Optimal detection of differential chaos shift keying

Recent advances in the development of communication schemes based on chaos suggest that differential chaos shift keying (DCSK) is one of the most promising candidates for a feasible implementation. Traditionally, the demodulation-decoding of DCSK has been achieved by means of a noncoherent approach based on a correlation detector. This approach in general works for any differential noise shift keying (DNSK) out of which DCSK is a subclass, i.e., it does not exploit the chaotic dynamics involved. In this paper, it will be shown that the simple correlation detector can be augmented by information based on the chaotic dynamics to improve the performance, yielding a statistically optimal detection. Introducing a rigorous probabilistic framework, the optimal receiver for additive white Gaussian noise (AWGN) will be derived, and it is shown that it decomposes into a part based on correlation and a part based on the chaotic dynamics.