Method for Recognition of Communication Interference Signals under Small-Sample Conditions

Abstract

To address the difficulty in obtaining a large number of labeled jamming signals in complex electromagnetic environments, this paper proposes a small-sample communication jamming signal recognition method based on WDCGAN-SA (Wasserstein Deep Convolution Generative Adversarial Network–Self Attention) and C-ResNet (Convolution Block Attention Module–Residual Network). Firstly, leveraging the DCGAN architecture, we integrate the Wasserstein distance measurement and gradient penalty mechanism to design the jamming signal generation model WDCGAN for data augmentation. Secondly, we introduce a self-attention mechanism to make the generation model focus on global correlation features in time–frequency maps while optimizing training strategies to enhance the quality of generated samples. Finally, real samples are mixed with generated samples and fed into the classification network, incorporating cross-channel and spatial information in the classification network to improve jamming signal recognition rates. The simulation results demonstrate that under small-sample conditions with a Jamming-to-Noise Ratio (JNR) ranging from −10 dB to 10 dB, the proposed algorithm significantly outperforms GAN, WGAN and DCGAN comparative algorithms in recognizing six types of communication jamming signals.

1. Introduction

Due to the openness of wireless channels, information transmission via wireless communication devices is highly susceptible to attacks by noise or deliberate malicious jamming. Typical patterns of malicious jamming include single-tone, multi-tone, narrowband, and linear sweeping frequency—all of which can significantly reduce the security and reliability of communication transmissions. Therefore, identifying such malicious jamming provides prior knowledge for subsequent anti-jamming decision-making and the selection of anti-jamming waveforms, thereby ensuring the reliability and security of communication transmissions. This is of great importance for communication anti-jamming efforts [1].

In recent years, deep learning has made extraordinary progress in many fields, including signal recognition, due to its exceptional data processing capabilities. Reference [2] utilizes an improved deep convolutional neural network (CNN) to automatically extract features of modulation signals from a large amount of training data, accomplishing modulation signal classification in complex communication channels. Reference [3] uses a deep, sparse denoising autoencoder to extract features for suppressing interference in satellite navigation systems. A total of 60,000 labeled signal samples are used for training, and the extracted features are integrated into a stacked model composed of support vector machines and random forests to classify interference signals. When the signal-to-noise ratio is greater than 11 dB, the recognition rate reaches 100%. One study [4] used Variational Mode Decomposition (VMD), Local Mean Decomposition (LMD), and Wavelet Thresholding (WT) methods to perform three-stage decomposition denoising on the original radar signal and converted the processed signal into a time–frequency image through Choi Williams Distribution (CWD). Then, a neural network equipped with dilated convolution learned from a large number of time–frequency images and achieved a recognition rate of 75.3% under low SNR conditions. Another study [5] proposed a WIR converter consisting of a Local Attention Fusion Layer (LAFL) and a Patch Aggregation Module (PAM). This model applies Transformer technology to the field of wireless signal recognition (WIR) and uses a region partitioning strategy to independently calculate self-attention within each partitioned region, thereby reducing computational complexity. After extensive sample training, this method has higher recognition accuracy compared to traditional wireless signal recognition techniques.

Deep learning-based signal recognition methods typically require a large number of training samples to uncover deep data features. However, in complex electromagnetic environments, the quantity of communication jamming signal samples available for training is often limited. When the number of samples is insufficient, the capability of deep learning to automatically extract and learn features significantly decreases, leading to severe degradation in recognition performance. Therefore, accurately recognizing communication jamming signals under small sample conditions is critical. The introduction of Generative Adversarial Networks (GAN) [6] has provided a new direction for addressing small sample problems, and researchers have already applied GANs to modulation signal recognition, fault diagnosis, and other fields. The authors of [7] proposed a GAN-based joint data augmentation method that uses a similarity principle to establish a filtering mechanism, obtaining high-quality generated signals, and inputting the augmented dataset into a designed CNN network to accomplish classification and recognition, achieving good electromagnetic signal classification performance under small sample dataset conditions. The authors of [8] designed a semi-supervised learning framework based on GAN that directly processed IQ signal data and fully utilized unlabeled samples to achieve the end-to-end precise classification of a small number of electromagnetic signals.

