title: A matched filter for chaos.
abstract: 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.
authors.affiliation: US Army Research, Development and Engineering Command, RDMR-WSS, Redstone Arsenal, Alabama 35898, USA. ned.corron@us.army.mil
authors.forename: Ned J
authors.initials: NJ
authors.lastname: Corron
authors.forename: Jonathan N
authors.initials: JN
authors.lastname: Blakely
authors.forename: Mark T
authors.initials: MT
authors.lastname: Stahl