{"id":"https://openalex.org/W3190864051","doi":"https://doi.org/10.1109/taes.2021.3103150","title":"Fast Detection of the Number of Signals Based on Ritz Values: A Noise-Power-Aided Approach","display_name":"Fast Detection of the Number of Signals Based on Ritz Values: A Noise-Power-Aided Approach","publication_year":2021,"publication_date":"2021-08-10","ids":{"openalex":"https://openalex.org/W3190864051","doi":"https://doi.org/10.1109/taes.2021.3103150","mag":"3190864051"},"language":"en","primary_location":{"id":"doi:10.1109/taes.2021.3103150","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2021.3103150","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Transactions on Aerospace and Electronic Systems","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/A5100447279","display_name":"Ming Zhang","orcid":"https://orcid.org/0000-0002-5796-4754"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming Zhang","raw_affiliation_strings":["Xi\u2019an Jiaotong University, Xi\u2019an, China","Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-5796-4754","affiliations":[{"raw_affiliation_string":"Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087955356","display_name":"Shitao Zhu","orcid":"https://orcid.org/0000-0002-2201-867X"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shitao Zhu","raw_affiliation_strings":["Xi\u2019an Jiaotong University, Xi\u2019an, China","Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-2201-867X","affiliations":[{"raw_affiliation_string":"Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042100389","display_name":"Xiaoming Chen","orcid":"https://orcid.org/0000-0003-3151-1690"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoming Chen","raw_affiliation_strings":["Xi\u2019an Jiaotong University, Xi\u2019an, China","Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0003-3151-1690","affiliations":[{"raw_affiliation_string":"Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002236287","display_name":"Anxue Zhang","orcid":"https://orcid.org/0000-0002-3254-6679"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Anxue Zhang","raw_affiliation_strings":["Xi\u2019an Jiaotong University, Xi\u2019an, China","Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-3254-6679","affiliations":[{"raw_affiliation_string":"Xi\u2019an Jiaotong University, Xi\u2019an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":0.2814,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.54566997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"58","issue":"1","first_page":"651","last_page":"662"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9994999766349792,"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/T10891","display_name":"Radar Systems and Signal Processing","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9990000128746033,"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/notation","display_name":"Notation","score":0.687950074672699},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.521587073802948},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5039719939231873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5038420557975769},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4965279698371887},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35680291056632996},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3436477780342102},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34087568521499634},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22097864747047424},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1350768804550171},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11708995699882507},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06619229912757874}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.687950074672699},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.521587073802948},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5039719939231873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5038420557975769},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4965279698371887},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35680291056632996},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3436477780342102},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34087568521499634},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22097864747047424},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1350768804550171},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11708995699882507},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06619229912757874},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/taes.2021.3103150","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2021.3103150","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Transactions