{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T08:18:12Z","timestamp":1772785092153,"version":"3.50.1"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T00:00:00Z","timestamp":1703635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s00034-023-02565-2","type":"journal-article","created":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T02:01:52Z","timestamp":1703642512000},"page":"2409-2427","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the NP-VSS-NLMS Algorithm: Model, Design Guidelines, and Numerical Results"],"prefix":"10.1007","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7356-6708","authenticated-orcid":false,"given":"Augusto Cesar","family":"Becker","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0881-4888","authenticated-orcid":false,"given":"Eduardo Vinicius","family":"Kuhn","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6766-3261","authenticated-orcid":false,"given":"Marcos Vinicius","family":"Matsuo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0036-5865","authenticated-orcid":false,"given":"Jacob","family":"Benesty","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,27]]},"reference":[{"issue":"3","key":"2565_CR1","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1016\/j.dsp.2008.10.002","volume":"19","author":"MSE Abadi","year":"2009","unstructured":"M.S.E. Abadi, J.H. Hus\u00f8y, On the application of a unified adaptive filter theory in the performance prediction of adaptive filter algorithms. Digit. Signal Process. 19(3), 410\u2013432 (2009)","journal-title":"Digit. Signal Process."},{"issue":"3","key":"2565_CR2","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1109\/78.558478","volume":"45","author":"T Aboulnasr","year":"1997","unstructured":"T. Aboulnasr, K. Mayyas, A robust variable step-size LMS-type algorithm: analysis and simulations. IEEE Trans. Signal Process. 45(3), 631\u2013639 (1997)","journal-title":"IEEE Trans. Signal Process."},{"key":"2565_CR3","volume-title":"Stochastic Approximation and Nonlinear Regression","author":"AE Albert","year":"1967","unstructured":"A.E. Albert, L.S. Gardner Jr., Stochastic Approximation and Nonlinear Regression, 1st edn. (MIT Press, Cambridge, MA, 1967)","edition":"1"},{"key":"2565_CR4","volume-title":"Adaptive Control","author":"KJ Astr\u00f6m","year":"2008","unstructured":"K.J. Astr\u00f6m, B. Wittenmark, Adaptive Control, 2nd edn. (Dover Publications, Mineola, NY, 2008)","edition":"2"},{"key":"2565_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2021.103359","volume":"122","author":"KJ Bakri","year":"2022","unstructured":"K.J. Bakri, E.V. Kuhn, R. Seara, J. Benesty, C. Paleologu, S. Ciochin\u0103, On the stochastic modeling of the LMS algorithm operating with bilinear forms. Digit. Signal Process. 122, 103359 (2022)","journal-title":"Digit. Signal Process."},{"key":"2565_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-15600-8","volume-title":"Array Processing-Kronecker Product Beamforming","author":"J Benesty","year":"2019","unstructured":"J. Benesty, I. Cohen, J. Chen, Array Processing-Kronecker Product Beamforming (Springer, Cham, 2019)"},{"key":"2565_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04437-7","volume-title":"Advances in Network and Acoustic Echo Cancellation","author":"J Benesty","year":"2001","unstructured":"J. Benesty, T. G\u00e4nsler, D.R. Morgan, M.M. Sondhi, S.L. Gay, Advances in Network and Acoustic Echo Cancellation (Springer, Berlin, 2001)"},{"key":"2565_CR8","doi-asserted-by":"crossref","unstructured":"J.\u00a0Benesty, C.\u00a0Paleologu, S.\u00a0Ciochin\u0103, E.V. Kuhn, K.J. Bakri, R.\u00a0Seara, LMS and NLMS algorithms for the identification of impulse responses with intrinsic symmetric or antisymmetric properties. In Proceedings of the IEEE International Conference on Acoustic, Speech, Signal Process (ICASSP), pp. 5662\u20135666, Singapore, Singapore, May (2022)","DOI":"10.1109\/ICASSP43922.2022.9747430"},{"key":"2565_CR9","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1109\/LSP.2006.876323","volume":"13","author":"J Benesty","year":"2006","unstructured":"J. Benesty, H. Rey, L.R. Vega, S. Tressens, A nonparametric VSS-NLMS algorithm. IEEE Signal Process. Lett. 13, 581\u2013584 (2006)","journal-title":"IEEE Signal Process. Lett."