## 1 Introduction
The features selected can be grouped into the following categories: time-domain features based on instantaneous amplitude, phase, and frequency [12]; frequency-domain features based on a cyclic spectrum [13] and higher-order cumulants [14]; and transform-domain features based on constellation diagrams [15] and wavelet transforms [16]. Traditional classifiers like support vector machines (SVMs) [17] and decision tree (DT) [18] struggle to learn complex feature representations from data. In addition, feature extraction necessitates artificial design, which lead to significant human resource engagement. Feature engineering is indeed a laborious task requiring specialized expertise. Most crucially, the designed features may be confined to specific modulation schemes. Deep learning algorithms have demonstrated substantial advantages in applications such as image recognition, speech recognition, and facial recognition. Concurrently, they are employed in the field of wireless communication for tasks like spectrum prediction [19], specific emitter identification [20; 21; 22; 23; 24], and automatic modulation classification [25; 26]. Deep learning AMC (DL-AMC) methods are data-driven approaches [26]. The depth of the network used is much deeper than the previous network. This allows them to extract more complex features. Unlike previous approaches, it can automatically extract features from raw data and makes effective decisions without manual intervention. These methods include convolutional neural networks (CNNs) [27; 28] and recurrent neural networks (RNNs) [29]. The core idea of a CNN is to extract features from input data through a series of convolution layers, pooling layers, and fully connected layers. An RNN is a deep learning model that excels in processing sequential data. Its core idea is to introduce recurrent units into the network, making the output of the network dependent not only on the current step but also on the output of the previous step. For deep learning methods, sample annotation is expensive and their performance highly depends on the quality of the data. Motivated by this, some methods such as few-shot learning [30], conditional generative adversarial networks (CGANs) [31], and semi-supervised learning have been considered. Few-shot learning's objective is to develop precise models with fewer samples. A CGAN is a type of generative adversarial network that involves the conditional generation of images by a generator model. This enables discernible image generation of a specified type. Semi-supervised learning employs minimal labeled data, coupled with substantial unlabeled data for training, as shown in Figure 1. In this paper, we propose a semi-supervised automatic modulation classification (SSL-AMC) method based on consistency regularization and pseudo-labeling. Consistency regularization effectively mitigates overfitting by requiring model output consistency amidst slight data variations. The common method is input perturbation, which involves making small random changes to input data. This can encourage the model to produce stable responses to minor variations. Pseudo-labeling is a semi-supervised learning method that leverages the model's predictions on unlabeled data and adds them as pseudo-labels to the unlabeled data, overcoming the problem of sparsely labeled data. We use a wide residual network (WRN) as a backbone network. A WRN is a variant of convolution neural networks that introduces a wider network structure based on residual networks; i.e., it increases the number of channels. Our experimental results demonstrate that the proposed method achieves a high recognition accuracy with limited labeled signal samples. The main contributions of this paper are summarized as follows:  
* We present a semi-supervised AMC method based on consistency regularization and pseudo-labeling. Consistency regularization is used to encourage the model to extract generalized features from the signal data. Pseudo-labeling is used to make manual predictions for unlabeled data.