{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T06:24:38Z","timestamp":1766298278877,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2016,10,24]],"date-time":"2016-10-24T00:00:00Z","timestamp":1477267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A robust sparse least-mean mixture-norm (LMMN) algorithm is proposed, and its performance is appraised in the context of estimating a broadband multi-path wireless channel. The proposed algorithm is implemented via integrating a correntropy-induced metric (CIM) penalty into the conventional LMMN algorithm to modify the basic cost function, which is denoted as the CIM-based LMMN (CIM-LMMN) algorithm. The proposed CIM-LMMN algorithm is derived in detail within the kernel framework. The updating equation of CIM-LMMN can provide a zero attractor to attract the non-dominant channel coefficients to zeros, and it also gives a tradeoff between the sparsity and the estimation misalignment. Moreover, the channel estimation behavior is investigated over a broadband sparse multi-path wireless channel, and the simulation results are compared with the least mean square\/fourth (LMS\/F), least mean square (LMS), least mean fourth (LMF) and the recently-developed sparse channel estimation algorithms. The channel estimation performance obtained from the designated sparse channel estimation demonstrates that the CIM-LMMN algorithm outperforms the recently-developed sparse LMMN algorithms and the relevant sparse channel estimation algorithms. From the results, we can see that our CIM-LMMN algorithm is robust and is superior to these mentioned algorithms in terms of both the convergence speed rate and the channel estimation misalignment for estimating a sparse channel.<\/jats:p>","DOI":"10.3390\/e18100380","type":"journal-article","created":{"date-parts":[[2016,10,24]],"date-time":"2016-10-24T10:46:39Z","timestamp":1477305999000},"page":"380","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Robust Sparse Adaptive Filtering Algorithm with a Correntropy Induced Metric Constraint for Broadband Multi-Path Channel Estimation"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2450-6028","authenticated-orcid":false,"given":"Yingsong","family":"Li","sequence":"first","affiliation":[{"name":"College of Information and Communications Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhan","family":"Jin","sequence":"additional","affiliation":[{"name":"College of Information and Communications Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"College of Communication and Information Engineering, Qiqihar University, Qiqihar 161006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanyan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information and Communications Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Engineering, Huazhong Agricultural University, Wuhan 430070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,24]]},"reference":[{"key":"ref_1","unstructured":"Haykin, S. 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