PHM-Net: A Physics-Informed Hierarchical Multi-Scale Network for Automatic Modulation Classification

Automatic Modulation Classification (AMC) is essential for waveform-level signal characterization. It supports spectrum sensing, signal identification, and adaptive resource allocation in cognitive radio and next-generation wireless systems. However, channel impairments such as multipath propagation, frequency offset, fast fading, and noise degrade modulation signatures, making reliable AMC challenging. Existing deep learning-based approaches often rely on purely data-driven learning, leading to insufficient modeling of modulation-relevant features, loss of transient characteristics, and limited exploitation of hierarchical relationships among modulation types. To address these issues, this paper proposes PHM-Net, a physics-informed hierarchical multi-scale network for robust AMC. The model employs a hierarchical backbone with residual encoder blocks. A Transient Feature Gating (TFG) module enhances modulation-relevant representations, a Cross-Resolution Signal Aggregation (CRSA) module fuses multi-stage features, and a Physics-Informed Hierarchical Loss (PI-HL) enforces consistency between coarse- and fine-grained predictions. Experimental results on three benchmark datasets (RML2016.10a, RML2016.10b, and RML2018.01a) show that PHM-Net consistently achieves the highest average accuracy among all compared models. On RML2018.01a, which contains 1024-sample sequences and 24 classes, PHM-Net achieves an average accuracy of 64.59% and a best-case accuracy of 98.42%, surpassing AMC_Net by 11.14 and 17.09 percentage points and CNN-Transformer by 9.43 and 11.15 percentage points, respectively. PHM-Net provides a robust and interpretable solution for AMC under complex channel conditions.