{"id":"https://openalex.org/W2150710838","doi":"https://doi.org/10.1109/pimrc.2009.5450219","title":"On the Nash equilibrium solutions of integer bit loading OFDMA resource allocation games","display_name":"On the Nash equilibrium solutions of integer bit loading OFDMA resource allocation games","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2150710838","doi":"https://doi.org/10.1109/pimrc.2009.5450219","mag":"2150710838"},"language":"en","primary_location":{"id":"doi:10.1109/pimrc.2009.5450219","is_oa":false,"landing_page_url":"https://doi.org/10.1109/pimrc.2009.5450219","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications","raw_type":"proceedings-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/A5111899402","display_name":"Zhenyu Liang","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I115228651","display_name":"Agency for Science, Technology and Research","ror":"https://ror.org/036wvzt09","country_code":"SG","type":"government","lineage":["https://openalex.org/I115228651"]},{"id":"https://openalex.org/I3005327000","display_name":"Institute for Infocomm Research","ror":"https://ror.org/053rfa017","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3005327000","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Zhenyu Liang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore","Institute of Infocomm Research, Agency for Science, Technology and Research, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Institute of Infocomm Research, Agency for Science, Technology and Research, Singapore","institution_ids":["https://openalex.org/I3005327000","https://openalex.org/I115228651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111955028","display_name":"Yong Huat Chew","orcid":null},"institutions":[{"id":"https://openalex.org/I115228651","display_name":"Agency for Science, Technology and Research","ror":"https://ror.org/036wvzt09","country_code":"SG","type":"government","lineage":["https://openalex.org/I115228651"]},{"id":"https://openalex.org/I3005327000","display_name":"Institute for Infocomm Research","ror":"https://ror.org/053rfa017","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3005327000","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yong Huat Chew","raw_affiliation_strings":["Institute of Infocomm Research, Agency for Science, Technology and Research, Singapore"],"affiliations":[{"raw_affiliation_string":"Institute of Infocomm Research, Agency for Science, Technology and Research, Singapore","institution_ids":["https://openalex.org/I3005327000","https://openalex.org/I115228651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102480245","display_name":"Chi Chung Ko","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Chi Chung Ko","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111899402"],"corresponding_institution_ids":["https://openalex.org/I115228651","https://openalex.org/I165932596","https://openalex.org/I3005327000"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16313873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":null,"first_page":"1692","last_page":"1696"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9991999864578247,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9991999864578247,"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/T11499","display_name":"ICT Impact and Policies","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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":0.9914000034332275,"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/nash-equilibrium","display_name":"Nash equilibrium","score":0.678917646408081},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6342542171478271},{"id":"https://openalex.org/keywords/telecommunications-link","display_name":"Telecommunications link","score":0.6290667653083801},{"id":"https://openalex.org/keywords/resource-allocation","display_name":"Resource allocation","score":0.5861842036247253},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5766050815582275},{"id":"https://openalex.org/keywords/frequency-division-multiple-access","display_name":"Frequency-division multiple access","score":0.5627318024635315},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5518973469734192},{"id":"https://openalex.org/keywords/base-station","display_name":"Base station","score":0.5121524333953857},{"id":"https://openalex.org/keywords/orthogonal-frequency-division-multiplexing","display_name":"Orthogonal frequency-division multiplexing","score":0.4863284230232239},{"id":"https://openalex.org/keywords/orthogonal-frequency-division-multiple-access","display_name":"Orthogonal frequency-division multiple