This work reports the potential of first-order, non-autonomous chaotic circuits for bistatic radar applications. Unlike most chaotic systems, 1st order chaotic systems offer closed-form analytic solutions that aid in designing simple matched filters. In this work, a signal generated by a 1st chaotic oscillator is transmitted towards both the receiver and the target, enabling the use of this waveform for two purposes. First, the waveform serves to synchronize the bistatic radar receiver. Second, the waveform assists in acquiring an estimate of the target’s range. For the first time, we show that two 1st order chaotic circuits can be synchronized using a simple resistive coupling. The cross-correlation between the two synchronized circuits is of high quality, exhibiting a narrow main lobe width and low sidelobe levels. Consequently, these 1st order systems can generate high-range resolution profiles in bistatic configurations. Lastly, analytical expressions show that the cross-ambiguity function between the echo received from the target and synchronized waveforms yields a near thumb-tack shape, emphasizing the value of a noise-like waveform for radar-ranging applications.
This work focuses on implementing a class of exactly solvable chaotic oscillators at speeds that allow real world radar applications. The implementation of a chaotic radar using a solvable system has many advantages due to the generation of aperiodic, random-like waveforms with an analytic representation. These advantages include high range resolution, no range ambiguity, and spread spectrum characteristics. These systems allow for optimal detection of a noise-like signal by the means of a linear matched filter using simple and inexpensive methods. This paper outlines the use of exactly solvable chaos in ranging systems, while addressing electronic design issues related to the frequency dependence of the system's stretching function introduced by the use of negative impedance converters (NICs).
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