## 4 Our Proposed Method  
### Proposed Semi-Supervised AMC Method Based on Consistency Regularization and Pseudo Labeling  
The structure of our proposed semi-supervised AMC method is illustrated in Figure 4. For simplicity, our proposed method is recognized as Fixmatch. Semi-supervised learning is commonly employed for tasks where data annotation expenses are considerable or the data contain a substantial number of unlabeled samples, such as medical image analysis and agriculture and environmental surveillance. Semi-supervised learning essentially utilizes unlabeled samples to improve model performance. In this article, the fundamental concept of the proposed method is to incorporate unlabeled signal samples during model training. The specific steps are to train the model using labeled and unlabeled data, respectively, generating supervised and unsupervised losses, and backpropagating to adjust model parameters. The following discussions concentrate on how to construct supervised and unsupervised losses. The initial I/Q signals are post-processed with data to obtain the time-frequency signal images. The time-frequency signal images are divided into labeled and unlabeled signal images. The supervised loss is derived by comparing the projected value of labeled data through the model with the authentic label. It is represented as follows:  
\[L_{s}=\frac{1}{N}\sum_{i=1}^{N}L_{ce}(y_{i},P(y|x_{l}^{i})), \tag{8}\]  
where \(P(\cdot)\) denotes the model's prediction, \(N\) denotes the number of labeled samples, \(y_{i}\) denotes true labels of labeled samples, and \(L_{ce}(\cdot)\) denotes the cross-entropy loss function. It is a loss function used in classification tasks to measure the difference between model predictions and true labels. We design unsupervised loss employing two semi-supervised methods, including consistency regularization and pseudo-labeling. We initially modify unlabeled signal samples twice with varying degrees of perturbation, which we refer to as weak data augmentation and strong data augmentation, respectively. Data augmentation is a technique that expands the training samples. The objective of data augmentation is to fortify the robustness of the model by modifying the data space. \"Strong\" and \"weak\" here denote the degree of perturbation of the data. The strong augmented and weak augmented images are fed into the model to obtain model predictions. \(A(\cdot)\) denotes strong data augmentation, which generally consists of operations including color transformation, contrast enhancement, etc. \(\alpha(\cdot)\) denotes weak data augmentation, which consists of operations including flipping. Since unlabeled samples do not possess labels, we utilize the weak augmentation branch to devise \"pseudo-labels\" for these unlabeled samples. The principle of pseudo-labeling [41] is to utilize the model itself to obtain artificial labels for unlabeled samples, which typically use hard labels, i.e., one-hot labels acquired by employing the argmax function. One-hot labels are only retained for labels whose maximum class probability surpasses the threshold. The formulation for pseudo-labeling is as follows:  
\[\hat{q}_{j}=\arg\max\Big{(}p\Big{(}y|\alpha\Big{(}x_{ul}^{j}\Big{)}\Big{)} \Big{)}. \tag{9}\]  
After obtaining the pseudo-labels, we obtain model predictions for the branch of strong data augmentation. The unsupervised loss is obtained by comparing model predictions for the branch of strong data augmentation with pseudo-labels. The reason for constructing the unsupervised loss in this way is that this embodies the idea of consistency regularization. Consistency regularization is an important part of current mainstream SSL, and is based on  
Figure 4: The structure of the proposed semi-supervised AMC method. the assumption that the same image with different perturbations through the network will output the same prediction.