Multivariate Shannon's entropy for adaptive IIR filtering via kernel density estimators

• Published in: Electronics letters Vol. 55; no. 15; pp. 859 - 861
• Main Authors: Fantinato, D.G, Silva, D.G, Attux, R, Neves, A
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 25.07.2019
• Subjects: adaptive filters; adaptive IIR; approximate gradient‐based approaches; entropy; equalisers; filtering theory; gradient methods; higher order statistics; IIR filters; information theoretic learning criterion; kernel density estimators; learning (artificial intelligence); mean square error methods; mean squared error criterion; MSE; multivariate entropy definition; noisy scenarios; optimisation; optimisation methods; Recursive Prediction Error‐based algorithm; Shannon's entropy; Shannon's error entropy; Signal processing; supervised channel equalisation problem; supervised infinite impulse response adaptive filtering; underlying signals; usual option; mean squared error criterion; IIR filters; kernel density estimators; Shannon's error entropy; multivariate entropy definition; optimisation; entropy; adaptive IIR; supervised infinite impulse response adaptive filtering; Recursive Prediction Error-based algorithm; equalisers; learning (artificial intelligence); mean square error methods; gradient methods; noisy scenarios; MSE; approximate gradient-based approaches; adaptive filters; optimisation methods; filtering theory; information theoretic learning criterion; higher order statistics; usual option; underlying signals; Shannon's entropy; supervised channel equalisation problem
• ISSN: 0013-5194; 1350-911X; 1350-911X
• DOI: 10.1049/el.2019.1430

In supervised infinite impulse response adaptive filtering, approximate gradient-based approaches are the usual option among optimisation methods. When based on the mean squared error (MSE) criterion, however, these approaches may present biased solutions in noisy scenarios. In that sense, instead of the MSE, the authors propose the use of Shannon's error entropy, an information theoretic learning criterion, which is able to extract higher order statistics from the underlying signals. In particular, a multivariate entropy definition is considered, which is applied to derive a Recursive Prediction Error-based algorithm. The performance analyses are carried out in the context of the supervised channel equalisation problem, with results very favourable to the proposal, in high and low noise level environments.