access","score":0.4656323492527008},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4104590117931366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2853970527648926},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.24111106991767883},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.08688041567802429}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.678917646408081},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6342542171478271},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.6290667653083801},{"id":"https://openalex.org/C29202148","wikidata":"https://www.wikidata.org/wiki/Q287260","display_name":"Resource allocation","level":2,"score":0.5861842036247253},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5766050815582275},{"id":"https://openalex.org/C2776208322","wikidata":"https://www.wikidata.org/wiki/Q844071","display_name":"Frequency-division multiple access","level":4,"score":0.5627318024635315},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5518973469734192},{"id":"https://openalex.org/C68649174","wikidata":"https://www.wikidata.org/wiki/Q1379116","display_name":"Base station","level":2,"score":0.5121524333953857},{"id":"https://openalex.org/C40409654","wikidata":"https://www.wikidata.org/wiki/Q375889","display_name":"Orthogonal frequency-division multiplexing","level":3,"score":0.4863284230232239},{"id":"https://openalex.org/C2775907427","wikidata":"https://www.wikidata.org/wiki/Q2697649","display_name":"Orthogonal frequency-division multiple access","level":4,"score":0.4656323492527008},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4104590117931366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2853970527648926},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.24111106991767883},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.08688041567802429},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":2,"locations":[{"id":"doi:10.1109/pimrc.2009.5450219","is_oa":false,"landing_page_url":"https://doi.org/10.1109/pimrc.2009.5450219","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications","raw_type":"proceedings-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/71234","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/71234","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Conference Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1605726653","https://openalex.org/W1991799203","https://openalex.org/W2022537828","https://openalex.org/W2035681301","https://openalex.org/W2087466196","https://openalex.org/W2098293824","https://openalex.org/W2099156432","https://openalex.org/W2104173866","https://openalex.org/W2110326345","https://openalex.org/W2142473263","https://openalex.org/W2148911784","https://openalex.org/W2950348070","https://openalex.org/W6636327924","https://openalex.org/W6674595165","https://openalex.org/W6675826651"],"related_works":["https://openalex.org/W2907156721","https://openalex.org/W2025189274","https://openalex.org/W2092365485","https://openalex.org/W1585503616","https://openalex.org/W2063285884","https://openalex.org/W2383112630","https://openalex.org/W1843974825","https://openalex.org/W1543564974","https://openalex.org/W2004574319","https://openalex.org/W1654541684"],"abstract_inverted_index":{"We":[0,72],"address":[1,73],"the":[2,10,20,34,37,42,45,48,52,74,82,98,104,115,122],"allocation":[3],"of":[4,14,28,47,68,76,81,100,117],"subcarriers,":[5],"bits":[6,43,69],"and":[7,44,89],"power":[8,49],"among":[9],"base":[11],"stations":[12],"(BSs)":[13],"downlink":[15],"multi-cell":[16],"OFDMA":[17,93,123],"systems":[18],"using":[19],"non-cooperative":[21],"game":[22],"theoretic":[23],"approach.":[24],"The":[25],"utility":[26],"function":[27],"a":[29,118],"player":[30],"is":[31,61],"defined":[32],"as":[33],"difference":[35],"between":[36],"revenue":[38],"generated":[39],"from":[40],"transmitting":[41],"cost":[46],"consumed.":[50],"Unlike":[51],"commonly":[53],"adopted":[54],"water-filling":[55],"approach":[56],"where":[57],"continuous":[58],"bit":[59],"loading":[60],"used,":[62],"we":[63,112],"consider":[64],"assigning":[65],"integer":[66],"number":[67],"to":[70,97],"subcarriers.":[71],"existence":[75,99,116],"pure":[77,101],"Nash":[78],"equilibrium":[79],"(NE)":[80],"static":[83],"games":[84,106,124],"for":[85,103,121],"two-cell":[86],"modulation":[87,92],"adaptive":[88],"three-cell":[90],"single":[91],"systems.":[94],"Theorems":[95],"related":[96],"NE":[102],"two":[105],"are":[107],"developed.":[108],"Using":[109],"these":[110],"results,":[111],"show":[113],"that":[114],"stable":[119],"solution":[120],"cannot":[125],"be":[126,133],"guaranteed":[127],"if":[128],"minimum":[129],"rate":[130],"requirements":[131],"must":[132],"satisfied.":[134]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}