Analytic range-Doppler ambiguities for nonautonomous solvable chaos

Chandra S. Pappu, Aubrey N. Beal, Jonathan N. Blakely and Ned J. Corron

Chaos, Solitons & Fractals, 2025, vol. 197, issue C

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.

Keywords: Solvable chaos; Correlations; Narrow ambiguity function; Wideband ambiguity function; Chaos radar; Chaos sonar (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004473

DOI: 10.1016/j.chaos.2025.116434

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