Weak Signal Frequency Detection Using Chaos Theory: A Comprehensive Analysis

As a potential technology in weak signal detection (WSD), the chaos theory benefits from its characteristics of the sensitivity to the initial condition and the immunity to the Additive White Gaussian Noise (AWGN). Traditional methods based on chaos theory perform well on single non-variable-frequency signal detection (SNVFSD), which is a common situation in texture flaw detection while it is a rare scenario in the communication field. In this paper, we give a comprehensive analysis of the chaos-based approach for weak signal frequency detection. To better understand the advantages and limitations of the chaos theory, we present the research results for several typical communication scenarios. Specifically, we proposed several chaos-based approaches to get a satisfying performance in the following situations: single variable-frequency signal detection (SVFSD), multiple non-variable-frequency signals detection (MNVFSD), multiple variable-frequency signals detection (MVFSD). To enhance the generalization performance to real application, the critical state's characteristics, Lyapunov Exponents (LE) and Melnikov method are analyzed to employed in these proposed chaos-based approaches. By theoretical analysis and numerical simulations, we study the performance of chaos-based detection systems in terms of SVFSD, MNVFSD, MVFSD. Our results show that these proposed schemes can obtain a satisfying performance in terms of accuracy and robustness, and the extensive simulations demonstrate their effectiveness.

Automated summary

Chaos theory benefits from its sensitivity and immunity in weak signal detection, showing promising performance in various communication scenarios. Through different chaos-based approaches, satisfactory performance has been achieved, as demonstrated by theoretical analysis and numerical simulations, indicating excellent accuracy and robustness.