COMMUNICATIONS USING CHAOTIC FREQUENCY-MODULATION

Chaotic Frequency Modulation (CFM) provides the basis for a nonlinear communications system with (1) good noise suppression and (2) analogue signal encryption for private and secure communications links. CFM is a generalization of conventional Wideband Frequency Modulation (WFM) where the information about modulation samples m(k) axe contained in the lengths of the periods p(k) for the kth cycle of the WFM waveform. A WFM modulator produces wave-form periods described by an invertible function of the form p(k) = F(m(k)). Chaotic FM uses a map of the pulse periods to produce a noise-like pulse train even with a constant signal. The basis for CFM is a function p(k) = F(m(k); p(k-1), p(k-2), ..., p(k-1)), where i is the dimensionality of the map. A practical realization for a CFM transmitter employs an autonomous chaotic relaxation oscillator (ACRO) circuit for use as a chaotic voltage-controlled oscillator (CVCO). The ACRO is simple to construct, consisting of only two capacitors, one inductor, a bistable nonlinear element, and a modulated current source. The CVCO period (p(k)) is a nonlinear function of the current (m(k)) and the two previous pulse periods. Demodulation requires the use of at least three successive waveform-periods. Experimental and theoretical studies of the CVCO circuit have shown that (1) the ACRO return maps of pulse periods are embedded in three dimensions, (2) chaotic outputs axe difficult to decode without prior knowledge of the circuit parameters, and (3) demodulation may be accomplished with a digital signal processor.