The authors of [9] introduced Uni QGAN, a unified generative adversarial network for enhancing modulation classification, which employs multi-condition embedding and multi-domain classification techniques to handle IQ constellation diagrams under various signal-to-noise ratios simultaneously, effectively reducing training overhead and enhancing recognition accuracy at low signal-to-noise ratios. Another study [10] combined deep convolutional generative adversarial networks with conditional generative adversarial networks (CGAN) to expand the modulation signal dataset, enhancing the recognition capabilities under small sample conditions. The authors of [11] proposed a method combining numerical simulation and generative adversarial networks to input simulated samples and actual measured fault samples into GAN, generating high-quality synthetic fault samples and expanding the fault sample library for gear fault detection. The authors of [12] introduced an Adversarial Class Imbalance Learning (ACIL) method that combined CGAN with auxiliary classifiers under uneven data class distribution, using the interaction between the generator, discriminator, and auxiliary classifier to generate fault samples, enabling the model to better learn the distribution of fault samples. The authors of [13] proposed multi-module learning with gradient penalty GAN, which, through adversarial training of generators, discriminators, and classifiers, generated mechanical signals highly similar to real signals, thereby improving recognition accuracy under small sample conditions. Another group [14] proposed a filter-style GAN to separate hidden features in the feature space, reorganizing features into new signals.

Although the idea of using generative adversarial networks for data augmentation has been applied in the aforementioned fields, research in the field of communication jamming signal recognition is still limited; thus, utilizing GANs to solve low recognition rates under small sample conditions in communication interference merits further exploration. To improve the recognition rate of small-sample interference signals, the following issues need to be addressed: 1. Due to the specificity of adversarial training, traditional GAN’s loss function struggles to ensure training stability. 2. Traditional GANs have difficulty learning global correlation features in the time–frequency graphs of communication interference signals. 3. Time–frequency graphs contain large areas of noise information, and the ResNet network fails to focus on the key features of interference signals. The innovations of this article are summarized as follows:

• Design a novel adversarial loss function that combines the Wasserstein distance with a gradient penalty mechanism to alleviate the gradient vanishing issue during the training of GAN models.
• Design an attention mechanism-embedded generative model, WDCGAN-SA, which integrates self-attention mechanisms with improved generative adversarial networks to guide the generative model to focus on the global correlation features of the jamming signal’s time–frequency plots; modify the training strategy by optimizing the alternating training mode of the generator and discriminator in traditional GAN networks to multiple discriminator trainings for one generator training, improving the quality of sample generation.
• On the basis of a deep residual network, by merging cross-channel and spatial information, the classification model focuses more on the key features of the jamming signal’s time–frequency plots, enhancing recognition accuracy.

The structure of this article is organized as follows: Section 2 presents the system model and data pre-processing methods; Section 3 provides a detailed introduction to the data augmentation network WDCGAN-SA; Section 4 elaborates on the classification network C-Resnet; Section 5 presents comprehensive experiments on six types of communication jamming signals; Section 6 concludes the paper.

2. System Model and Data Pre-Processing

This section proposes a communication jamming signals recognition method based on WDCGAN-SA and C-ResNet, aiming to improve the recognition rate of interference signals under small-sample conditions. The model comprises three parts: the pre-processing module, the feature enhancement network (WDCGAN-SA), and the classification network (C-ResNet).

(1)

In the data pre-processing module, communication jamming signals are transformed into time–frequency plots using Short-Time Fourier Transform (STFT). This method primarily aims to convert one-dimensional time-domain signals into two-dimensional time–frequency plots, fully leveraging the advantages of deep learning to capture the characteristic patterns of frequency changes over time.

(2)

In the data enhancement network, we designed a training strategy that combines the Wasserstein distance and gradient penalty mechanism for stable training. After receiving the pre-processed two-dimensional time–frequency plots as input, a self-attention module is added to focus the model on the global key features of the time–frequency plots of communication jamming signals. Finally, changing the training strategy improves the quality of sample generation.

(3)

Finally, in the C-ResNet classification network, the original images and generated images are combined to form a new dataset, which is then fed into a classification module that integrates cross-channel and spatial information for recognition. This model can capture the key features of the time–frequency plots, generating richer and more discriminative feature representations, thereby improving recognition accuracy.

