Signal reconstruction with applications to chaos-based communications

Abstract

This thesis addresses the signal reconstruction problem relevant to chaos-based communication systems. Six specific phases of studies are described. The first phase reviews the basic properties of chaotic signals, establishing the suitability of chaotic signals for use in communication. Existing theories, techniques, methods and practical issues related to chaos-based communications are discussed. The second phase reviews the state of the art in signal reconstruction, with special emphasis laid on deterministic chaotic signals. The problems associated with applying the reconstruction theory are described. To tackle the practical problems of reconstructing chaotic dynamics from non-ideal observed samples, neural networks are used as modelling tools. In the third phase, the background theories of neural networks are reviewed, the focus being two specific kinds of neural networks: radial-basis-function neural networks and recurrent neural networks. In the fourth phase, the reconstruction theory is generalized to time-varying (continuous-time and discrete-time) chaotic systems based on the observer approach. In the fifth phase, an original contribution to reconstruction of chaotic dynamics from noisy observed samples is described in detail. Specifically, a modified radial-basis-function neural network incorporating a (adaptive) learning algorithm is used to realize the reconstruction task. Also, a specific application in chaos-based digital communication systems is discussed. In the sixth phase, the reconstruction of chaotic dynamics from distorted and noisy observed samples is studied. Essentially, the channel equalization problem in chaos-based communication systems is addressed. This problem is formulated in the light of signal reconstruction, and is solved by using a modified recurrent neural network incorporating a learning algorithm.