{"id":"https://openalex.org/W3161704471","doi":"https://doi.org/10.3390/a14050155","title":"Energy-Efficient Power Allocation in Non-Linear Energy Harvesting Multiple Relay Systems","display_name":"Energy-Efficient Power Allocation in Non-Linear Energy Harvesting Multiple Relay Systems","publication_year":2021,"publication_date":"2021-05-17","ids":{"openalex":"https://openalex.org/W3161704471","doi":"https://doi.org/10.3390/a14050155","mag":"3161704471"},"language":"en","primary_location":{"id":"doi:10.3390/a14050155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14050155","pdf_url":"https://www.mdpi.com/1999-4893/14/5/155/pdf?version=1621572957","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/14/5/155/pdf?version=1621572957","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100850002","display_name":"Huifang Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huifang Pan","raw_affiliation_strings":["Jiangsu Key Laboratory of Wireless Communications, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"],"affiliations":[{"raw_affiliation_string":"Jiangsu Key Laboratory of Wireless Communications, Nanjing University of Posts and Telecommunications, Nanjing 210003, China","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100743927","display_name":"Qi Zhu","orcid":"https://orcid.org/0000-0002-8190-8912"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Zhu","raw_affiliation_strings":["Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"],"affiliations":[{"raw_affiliation_string":"Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks, Nanjing University of Posts and Telecommunications, Nanjing 210003, China","institution_ids":["https://openalex.org/I41198531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100743927"],"corresponding_institution_ids":["https://openalex.org/I41198531"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5014,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6308551,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"5","first_page":"155","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11392","display_name":"Energy Harvesting in Wireless Networks","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/T11392","display_name":"Energy Harvesting in Wireless Networks","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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9987999796867371,"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/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9980999827384949,"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/relay","display_name":"Relay","score":0.7682321071624756},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.7497029304504395},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7074457406997681},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6777273416519165},{"id":"https://openalex.org/keywords/transmitter-power-output","display_name":"Transmitter power output","score":0.508553147315979},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.49955248832702637},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4812448024749756},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.47972527146339417},{"id":"https://openalex.org/keywords/maximum-power-transfer-theorem","display_name":"Maximum power transfer theorem","score":0.4421895146369934},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4402013421058655},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4349871873855591},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.42355164885520935},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.4232608377933502},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.33195650577545166},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21776968240737915},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.1331983208656311},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.12431347370147705},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.12427586317062378},{"id":"https://openalex.org/keywords/transmitter","display_name":"Transmitter","score":0.07376393675804138}],"concepts":[{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.7682321071624756},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.7497029304504395},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7074457406997681},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6777273416519165},{"id":"https://openalex.org/C65422117","wikidata":"https://www.wikidata.org/wiki/Q358527","display_name":"Transmitter power output","level":4,"score":0.508553147315979},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.49955248832702637},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4812448024749756},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.47972527146339417},{"id":"https://openalex.org/C67186554","wikidata":"https://www.wikidata.org/wiki/Q17103352","display_name":"Maximum power transfer