{"id":"https://openalex.org/W4206349701","doi":"https://doi.org/10.1109/tsp.2021.3137966","title":"Joint ML/MAP Estimation of the Frequency and Phase of a Single Sinusoid With Wiener Carrier Phase Noise","display_name":"Joint ML/MAP Estimation of the Frequency and Phase of a Single Sinusoid With Wiener Carrier Phase Noise","publication_year":2021,"publication_date":"2021-12-23","ids":{"openalex":"https://openalex.org/W4206349701","doi":"https://doi.org/10.1109/tsp.2021.3137966"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3137966","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3137966","pdf_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09662238.pdf","source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09662238.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073201721","display_name":"Qian Wang","orcid":"https://orcid.org/0000-0001-5544-4512"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qian Wang","raw_affiliation_strings":["College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036478038","display_name":"Zhi Quan","orcid":null},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi Quan","raw_affiliation_strings":["College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021492036","display_name":"Suzhi Bi","orcid":"https://orcid.org/0000-0001-6212-690X"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suzhi Bi","raw_affiliation_strings":["College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083124337","display_name":"Pooi\u2010Yuen Kam","orcid":"https://orcid.org/0000-0001-5543-5034"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pooi-Yuen Kam","raw_affiliation_strings":["Center for Advanced Microelectronic Devices, NUS Research Institute, Suzhou, China","School of Science and Engineering, Chinese University of Hong Kong, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Center for Advanced Microelectronic Devices, NUS Research Institute, Suzhou, China","institution_ids":[]},{"raw_affiliation_string":"School of Science and Engineering, Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073201721"],"corresponding_institution_ids":["https://openalex.org/I180726961"],"apc_list":null,"apc_paid":null,"fwci":1.829,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.85646749,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"70","issue":null,"first_page":"337","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9984999895095825,"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/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9984999895095825,"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/T10655","display_name":"GNSS positioning and interference","score":0.9961000084877014,"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/T12004","display_name":"Advanced Frequency and Time Standards","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cram\u00e9r\u2013rao-bound","display_name":"Cram\u00e9r\u2013Rao bound","score":0.8143454790115356},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.717463493347168},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7160253524780273},{"id":"https://openalex.org/keywords/maximum-a-posteriori-estimation","display_name":"Maximum a posteriori estimation","score":0.6874380111694336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5642956495285034},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5037011504173279},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5010757446289062},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5008001327514648},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.4961896538734436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4602564573287964},{"id":"https://openalex.org/keywords/phase-noise","display_name":"Phase noise","score":0.4435086250305176},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.4387504458427429},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.43199554085731506},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42930740118026733},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.4258010983467102},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.3365171253681183},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30270445346832275},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12220162153244019},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.09717267751693726},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09218734502792358},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08250004053115845}],"concepts":[{"id":"https://openalex.org/C4978587","wikidata":"https://www.wikidata.org/wiki/Q1138810","display_name":"Cram\u00e9r\u2013Rao bound","level":3,"score":0.8143454790115356},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.717463493347168},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7160253524780273},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.6874380111694336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5642956495285034},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5037011504173279},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5010757446289062},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5008001327514648},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.4961896538734436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4602564573287964},{"id":"https://openalex.org/C89631360","wikidata":"https://www.wikidata.org/wiki/Q1428766","display_name":"Phase