22.1 Introduction

Over the past five years, much research effort has been devoted to the study of digital modulation schemes using chaotic basis functions. It is now possible to make definitive statements about the noise performance of these schemes. The aim of this chapter is to present theoretical performance bounds for correlator-based chaotic digital communications schemes, to summarize the performance of some representative schemes relative to these limits, and to highlight the expected best case performance in real applications.

In Section 22.2, we extend the basis function approach to modulation and demodulation using chaotic basis functions and highlight the problem associated with estimating statistical properties of chaotic signals from sample functions of finite length.

The estimation problem, which results from an inherent characteristic of a chaotic communications system, namely that the basis functions vary from symbol to symbol even if the same symbol is transmitted repeatedly, potentially degrades the performance of every chaotic digital modulation scheme. We discuss this problem in Sec. 22.3 and show that it can be solved by using orthonormal basis functions.

The digital chaotic modulation schemes which we consider in this work are analyzed in the context of a receiver model which is described in Sec. 22.4

In Section 22.5, we show that a coherent chaotic modulation scheme with one basis function, referred to as antipodal Chaos-Shift Keying (CSK), can theoretically achieve the noise performance of Binary Phase-Shift Keying (BPSK). In practice, this performance cannot be reached because at least two problems must be overcome: the...