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Entropy 2019, 21(2), 162;

A Robust Adaptive Filter for a Complex Hammerstein System

1,2,* , 1
College of Electronic and Information Engineering, Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Southwest University, Chongqing 400715, China
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China.
Authors to whom correspondence should be addressed.
Received: 22 December 2018 / Revised: 2 February 2019 / Accepted: 6 February 2019 / Published: 9 February 2019
(This article belongs to the Special Issue Information Theory in Complex Systems)
PDF [887 KB, uploaded 9 February 2019]


The Hammerstein adaptive filter using maximum correntropy criterion (MCC) has been shown to be more robust to outliers than the ones using the traditional mean square error (MSE) criterion. As there is no report on the robust Hammerstein adaptive filters in the complex domain, in this paper, we develop the robust Hammerstein adaptive filter under MCC to the complex domain, and propose the Hammerstein maximum complex correntropy criterion (HMCCC) algorithm. Thus, the new Hammerstein adaptive filter can be used to directly handle the complex-valued data. Additionally, we analyze the stability and steady-state mean square performance of HMCCC. Simulations illustrate that the proposed HMCCC algorithm is convergent in the impulsive noise environment, and achieves a higher accuracy and faster convergence speed than the Hammerstein complex least mean square (HCLMS) algorithm.
Keywords: complex; Hammerstein; adaptive filters; impulsive noise; stability complex; Hammerstein; adaptive filters; impulsive noise; stability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Qian, G.; Luo, D.; Wang, S. A Robust Adaptive Filter for a Complex Hammerstein System. Entropy 2019, 21, 162.

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