noise","level":2,"score":0.4435086250305176},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.4387504458427429},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.43199554085731506},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42930740118026733},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.4258010983467102},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.3365171253681183},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30270445346832275},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12220162153244019},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.09717267751693726},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09218734502792358},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08250004053115845},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2021.3137966","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3137966","pdf_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09662238.pdf","source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/tsp.2021.3137966","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3137966","pdf_url":"https://ieeexplore.ieee.org/ielx7/78/9675017/09662238.pdf","source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1084572967","display_name":null,"funder_award_id":"2019YFB1","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3234064677","display_name":null,"funder_award_id":"2019YFB1803305","funder_id":"https://openalex.org/F4320336026","funder_display_name":"National Key Research and Development Program of China Stem Cell and Translational Research"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7768016019","display_name":null,"funder_award_id":"61571316","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/F4320336026","display_name":"National Key Research and Development Program of China Stem Cell and Translational Research","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4206349701.pdf","grobid_xml":"https://content.openalex.org/works/W4206349701.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1536252645","https://openalex.org/W1536435668","https://openalex.org/W1785968703","https://openalex.org/W1989419222","https://openalex.org/W1997994486","https://openalex.org/W2001188690","https://openalex.org/W2001605516","https://openalex.org/W2010492472","https://openalex.org/W2016999686","https://openalex.org/W2025934813","https://openalex.org/W2031186754","https://openalex.org/W2034461574","https://openalex.org/W2074374994","https://openalex.org/W2075215163","https://openalex.org/W2080611403","https://openalex.org/W2099743383","https://openalex.org/W2100161595","https://openalex.org/W2102303896","https://openalex.org/W2111855076","https://openalex.org/W2124684882","https://openalex.org/W2138679438","https://openalex.org/W2149392240","https://openalex.org/W2159486133","https://openalex.org/W2160298987","https://openalex.org/W2162296825","https://openalex.org/W2164237438","https://openalex.org/W2335435021","https://openalex.org/W2338754419","https://openalex.org/W2760612493","https://openalex.org/W2765249322","https://openalex.org/W2790438735","https://openalex.org/W2809373218","https://openalex.org/W2885064626","https://openalex.org/W2951214606","https://openalex.org/W3128673098"],"related_works":["https://openalex.org/W2022738044","https://openalex.org/W3111419928","https://openalex.org/W1911817635","https://openalex.org/W2353656796","https://openalex.org/W2011915004","https://openalex.org/W2074565401","https://openalex.org/W1967187784","https://openalex.org/W2149123792","https://openalex.org/W3093327599","https://openalex.org/W2242778450"],"abstract_inverted_index":{"We":[0,28],"address":[1],"here":[2],"the":[3,8,30,42,47,60,70,75,82,85,106,109,113,140,146,150,155,161,168,173,177,181,190,196,201,204,216,218,222],"issue":[4],"of":[5,11,41,59,74,84,104,111,163,200,215],"jointly":[6],"estimating":[7],"angle":[9],"parameters":[10],"a":[12,54,122,136,213,234],"single":[13],"sinusoid":[14],"with":[15,51,81],"Wiener":[16],"carrier":[17,44,49,62,164],"phase":[18,63,90,107,165,182,223,242],"noise":[19,26,91,183,224],"and":[20,46,72,108,149,167,180,195,221],"observed":[21],"in":[22,133,160,237,240],"additive,":[23],"white,":[24],"Gaussian":[25],"(AWGN).":[27],"develop":[29],"theoretical":[31],"foundation":[32],"for":[33,138,145,154],"time-domain,":[34],"phase-based,":[35],"joint":[36],"maximum":[37,53],"likelihood":[38],"(ML)":[39],"estimation":[40,58,238],"unknown":[43],"frequency":[45],"initial":[48],"phase,":[50],"simultaneous":[52],"posteriori":[55],"probability":[56],"(MAP)":[57],"time-varying":[61],"noise.":[64,243],"The":[65,209],"derivation":[66],"is":[67,186,226],"based":[68],"on":[69,172],"amplitude":[71],"phase-form":[73],"noisy":[76],"received":[77,114],"signal":[78,115],"model":[79,92],"together":[80],"use":[83],"best,":[86],"linearized,":[87],"additive":[88],"observation":[89,178,219],"due":[93],"to":[94],"AWGN.":[95],"Our":[96],"newly":[97],"derived":[98,159],"estimators":[99,148,202],"are":[100,158,193],"closed-form":[101],"expressions,":[102],"consisting":[103],"both":[105],"magnitude":[110],"all":[112,120],"samples.":[116],"More":[117],"importantly,":[118],"they":[119],"have":[121],"low-complexity,":[123],"sample-by-sample":[124],"iterative":[125],"processing":[126],"structure,":[127],"which":[128,232],"can":[129],"be":[130],"implemented":[131],"iteratively":[132],"real-time.":[134],"As":[135],"basis":[137],"comparison,":[139],"Cramer-Rao":[141],"lower":[142],"bound":[143],"(CRLB)":[144],"ML":[147],"Bayesian":[151],"CRLB":[152],"(BCRLB)":[153],"MAP":[156],"estimator":[157],"presence":[162],"noise,":[166],"results":[169],"simply":[170],"depend":[171],"signal-to-noise":[174],"ratio":[175],"(SNR),":[176],"length":[179,220],"variance.":[184],"It":[185],"theoretically":[187],"shown":[188],"that":[189],"estimates":[191],"obtained":[192],"unbiased,":[194],"mean-square":[197],"error":[198],"(MSE)":[199],"attain":[203],"CRLB/BCRLB":[205],"at":[206],"high":[207],"SNR.":[208],"MSE":[210],"performance":[211],"as":[212],"function":[214],"SNR,":[217],"variance":[225],"verified":[227],"using":[228],"Monte":[229],"Carlo":[230],"simulation,":[231],"shows":[233],"remarkable":[235],"improvement":[236],"accuracy":[239],"large":[241]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
