{"id":"https://openalex.org/W3127747887","doi":"https://doi.org/10.1109/lsp.2021.3055460","title":"The NLMS Is Steady-State Schur-Convex","display_name":"The NLMS Is Steady-State Schur-Convex","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3127747887","doi":"https://doi.org/10.1109/lsp.2021.3055460","mag":"3127747887"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2021.3055460","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2021.3055460","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing 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/A5102002504","display_name":"Anum Ali","orcid":"https://orcid.org/0000-0001-5332-8745"},"institutions":[{"id":"https://openalex.org/I4210101778","display_name":"Samsung (United States)","ror":"https://ror.org/01bfbvm65","country_code":"US","type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4210101778"]},{"id":"https://openalex.org/I4210133173","display_name":"Research!America (United States)","ror":"https://ror.org/044pgyv50","country_code":"US","type":"company","lineage":["https://openalex.org/I4210133173"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anum Ali","raw_affiliation_strings":["Standards and Mobility Innovation Laboratory, Samsung Research America, Plano, TX, USA"],"raw_orcid":"https://orcid.org/0000-0001-5332-8745","affiliations":[{"raw_affiliation_string":"Standards and Mobility Innovation Laboratory, Samsung Research America, Plano, TX, USA","institution_ids":["https://openalex.org/I4210101778","https://openalex.org/I4210133173"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057263563","display_name":"Muhammad Moinuddin","orcid":"https://orcid.org/0000-0003-4735-0692"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Muhammad Moinuddin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia","Center of Excellence in Intelligent Engineering Systems, King Abdulaziz University, Jeddah, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-4735-0692","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Center of Excellence in Intelligent Engineering Systems, King Abdulaziz University, Jeddah, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066119580","display_name":"Tareq Y. Al-Naffouri","orcid":"https://orcid.org/0000-0001-6955-4720"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tareq Y. Al-Naffouri","raw_affiliation_strings":["Computer Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6955-4720","affiliations":[{"raw_affiliation_string":"Computer Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6904,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62812482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"28","issue":null,"first_page":"389","last_page":"393"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9995999932289124,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/majorization","display_name":"Majorization","score":0.8145138621330261},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.7274671196937561},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6284156441688538},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6021145582199097},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5613324642181396},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5027449131011963},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46714848279953003},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4525432586669922},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.43513181805610657},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4283064901828766},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4080749452114105},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36427542567253113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31702759861946106},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31130069494247437},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30460578203201294},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.293914258480072},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11220580339431763},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09711924195289612},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07050231099128723}],"concepts":[{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.8145138621330261},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.7274671196937561},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6284156441688538},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6021145582199097},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5613324642181396},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5027449131011963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46714848279953003},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4525432586669922},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43513181805610657},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4283064901828766},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4080749452114105},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36427542567253113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31702759861946106},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31130069494247437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30460578203201294},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.293914258480072},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11220580339431763},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09711924195289612},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07050231099128723},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical 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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2021.3055460","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2021.3055460","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/667111","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/667111","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2345601897","display_name":null,"funder_award_id":"DF-211-135-1441","funder_id":"https://openalex.org/F4320322322","funder_display_name":"King Abdulaziz University"}],"funders":[{"id":"https://openalex.org/F4320322322","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74"},{"id":"https://openalex.org/F4320335726","display_name":"Deanship of Scientific Research, King Saud University","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1492221128","https://openalex.org/W1968020335","https://openalex.org/W1975688973","https://openalex.org/W1999542175","https://openalex.org/W2030319782","https://openalex.org/W2041495894","https://openalex.org/W2092124777","https://openalex.org/W2107084304","https://openalex.org/W2116474882","https://openalex.org/W2119099945","https://openalex.org/W2119596571","https://openalex.org/W2128817619","https://openalex.org/W2133247229","https://openalex.org/W2144174236","https://openalex.org/W2151578276","https://openalex.org/W2157977263","https://openalex.org/W2166722852","https://openalex.org/W2167296576","https://openalex.org/W2178703507","https://openalex.org/W2407385664","https://openalex.org/W2797325582","https://openalex.org/W2883912978","https://openalex.org/W2955198501","https://openalex.org/W3000411373","https://openalex.org/W3020982396","https://openalex.org/W4236087597","https://openalex.org/W4300694379","https://openalex.org/W6629420886","https://openalex.org/W6683919474","https://openalex.org/W6737056381","https://openalex.org/W6842073646","https://openalex.org/W6844645866","https://openalex.org/W7045474554"],"related_works":["https://openalex.org/W371413493","https://openalex.org/W1988514170","https://openalex.org/W4320039931","https://openalex.org/W4313303878","https://openalex.org/W4214702501","https://openalex.org/W2050374035","https://openalex.org/W2524413221","https://openalex.org/W4246164825","https://openalex.org/W1932856329","https://openalex.org/W3159088589"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,26,41,59],"study":[4],"the":[5,10,18,28,34,47,51,56,65,71],"impact":[6],"of":[7,17,30,50,64],"input-spread":[8,72],"on":[9],"steady-state":[11,68],"excess":[12],"mean":[13,21],"squared":[14],"error":[15],"(EMSE)":[16],"normalized":[19],"least":[20],"squares":[22],"(NLMS)":[23],"algorithm.":[24],"First,":[25],"use":[27,42],"concept":[29],"majorization":[31,48],"to":[32,37,44],"order":[33,49],"input-regressors":[35,52],"according":[36],"their":[38],"spread.":[39],"Second,":[40],"Schur-convexity":[43],"show":[45],"that":[46],"is":[53],"preserved":[54],"in":[55,67],"EMSE.":[57],"Effectively,":[58],"provide":[60],"an":[61],"analytical":[62],"justification":[63],"increase":[66],"EMSE":[69],"as":[70],"increases.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}