},{"issue":"1","key":"2565_CR10","first-page":"24","volume":"21","author":"D Bismor","year":"2016","unstructured":"D. Bismor, K. Czyz, Z. Ogonowski, Review and comparison of variable step-size LMS algorithms. Int. J. Acoust. Vib. 21(1), 24\u201339 (2016)","journal-title":"Int. J. Acoust. Vib."},{"key":"2565_CR11","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.sigpro.2015.06.016","volume":"118","author":"S Ciochina","year":"2016","unstructured":"S. Ciochina, C. Paleologu, J. Benesty, An optimized NLMS algorithm for system identification. Signal Process. 118, 115\u2013121 (2016)","journal-title":"Signal Process."},{"key":"2565_CR12","doi-asserted-by":"crossref","unstructured":"M.H. Costa, J.C.M. Bermudez, An improved model for the normalized LMS algorithm with Gaussian inputs and large number of coefficients. In Proceedings of the IEEE International Conference on Acoustic, Speech, Signal Processing (ICASSP), volume\u00a02, pp. 1385\u20131388, Orlando, FL, May (2002)","DOI":"10.1109\/ICASSP.2002.5745810"},{"key":"2565_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4106-9","volume-title":"Adaptive Filtering: Algorithms and Practical Implementation","author":"PSR Diniz","year":"2013","unstructured":"P.S.R. Diniz, Adaptive Filtering: Algorithms and Practical Implementation, 4th edn. (Springer, New York, NY, 2013)","edition":"4"},{"key":"2565_CR14","doi-asserted-by":"publisher","DOI":"10.1002\/9781118591352","volume-title":"Adaptive Filters: Theory and Applications","author":"B Farhang-Boroujeny","year":"2013","unstructured":"B. Farhang-Boroujeny, Adaptive Filters: Theory and Applications, 2nd edn. (Wiley, Chichester, 2013)","edition":"2"},{"key":"2565_CR15","volume-title":"Adaptive Filter Theory","author":"S Haykin","year":"2014","unstructured":"S. Haykin, Adaptive Filter Theory, 5th edn. (Prentice Hall, Upper Saddle River, NJ, 2014)","edition":"5"},{"key":"2565_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5477-9","volume-title":"Introduction to Perturbation Methods","author":"MH Holmes","year":"2013","unstructured":"M.H. Holmes, Introduction to Perturbation Methods, 2nd edn. (Springer, New York, NY, 2013)","edition":"2"},{"issue":"4","key":"2565_CR17","doi-asserted-by":"publisher","first-page":"2055","DOI":"10.1109\/TSP.2011.2181505","volume":"60","author":"H-C Huang","year":"2012","unstructured":"H.-C. Huang, J. Lee, A new variable step-size NLMS algorithm and its performance analysis. IEEE Trans. Signal Process. 60(4), 2055\u20132060 (2012)","journal-title":"IEEE Trans. Signal Process."},{"key":"2565_CR18","unstructured":"ITU-T Recommendation G.168 \u2013 Digital Network Echo Cancellers. Switzerland, International Telecommunications Union - Telecommunication Standardization Sector, Geneva (2015)"},{"key":"2565_CR19","volume-title":"Handbook of Mathematical Formulas and Integrals","author":"A Jeffrey","year":"2008","unstructured":"A. Jeffrey, H.-H. Dai, Handbook of Mathematical Formulas and Integrals, 4th edn. (Academic Press, Burlington, MA, 2008)","edition":"4"},{"key":"2565_CR20","unstructured":"S.\u00a0Kaczmarz, Angen\u00e4herte aufl\u00f6sung von systemen linearer gleichungen. Bull. Int. Acad. Pol. Sci. Lettres A, 35(III), 355\u2013357 (1937)"},{"issue":"4","key":"2565_CR21","doi-asserted-by":"publisher","first-page":"1304","DOI":"10.1109\/TSP.2008.2010375","volume":"57","author":"JE Kolodziej","year":"2009","unstructured":"J.E. Kolodziej, O.J. Tobias, R. Seara, D.R. Morgan, On the constrained stochastic gradient algorithm: Model, performance, and improved version. IEEE Trans. Signal Process. 57(4), 1304\u20131315 (2009)","journal-title":"IEEE Trans. Signal Process."