Communication systems using chaotic signals.

Author(s)

Marcio Eisencraft

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Escola Politécnica (EP/BC)
• Defense date: 2001-02-01

Examining board members

Max Gerken; Jose Roberto Castilho Piqueira; Joao Marcos Travassos Romano

• Advisor: Max Gerken

Abstract

Chaotic signals are deterministic, nonperiodic and exhibit sensitive dependence on initial conditions. This dependence means that the states of two identical chaotic systems started with two conditions whose difference is arbitrarily small will be distant in the phase space after a finite time. These signals may be interesting in some Telecommunication Engineering fields because their Fourier spectrum is plane, they are difficult to predict and they are noise-like. Due to the sensitive dependence on initial conditions, it may seem that the synchronism of two chaotic systems is impossible. However, as Pecora and Carroll have shown, this synchronism is possible if the systems satisfy some necessary and sufficient conditions. This result has inspired the development of many communication systems based on coherent detection of chaotic signals. In general, they are composed of a transmitter subsystem that generates a chaotic signal depending on the information to be transmitted and a receptor subsystem that can generate a chaotic signal synchronized with the one on the transmitter and can recover the information signal. These systems are known to work well under ideal conditions. The main objective of this work is to study, theoretically and numerically, Pecora and Carroll's criterion and some of the communication systems using chaotic signals proposed in the literature, specially their behavior when additive white gaussian noise is added to the transmitted signal and the channel is band-limited. Specifically, the analog communication systems proposed by Cuomo and Oppenheim, by Wu and Chua and the Chaotic Phase Shift Keying (CPSK) system proposed by Ushio are analyzed in some detail. We show that when the mentioned non-ideal conditions are present the above systems have poor performance when considering the signal-to-noise ratio at the output of the receiver. In this work a solution is presented for the case of transmission over a bandlimited channel and a method for improving the results in the case of noisy channels is analyzed. We conclude that, regardless all the potential properties chaotic signals may have for communication applications, research and development are still necessary so that systems based on them can surpass in practical situations the usual systems used nowadays. (AU)