The Role of Synchronization in Digital Communications Using Chaos—Part I: Fundamentals of Digital Communications

In a digital communications system, data is transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample functions sent through the channel are weighted sums of one or more sinusoids; in a chaotic communications system, the sample functions are segments of chaotic waveforms. At the receiver, the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by noncoherent detection, where one or more characteristics of the sample functions are estimated. In a coherent receiver, synchronization is the most commonly used technique for recovering the sample functions from the received waveform. These sample functions are then used as reference signals for a correlator. Synchronization-based receivers have advantages over noncoherent ones in terms of noise performance and bandwidth efficiency. These advantages are lost if synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communication without synchronization may be preferable. The main aim of this paper is to provide a unified approach for the analysis and comparison of conventional and chaotic communications systems. In Part I, the operation of sinusoidal communications techniques is surveyed in order to clarify the role of synchronization and to classify possible demodulation methods for chaotic communications. In Part II, chaotic synchronization schemes are described in detail and proposed chaotic communications techniques are summarized. In Part III, examples of chaotic communications schemes with and without synchronization are given, and the performance of these schemes is evaluated in the context of noisy, bandlimited channels.