The overall framework of the proposed method is illustrated in Figure 1.

Pre-Processing Module

When nodes 1 and 2 communicate with each other, the jamming device utilizes jamming signals to attack the communication channel. The jamming signals include Single-Tone Jamming (STJ), Multi-Tone Jamming (MTJ), NarrowBand Jamming (NBJ), BroadBand Jamming (BBJ), Comb-Frequency Jamming (CFJ), and Linear-Sweeping Frequency Jamming (LSFJ). After node 1 sends information, the signal received by node 2 can be expressed as:

$$Y\left(n\right)=S\left(n\right)+J\left(n\right)+N\left(n\right)$$

(1)

where $S\left(n\right)$, $J\left(n\right)$ and $N\left(n\right)$ represent the transmitted signals, jamming signals and Gaussian white noise. Due to high-intensity jamming signals, users are incapable of receiving the acknowledgment character (ACK). Suppose that the receiver will not send a signal until it receives the ACK. Then, the signal received by node 2 can be expressed as:

$$Y\left(n\right)=J\left(n\right)+N\left(n\right)$$

(2)

Node 2 performs a time–frequency transformation on the received signal $Y\left(n\right)$, converting the one-dimensional time-domain signal into a two-dimensional time–frequency image. The two-dimensional time–frequency image can analyze the frequency changes of communication jamming signals over time [15]. In this paper, the Short-Time Fourier Transform (STFT) is chosen as the time–frequency transformation method. The formula for STFT is:

$$STFT\left(t,f\right)={\displaystyle {\int }_{-\infty }^{+\infty }\left[x\left(\tau \right)\varpi \left(\tau -t\right)\right]}{e}^{-j2\pi f\tau }d\tau$$

(3)

where $x\left(t\right)$ represents the original jamming signal, and $\varpi \left(t\right)$ is the window function.

Figure 2 shows the time–frequency plots of jamming signals generated at a JNR of 0 dB, revealing distinct time–frequency distribution characteristics for different types of jamming signals. In (a), Single-Tone Jamming exhibits a single spectral line on the time–frequency plot due to its interference at a single frequency point. In (b), Multi-Tone Jamming results in multiple spectral lines due to interference at multiple frequency points. (c) Narrow Band Jamming and (d) Broad Band Jamming are distinguished on the time–frequency plot by the thickness and thinness of the spectral lines, respectively, corresponding to the bandwidth occupied. (e) Comb Frequency Jamming also shows multiple spectral lines but with dispersed energy. (f) Linear Sweeping Frequency Jamming exhibits spectral lines with varying slopes based on the sweep speed.

3. Data Enhancement Network

The data enhancement network is primarily divided into two parts: designing adversarial loss functions and constructing the generative model WDCGAN-SA with self-attention embedding.

3.1. Adversarial Loss Function Design

The loss functions for the original GAN network’s generator and discriminator are as follows:

$$\underset{\theta G}{\min } \underset{\theta D}{\max }V\left(G,D\right)=E_{x\sim P_x}\left[\log D\left(x\right)\right]+E_{z\sim P_z}\left[\log \left(1-D\left(G\left(z\right)\right)\right)\right]$$

(4)

where $P_{\mathbf{x}}$ and $P_{\mathbf{z}}$ represent the sample distributions of real data $x$ and random noise $z$ respectively. $D$ is the discriminator, and $G$ is the generator.

During the optimization process, the optimization goal of the discriminator $D$ is for the probability value of $D\left(x\right)$ to approach 1 and for the probability value of $D\left(G\left(z\right)\right)$ to approach 0. Conversely, the optimization goal of the generator $G$ is for the probability value of $D\left(G\left(z\right)\right)$ to approach 0. Therefore, the training process of GAN is transformed into a Minimax problem, as shown in Equation (4). Additionally, Equation (4) can be derived to transform into the Jensen–Shannon Divergence, so the actual computed loss function is:

$$\underset{\theta G}{\min } \underset{\theta D}{\max }V\left(G,D\right)=2JS\left(P_x‖P_z\right)-2\log 2$$

(5)

where $JS\left(P_x‖P_z\right)$ denotes the computation of the Jensen–Shannon Divergence between the distributions of real data $x$ and random noise $z$.