},{"key":"2565_CR22","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.dsp.2014.03.006","volume":"30","author":"EV Kuhn","year":"2014","unstructured":"E.V. Kuhn, J.E. Kolodziej, R. Seara, Stochastic modeling of the NLMS algorithm for complex Gaussian input data and nonstationary environment. Digit. Signal Process. 30, 55\u201366 (2014)","journal-title":"Digit. Signal Process."},{"key":"2565_CR23","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.sigpro.2018.01.014","volume":"147","author":"EV Kuhn","year":"2018","unstructured":"E.V. Kuhn, J.G.F. Zipf, R. Seara, On the stochastic modeling of a VSS-NLMS algorithm with high immunity against measurement noise. Signal Process. 147, 120\u2013132 (2018)","journal-title":"Signal Process."},{"issue":"7","key":"2565_CR24","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.1109\/78.143435","volume":"40","author":"RH Kwong","year":"1992","unstructured":"R.H. Kwong, E.W. Johnston, A variable step size LMS algorithm. IEEE Trans. Signal Process. 40(7), 1633\u20131642 (1992)","journal-title":"IEEE Trans. Signal Process."},{"issue":"9","key":"2565_CR25","doi-asserted-by":"publisher","first-page":"1697","DOI":"10.1016\/S0165-1684(00)00082-7","volume":"80","author":"A Mader","year":"2000","unstructured":"A. Mader, H. Puder, G.U. Schmidt, Step-size control for acoustic echo cancellation filters: An overview. Signal Process. 80(9), 1697\u20131719 (2000)","journal-title":"Signal Process."},{"key":"2565_CR26","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.sigpro.2019.02.001","volume":"160","author":"MV Matsuo","year":"2019","unstructured":"M.V. Matsuo, E.V. Kuhn, R. Seara, Stochastic analysis of the NLMS algorithm for nonstationary environment and deficient length adaptive filter. Signal Process. 160, 190\u2013201 (2019)","journal-title":"Signal Process."},{"key":"2565_CR27","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.sigpro.2016.03.018","volume":"128","author":"MV Matsuo","year":"2016","unstructured":"M.V. Matsuo, R. Seara, On the stochastic analysis of the NLMS algorithm for white and correlated Gaussian inputs in time-varying environments. Signal Process. 128, 291\u2013302 (2016)","journal-title":"Signal Process."},{"issue":"4","key":"2565_CR28","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/j.jfranklin.2011.01.003","volume":"348","author":"K Mayyas","year":"2011","unstructured":"K. Mayyas, F. Momani, An LMS adaptive algorithm with a new step-size control equation. J. Franklin Inst. 348(4), 589\u2013605 (2011)","journal-title":"J. Franklin Inst."},{"issue":"6","key":"2565_CR29","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1109\/18.45287","volume":"35","author":"DR Morgan","year":"1989","unstructured":"D.R. Morgan, Comments on \u2018Convergence and performance analysis of the normalized LMS algorithm with uncorrelated Gaussian data\u2019. IEEE Trans. Inform. Theory 35(6), 1299 (1989)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"2565_CR30","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1109\/TAC.1967.1098599","volume":"12","author":"JI Nagumo","year":"1967","unstructured":"J.I. Nagumo, A. Noda, A learning method for system identification. IEEE Trans. Autom. Control 12(3), 282\u2013287 (1967)","journal-title":"IEEE Trans. Autom. Control"},{"key":"2565_CR31","volume-title":"Probability, Random Variables, and Stochastic Processes","author":"A Papoulis","year":"2002","unstructured":"A. Papoulis, S.U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edn. (McGraw-Hill, New York, NY, 2002)","edition":"4"},{"issue":"3","key":"2565_CR32","doi-asserted-by":"publisher","first-page":"1149","DOI":"10.1109\/78.205720","volume":"41","author":"M Rupp","year":"1993","unstructured":"M. Rupp, The behavior of LMS and NLMS algorithms in the presence of spherically invariant processes. IEEE Trans. Signal Process. 41(3), 1149\u20131160 (1993)","journal-title":"IEEE Trans. Signal Process."},{"issue":"7","key":"2565_CR33","doi-asserted-by":"publisher","first-page":"2809","DOI":"10.1007\/s13369-017-2453-y","volume":"42","author":"MOB Saeed","year":"2017","unstructured":"M.O.B. Saeed, LMS-based variable step-size algorithms: A unified analysis approach. Arab. J. Sci. Eng. 42(7), 2809\u20132816 (2017)","journal-title":"Arab. J. Sci. Eng."