Applying Ergodic Theory to Improve the Noise Performance of Differential Chaos Shift Keying

This chapter provides an overview of the state of the art of current chaos communication schemes and introduces the use of signal processing to improve the communication performances. Popular communication schemes in the literature, including chaotic spreading sequence (CSS), chaotic carrier (CC), chaos masking (CM), chaos shift keying (CSK), differential chaos shift keying (DCSK) and chaotic parameter modulation (CPM), are discussed here and they are classified into three main categories according to the way how chaos is applied, that is, the use of chaotic signal, basis function and chaotic parameters. Their architecture and operations are addressed. Compared to the conventional digital communication systems, all these schemes are found to have inferior noise performance. We propose here by exploiting the ergodic property of chaotic signals, the noise performance of chaos communication can be enhanced. Using the most popular DCSK for demonstration, it is shown here that the ergodic DCSK (E-DCSK) has an improved noise performance. The theoretical noise performance, bit error rate (BER), of the proposed E-DCSK is derived, and is compared to those of other chaos communication schemes. The performance of E-DCSK in different noise channels is also investigated.