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Use of Chebyshev Polynomial Kalman Filter for pseudo-blind demodulation of CD3S signals

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Abstract

Chaos based communication represents an attractive solution in order to design secure multiple access digital communication systems. In this paper we investigate the use of piecewise linear chaotic maps as chaotic generators combined, on the receiver side, with Chebyshev Polynomial Kalman Filters in a dual scheme configuration for demodulation purpose. Piecewise linear maps results into enhanced robustness properties of the spreading chaotic sequence, while approximation of nonlinear systems through Chebyshev polynomial series allows closed form estimation of mean and variance. Therefore, statistical moments can be computed by means of simple algebraic operations on matrices in compact form. In this work we extend these concepts to a dual Chebyshev Polynomial Kalman Filter scheme, suitable for signal recovery in chaos based spread spectrum systems. Numerical simulations show that the proposed method achieves lower error levels on a wide range of the bit-energy-tonoise- power-spectral-density ratio with respect to a state-of-the-art method based on unscented Kalman filters.

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Author information

Authors and Affiliations

  1. Department of Electronics, University of Jijel, Jijel, Algeria

    Moussa Yahia

  2. Department of Management, Universitá Politecnica delle Marche, Ancona, Italy

    Davide Radi

  3. DESP, University of Urbino, Urbino, Italy

    Laura Gardini

  4. DiSBeF, University of Urbino, Urbino, Italy

    Valerio Freschi

Authors
  1. Moussa Yahia
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  2. Davide Radi
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  3. Laura Gardini
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  4. Valerio Freschi
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Corresponding author

Correspondence to Valerio Freschi.

Additional information

Recommended by Associate Editor Young Soo Suh under the direction of Editor Duk-Sun Shim.

The first author acknowledges the University of Jijel, Algeria, for financial support. The authors are grateful to Prof. Federico Bizzarri (Politecnico di Milano) for his valuable advices during the preparation of this article and for his helpful comments on early drafts of it.

Moussa Yahia was born in Fej-M‘zala, Jijel, Algeria. He received his Ph.D. degree in Electronics from the University of Constantine 1, Algeria. Currently, he is an Assistant Professor in the Department of Electronics, University of Jijel, Algeria. His research activities concern nonlinear signal processing, secure communications relying on chaotic dynamics.

Davide Radi received both his B.S. degree in Information Technology Management for Business and his M.Sc. degree in Economics from the University of Urbino Carlo Bo, Urbino, Italy, in 2007 and 2010, respectively, and his D.Phil. degree in Economics, Applied Mathematics and Operational research from the University of Bergamo, Bergamo, Italy, in 2014. His current position is with Marche Polytechnic University, Ancona, Italy. His research interests include nonlinear dynamical systems and their applications.

Laura Gardini was born in Ravenna, Italy, in 1952, she graduated in mathematics in 1975 at the University of Bologna. She worked as a researcher for the ENI group, and became a Universitary Resercher in 1988. She is a Full professor of Mathematics for Economics and Social Sciences since 1994, she now lives and works in Urbino. Her research interests are Discrete Dynamical Systems and their applications to the modeling of economic, financial, social, biological, engineering and physical systems. The main results have been obtained in the global properties of noninvertible maps, homoclinic bifurcations, dynamics and bifurcations of piecewise-smooth and discontinuous systems.

Valerio Freschi graduated in Electrical Engineering at University of Ancona (Italy) in 1999 and received his PhD in Computer Science Engineering from University of Ferrara (Italy) in 2006. Since 2009 he is an Assistant Professor in the Department of Basic Sciences and Foundations (DiSBeF) at University of Urbino, Italy. His research interests include wireless embedded systems, sensor networks, graph algorithms, bioinformatics, optimization.

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Yahia, M., Radi, D., Gardini, L. et al. Use of Chebyshev Polynomial Kalman Filter for pseudo-blind demodulation of CD3S signals. Int. J. Control Autom. Syst. 13, 1193–1200 (2015). https://doi.org/10.1007/s12555-014-0283-1

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  • DOI: https://doi.org/10.1007/s12555-014-0283-1

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