Exact calculation of bit error rates in communication systems with chaotic modulation

The paper explores the calculation of exact bit error rates (BERs) for some single-user chaotic-shift-keying (CSK) communications systems, in contrast to approximate Gaussian-based approximations in current use. The conventional signalto-noise-ratio approach is shown to give only lower bounds on the BERs. An analytical Gaussian approach based on exact mean and variance of the decoder function gives inexact results. Exact BERs are given here for several CSK systems with spreading sequences from different types of chaotic map. They achieve exactness from fully exploiting the dynamical and statistical features of the systems and the results correspond theoretically to impractically large Monte Carlo simulations. A further aspect of the paper is the derivation of likelihood optimal bit decoders which can be superior to correlation decoders. The inapplicability of Gaussian assumptions is viewed through some exact distributional results for one system.