{"id":"https://openalex.org/W2396665165","doi":"https://doi.org/10.1109/lcomm.2016.2572682","title":"Wireless Energy Transfer Beamforming With L\u00f6wner-John Ellipsoidal Approximation","display_name":"Wireless Energy Transfer Beamforming With L\u00f6wner-John Ellipsoidal Approximation","publication_year":2016,"publication_date":"2016-05-24","ids":{"openalex":"https://openalex.org/W2396665165","doi":"https://doi.org/10.1109/lcomm.2016.2572682","mag":"2396665165"},"language":"en","primary_location":{"id":"doi:10.1109/lcomm.2016.2572682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcomm.2016.2572682","pdf_url":null,"source":{"id":"https://openalex.org/S147316732","display_name":"IEEE Communications Letters","issn_l":"1089-7798","issn":["1089-7798","1558-2558","2373-7891"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications Letters","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/A5100374424","display_name":"Bo Li","orcid":"https://orcid.org/0000-0002-3793-9156"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Li","raw_affiliation_strings":["Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101906657","display_name":"Zhimin Zeng","orcid":"https://orcid.org/0009-0008-5717-9167"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhimin Zeng","raw_affiliation_strings":["Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038087450","display_name":"Norman C. Beaulieu","orcid":"https://orcid.org/0000-0001-9233-219X"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Norman C. Beaulieu","raw_affiliation_strings":["Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102913097","display_name":"Tiankui Zhang","orcid":"https://orcid.org/0000-0002-0694-5844"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tiankui Zhang","raw_affiliation_strings":["Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I139759216"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0302463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"8","first_page":"1667","last_page":"1670"},"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":0.9994999766349792,"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/T10069","display_name":"Antenna Design and Analysis","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/beamforming","display_name":"Beamforming","score":0.8073943853378296},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.6786165237426758},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6485437154769897},{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.6390402913093567},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.5699702501296997},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.5635783076286316},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5205010771751404},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5102572441101074},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.432860404253006},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4118083417415619},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31020769476890564},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.2373323142528534},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.201887309551239},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07751980423927307}],"concepts":[{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.8073943853378296},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.6786165237426758},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6485437154769897},{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.6390402913093567},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.5699702501296997},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.5635783076286316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5205010771751404},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5102572441101074},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.432860404253006},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4118083417415619},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31020769476890564},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.2373323142528534},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.201887309551239},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07751980423927307},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lcomm.2016.2572682","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcomm.2016.2572682","pdf_url":null,"source":{"id":"https://openalex.org/S147316732","display_name":"IEEE Communications Letters","issn_l":"1089-7798","issn":["1089-7798","1558-2558","2373-7891"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.9100000262260437,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G3084443806","display_name":null,"funder_award_id":"No. 61461029","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4841914214","display_name":null,"funder_award_id":"2014ZD03\u201001","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5017591519","display_name":null,"funder_award_id":"No. 61502046","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1965098391","https://openalex.org/W1981044874","https://openalex.org/W1992034250","https://openalex.org/W1996215314","https://openalex.org/W2058705882","https://openalex.org/W2094000142","https://openalex.org/W2113754957","https://openalex.org/W2126351339","https://openalex.org/W2311985995","https://openalex.org/W3100823853","https://openalex.org/W4250589301","https://openalex.org/W4361793249"],"related_works":["https://openalex.org/W2548963335","https://openalex.org/W2159941915","https://openalex.org/W1995129237","https://openalex.org/W1761601995","https://openalex.org/W2904599916","https://openalex.org/W4321608401","https://openalex.org/W4300468626","https://openalex.org/W2909457694","https://openalex.org/W3040536194","https://openalex.org/W4385695889"],"abstract_inverted_index":{"The":[0,89],"physical":[1,29],"layer":[2],"beamforming":[3,30],"design":[4,31],"of":[5,17,25,65,121],"downlink":[6,123],"wireless":[7],"energy":[8,119],"transfer":[9],"(WET)":[10],"is":[11,32,50,55,84,92,105],"investigated.":[12],"To":[13],"minimize":[14],"the":[15,22,28,48,53,63,78,98,113,118,122],"power":[16],"WET":[18,124],"with":[19,62,126],"respect":[20],"to":[21,46,77,97],"terminals'":[23],"quality":[24],"service":[26],"requirements,":[27],"modeled":[33],"as":[34,86],"a":[35,66,71],"non-convex":[36],"quadratically":[37],"constrained":[38],"quadratic":[39],"program":[40,73],"(QCQP)":[41],"problem.":[42],"A":[43],"two-step":[44],"method":[45,91,115],"solve":[47],"QCQP":[49,54],"proposed.":[51],"First,":[52],"tightened":[56],"into":[57],"an":[58],"ellipsoidal":[59,81],"approximation":[60,79],"problem":[61],"aid":[64],"L\u00f6wner-John":[67],"ellipsoid,":[68],"by":[69],"solving":[70],"semidefinite":[72,100],"(SDP).":[74],"Second,":[75],"due":[76],"problem's":[80],"nature,":[82],"it":[83],"solved":[85],"another":[87],"SDP.":[88],"proposed":[90,114],"compared":[93,125],"using":[94],"numerical":[95],"results":[96],"conventional":[99],"relaxation":[101],"(SDR)":[102],"approach.":[103],"It":[104],"demonstrated":[106],"that":[107],"for":[108],"equivalent":[109],"computing":[110],"time":[111],"cost,":[112],"usefully":[116],"improves":[117],"efficiency":[120],"SDR.":[127]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
