{"id":"https://openalex.org/W3114704532","doi":"https://doi.org/10.23919/eusipco47968.2020.9287604","title":"A Multi-Stage Parallel LMS Structure and its Stability Analysis Using Transfer Function Approximation","display_name":"A Multi-Stage Parallel LMS Structure and its Stability Analysis Using Transfer Function Approximation","publication_year":2020,"publication_date":"2020-12-18","ids":{"openalex":"https://openalex.org/W3114704532","doi":"https://doi.org/10.23919/eusipco47968.2020.9287604","mag":"3114704532"},"language":"en","primary_location":{"id":"doi:10.23919/eusipco47968.2020.9287604","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco47968.2020.9287604","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 28th European Signal Processing Conference (EUSIPCO)","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/A5021771385","display_name":"Ghattas Akkad","orcid":"https://orcid.org/0000-0001-8006-6090"},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I4210123702","display_name":"Laboratoire des Sciences et Techniques de l\u2019Information de la Communication et de la Connaissance","ror":"https://ror.org/0266kfd37","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I180375564","https://openalex.org/I201181511","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I4210123702","https://openalex.org/I4210127572","https://openalex.org/I4210145102","https://openalex.org/I4210148559","https://openalex.org/I4210159245","https://openalex.org/I4405260085"]},{"id":"https://openalex.org/I4210148559","display_name":"\u00c9cole nationale sup\u00e9rieure de techniques avanc\u00e9es Bretagne","ror":"https://ror.org/059n54003","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102","https://openalex.org/I4210148559"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G. Akkad","raw_affiliation_strings":["UMR 6285, ENSTA Bretagne, Lab-STICC, Brest, France","ENSTA Bretagne - \u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne (2 rue Fran\u00e7ois Verny, 29806 Brest cedex 9 - France)","Lab-STICC_SI3 - Equipe Security, Intelligence and Integrity of Information (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UMR 6285, ENSTA Bretagne, Lab-STICC, Brest, France","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I4210123702","https://openalex.org/I4210148559"]},{"raw_affiliation_string":"ENSTA Bretagne - \u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne (2 rue Fran\u00e7ois Verny, 29806 Brest cedex 9 - France)","institution_ids":["https://openalex.org/I4210148559"]},{"raw_affiliation_string":"Lab-STICC_SI3 - Equipe Security, Intelligence and Integrity of Information (France)","institution_ids":["https://openalex.org/I161929037"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015623576","display_name":"Ali Mansour","orcid":"https://orcid.org/0000-0003-4144-8832"},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I4210123702","display_name":"Laboratoire des Sciences et Techniques de l\u2019Information de la Communication et de la Connaissance","ror":"https://ror.org/0266kfd37","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I180375564","https://openalex.org/I201181511","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I4210123702","https://openalex.org/I4210127572","https://openalex.org/I4210145102","https://openalex.org/I4210148559","https://openalex.org/I4210159245","https://openalex.org/I4405260085"]},{"id":"https://openalex.org/I4210148559","display_name":"\u00c9cole nationale sup\u00e9rieure de techniques avanc\u00e9es Bretagne","ror":"https://ror.org/059n54003","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102","https://openalex.org/I4210148559"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Mansour","raw_affiliation_strings":["UMR 6285, ENSTA Bretagne, Lab-STICC, Brest, France","Lab-STICC_SI3 - Equipe Security, Intelligence and Integrity of Information (France)","ENSTA Bretagne - \u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne (2 rue Fran\u00e7ois Verny, 29806 Brest cedex 9 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UMR 6285, ENSTA Bretagne, Lab-STICC, Brest, France","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I4210123702","https://openalex.org/I4210148559"]},{"raw_affiliation_string":"Lab-STICC_SI3 - Equipe Security, Intelligence and Integrity of Information (France)","institution_ids":["https://openalex.org/I161929037"]},{"raw_affiliation_string":"ENSTA Bretagne - \u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es Bretagne (2 rue Fran\u00e7ois Verny, 29806 Brest cedex 9 - France)","institution_ids":["https://openalex.org/I4210148559"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110732240","display_name":"Bachar El-Hassan","orcid":null},"institutions":[{"id":"https://openalex.org/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"B. ElHassan","raw_affiliation_strings":["Faculty of Engineering, Lebanese University, Tripoli, Lebanon","DEPT. OF COMPUT. & COMMUN. - Lebanese Univ., Tripoli, Lebanon (Liban)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Lebanese University, Tripoli, Lebanon","institution_ids":["https://openalex.org/I160368002"]},{"raw_affiliation_string":"DEPT. OF COMPUT. & COMMUN. - Lebanese Univ., Tripoli, Lebanon (Liban)","institution_ids":["https://openalex.org/I160368002"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046149825","display_name":"Elie Inaty","orcid":"https://orcid.org/0000-0001-7611-3018"},"institutions":[{"id":"https://openalex.org/I168913471","display_name":"University of Balamand","ror":"https://ror.org/01xvwxv41","country_code":"LB","type":"education","lineage":["https://openalex.org/I168913471"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"E. Inaty","raw_affiliation_strings":["University of Balamand, Koura, Lebanon","UOB - University of Balamand [Liban] (Liban)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Balamand, Koura, Lebanon","institution_ids":["https://openalex.org/I168913471"]},{"raw_affiliation_string":"UOB - University of Balamand [Liban] (Liban)","institution_ids":["https://openalex.org/I168913471"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1851","last_page":"1855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/least-mean-squares-filter","display_name":"Least mean squares filter","score":0.6991699934005737},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6515887379646301},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5609644651412964},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5345809459686279},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5281650424003601},{"id":"https://openalex.org/keywords/adaptive-beamformer","display_name":"Adaptive