{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T12:57:23Z","timestamp":1778677043757,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T00:00:00Z","timestamp":1566345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a kernel recursive maximum Versoria-like criterion (KRMVLC) algorithm has been constructed, derived, and analyzed within the framework of nonlinear adaptive filtering (AF), which considers the benefits of logarithmic second-order errors and the symmetry maximum-Versoria criterion (MVC) lying in reproducing the kernel Hilbert space (RKHS). In the devised KRMVLC, the Versoria approach aims to resist the impulse noise. The proposed KRMVLC algorithm was carefully derived for taking the nonlinear channel equalization (NCE) under different non-Gaussian interferences. The achieved results verify that the KRMVLC is robust against non-Gaussian interferences and performs better than those of the popular kernel AF algorithms, like the kernel least-mean-square (KLMS), kernel least-mixed-mean-square (KLMMN), and Kernel maximum Versoria criterion (KMVC).<\/jats:p>","DOI":"10.3390\/sym11091067","type":"journal-article","created":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T11:19:06Z","timestamp":1566386346000},"page":"1067","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Kernel Recursive Maximum Versoria-Like Criterion Algorithm for Nonlinear Channel Equalization"],"prefix":"10.3390","volume":"11","author":[{"given":"Qishuai","family":"Wu","sequence":"first","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2450-6028","authenticated-orcid":false,"given":"Yingsong","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Key Laboratory of Microwave Remote Sensing, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Xue","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Liu, W., Pr\u00edncipe, J.C., and Haykin, S. (2010). Kernel Adaptive Filtering: A Comprehensive Introduction, John Wiley & Sons.","DOI":"10.1002\/9780470608593"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1109\/TSP.2007.907881","article-title":"The kernel least mean square algorithm","volume":"56","author":"Liu","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1016\/j.aeue.2016.04.001","article-title":"Sparse-aware set-membership NLMS algorithms and their application for sparse channel estimation and echo cancelation","volume":"70","author":"Li","year":"2016","journal-title":"AEU Int. J. Electron. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6412","DOI":"10.1109\/ACCESS.2018.2889877","article-title":"Controllable sparse antenna array for adaptive beamforming","volume":"7","author":"Shi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1007\/s11071-017-3707-7","article-title":"Time series prediction using kernel adaptive filter with least mean absolute third loss function","volume":"90","author":"Lu","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2275","DOI":"10.1109\/TSP.2004.830985","article-title":"The kernel recursive least squares algorithm","volume":"52","author":"Engel","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/TNNLS.2011.2178446","article-title":"Quantized kernel least mean square algorithm","volume":"23","author":"Chen","year":"2012","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1109\/TNNLS.2013.2258936","article-title":"Quantized kernel recursive least squares algorithm","volume":"24","author":"Chen","year":"2013","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1950","DOI":"10.1109\/TNET.2012.2187923","article-title":"An information theoretic approach of designing sparse kernel adaptive filters","volume":"20","author":"Liu","year":"2009","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_10","first-page":"3081","article-title":"Extended kernel recusive least squares algorithm","volume":"57","author":"Liu","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1109\/LSP.2015.2503000","article-title":"Regularized kernel least mean square algorithm with multiple-delay feedback","volume":"23","author":"Wang","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1109\/LSP.2014.2377726","article-title":"Kernel least mean square with single feedback","volume":"22","author":"Zhao","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.neucom.2016.01.004","article-title":"Kernel least mean square with adaptive kernel size","volume":"191","author":"Chen","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1049\/el.2013.3997","article-title":"Combination of affine projection sign algorithms for robust adaptive filtering in non-gaussian impulsive interference","volume":"50","author":"Shi","year":"2014","journal-title":"Electron. