An augmented echo state network for nonlinear adaptive filtering of complex noncircular signals

Yili Xia*, Beth Jelfs, Marc M. Van Hulle, Jos C. Principe, Danilo P. Mandic

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

89 Citations (Scopus)


A novel complex echo state network (ESN), utilizing full second-order statistical information in the complex domain, is introduced. This is achieved through the use of the so-called augmented complex statistics, thus making complex ESNs suitable for processing the generality of complex-valued signals, both second-order circular (proper) and noncircular (improper). Next, in order to deal with nonstationary processes with large nonlinear dynamics, a nonlinear readout layer is introduced and is further equipped with an adaptive amplitude of the nonlinearity. This combination of augmented complex statistics and enhanced adaptivity within ESNs also facilitates the processing of bivariate signals with strong component correlations. Simulations in the prediction setting on both circular and noncircular synthetic benchmark processes and real-world noncircular and nonstationary wind signals support the analysis.

Original languageEnglish
Article number5634130
Pages (from-to)74-83
Number of pages10
JournalIEEE Transactions on Neural Networks
Issue number1
Publication statusPublished - Jan 2011
Externally publishedYes


  • Augmented complex statistics
  • complex noncircularity
  • echo state networks
  • widely linear modeling
  • wind prediction

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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