Due to the discrete nature of the Jensen–Shannon divergence, the phenomenon of gradient vanishing can occur during the optimization process [16]. However, Wasserstein distance can provide a smoother reflection of the differences between two distributions. Therefore, using a Wasserstein distance metric instead of Jensen–Shannon divergence to design a loss function can effectively alleviate the issue of gradient vanishing. The Wasserstein distance is defined as shown below:

$$W\left(P_x,P_y\right)=\underset{\gamma ~\Pi \left(P_x,P_y\right)}{\inf }{E}_{\left(x,y\right)~\gamma }\left[‖x-y‖\right]$$

(6)

where $\gamma \sim \prod \left(P_x,P_y\right)$ represents the joint distribution set of real samples $x$ and generated samples $y$, while $\inf$ represents the infimum, which is the minimum value among all possible joint distribution sets. Therefore, the Wasserstein distance focuses on finding the expected value within the joint distribution that minimizes $E_{\left(x,y\right)~\gamma }\left[‖x-y‖\right]$.

However, during the design process of GANs based on the Wasserstein distance, using weight clipping to enforce the discriminator to be in the 1-Lipschitz function space can lead to the phenomenon of gradient explosion [17]. Instead of weight clipping, gradient penalty, which satisfies the 1-Lipschitz function condition, can effectively alleviate gradient explosion and stabilize training. The gradient penalty can be shown as:

$$gp=\lambda \times \underset{\tilde{x}~P_{\tilde{x}}}{E}\left[{\left({‖{\nabla }_{\tilde{x}}D\left(\tilde{x}\right)‖}_2-1\right)}^2\right]$$

(7)

where $\tilde{x}=\mathsf{\epsilon }x+\left(1-\mathsf{\epsilon }\right)y, \mathsf{\epsilon }~\mathrm{Uniform}\left[0,1\right]$, $\tilde{x}$ represents uniform sampling between the distributions of real sample $x$ and generated sample $y$; ${\nabla }_{\tilde{x}}D\left(\tilde{x}\right)$ denotes the gradient computation of the discriminator’s output with respect to $\tilde{x}$; ${‖{\nabla }_{\tilde{x}}D\left(\tilde{x}\right)‖}_2$ represents the L2 norm of $‖·‖$.

Based on the derivation, a new adversarial loss function is constructed as shown in Equation (8):

$$L\left(G,D\right)=-\underset{x~P_x}{E}\left[D\left(x\right)\right]+\underset{y~P_y}{E}\left[D\left(y\right)\right]+\lambda \times \underset{\tilde{x}~P_{\tilde{x}}}{E}\left[{\left({‖{\nabla }_{\tilde{x}}D\left(\tilde{x}\right)‖}_2-1\right)}^2\right]$$

(8)

3.2. The Generative Model WDCGAN-SA

Most models based on generative adversarial networks use convolutional layers to model images. However, the receptive field of convolutional operations is limited, particularly when capturing global correlation features in images. Accumulating multiple layers of convolutions to capture relationships between distant pixels also significantly increases the model’s computational complexity. The self-attention mechanism can be used to compute dependencies between different areas within an image [18]. Therefore, embedding self-attention modules within the convolutional layers of both the generator and discriminator helps guide the learning of global correlation features to compensate for the limitations of convolutional operations. The self-attention module is illustrated in Figure 3.

In the figure above, two $1\times 1$ convolution kernels, $f$ and $g$, are first used to extract features from the feature map $x$, respectively generating feature tensors $f\left(x\right)$ and $g\left(x\right)$ for calculating the attention weight map $\beta$. The definition of ${\beta }_{i,j}$ is as follows:

$${\beta }_{i,j}=\frac{\exp \left(x_{ij}\right)}{{\displaystyle \sum _{i=1}^n\left(s_{ij}\right)}}, \mathrm{where} s_{ij}=f{\left(x_i\right)}^{\mathrm{T}}g\left(x_j\right)$$

(9)

where $s_{ij}$ represents the correlation between the i-th and j-th pixels in the convolutional feature map, which is normalized by the Softmax function to obtain ${\beta }_{i,j}$, representing the weights indicating the degree of attention required for the interrelations between elements in the convolutional feature map.

