This paper presents the mathematical expression of continuous chaotic frequency modulated signal (CCFMS), and theoretically derives the autocorrelation function and root mean square bandwidth of CCFMS. The results show that the sidelobe suppression performance of the CCFMS autocorrelation function is excellent; its root mean square bandwidth is proportional to the frequency modulation index and the root mean square of the chaotic signal. The performance of CCFMS generated by typical chaos is simulated and calculated, and it is further proved that CCFMS has a higher time peak sidelobe ratio, a flat power spectrum shape, an approximately pin-shaped ambiguity function, and the same peak-to-average power ratio as the sinusoidal transmission signal. The anti-noise interference performance of CCFMS radar is analyzed, and the signal-to-interference ratio improvement factor is increased by about 5.5 dB compared with the linear frequency modulation signal radar.
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