},{"key":"2565_CR34","doi-asserted-by":"publisher","DOI":"10.1002\/9780470374122","volume-title":"Adaptive Filters","author":"AH Sayed","year":"2008","unstructured":"A.H. Sayed, Adaptive Filters (Wiley, Hoboken, NJ, 2008)"},{"issue":"2","key":"2565_CR35","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1109\/LSP.2003.821722","volume":"11","author":"H-C Shin","year":"2004","unstructured":"H.-C. Shin, A.H. Sayed, W.-J. Song, Variable step-size NLMS and affine projection algorithms. IEEE Signal Process. Lett. 11(2), 132\u2013135 (2004)","journal-title":"IEEE Signal Process. Lett."},{"key":"2565_CR36","volume-title":"Discrete Random Signals and Statistical Signal Processing","author":"CW Therrien","year":"1992","unstructured":"C.W. Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice Hall, Englewood Cliffs, NJ, 1992)"},{"key":"2565_CR37","doi-asserted-by":"publisher","first-page":"1774","DOI":"10.1109\/LSP.2022.3195662","volume":"29","author":"DG Tiglea","year":"2022","unstructured":"D.G. Tiglea, R. Candido, M.T.M. Silva, A variable step size adaptive algorithm with simple parameter selection. IEEE Signal Process. Lett. 29, 1774\u20131778 (2022)","journal-title":"IEEE Signal Process. Lett."},{"issue":"2","key":"2565_CR38","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1080\/00031305.2012.687494","volume":"66","author":"JM VerHoef","year":"2012","unstructured":"J.M. VerHoef, Who invented the delta method? Am Stat. 66(2), 124\u2013127 (2012)","journal-title":"Am Stat."},{"key":"2565_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2023.109060","volume":"210","author":"W Wang","year":"2023","unstructured":"W. Wang, H. Zhang, A new and effective nonparametric variable step-size normalized least-mean-square algorithm and its performance analysis. Signal Process. 210, 109060 (2023)","journal-title":"Signal Process."},{"key":"2565_CR40","first-page":"96","volume":"4","author":"B Widrow","year":"1960","unstructured":"B. Widrow, M.E. Hoff, Adaptive switching circuits. Proc. IRE WESCON Conv. Rec. 4, 96\u2013104 (1960)","journal-title":"Proc. IRE WESCON Conv. Rec."},{"issue":"4","key":"2565_CR41","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1109\/PROC.1975.9807","volume":"63","author":"B Widrow","year":"1975","unstructured":"B. Widrow, J. McCool, M. Ball, The complex LMS algorithm. Proc. IEEE 63(4), 719\u2013720 (1975)","journal-title":"Proc. IEEE"},{"issue":"1","key":"2565_CR42","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.sigpro.2008.07.013","volume":"89","author":"S Zhao","year":"2009","unstructured":"S. Zhao, Z. Man, S. Khoo, H.R. Wu, Variable step-size LMS algorithm with a quotient form. Signal Process. 89(1), 67\u201376 (2009)","journal-title":"Signal Process."},{"key":"2565_CR43","doi-asserted-by":"crossref","unstructured":"J.G.F. Zipf, O.J. Tobias, R.\u00a0Seara, Non-parametric VSS-NLMS algorithm with control parameter based on the error correlation. In IEEE International Telecommunication Symposium (ITS), pp. 1\u20135, Manaus, AM, Brazil (2010)","DOI":"10.14209\/sbrt.2010.108"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-023-02565-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-023-02565-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-023-02565-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T12:16:37Z","timestamp":1709036197000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-023-02565-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,27]]},"references-count":43,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["2565"],"URL":"https:\/\/doi.org\/10.1007\/s00034-023-02565-2","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,27]]},"assertion":[{"value":"6 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 November 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 November 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests and Funding"}}]}}