From the equation above, it can be inferred that the attention weight map $\beta$ can focus on the global information of the feature map. By element-wise multiplication of $\beta$ and the feature tensor $h\left(x\right)$, followed by feature extraction using a $1\times 1$ convolutional kernel, the self-attention feature map $o$ is obtained. Then, by weighted fusion of $o$ with the original convolutional feature map $x$, the output feature map $y$ after self-attention module extraction is obtained. This computational process can be represented as follows:

$$y_i=\gamma o_j+x_j, \mathrm{where} o_j=v\left({\displaystyle \sum _{j=1}^n{\beta }_{j,i}\times h\left(x_i\right)}\right)$$

(10)

where $o_j\in o=\left(o_1,o_2,\dots ,o_j,\dots ,o_n\right)$, $\gamma$ serves as the scale parameter initialized to 0, allowing the model to progressively extend from capturing local information to learning the global information of the feature map.

The model for data enhancement of communication jamming signals based on the self-attention mechanism is illustrated in Figure 4. The composition of the generator network and the parameters are as described in (a). The generator takes random noise with dimensions of $100\times 1\times 1$ as input, which first passes through a fully connected layer for expansion, and then is reshaped into a $512\times 4\times 4$ matrix. This noise is subsequently transformed into a $3\times 64\times 64$ image through multiple transposed convolution layers and outputted. Self-attention modules are embedded before and after the third transposed convolution layer to guide the generator to focus on the global key features of the time–frequency graph of the communication jamming signals. Gaussian Error Linear Units (GELU) are used in the transposed convolution layers as activation functions to provide more continuous gradient information. The output layer employs a tanh activation function to ensure the pixel values of the output image are within a reasonable range.

The discriminator network’s composition and input-output parameters are depicted in (b). The input to the discriminator consists of mixed images from the generator’s output and real images. After symmetric convolutional feature extraction relative to the generator, the output is a $512\times 4\times 4$ feature tensor. This tensor is reshaped into a one-dimensional feature vector, which is then fed into a fully connected layer to produce an output of 1 or 0, used to determine whether the image is a real or generated sample. Attention modules are placed in the same positions as in the generator to ensure that the discriminator can also capture the global feature information of the input images. The activation function used is the Leaky Rectified Linear Unit (LReLU) to address the issue of ‘dead zones’ in activation functions and to mitigate the problem of vanishing gradients.

Traditional DCGAN network training strategies typically involve alternating training between the generator and discriminator. In the early stages of this approach, the competition between the generator and discriminator can lead to the model falling into local optima or experiencing training oscillations. Additionally, under this strategy, the discriminator is not trained sufficiently often, hindering its ability to fully learn the distribution characteristics of the data, making it difficult to differentiate between real and generated samples. Consequently, the training strategy is modified to involve multiple training cycles for the discriminator for every single cycle of the generator. This frequent training of the discriminator not only enhances its ability to distinguish between real and generated samples but also provides timely guidance to the generator to produce samples that more closely resemble real data. The model training is complete when the generator and discriminator are trained against each other until convergence. The proposed algorithm is depicted in Algorithm 1.