beamformer","score":0.5130828619003296},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48067009449005127},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4419357180595398},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.424507737159729},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.4176325798034668},{"id":"https://openalex.org/keywords/adaptive-filter","display_name":"Adaptive filter","score":0.41697677969932556},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3425702452659607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33352571725845337},{"id":"https://openalex.org/keywords/beamforming","display_name":"Beamforming","score":0.324901282787323},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1492525339126587},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.10594058036804199},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.09960553050041199},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.06847560405731201},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06700605154037476}],"concepts":[{"id":"https://openalex.org/C32617633","wikidata":"https://www.wikidata.org/wiki/Q1426666","display_name":"Least mean squares filter","level":3,"score":0.6991699934005737},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6515887379646301},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5609644651412964},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5345809459686279},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5281650424003601},{"id":"https://openalex.org/C33378366","wikidata":"https://www.wikidata.org/wiki/Q4680719","display_name":"Adaptive beamformer","level":3,"score":0.5130828619003296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48067009449005127},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4419357180595398},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.424507737159729},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.4176325798034668},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.41697677969932556},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3425702452659607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33352571725845337},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.324901282787323},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1492525339126587},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.10594058036804199},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.09960553050041199},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.06847560405731201},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06700605154037476},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.23919/eusipco47968.2020.9287604","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco47968.2020.9287604","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 28th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-03127370v1","is_oa":false,"landing_page_url":"https://ensta.hal.science/hal-03127370","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://eusipco2020.org/","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1566559202","display_name":"Multilayer Analog Digital System for Cyberdefence & Radio Surveillance.","funder_award_id":"ANR-19-ASTR-0005","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W87496662","https://openalex.org/W1561251331","https://openalex.org/W1939850887","https://openalex.org/W1974478639","https://openalex.org/W2104233251","https://openalex.org/W2107086705","https://openalex.org/W2155595938","https://openalex.org/W2586777836","https://openalex.org/W2971659000","https://openalex.org/W2983916441","https://openalex.org/W3028021402","https://openalex.org/W3147634857","https://openalex.org/W6675716170","https://openalex.org/W6959277134"],"related_works":["https://openalex.org/W818226659","https://openalex.org/W2009075871","https://openalex.org/W2132841313","https://openalex.org/W2518591292","https://openalex.org/W2105408150","https://openalex.org/W1976800395","https://openalex.org/W2606661315","https://openalex.org/W2287235845","https://openalex.org/W2548445082","https://openalex.org/W2072054645"],"abstract_inverted_index":{"Generally,":[0],"the":[1,26,45,55,59,66,96,116,125,147,158,167,176,182,188,193,200,204],"least":[2],"mean":[3],"square":[4],"(LMS)":[5],"adaptive":[6],"algorithm":[7],"is":[8,135,169],"widely":[9],"used":[10],"in":[11,65,72,80,171,206],"antenna":[12,119],"array":[13],"beamforming":[14],"given":[15],"its":[16,21],"target":[17],"tracking":[18],"capability":[19],"and":[20,38,69,106,140,179,210,219],"low":[22,73,211],"computational":[23,67,108],"requirements.":[24],"However,":[25],"classical":[27,46],"LMS":[28,47,88,97,123,127,149],"implementation":[29],"still":[30],"suffers":[31],"from":[32],"a":[33,52,62,85,101,107],"trade-off":[34],"between":[35],"convergence":[36,98,209],"speed":[37],"residual":[39],"error":[40,92,105,134,214],"floor.":[41],"Numerous":[42],"variants":[43,218],"to":[44,75,142,156,166,173,180,216],"have":[48],"been":[49],"suggested":[50],"as":[51],"solution":[53],"for":[54,94,191,220],"previous":[56,217],"problem":[57],"at":[58],"cost":[60],"of":[61,110,118,146,187,203],"considerable":[63],"increase":[64],"complexity":[68,109],"degraded":[70],"performance":[71,202],"signal":[74],"noise":[76],"ratio":[77],"(SNR).":[78],"Thus,":[79],"this":[81],"paper,":[82],"we":[83],"propose":[84],"multi-stage":[86],"parallel":[87,122],"structure":[89],"with":[90,144],"an":[91],"feedback":[93],"accelerating":[95],"while":[99],"maintaining":[100],"minimal":[102],"steady":[103,212],"state":[104,213],"order":[111,172],"O(N),":[112],"where":[113],"N":[114],"represents":[115],"number":[117],"elements.":[120],"In":[121],"(pLMS),":[124],"second":[126],"stage":[128,150],"(LMS":[129,151],"<sub":[130,152],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[131,153],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[132],")":[133,155],"delayed":[136],"by":[137],"one":[138],"sample":[139],"fed-back":[141],"combine":[143],"that":[145],"first":[148],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[154],"form":[157],"total":[159],"pLMS":[160,168,177,194,205],"error.":[161],"A":[162],"transfer":[163],"function":[164],"approximation":[165],"derived":[170],"numerically":[174],"assess":[175],"stability":[178],"determine":[181],"approximate":[183],"maximum":[184],"parametric":[185],"value":[186],"step":[189],"size":[190],"which":[192],"remains":[195],"stable.":[196],"Simulation":[197],"result":[198],"highlight":[199],"superior":[201],"demonstrating":[207],"accelerated":[208],"compared":[215],"different":[221],"SNR":[222],"environment.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}