theorem","level":3,"score":0.4421895146369934},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4402013421058655},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4349871873855591},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.42355164885520935},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.4232608377933502},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.33195650577545166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21776968240737915},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.1331983208656311},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.12431347370147705},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.12427586317062378},{"id":"https://openalex.org/C47798520","wikidata":"https://www.wikidata.org/wiki/Q190157","display_name":"Transmitter","level":3,"score":0.07376393675804138},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a14050155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14050155","pdf_url":"https://www.mdpi.com/1999-4893/14/5/155/pdf?version=1621572957","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ab52323343a94619ac7f8bf0f4710464","is_oa":true,"landing_page_url":"https://doaj.org/article/ab52323343a94619ac7f8bf0f4710464","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 14, Iss 5, p 155 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/14/5/155/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a14050155","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":"Algorithms; Volume 14; Issue 5; Pages: 155","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a14050155","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14050155","pdf_url":"https://www.mdpi.com/1999-4893/14/5/155/pdf?version=1621572957","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.9100000262260437}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3161704471.pdf","grobid_xml":"https://content.openalex.org/works/W3161704471.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1967956032","https://openalex.org/W2051876295","https://openalex.org/W2054211624","https://openalex.org/W2101481747","https://openalex.org/W2140973383","https://openalex.org/W2153794195","https://openalex.org/W2170074621","https://openalex.org/W2170263567","https://openalex.org/W2177372563","https://openalex.org/W2337224938","https://openalex.org/W2588454501","https://openalex.org/W2592458917","https://openalex.org/W2610768674","https://openalex.org/W2740839525","https://openalex.org/W2801136569","https://openalex.org/W2804909802","https://openalex.org/W2921448492","https://openalex.org/W2923416685","https://openalex.org/W2951199095","https://openalex.org/W2953740496","https://openalex.org/W2996270571","https://openalex.org/W3101496806","https://openalex.org/W3106286659","https://openalex.org/W6682686835","https://openalex.org/W6703621072"],"related_works":["https://openalex.org/W2015244536","https://openalex.org/W1988754299","https://openalex.org/W2034024079","https://openalex.org/W2594574147","https://openalex.org/W834972196","https://openalex.org/W4230146972","https://openalex.org/W4387967834","https://openalex.org/W2477209608","https://openalex.org/W4205616904","https://openalex.org/W2597862030"],"abstract_inverted_index":{"In":[0,103],"this":[1,84,185],"paper,":[2],"to":[3,70,97],"maximize":[4],"the":[5,10,36,46,51,58,63,73,99,105,129,165,169,176,179],"energy":[6,38,49],"efficiency":[7],"(EE)":[8],"in":[9,34,184,187],"two-hop":[11],"multi-relay":[12],"cooperative":[13],"decoding":[14],"and":[15,23,57,76,121,168],"forwarding":[16],"(DF)":[17],"system":[18],"for":[19,148],"simultaneous":[20],"wireless":[21],"information":[22,56],"power":[24,29,61,75,101,107,119,124,180],"transmission":[25,53,60],"(SWIPT),":[26],"an":[27,65,92],"optimal":[28,100],"allocation":[30,108,125,181],"algorithm":[31,94,182],"is":[32,68,86,95,112,126,139],"proposed,":[33],"which":[35,133],"relay":[37,118],"harvesting":[39],"(EH)":[40],"adopts":[41],"a":[42,87,116,140],"nonlinear":[43,88],"model.":[44],"Under":[45],"constraints,":[47],"including":[48],"causality,":[50],"minimum":[52],"quality":[54],"of":[55,80,151,178,189],"total":[59],"at":[62,109],"relays,":[64],"optimization":[66],"problem":[67,85],"constructed":[69],"jointly":[71],"optimize":[72],"transmit":[74],"power-splitting":[77],"(PS)":[78],"ratios":[79],"multiple":[81,110],"relays.":[82],"Although":[83],"fractional":[89],"programming":[90,142],"problem,":[91],"iterative":[93],"developed":[96],"obtain":[98],"allocation.":[102],"particular,":[104],"joint":[106],"relays":[111],"first":[113],"decoupled":[114],"into":[115],"single":[117],"allocation,":[120],"then":[122],"single-relay":[123],"performed":[127],"by":[128,156],"Dinkelbach":[130],"iteration":[131],"algorithm,":[132],"can":[134],"be":[135],"proven":[136],"that":[137],"it":[138],"convex":[141],"problem.":[143],"Its":[144],"closed":[145],"form":[146],"solutions":[147],"different":[149],"polylines":[150],"EH":[152],"models":[153],"are":[154],"obtained":[155],"using":[157],"mathematical":[158],"methods,":[159],"such":[160],"as":[161],"monotonicity,":[162],"Lagrange":[163],"multipliers,":[164],"KKT":[166],"condition":[167],"Cardan":[170],"formula.":[171],"The":[172],"simulation":[173],"results":[174],"show":[175],"superiority":[177],"proposed":[183],"paper":[186],"terms":[188],"EE.":[190]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-05-24T00:00:00"}