Algorithm 1: WDCGAN-SA data enhancement algorithm

1.    Input: Random noise $z$ of dimensions $100\times 1\times 1$; real sample time–frequency plots $x$; number of discriminator iterations $\mathrm{m}=4$; coefficient for the gradient penalty term. 2.    Output: Generated sample time–frequency plots $\tilde{x}$. 3.    Initialize weight parameters: ${\theta }_d$ for the discriminator, ${\theta }_g$ for the generator. 4.    For epoch do: 5.    For 1:m do: 6.       Clear gradients; 7.       The generator accepts random noise $z$ as input and produces a minibatch of generated images $\tilde{x}$; 8.       $\mathrm{d}\text{\_}\mathrm{loss}\text{\_}\mathrm{real}=-E_{x\sim P_x}\left[D\left(x\right)\right]$; 9.       $\mathrm{d}\text{\_}\mathrm{loss}\text{\_}\mathrm{fake}=E_{\tilde{x}\sim P_{\tilde{x}}}\left[D\left(\tilde{x}\right)\right]$; 10.     Random interpolation sampling: $\widehat{x}=\epsilon x+\left(1-\epsilon \right)\tilde{x}, \epsilon \sim Uniform\left[0,1\right]$; 11.     $\mathrm{gradient}\text{\_}\mathrm{penalty}=\lambda \times \underset{\tilde{x}~P_{\tilde{x}}}{E}\left[{\left({‖{\nabla }_{\tilde{x}}D\left(\tilde{x}\right)‖}_2-1\right)}^2\right]$; 12.     $\mathrm{d}\text{\_}\mathrm{loss}=-E_{x\sim P_x}\left[D\left(x\right)\right]+E_{\tilde{x}\sim P_{\tilde{x}}}\left[D\left(\tilde{x}\right)\right]+\lambda \times \underset{\tilde{x}~P_{\tilde{x}}}{E}\left[{\left({‖{\nabla }_{\tilde{x}}D\left(\tilde{x}\right)‖}_2-1\right)}^2\right]$; 13.     $\mathrm{d}\text{\_}\mathrm{loss}$ backpropagation; 14.     $\mathrm{d}\text{\_}\mathrm{optimizer}$ update model parameters; 15.    end for 16.    Clear gradients; 17.    Generator $G$ randomly generates a minibatch of images $\tilde{x}$; 18.    Calculate $\mathrm{g}\text{\_}\mathrm{loss}=-E_{\tilde{x}\sim P_{\tilde{x}}}\left[D\left(\tilde{x}\right)\right]$; 19.    $\mathrm{g}\text{\_}\mathrm{loss}$ backpropagation; 20.    $\mathrm{g}\text{\_}\mathrm{optimizer}$ update model parameters; 21.  End for

4. C-ResNet Classification Network

4.1. Spatial and Channel Attention Mechanism

In the time–frequency plots of communication jamming signals, a significant portion of the area consists of noise information. To focus the classification network on the key feature areas of the jamming signals, the Convolutional Block Attention Module (CBAM) is introduced [19]. This spatial and channel attention mechanism includes a spatial and channel attention layers, which dynamically adjust the focus on different spatial positions. Lower weight parameters are assigned to the noise areas in the time–frequency plots, while higher weight parameters are allocated to the key feature areas of the signals.

The spatial attention layer enhances the response to key feature areas in the time–frequency plots by calculating the weights of different pixel positions. The input feature $F$ is first processed by two convolutional layers with a kernel size of $1\times 1$, followed by two layers of activation functions to produce an attention map. Finally, each spatial position of the original input feature map $F$ is weighted according to the corresponding attention map. The formula for the spatial attention layer is:

$${\mathit{F}}_{\mathbf{s}}^{\prime }=F\otimes \gamma \left(f\left(\sigma \left(f\left(F\right)\right)\right)\right)$$

(11)

Unlike the spatial attention layer, the channel attention layer employs global average pooling to capture the overall features of each channel and assigns weights to each channel based on their importance. The formula for the channel attention layer is:

$${\mathit{F}}_{\mathit{c}}^{\prime }=F\otimes \gamma \left(f\left(\sigma \left(f\left(Avgpool\left(F\right)\right)\right)\right)\right)$$

(12)

where $Avgpool$ represents the global average pooling.

