{"id":"https://openalex.org/W2103601777","doi":"https://doi.org/10.1109/wcnc.2009.4917520","title":"A Novel Complexity Metric of FH/SS Sequences Using Approximate Entropy","display_name":"A Novel Complexity Metric of FH/SS Sequences Using Approximate Entropy","publication_year":2009,"publication_date":"2009-04-01","ids":{"openalex":"https://openalex.org/W2103601777","doi":"https://doi.org/10.1109/wcnc.2009.4917520","mag":"2103601777"},"language":"en","primary_location":{"id":"doi:10.1109/wcnc.2009.4917520","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wcnc.2009.4917520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Wireless Communications and Networking Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5100697315","display_name":"Zan Li","orcid":"https://orcid.org/0000-0002-5207-6504"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zan Li","raw_affiliation_strings":["State Key Laboratory of Integrated Services Networks, XiDian University, Xi'an, China","[State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019 an, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, XiDian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"[State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019 an, China]","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101425172","display_name":"Jueping Cai","orcid":"https://orcid.org/0000-0002-1852-0982"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jueping Cai","raw_affiliation_strings":["XiDian University, Xi'an, China","Xidian University School of Microelectronics Xi'an China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"XiDian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"Xidian University School of Microelectronics Xi'an China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100369438","display_name":"Xiaojun Chen","orcid":"https://orcid.org/0000-0002-2818-4652"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaojun Chen","raw_affiliation_strings":["State Key Laboratory of Integrated Services Networks, XiDian University, Xi'an, China","[State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019 an, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, XiDian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"[State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019 an, China]","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064578488","display_name":"Xiaofeng Lu","orcid":"https://orcid.org/0000-0001-7208-6841"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaofeng Lu","raw_affiliation_strings":["State Key Laboratory of Integrated Services Networks, XiDian University, Xi'an, China","[State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019 an, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Integrated Services Networks, XiDian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"[State Key Laboratory of Integrated Services Networks, Xidian University, Xi\u2019 an, China]","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"93","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/approximate-entropy","display_name":"Approximate entropy","score":0.776270866394043},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.7146087884902954},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5899614095687866},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.587946355342865},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5762830376625061},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5611328482627869},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5304486155509949},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5157166123390198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4766809940338135},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4526888132095337},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4482116401195526},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.38993147015571594},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1999523937702179},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19965404272079468},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.17264103889465332},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.09361061453819275}],"concepts":[{"id":"https://openalex.org/C86859247","wikidata":"https://www.wikidata.org/wiki/Q4781760","display_name":"Approximate entropy","level":3,"score":0.776270866394043},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.7146087884902954},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5899614095687866},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.587946355342865},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5762830376625061},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5611328482627869},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5304486155509949},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5157166123390198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4766809940338135},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4526888132095337},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4482116401195526},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38993147015571594},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1999523937702179},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19965404272079468},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.17264103889465332},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.09361061453819275},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/wcnc.2009.4917520","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wcnc.2009.4917520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Wireless Communications and Networking Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1982035040","https://openalex.org/W1998727969","https://openalex.org/W2000841363","https://openalex.org/W2000983461","https://openalex.org/W2028490525","https://openalex.org/W2032108249","https://openalex.org/W2069641973","https://openalex.org/W2102624304","https://openalex.org/W2104436223","https://openalex.org/W2107925704","https://openalex.org/W2113619583","https://openalex.org/W2120411251","https://openalex.org/W2122741631","https://openalex.org/W2152254020","https://openalex.org/W2162442687","https://openalex.org/W2798333393","https://openalex.org/W4232834112"],"related_works":["https://openalex.org/W3034924094","https://openalex.org/W2006887475","https://openalex.org/W2377672665","https://openalex.org/W2055371868","https://openalex.org/W3035605494","https://openalex.org/W2951756867","https://openalex.org/W4299420056","https://openalex.org/W3123340132","https://openalex.org/W4323649933","https://openalex.org/W2376346938"],"abstract_inverted_index":{"High":[0],"complexity":[1,41,44,48,55,86],"of":[2,8,32,67,92,106,110,120,129,147,154],"frequency-hopping":[3],"(FH)/spread-spectrum":[4],"(SS)":[5],"sequence":[6,20,34,75,79,94],"is":[7,101],"great":[9],"importance":[10],"to":[11,22,63,88,142],"high-security":[12],"multiple-access":[13],"communication":[14],"systems,":[15],"for":[16],"it":[17],"makes":[18],"FH/SS":[19,33,93,149],"difficult":[21],"be":[23],"analyzed.":[24],"With":[25],"the":[26,30,39,46,52,65,68,73,77,90,97,104,107,111,117,121,137,144,148],"growing":[27],"development":[28],"in":[29,35,103],"design":[31],"much":[36],"wider":[37],"fields,":[38],"well-known":[40],"measures-the":[42],"linear":[43,47,54],"(LC),":[45],"profile":[49],"(LCP)":[50],"and":[51,76,132],"k-error":[53],"(k-error":[56],"LC)-are":[57],"widely":[58],"used":[59],"but":[60],"not":[61],"sufficient":[62],"evaluate":[64,89],"complexities":[66,146],"sequences":[69,112,150],"available,":[70],"such":[71],"as":[72],"cryptographical":[74],"chaotic":[78],"families.":[80],"In":[81],"this":[82],"paper,":[83],"a":[84,126],"new":[85],"metric":[87],"unpredictability":[91],"based":[95],"on":[96],"approximate":[98],"entropy":[99],"(ApEn)":[100],"proposed":[102,138],"view":[105],"maximal":[108],"randomness":[109],"with":[113,151],"arbitrary":[114],"length.":[115],"And":[116],"theoretical":[118],"bounds":[119],"ApEn":[122,139],"are":[123],"derived":[124],"from":[125],"probabilistic":[127],"point":[128],"view.":[130],"Simulations":[131],"analysis":[133],"results":[134],"show":[135],"that,":[136],"works":[140],"effectively":[141],"discern":[143],"changing":[145],"small":[152],"number":[153],"samples,":[155],"which":[156],"provide":[157],"superior":[158],"performance":[159],"over":[160],"its":[161],"candidates.":[162]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}