{"id":"https://openalex.org/W2794009752","doi":"https://doi.org/10.3390/s18020639","title":"Robust Rate Maximization for Heterogeneous Wireless Networks under Channel Uncertainties","display_name":"Robust Rate Maximization for Heterogeneous Wireless Networks under Channel Uncertainties","publication_year":2018,"publication_date":"2018-02-21","ids":{"openalex":"https://openalex.org/W2794009752","doi":"https://doi.org/10.3390/s18020639","mag":"2794009752","pmid":"https://pubmed.ncbi.nlm.nih.gov/29466315"},"language":"en","primary_location":{"id":"doi:10.3390/s18020639","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18020639","pdf_url":"https://www.mdpi.com/1424-8220/18/2/639/pdf?version=1519442152","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/1424-8220/18/2/639/pdf?version=1519442152","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060060834","display_name":"Yongjun Xu","orcid":"https://orcid.org/0000-0002-3588-0461"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]},{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongjun Xu","raw_affiliation_strings":["School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China","State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019an 710071, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101545228","display_name":"Yuan Hu","orcid":"https://orcid.org/0000-0001-7150-6875"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Hu","raw_affiliation_strings":["School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034845779","display_name":"Guoquan Li","orcid":"https://orcid.org/0000-0001-8022-743X"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guoquan Li","raw_affiliation_strings":["School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034845779"],"corresponding_institution_ids":["https://openalex.org/I10535382"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2598},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2598},"fwci":1.3888,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.81904601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"2","first_page":"639","last_page":"639"},"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9998000264167786,"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":0.9957000017166138,"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/macrocell","display_name":"Macrocell","score":0.8070663809776306},{"id":"https://openalex.org/keywords/femtocell","display_name":"Femtocell","score":0.7849379181861877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7058103680610657},{"id":"https://openalex.org/keywords/wireless-network","display_name":"Wireless network","score":0.5461155772209167},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.5090024471282959},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5070362091064453},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.49720123410224915},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4772634208202362},{"id":"https://openalex.org/keywords/channel-state-information","display_name":"Channel state information","score":0.4659005105495453},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.45627373456954956},{"id":"https://openalex.org/keywords/heterogeneous-network","display_name":"Heterogeneous network","score":0.45104101300239563},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4505607485771179},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.44054871797561646},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.42373907566070557},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17218530178070068},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.15495142340660095},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.129039466381073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.10087653994560242}],"concepts":[{"id":"https://openalex.org/C2778291847","wikidata":"https://www.wikidata.org/wiki/Q1163937","display_name":"Macrocell","level":3,"score":0.8070663809776306},{"id":"https://openalex.org/C152504517","wikidata":"https://www.wikidata.org/wiki/Q572455","display_name":"Femtocell","level":3,"score":0.7849379181861877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7058103680610657},{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"score":0.5461155772209167},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.5090024471282959},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5070362091064453},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.49720123410224915},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4772634208202362},{"id":"https://openalex.org/C148063708","wikidata":"https://www.wikidata.org/wiki/Q5072511","display_name":"Channel state information","level":3,"score":0.4659005105495453},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.45627373456954956},{"id":"https://openalex.org/C158207573","wikidata":"https://www.wikidata.org/wiki/Q5747224","display_name":"Heterogeneous network","level":4,"score":0.45104101300239563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4505607485771179},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.44054871797561646},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.42373907566070557},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17218530178070068},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.15495142340660095},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.129039466381073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.10087653994560242},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/s18020639","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18020639","pdf_url":"https://www.mdpi.com/1424-8220/18/2/639/pdf?version=1519442152","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:29466315","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29466315","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:mdpi.com:/1424-8220/18/2/639/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s18020639","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 