on Aerospace and Electronic Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2040244212","display_name":null,"funder_award_id":"2018M640990","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6872402133","display_name":null,"funder_award_id":"61801368","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/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W569291674","https://openalex.org/W595851582","https://openalex.org/W615589970","https://openalex.org/W637574335","https://openalex.org/W653761051","https://openalex.org/W1586554030","https://openalex.org/W1814500939","https://openalex.org/W1980129653","https://openalex.org/W1993994096","https://openalex.org/W1996639130","https://openalex.org/W1999641116","https://openalex.org/W2013438974","https://openalex.org/W2034248602","https://openalex.org/W2035838573","https://openalex.org/W2054658115","https://openalex.org/W2057077708","https://openalex.org/W2058864484","https://openalex.org/W2096710051","https://openalex.org/W2103519107","https://openalex.org/W2103657994","https://openalex.org/W2117686912","https://openalex.org/W2123226256","https://openalex.org/W2125906265","https://openalex.org/W2129854524","https://openalex.org/W2130882239","https://openalex.org/W2131634726","https://openalex.org/W2140262081","https://openalex.org/W2147358934","https://openalex.org/W2150307184","https://openalex.org/W2150580621","https://openalex.org/W2156755023","https://openalex.org/W2165252709","https://openalex.org/W2166426208","https://openalex.org/W2168175751","https://openalex.org/W2293035877","https://openalex.org/W2316564661","https://openalex.org/W2507598686","https://openalex.org/W2522297021","https://openalex.org/W2612848743","https://openalex.org/W2912347931","https://openalex.org/W2944265668","https://openalex.org/W2963415778","https://openalex.org/W3084266373","https://openalex.org/W3103955503","https://openalex.org/W3110071460","https://openalex.org/W4256183008","https://openalex.org/W4302437260","https://openalex.org/W4312258136","https://openalex.org/W4320800818","https://openalex.org/W4379510236"],"related_works":["https://openalex.org/W2132719248","https://openalex.org/W3053349720","https://openalex.org/W1997716701","https://openalex.org/W2083479055","https://openalex.org/W4313595731","https://openalex.org/W1994932819","https://openalex.org/W2920316261","https://openalex.org/W2065402448","https://openalex.org/W2118497999","https://openalex.org/W4282942030"],"abstract_inverted_index":{"Detecting":[0],"the":[1,15,24,42,46,52,55,60,66,71,75,85,89,96,106,114,121,128,132,139,143,160,165,179,183,187],"number":[2,25],"of":[3,14,26,54,70,163,189],"signals":[4],"(NOS)":[5],"is":[6,63],"afundamental":[7],"problem":[8],"in":[9,74],"array":[10],"processing.":[11],"However,":[12],"most":[13],"existing":[16,184],"methods":[17,185],"have":[18],"a":[19,33,38,81,110,135,153],"computational":[20],"complexity":[21,39],"of$O(M^3)$,":[22],"where$M$is":[23],"sensors.":[27],"In":[28],"this":[29],"article,":[30],"we":[31,93,125],"propose":[32],"fast":[34],"detection":[35],"algorithm":[36,145,181],"with":[37,134],"of$O(DM^2)$,":[40],"where$D$is":[41],"NOS.":[43],"Different":[44],"from":[45],"conventional":[47],"approaches":[48],"that":[49,95,178],"depend":[50],"on":[51,65],"eigenvalues":[53,69],"sample":[56,191],"covariance":[57],"matrix":[58],"(SCM),":[59],"proposed":[61,144,180],"method":[62],"based":[64],"Ritz":[67,116,166],"values\u2014the":[68],"projected":[72],"SCM":[73],"Krylov":[76,86,107],"subspace.":[77],"We":[78],"first":[79],"present":[80],"scheme":[82],"to":[83,101,120,171],"construct":[84],"subspace":[87,108],"via":[88],"Lanczos":[90],"tridiagonalization.":[91],"Then,":[92],"prove":[94],"first$D$Ritz":[97],"values":[98,167],"are":[99],"equal":[100],"the$D$signal":[102],"eigenvalues.":[103],"Furthermore,":[104],"if":[105],"has":[109,152],"dimension":[111],"greater":[112],"than$D$,":[113],"minimum":[115],"value":[117],"(MRV)":[118],"converges":[119],"noise":[122,140],"power.":[123,141],"Therefore,":[124],"can":[126],"detect":[127],"NOS":[129],"by":[130,138,158],"comparing":[131],"MRV":[133],"threshold":[136],"determined":[137],"Because":[142],"does":[146],"not":[147,169],"perform":[148],"eigenvalue":[149],"decomposition,":[150],"it":[151],"simple":[154],"implementation":[155],"structure.":[156],"Moreover,":[157],"using":[159],"Sylvester\u2019s":[161],"law":[162],"inertia,":[164],"do":[168],"need":[170],"be":[172],"computed":[173],"either.":[174],"Simulation":[175],"results":[176],"show":[177],"outperforms":[182],"under":[186],"conditions":[188],"small":[190],"size":[192],"and":[193],"low":[194],"signal-to-noise":[195],"ratio.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}