Theoretical noise performance of correlator-based chaotic communications schemes

In wireless local area networks and indoor communications, multipath propagation limits the performance of data communications systems. To overcome the multipath propagation problem, a spread spectrum system has to be used. The chaotic communications technique, where inherently wideband chaotic basis functions are used, offers a cheap alternative to conventional spread spectrum communications. Unfortunately, analytic expressions for the noise performance of chaotic modulation schemes are not available in the literature. This has so far prevented a full exploitation of the features of chaotic modulation schemes. By generalizing the waveform communications concept, this paper develops exact expressions for the noise performance of the coherent antipodal chaos shift keying (CSK), coherent differential chaos shift keying (DCSK), and differentially coherent DCSK modulation schemes. We show that the properties of the basis functions have no effect on the noise performance of a modulation scheme, provided that the energy per bit is constant. In this sense, the concept of waveform communications is generalized. Finally, our theoretical results are verified by computer simulations.