A Matched Filter Developed for Chaotic Waveforms

A matched filter developed for use in chaos-based communications systems is presented. A matched filter is the optimum filter for maximizing the signal-to-noise ratio of a received signal in the presence of additive Gaussian white noise (AGWN). Chaos-based communications systems encode information into a chaotic waveform using arbitrary small perturbations to control the trajectory of the chaotic oscillator. Chaotic waveforms are deterministic, are sensitive to initial conditions, have aperiodic long-term behavior, have a spread frequency spectrum, and are theoretically immune to interference. There has been great interest in using chaotic waveforms in communication applications. One reason for this interest is that the spread spectrum of a chaotic waveform gives the appearance of noise when observed over a prolonged period of time. This masks the waveform from anyone without prior knowledge of its presence. Another reason is that to retrieve the information encoded in the chaotic waveform, complete knowl...