Adaptive Blind Equalization of Nonlinear Channels and Chaotic Systems using Coupled EKF and RLS Estimator

Abstract

A novel approach, which employs coupled extended Kalman filter (EKF) and recursive least squares (RLS) estimator is proposed for adaptive blind equalization of nonlinear channels and chaotic systems. The conventional models of nonlinear FIR Volterra channels, nonlinear IIR channels, and chaotic communication systems are cast into regression models to formulate RLS algorithm to estimate the unknown channel parameters. The state-space representation of the channels have been formulated to develop the EKF to estimate the state from which the input sequence can be recovered. Then, the EKF and RLS estimator are coupled to estimate jointly the channel parameters and the state. The stability problem of the estimator is also addressed. The proposed estimator is corroborated with simulation examples on adaptive blind equalization of nonlinear FIR Volterra channels, nonlinear IIR channels, and chaotic communication systems. Simulation results show that the proposed estimator is effective in recovering the input sequence as well as the channel parameters blindly from the channel output measurement.

Indexing terms:

• Adaptive blind equalization
• Nonlinear channels equalization
• Chaotic systems equalization
• Coupled estimator
• EKF
• RLS

Additional information

Notes on contributors

K Deergha Rao

K Deergha Rao received his BE and ME (Control Systems) degrees in Electrical Engineering from Andhra University, Visakhapatnam, India, in 1977 and 1980 respectively, and PhD degree in Electronics and Communication Engineering from Osmania University, Hyderabad, India, in 1993.

He is presently a Principal scientist/Professor in the Research and Training Unit for Navigational Electronics, Osmania University. He served as Post Doctoral Fellow and Part-Time Professor from March 1999 to March 2003 in the Department of ECE, Concordia University Montreal, Canada. His research interests are in GPS Signal Processing, Guidance and Control, Adaptive blind equalization, Adaptive interference cancellation in spread spectrum systems, Robust detection and estimation, Chaotic transmission and Cryptography, Robust image restoration and transmission. He has published 85 technical papers in these areas.

E I Plotkin

Eugene I Plotkin, Fellow IEEE, received his PhD degree in Electrical Engineering in 1963 from the St Petersburg Telecommunications University, St Petersburg, Russia. In 1973 he joined Ben-Gurion University, Israel, and served as Chiarman of the Department of Electrical and Computer Engineering from 1982 to 1985. Since 1986 he has been with the Department of Electrical and Computer Engineering at Concordia University, Montreal, Canada, where he is currently a Professor of Electrical Engineering. His main interests are in the areas of Nonlinear and Time-Varying Structural Signal Processing, and Image Processing. Dr Plotkin is the author and coauthor of more than 180 technical papers in the areas of Signal/Image Processing, Communications. Dr Plotkin is a Member of the Acoustical Society of America and is a co-recipient of the IEEE CAS 1986 Guillemin-Cauer Best Paper Award.

M N S Swamy

MNS Swamy received BSc (Hons) degree in Mathematics from Mysore University, India, in 1954, the Diploma in Electrical Communication Engineering from the Indian Institute of Science, Bangalore in 1957, and the MSc and PhD degrees in Electrical Engineering from the University of Saskatchewan, Saskatoon, Canada, in 1960 and 1963 respectively. In August 2001 he received the Doctor of Science degree in Engineering (Honoris Causa) from Ansted University, Penang, Malaysia, “In recognition of his exemplary contributions to the research in Electrical and Computer Engineering and to Engineering Education, as well as his dedication to the promotion of Signal Processing and Communications Applications.”

He is presently a Research Professor and the Director of the Center for Signal Processing and Communications in the Department of Electrical and Computer Engineering at Concordia University, Montreal, Canada, where he served as the Chair of the Department of Electrical Engineering from 1970 to 1977, and Dean of Engineering and Computer Science from 1977 to 1993. Since July 2001, he holds the Concordia Chair (Tier I) in Signal Processing. He has also taught in the Electrical Engineering Department of the Technical University of Nova Scotia, Halifax, and the University of Calgary, Calgary, as well as in the Department of Mathematics at the University of Saskatchewan. He has published extensively in the areas of number theory, circuits, systems and signal processing, and holds four patents. He is the co-author of two book chapters and three books.

Dr Swamy is a Fellow of the Institute of Electrical Engineers (UK), the Engineering Institute of Canada, the Institution of Engineers (India), and the Institution of Electronic and Telecommunication Engineers (India). Presently, he is the Past-President of the CAS Society. He has served the IEEE CAS Society in various capacities such as President during 2004. He is the recipient of many IEEE-CAS Society awards including the Education Award in 2000, Golden Jubilee Medal in 2000, and the 1986 Guillemin-Cauer Best Paper Award.