• Three Cauchy-Score-function-based concepts are proposed, and four properties are discussed with proofs. • A lightweight neural network structure, termed FC-MLP, is designed. • A novel AMC method is proposed under a dual-layer decision tree framework. • Different channel models and mixed noise are considered. • A new dataset, RDL2021.12, is generated and provided. Automatic modulation classification (AMC), also termed blind signal modulation recognition, plays a critical role in various civilian and military applications. Although existing approaches have made substantial contributions in this area, most fail to simultaneously consider mixed noise, different channel modes and low-power scenarios. In this paper, a novel cyclic correlation spectrum based on the Cauchy Score function is first proposed as the robust pattern for the outliers in the Gaussian and non-Gaussian mixed noise. Besides, its properties are studied and proved for further potential applications in wireless signal processing. Furthermore, a modified lightweight neural network, termed feature-coupling multi-layer perceptron (FC-MLP), is designed to avoid the potential risk of overfitting and meet the needs when applied in low-power chips. In addition, a novel AMC method is proposed under a dual-layer decision tree framework, and different patterns are adopted in different layers to make full use of the robustness of the proposed pattern and the information embedded in the time sequence. Meanwhile, different classifiers are also chosen according to the characteristics of the patterns. In the simulations, state-of-the-art machine learning techniques, neural networks and patterns are employed as comparison candidates to verify the superiority of the proposed pattern, the lightweight classifier and the novel AMC approach in the scenario of Rayleigh channel or Rician channel with additive mixed noise.