4.2. Constructing the C-ResNet Classification Model

Therefore, given the presence of significant noise information in the time–frequency plots of jamming signals, this section designs a classification network called C-ResNet, based on deep residual networks and spatial-channel attention mechanisms, to enhance classification performance. The network structure and parameters are shown in Figure 5. The network model includes 23 convolutional layers (containing 11 residual blocks), two CBAM attention layers, two pooling layers, and one fully connected layer. When the input and output dimensions of the residual blocks are the same, solid line skip connections are used, and the numbers beside the skip lines indicate the number of identical stacked blocks; when the input and output dimensions of the residual blocks differ, dashed line skip connections are used. The parameters in the diagram denote the kernel size, convolution dimension, number of convolution kernels, and whether an additional linear mapping is needed to match the output dimensions; for example, {3 × 3, Conv2d, 128/2} indicates a kernel size of $3\times 3$, using 2D convolution, with 128 kernels and requiring an additional linear mapping to match the output dimensions. The activation functions are all RELU functions, and the pooling layers include both max pooling and adaptive pooling. To avoid impacting the network structure, a CBAM module is added at both the first and the last layers, which improves classification efficiency and facilitates the loading of pre-trained parameters. In the C-ResNet classification model, the cross-entropy function is used as the loss function to measure the discrepancy between the predicted probability distribution and the actual label probability distribution. The generated time–frequency plots and the real time–frequency plots are combined to form a new dataset, which is then fed into the C-ResNet classification model. The model is trained using the cross-entropy loss function to complete the classification. The cross-entropy loss function is shown in Equation (13).

$$H\left(\mathrm{p},q\right)=-{\displaystyle \sum _{i=1}^{n}p\left(x_i\right)}\log \left(q\left(x_i\right)\right)$$

(13)

where $p\left(x_i\right)$ represents the probability distribution of the true labels, while $q\left(x_i\right)$ represents the distribution predicted by the model.

5. Simulation and Analysis

5.1. Experimental Data

The experiment used six typical communication jamming signals to evaluate the recognition performance of the proposed signal identification method. These include Single-Tone Jamming, Multi-Tone Jamming, Narrow-Band Jamming, Broad-Band Jamming, Comb-Frequency Jamming, and Linear Sweeping Frequency Jamming. The specific parameters of each interference signal are detailed in

Table 1. The parameter settings for the six types of communication jamming signals.

Jamming Types	Label	Parameters Setting
Single-Tone	Jam 0	The frequency points $f$ are randomly selected between 1 and 5 MHz.
Multi-Tone	Jam 1	The number N of audio is a random integer between 2 and 8, and the frequency points $f$ are same as jam1.
Narrow Band	Jam 2	The center frequency point $f_c$ is randomly selected between 1 and 5 MHz, and the bandwidth is set to 0.25 MHz.
Broad Band	Jam 3	The bandwidth is randomly selected between 2 and 3 MHz.
Comb Frequency	Jam 4	The start frequency point $f_s$ is positioned at 2.5 MHz, the number N of frequency point randomly selected between 3 and 5, and the interval between frequency points is set to 0.25 MHz.
Linear Sweeping Frequency	Jam 5	The frequency linearly varies with a starting frequency between 10 and 100 MHz and a sweep rate uniformly distributed within [0.1, 1] THz/s.

. For each type of jamming signal, 140 samples were generated at each Jamming-to-Noise Ratio (JNR) level ranging from −10 dB to 10 dB with a step size of 2 dB. The samples were divided into a 7:3 ratio for training and testing, resulting in 98 training samples per interference signal type, totaling 588 samples, and 42 testing samples per interference signal type, totaling 252 samples.

5.2. Performance of Data Enhancement in the Model

In this section, the DCGAN algorithm is compared with the data enhancement algorithm proposed in this article. Figure 6 displays real samples of six types of jamming signals at a JNR of 10 dB, along with samples generated by WDCGAN-SA and DCGAN. Analysis of Figure 6 indicates that both generative adversarial network models can produce synthetic samples that mimic the true distribution. However, upon detailed examination, it is observed that the multi-tone jamming and comb frequency jamming signals generated by the DCGAN model exhibit very blurry features; the signal feature outlines in single-tone jamming and linear sweeping frequency jamming are extremely coarse. Conversely, the samples produced by the WDCGAN-SA model provide a clearer and more precise description of the signal features with smoother outlines, achieving a closer approximation to the real samples.

5.3. Comparative Experiments of Different Classification Networks

To verify the performance of the classifier C-ResNet proposed in this paper, combination experiments were conducted with the WDCGAN-SA enhancement network and different classifiers. The classifiers include the C-ResNet proposed in this paper, Convolutional Neural Network (CNN), k-Nearest Neighbor (KNN), Support Vector Machine (SVM), and Random Forest (RF). For each category, 98 real samples and 90 generated samples were mixed and used as the training set, which was then input into the aforementioned five classification networks for comparative experiments. Figure 7 presents the results of the combination experiments between the WDCGAN-SA enhancement network and the five classifiers.

