A new chaos detector and applications to communications

This dissertation proposes a new detector for chaos. This new detector is simpler and less computationally intensive than previous methods using Lyapunov exponents, correlation or attractor dimension, or entropy. It can detect chaos embedded in noise (as low as 4 dB signal to noise ratio in stationary additive white Gaussian noise), in short data sets (as short as 200 time series samples), and with severe data level quantization (data quantized to 5 bits or 32 levels). The theory behind the new detector is given and examples of its application to the Logistic, Henon, and Lozi Maps are given. Conventional electrical engineering tools (such as the Discrete Fourier Transform) fail to help in the detection of chaos. The reasons for this are given. Well known signals such as sinusoids, several types of noise, as well as amplitude modulated signals and phase shift keyed signals are applied to the new chaos detector to document the outputs. A new type of direct sequence spread spectrum communications is described and analyzed. The new system uses chaotic iterates as the frequency spreading function. This new system is more difficult to exploit than typical spread spectrum systems using linear feedback shift registers. Two new binary signalling communications schemes using chaotic iterates and the new chaos detector are described and analyzed. These systems offer secure communications and low detectability and exploitation because of their noise-like properties. Statistical analysis of chaotic data is compared to the chaos detector's performance. Computer simulations of the above are given.