Analytic range-Doppler ambiguities for nonautonomous solvable chaos

Abstract

We present the correlation properties and ambiguity surfaces for a first-order, nonautonomous, chaotic oscillator with a closed-form analytic solution. Unlike most chaotic systems, the solutions of this oscillator take the form of a linear superposition of fixed basis functions weighted by a phase-coded symbol sequence. These solutions enable the analytic investigation of important receiver metrics of systems in a manner that is seldom available when considering chaotic systems. These new, low-order systems exhibit less structure in their basis functions and produce favorable correlation properties with significant mainlobe peak and sidelobe levels below $-20dB$ to $-30dB$. Further, averaged ambiguity function results show a ‘thumbtack’ profile with a low-variance, single, localized peak. Consequently, our work validates the ability of these waveforms to resolve multiple-point targets on range-Doppler planes. These desirable characteristics indicate that nonautonomous solvable chaos has significant potential in supporting novel radar, sonar, and remote sensing technologies.