The performance of chaos shift keying: synchronization versus symbolic backtracking

Since Chaos Shift Keying (CSK) has been proposed by Herve Dedieu et al. (see IEEE Trans. Circuits Syst., vol. CAS-40, no. 10, p. 634 et seq., 1993) there has been a number of papers published, dealing with different variations of CSK. However, there is also a deficiency of work devoted to determine the performance of such systems, mainly due to a difficult parameterization. We suggest in this paper the use of discrete-time piecewise linear chaotic systems for performance comparisons of CSK. Synchronization of chaotic systems with an average diverging vector field is in general more sensitive to noise than with a passive system, possessing a converging vector field. We propose therefore a CSK implementation that we term “symbolic backtracking”. Symbolic backtracking is an algorithm that uses the ideas of symbolic dynamics to estimate the initial condition of a finite-length, noise perturbed chaotic trajectory. By “tracking” the signal backwards in time the vector field along the trajectory becomes convergent and we expect therefore better performance measures than for a “forward-oriented” synchronization technique. We compare finally the performance of CSK with conventional error feedback synchronization against CSK using symbolic backtracking