.47572973370552063},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3643476665019989},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.24110913276672363},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.12765640020370483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.11737501621246338},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11276650428771973}],"concepts":[{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.5844659805297852},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5359889268875122},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.47572973370552063},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3643476665019989},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.24110913276672363},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.12765640020370483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.11737501621246338},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11276650428771973}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/s16111854","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s16111854","pdf_url":"https://www.mdpi.com/1424-8220/16/11/1854/pdf?version=1478250646","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},{"id":"pmid:27827917","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/27827917","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:eb9783085f3d46709ca5f75000361144","is_oa":true,"landing_page_url":"https://doaj.org/article/eb9783085f3d46709ca5f75000361144","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 16, Iss 11, p 1854 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1424-8220/16/11/1854/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s16111854","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors; Volume 16; Issue 11; Pages: 1854","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:5134513","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5134513","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s16111854","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s16111854","pdf_url":"https://www.mdpi.com/1424-8220/16/11/1854/pdf?version=1478250646","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8899999856948853,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G129007841","display_name":"\u8f66\u8f7d\u81ea\u7ec4\u7f51\u5b9e\u65f6\u534f\u4f5c\u5b9a\u4f4d\u7cfb\u7edf\u53ca\u591a\u6570\u636e\u6e90\u878d\u5408\u7b97\u6cd5\u7814\u7a76","funder_award_id":"61272061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2094848848","display_name":null,"funder_award_id":"61272061 and 61301148","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2916571697","display_name":null,"funder_award_id":"2016JJ3041","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G8032331688","display_name":"\u9762\u5411\u975e\u89c6\u8ddd\u4e0e\u5bc6\u96c6\u591a\u5f84\u7684\u590d\u6742\u573a\u666f\u4e0b\u65e0\u7ebf\u5b9a\u4f4d\u673a\u5236\u4e0e\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61301148","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"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320323230","display_name":"Xidian University","ror":"https://ror.org/05s92vm98"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2548918789.pdf","grobid_xml":"https://content.openalex.org/works/W2548918789.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W268112365","https://openalex.org/W1483783971","https://openalex.org/W1499559950","https://openalex.org/W1511497032","https://openalex.org/W1649222721","https://openalex.org/W1982333910","https://openalex.org/W1983816900","https://openalex.org/W1992806133","https://openalex.org/W1997204636","https://openalex.org/W1998944109","https://openalex.org/W2034420299","https://openalex.org/W2054106511","https://openalex.org/W2067181210","https://openalex.org/W2087240286","https://openalex.org/W2100195693","https://openalex.org/W2101121986","https://openalex.org/W2104557602","https://openalex.org/W2118166339","https://openalex.org/W2127564408","https://openalex.org/W2130891087","https://openalex.org/W2150166076","https://openalex.org/W2189297450","https://openalex.org/W2211147027","https://openalex.org/W2226672079","https://openalex.org/W2248817212","https://openalex.org/W2292994152","https://openalex.org/W2293202428","https://openalex.org/W2294469601","https://openalex.org/W2296148671","https://openalex.org/W2303365748","https://openalex.org/W2329627572","https://openalex.org/W2329681656","https://openalex.org/W2337454810","https://openalex.org/W2610335499","https://openalex.org/W3100357572","https://openalex.org/W3101445254","https://openalex.org/W3104194621","https://openalex.org/W3104869988","https://openalex.org/W6663905091"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829","https://openalex.org/W2530322880","https://openalex.org/W4387123727"],"abstract_inverted_index":{"In":[0],"this":[1,143],"paper,":[2],"we":[3,38,105,122,145],"investigate":[4,86],"the":[5,40,52,60,70,91,98,114,124,154,158,165,175,207,212,216,224,231,237],"coverage":[6,74,80,176,232],"performance":[7,81,136,177,233],"and":[8,22,30,50,65,85,100,112,137,178,199,210],"energy":[9,125,179,208,238],"efficiency":[10,126,209],"of":[11,20,25,34,73,134,157,226],"multi-tier":[12,41,130,227],"heterogeneous":[13],"cellular":[14],"networks":[15],"(HetNets)":[16],"which":[17,201],"are":[18],"composed":[19],"macrocells":[21],"different":[23,83],"types":[24],"small":[26,92,166,190],"cells,":[27],"i.e.,":[28],"picocells":[29],"femtocells.":[31],"By":[32,96],"virtue":[33],"stochastic":[35],"geometry":[36],"tools,":[37],"model":[39],"HetNets":[42,131,228],"based":[43,150],"on":[44,174],"a":[45,107,147,171],"Poisson":[46],"point":[47],"process":[48],"(PPP)":[49],"analyze":[51],"Signal":[53],"to":[54,78,152,205],"Interference":[55],"Ratio":[56],"(SIR)":[57],"via":[58],"studying":[59],"cumulative":[61],"interference":[62],"from":[63],"pico-tier":[64,198],"femto-tier.":[66],"We":[67],"then":[68],"derive":[69,113],"analytical":[71],"expressions":[72],"probabilities":[75],"in":[76,82,132],"order":[77],"evaluate":[79],"tiers":[84],"how":[87],"it":[88],"varies":[89],"with":[90],"cells'":[93,167],"deployment":[94,168],"density.":[95],"taking":[97],"fairness":[99],"user":[101],"experience":[102],"into":[103],"consideration,":[104],"propose":[106],"disjoint":[108],"channel":[109,116],"allocation":[110,139],"scheme":[111],"system":[115,217],"throughput":[117,135],"for":[118,129,223,229],"various":[119],"tiers.":[120],"Further,":[121],"formulate":[123],"optimization":[127],"problem":[128],"terms":[133],"resource":[138],"fairness.":[140],"To":[141],"solve":[142],"problem,":[144],"devise":[146],"linear":[148],"programming":[149],"approach":[151],"obtain":[153],"available":[155],"area":[156],"feasible":[159],"solutions.":[160],"System-level":[161],"simulations":[162],"demonstrate":[163],"that":[164,185],"density":[169,195],"has":[170],"significant":[172],"effect":[173],"efficiency.":[180,239],"Simulation":[181],"results":[182],"also":[183],"reveal":[184],"there":[186],"exits":[187],"an":[188],"optimal":[189],"cell":[191],"base":[192],"station":[193],"(SBS)":[194],"ratio":[196],"between":[197],"femto-tier":[200],"can":[202],"be":[203],"applied":[204],"maximize":[206],"at":[211],"same":[213],"time":[214],"enhance":[215],"performance.":[218],"Our":[219],"findings":[220],"provide":[221],"guidance":[222],"design":[225],"improving":[230],"as":[234,236],"well":[235]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
