Deep learning technologies have achieved significant performance improvements in the field of synthetic aperture radar (SAR) image target recognition over traditional methods. However, the inherent "black box" property of deep learning models leads to a lack of transparency in decision-making processes, making them difficult to be convincingly applied in practice. This is especially true in SAR applications, where the credibility and reliability of model predictions are crucial. The complexity and insufficient explainability of deep networks have become a bottleneck for their application. To tackle this issue, this study proposes a physically explainable framework for complex-valued SAR image recognition, designed based on the physical process of microwave propagation. This framework utilizes complex-valued SAR data to explore the amplitude and phase information and its intrinsic physical properties. The network architecture is fully parameterized, with all learnable parameters endowed with clear physical meanings, and the computational process is completed entirely in the frequency domain. Experiments on both the complex-valued MSTAR dataset and a self-built Qilu-1 complex-valued dataset were conducted to validate the effectiveness of framework. In conditions of target overlap, our model discerns categories others find challenging. Against 0dB forest background noise, it boasts a 20% accuracy improvement over traditional neural networks. When targets are 60% masked by noise, it still outperforms other models by 9%. An end-to-end complex-valued synthetic aperture radar automatic target recognition (SAR-ATR) system has also been constructed to perform recognition tasks in interference SAR scenarios. The results demonstrate that the proposed method possesses a strong physical decision logic, high physical explainability and robustness, as well as excellent dealiasing capabilities.