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Analytic range-Doppler ambiguities for nonautonomous solvable chaos

Author

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

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.

Suggested Citation

  • Pappu, Chandra S. & Beal, Aubrey N. & Blakely, Jonathan N. & Corron, Ned J., 2025. "Analytic range-Doppler ambiguities for nonautonomous solvable chaos," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004473
    DOI: 10.1016/j.chaos.2025.116434
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    References listed on IDEAS

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    1. Pappu, Chandra S. & Carroll, Thomas L., 2021. "Quasi-FM Waveform Using Chaotic Oscillator for Joint Radar and Communication Systems," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Pappu, Chandra S. & Carroll, Thomas L., 2023. "Chaotic waveform for optimal joint radar communication systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
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