Ambiguity in range–Doppler determination using waveforms of a solvable chaotic oscillator

•The ambiguity function for waveforms of a chaotic oscillator is calculated exactly.•Specific examples illustrate best case and worst case ambiguity.•Statistical properties of the ambiguity function are derived analytically.•Mean ambiguity function indicates little ambiguity in range–Doppler determination.

The ambiguity function is derived analytically for waveforms from a chaotic oscillator that has an analytic solution. The chaotic solutions of this oscillator can be expressed as a superposition of basis functions, similar to conventional communication or phase coded radar waveforms. Example waveforms are considered to illustrate the variety of ambiguity functions obtainable from a free running oscillator. The mean and the variance of the ambiguity function for waveforms generated by a free running oscillator are derived to determine typical performance. The mean ambiguity function is shown to have a single, localized peak with low variance indicating that solvable chaos has significant potential as the basis of novel remote sensing technologies.