The role of synchronization in digital communications using chaos -: Part III:: Performance bounds for correlation receivers

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 typical conventional system, the analog sample functions sent through the channel are weighted sums of one or more sinusoids, called basis functions; in a chaotic communications system, the sample functions are segments of chaotic waveforms. At the receiver, the symbols 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 determined based on the received signal. 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 correlators. Synchronization-based coherent receivers have advantages over noncoherent receivers in terms of bandwidth efficiency (in narrow-band systems), data rate (in chaotic systems), and noise performance (both). These advantages are lost if carrier synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communications without synchronization may be preferable. This three-part paper shows in a tutorial manner how the theory of conventional telecommunications systems can be applied to chaotic modulation schemes. In addition, it discusses the latest results in the field of chaotic communications. In Part I [1], the theory and operation of conventional communications systems are surveyed and possible fields of application of chaotic communications are identified. In Part II [2], the theory of conventional telecommunications is extended to chaotic communications, chaotic modulation techniques and receiver configurations are surveyed, and chaotic synchronization schemes are described. In Part III, examples are given of chaotic communications schemes with and without synchronization, and the performance of correlator-based systems is evaluated in the context of noisy, bandlimited channels.