{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:08:18Z","timestamp":1760231298229,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006595","name":"the Romanian Ministry of Education and Research, CNCS\u2013UEFISCDI","doi-asserted-by":"publisher","award":["PN-III-P1-1.1-PD-2019-0340"],"award-info":[{"award-number":["PN-III-P1-1.1-PD-2019-0340"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a stochastic model for the least-mean-square algorithm with symmetric\/antisymmetric properties (LMS-SAS), operating in a system identification setup with Gaussian input data. Specifically, model expressions are derived to describe the mean weight behavior of the (global and virtual) adaptive filters, learning curves, and evolution of some correlation-like matrices, which allow predicting the algorithm behavior. Simulation results are shown and discussed, confirming the accuracy of the proposed model for both transient and steady-state phases.<\/jats:p>","DOI":"10.3390\/sym14091908","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T22:37:28Z","timestamp":1663108648000},"page":"1908","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic Model for the LMS Algorithm with Symmetric\/Antisymmetric Properties"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7356-6708","authenticated-orcid":false,"given":"Augusto Cesar","family":"Becker","sequence":"first","affiliation":[{"name":"LAPSE\u2014Electronics and Signal Processing Laboratory, Department of Electronics Engineering, Federal University of Technology-Paran\u00e1, Toledo 85902-490, PR, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0881-4888","authenticated-orcid":false,"given":"Eduardo Vinicius","family":"Kuhn","sequence":"additional","affiliation":[{"name":"LAPSE\u2014Electronics and Signal Processing Laboratory, Department of Electronics Engineering, Federal University of Technology-Paran\u00e1, Toledo 85902-490, PR, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6766-3261","authenticated-orcid":false,"given":"Marcos Vinicius","family":"Matsuo","sequence":"additional","affiliation":[{"name":"GEPS\u2014Electronics and Signal Processing Group, Department of Control, Automation, and Computation, Federal University of Santa Catarina, Blumenau 89036-004, SC, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0036-5865","authenticated-orcid":false,"given":"Jacob","family":"Benesty","sequence":"additional","affiliation":[{"name":"National Institute of Scientific Research\u2014Energy, Materials, and Telecommunications, University of Quebec, Montreal, QC H5A 1K6, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0379-2360","authenticated-orcid":false,"given":"Constantin","family":"Paleologu","sequence":"additional","affiliation":[{"name":"Department of Telecommunications, Faculty of Electronics, Telecommunications, and Information Technology, University Politehnica of Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5945-5179","authenticated-orcid":false,"given":"Laura-Maria","family":"Dogariu","sequence":"additional","affiliation":[{"name":"Department of Telecommunications, Faculty of Electronics, Telecommunications, and Information Technology, University Politehnica of Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3982-1837","authenticated-orcid":false,"given":"Silviu","family":"Ciochin\u0103","sequence":"additional","affiliation":[{"name":"Department of Telecommunications, Faculty of Electronics, Telecommunications, and Information Technology, University Politehnica of Bucharest, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,12]]},"reference":[{"key":"ref_1","unstructured":"\u00c5str\u00f6m, K.J., and Wittenmark, B. 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