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.