18; Issue 2; Pages: 639","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:5855866","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5855866","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/s18020639","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18020639","pdf_url":"https://www.mdpi.com/1424-8220/18/2/639/pdf?version=1519442152","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":[],"awards":[{"id":"https://openalex.org/G350329519","display_name":null,"funder_award_id":"CSTC2016JCYJA2197","funder_id":"https://openalex.org/F4320323172","funder_display_name":"Natural Science Foundation of Chongqing"},{"id":"https://openalex.org/G5306106478","display_name":null,"funder_award_id":"61601071","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5399272143","display_name":null,"funder_award_id":"61601071,61301124","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6960205627","display_name":null,"funder_award_id":"61301124","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/F4320321135","display_name":"Chongqing University","ror":"https://ror.org/023rhb549"},{"id":"https://openalex.org/F4320321550","display_name":"Chongqing Science and Technology Commission","ror":"https://ror.org/05w9erc61"},{"id":"https://openalex.org/F4320322687","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26"},{"id":"https://openalex.org/F4320323172","display_name":"Natural Science Foundation of Chongqing","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323230","display_name":"Xidian University","ror":"https://ror.org/05s92vm98"},{"id":"https://openalex.org/F4320324805","display_name":"Chongqing Municipal Education Commission","ror":"https://ror.org/031nm5713"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2794009752.pdf","grobid_xml":"https://content.openalex.org/works/W2794009752.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W90623281","https://openalex.org/W1967905547","https://openalex.org/W1968226644","https://openalex.org/W2025453432","https://openalex.org/W2041488232","https://openalex.org/W2051696221","https://openalex.org/W2086028881","https://openalex.org/W2089326092","https://openalex.org/W2092836447","https://openalex.org/W2108359457","https://openalex.org/W2109159967","https://openalex.org/W2123059049","https://openalex.org/W2124907246","https://openalex.org/W2150763656","https://openalex.org/W2151851437","https://openalex.org/W2154782861","https://openalex.org/W2161272050","https://openalex.org/W2167818879","https://openalex.org/W2196429375","https://openalex.org/W2301746362","https://openalex.org/W2315400342","https://openalex.org/W2343710647","https://openalex.org/W2343755894","https://openalex.org/W2607844664","https://openalex.org/W2611776601","https://openalex.org/W2612428923","https://openalex.org/W2735248222","https://openalex.org/W2738776418","https://openalex.org/W2742072364","https://openalex.org/W2963341937","https://openalex.org/W4211216658","https://openalex.org/W4250589301","https://openalex.org/W6745201582"],"related_works":["https://openalex.org/W2040311827","https://openalex.org/W2034139677","https://openalex.org/W2206637726","https://openalex.org/W1519632632","https://openalex.org/W2479641731","https://openalex.org/W117540911","https://openalex.org/W2100031696","https://openalex.org/W2138783567","https://openalex.org/W1976777118","https://openalex.org/W1987099914"],"abstract_inverted_index":{"Heterogeneous":[0],"wireless":[1,10,34,49],"networks":[2,50],"are":[3,114],"a":[4,40,46],"promising":[5],"technology":[6],"in":[7,117],"next":[8],"generation":[9],"communication":[11,25,35],"networks,":[12],"which":[13,159],"has":[14],"been":[15],"shown":[16],"to":[17,80,104],"efficiently":[18],"reduce":[19],"the":[20,32,60,68,85,102,105,155,173,176,180,186],"blind":[21],"area":[22],"of":[23,62,89,97,110,119,122,144,175,182],"mobile":[24],"and":[26,83,107,138,167],"improve":[27],"network":[28],"coverage":[29],"compared":[30],"with":[31,133,141],"traditional":[33],"networks.":[36],"In":[37],"this":[38],"paper,":[39],"robust":[41,69,149],"power":[42],"allocation":[43],"problem":[44,72,126,151,158],"for":[45],"two-tier":[47],"heterogeneous":[48],"is":[51,73,127,152,160],"formulated":[52],"based":[53],"on":[54,185],"orthogonal":[55],"frequency-division":[56],"multiplexing":[57],"technology.":[58],"Under":[59],"consideration":[61],"imperfect":[63],"channel":[64,98,145,183],"state":[65],"information":[66],"(CSI),":[67],"sum-rate":[70],"maximization":[71],"built":[74],"while":[75],"avoiding":[76],"sever":[77],"cross-tier":[78],"interference":[79],"macrocell":[81,106],"user":[82,113],"maintaining":[84],"minimum":[86],"rate":[87],"requirement":[88],"each":[90,111],"femtocell":[91,112],"user.":[92],"To":[93],"be":[94],"practical,":[95],"both":[96],"estimation":[99,146],"errors":[100],"from":[101],"femtocells":[103],"link":[108],"uncertainties":[109,184],"simultaneously":[115],"considered":[116],"terms":[118],"outage":[120],"probabilities":[121],"users.":[123],"The":[124,148],"optimization":[125,150,157],"analyzed":[128],"under":[129],"no":[130],"CSI":[131,140],"feedback":[132],"some":[134],"cumulative":[135],"distribution":[136,143],"function":[137],"partial":[139],"Gaussian":[142],"error.":[147],"converted":[153],"into":[154],"convex":[156],"solved":[161],"by":[162,179],"using":[163],"Lagrange":[164],"dual":[165],"theory":[166],"subgradient":[168],"algorithm.":[169],"Simulation":[170],"results":[171],"demonstrate":[172],"effectiveness":[174],"proposed":[177],"algorithm":[178],"impact":[181],"system":[187],"performance.":[188]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}