Generalization of waveform communications: The Fourier analyzer approach

In digital communications, fixed, chaotic, and random waveforms are used. Although the theory of fixed waveform communications is well established, its generalization to include chaotic and random carriers has not yet been carried out. The lack of an exact model prevents the optimization of chaotic and random communication systems. Introducing the Fourier analyzer concepts, this paper develops a unified model which is equally valid for communications with fixed, chaotic and random carriers. It gives an exact measure for the a priori information which is exploited at the receiver to optimize the noise performance. The unified model may be used to determine the performance bounds of different waveform communication systems and offers a systematic approach for the development of optimum detector configurations. Using the model developed, a new classification of digital communication systems is proposed.