Chaos detection scheme for multiple variable-frequency signals with overlapping frequencies

As one of the most critical technologies in signal detection, weak signal detection has received a great deal of attention in many areas. Traditional methods perform well when the number of signal is single and the form of signal is simple, which are quite different from the situation in some real applications (e.g., the marine communication scenario). In this paper, we consider the problem of high-precision frequency detection of multiple variable-frequency signals with overlapping frequencies (MVFS-O) in the low signal-to-noise ratio scenario, whose key point is how to detect the parameters (frequency range and frequency modulation rate) of each signal. To solve the problem, a novel chaos detection scheme based on Duffing difference oscillator is proposed. In this scheme, the wide frequency detection range of the critical state is used to determine the frequency range of the signals quickly, and the Lyapunov exponent is used to discriminate the output state of the system qualitatively. Furthermore, combining with the time points of the periodic state of the system, we can obtain the FMR of the corresponding signal by analyzing overlapping frequency ratio. Numerical results are provided to verify the practical effectiveness of the proposed scheme.