Optimal Spreading Sequences for Chaos-Based Communication Systems

As a continuation from [2], some higherorder statistical dependency aspects of chaotic spreading sequences used in communication systems are presented. The autocorrelation function (ACF) of the mean-adjusted squares, termed the quadratic autocorrelation function, forms the building block of nonlinear dependence assessment of the family of spreading sequences under investigation. Explicit results are provided for the theoretical lower bound, the so-called Fréchet lower bound, of the quadratic ACF of that family. A method for producing a spreading sequence which attains the Fréchet bound is introduced. Key Words—quadratic autocorrelation, negative statistical dependency, Fréchet lower bound, chaos communication systems