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.

中文翻译：

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利用混沌理论检测微弱信号频率：综合分析


混沌理论作为弱信号检测（WSD）领域的一项潜在技术，受益于其对初始条件的敏感性和对加性高斯白噪声（AWGN）的抗扰性的特点。基于混沌理论的传统方法在单一非变频信号检测（SNVFSD）方面表现良好，这是纹理缺陷检测中常见的情况，而在通信领域是罕见的场景。在本文中，我们对基于混沌的微弱信号频率检测方法进行了全面分析。为了更好地理解混沌理论的优点和局限性，我们展示了几种典型通信场景的研究结果。具体来说，我们提出了几种基于混沌的方法，以在以下情况下获得令人满意的性能：单个变频信号检测（SVFSD）、多个非变频信号检测（MNVFSD）、多个变频信号检测（MVFSD） 。为了提高实际应用的泛化性能，对临界状态的特征、Lyapunov 指数（LE）和 Melnikov 方法进行了分析，并将其应用于这些提出的基于混沌的方法中。通过理论分析和数值模拟，我们研究了基于混沌的检测系统在SVFSD、MNVFSD、MVFSD方面的性能。我们的结果表明，这些提出的方案在准确性和鲁棒性方面可以获得令人满意的性能，并且广泛的仿真证明了它们的有效性。