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3183","DOI":"10.1109\/TWC.2014.042314.131432","article-title":"Adaptive sparse channel estimation under symmetric \u03b1-stable noise","volume":"13","author":"Pelekanakis","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1540","DOI":"10.1109\/49.339922","article-title":"Least mean p-power error criterion for adaptive FIR filter","volume":"12","author":"Pei","year":"1994","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.sigpro.2016.04.003","article-title":"Norm-adaption penalized least mean square\/fourth algorithm for sparse channel estimation","volume":"128","author":"Li","year":"2016","journal-title":"Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1049\/ip-vis:19960449","article-title":"Convergence and steady-state properties of the least-mean mixed-norm (LMMN) adaptive algorithm","volume":"143","author":"Tanrikulu","year":"1994","journal-title":"IEE Proc. Vis. Image Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1049\/el:19941060","article-title":"Least mean mixed-norm adaptive filtering","volume":"30","author":"Chambers","year":"1994","journal-title":"Electron. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Miao, Q.Y., and Li, C.G. (2012, January 3\u20135). Kernel least-mean mixed-norm algorithm. Proceedings of the International Conference on Automatic Control and Artificial Intelligence (ACAI), Xiamen, China.","DOI":"10.1049\/cp.2012.1214"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Luo, X., Deng, J., Liu, J., Li, A., Wang, W., and Zhao, W. (2016, January 24\u201329). A novel entropy optimized kernel least-mean mixed-norm algorithm. Proceedings of the 2016 International Joint Conference on Neural Networks (IJCNN), Vancouver, BC, Canada.","DOI":"10.1109\/IJCNN.2016.7727405"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1016\/j.jfranklin.2017.04.008","article-title":"Kernel recursive generalized mixed norm algorithm","volume":"355","author":"Ma","year":"2018","journal-title":"J. Frankl. Inst."},{"key":"ref_23","first-page":"1596","article-title":"Maximum versoria criterion-based robust adaptive filtering algorithm","volume":"355","author":"Huang","year":"2017","journal-title":"IEEE Trans. Circuits Syst. II Exp. Briefs"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Jain, S., Mitra, R., and Bhatia, V. (2018, January 16\u201319). Kernel adaptive filtering based on maximum versoria criterion. Proceedings of the 2018 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), Indore, India.","DOI":"10.1109\/ANTS.2018.8710152"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, Y., Jiang, Z., Shi, W., Han, X., and Chen, B. (2019). Blocked maximum correntropy criterion algorithm for cluster-sparse system identifi-cations. IEEE Trans. Circuits Syst. II Exp. Briefs.","DOI":"10.1109\/TCSII.2019.2891654"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Shi, W., Li, Y., and Wang, Y. (2019). Noise-free maximum correntropy criterion algorithm in non-Gaussian environment. IEEE Trans. Circuits Syst. II Exp. Briefs.","DOI":"10.1109\/TCSII.2019.2914511"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"65901","DOI":"10.1109\/ACCESS.2018.2878310","article-title":"Mixed norm constrained sparse APA algorithm for satellite and network echo channel estimation","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lerga, J., Sucic, V., and Sersic, D. (2009, January 16\u201318). Performance analysis of the LPA-RICI denoising method. Proceedings of the 2009 6th International Symposium on Image and Signal Processing and Analysis, Salzburg, Austria.","DOI":"10.1109\/ISPA.2009.5297758"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"351","DOI":"10.7305\/automatika.2014.12.525","article-title":"An ICI based algorithm for fast denoising of video signals","volume":"55","author":"Lerga","year":"2014","journal-title":"Automatika"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11760-016-0921-6","article-title":"Improved LPA-ICI-based estimators embedded in a signal denoising virtual instrument","volume":"11","author":"Segon","year":"2017","journal-title":"Signal Image Video Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1932","DOI":"10.1016\/j.jfranklin.2015.02.005","article-title":"Consistency of the robust recursive Hammerstein model identification algorithm","volume":"352","author":"Filipovic","year":"2015","journal-title":"J. Frankl. Inst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1067\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:12:45Z","timestamp":1760188365000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1067"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,21]]},"references-count":31,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["sym11091067"],"URL":"https:\/\/doi.org\/10.3390\/sym11091067","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,21]]}}}