A matched filter for chaos

Chaos - Tập 20 Số 2 - 2010
Ned J. Corron1, Jonathan N. Blakely1, Mark T. Stahl1
1U. S. Army Research, Development and Engineering Command , RDMR-WSS, Redstone Arsenal, Alabama 35898, USA

Tóm tắt

A novel chaotic oscillator is shown to admit an exact analytic solution and a simple matched filter. The oscillator is a hybrid dynamical system including both a differential equation and a discrete switching condition. The analytic solution is written as a linear convolution of a symbol sequence and a fixed basis function, similar to that of conventional communication waveforms. Waveform returns at switching times are shown to be conjugate to a chaotic shift map, effectively proving the existence of chaos in the system. A matched filter in the form of a delay differential equation is derived for the basis function. Applying the matched filter to a received waveform, the bit error rate for detecting symbols is derived, and explicit closed-form expressions are presented for special cases. The oscillator and matched filter are realized in a low-frequency electronic circuit. Remarkable agreement between the analytic solution and the measured chaotic waveform is observed.

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Chaos

Tập 20 Số 2

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