A tensor approach to higher order expectations of quantized chaotic trajectories. I. General theory and specialization to piecewise affine Markov systems

Author

Rovatti, Riccardo ; Mazzini, Gianluca ; Setti, Gianluca

Author_Institution

Dipt. di Elettronica Inf. e Sistemistica, Bologna Univ., Italy

Volume

47

Issue

11

fYear

2000

fDate

11/1/2000 12:00:00 AM

Firstpage

1571

Lastpage

1583

Abstract

The problem of computing any-order expectations of trajectories generated by discrete-time one-dimensional chaotic systems is addressed by means of a suitable generalization of the Perron-Frobenius operator and its quantization. Tools from tensor algebra are introduced and analytical expressions for the special case of piecewise-affine Markov maps are obtained. Results are further specialized for a family of maps with quite general features. As an example application, some cross- and self-interference terms are computed, which are involved in the evaluation of the performance of chaos-based DS-CDMA systems in an asynchronous multipath environment

Keywords

Markov processes; chaos; code division multiple access; correlation theory; multipath channels; radiofrequency interference; spread spectrum communication; tensors; Perron-Frobenius operator; asynchronous multipath environment; chaos-based DS-CDMA systems; cross-interference terms; discrete-time 1D chaotic systems; higher order expectations; one-dimensional chaotic systems; piecewise affine Markov systems; piecewise-affine Markov maps; quantized chaotic trajectories; self-interference terms; tensor algebra; tensor approach; Algebra; Art; Chaos; Chaotic communication; Loss measurement; Multiaccess communication; Pervasive computing; Quantization; Tensile stress; Trajectory;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.895325

Filename

895325