Analysis of the results depicted in Figure 7 reveals that at a JNR of −10 dB, the noise frequency in the time–frequency plots of the jamming signals is relatively high, resulting in more obscure signal characteristics. The recognition rates of several classification networks are low, ranging between 20% and 30%. Due to the incorporation of a spatial channel attention mechanism in the C-Resnet classification, which aids the model in focusing on important features, the recognition rate of the C-Resnet network at −10 dB is 34.01%, slightly higher than that of other networks. As the JNR increases, the clarity of the signal features improves, and the recognition rates of all networks gradually increase. Notably, at a JNR of 10 dB, the recognition rate of the proposed model is 96.01%, while the accuracy rates for traditional algorithms like KNN, SVM, and RF are 75.13%, 79.71%, and 71.22%, respectively. This discrepancy is primarily due to traditional classification networks being limited by manually extracted features, which result in lower recognition rates compared to deep neural networks. The overall recognition accuracy of the proposed network from −10 dB to 10 dB is higher than that of the CNN classification network.

Furthermore, at a JNR of 10 dB, the recognition accuracy of the proposed network is 96.01%, which is 4.23% higher than CNN’s 91.78%. Figure 8a,b are the confusion matrices for the CNN classifier and the C-ResNet classifier at a JNR of 10 dB, respectively. The confusion matrix indicates that the CNN classifier often misclassifies narrowband jamming as single-tone jamming and comb frequency jamming as multi-tone jamming. This misclassification occurs because both narrowband jamming and single-tone jamming have a single spectral line, while multi-tone jamming and comb frequency jamming have multiple spectral lines, leading to classification errors. In contrast, the C-ResNet classifier significantly reduces these misjudgments. In summary, under both low and high JNR conditions, the C-ResNet classification network demonstrates a higher recognition rate compared to traditional CNNs and other conventional classification networks.

5.4. Experiment on the Impact of Generated Sample Quantity on Accuracy

To further explore the impact of small sample sizes on recognition rates, real and generated samples were mixed in different proportions for sample augmentation. The dataset was expanded with 30, 60, and 90 generated samples per category and then fed into the C-ResNet network for identification. The accuracy of communication interference signal recognition before and after sample augmentation is shown in Figure 9.

From the above figure, it is evident that under the condition of having 98 real samples per category in the training set and at a JNR of 10 dB, the recognition accuracy for communication interference signals is 79.37%. By incorporating generated data to increase the sample size, the deep neural network is able to more thoroughly exploit the underlying features of the data. After augmenting the real samples with 30, 60, and 90 additional generated samples per category, respectively, the recognition accuracies for communication interference signals at a JNR of 10 dB improved to 88.29%, 92.87%, and 96.01%, respectively, indicating an overall increase of 15.64% in recognition rate before and after sample expansion. The experimental results demonstrate that the WDCGAN-SA+C-ResNet model proposed in this article effectively addresses the problem of low recognition rates for communication interference signals under small sample conditions.

5.5. Experiment on the Impact of Different Generative Networks on Accuracy

To further validate the advantages of the algorithm proposed in this paper, three types of generative networks—GAN, WGAN, and DCGAN—were selected to augment and expand the time–frequency diagrams of communication interference signals. The generator and discriminator in GAN consist of a series of fully connected layers; similarly, WGAN’s generator and discriminator are composed of fully connected layers, but it introduces the Wasserstein distance into the original GAN framework. DCGAN, a Deep Convolutional Generative Adversarial Network, is a hybrid of CNN and GAN. Figure 10a–c, respectively, show the recognition accuracies after augmenting the real samples with 30, 60, and 90 generated samples per category using these four generative networks, followed by classification through C-ResNet.

Analysis of the figures reveals that with an increase in sample size, the recognition rates of all four networks improve to varying degrees. However, since the GAN network’s generator and discriminator are comprised of a series of fully connected layers, the quality of sample generation is relatively poor. Consequently, the recognition rates remain the lowest under all conditions of sample expansion, with 30, 60, or 90 samples per category. WGAN, which introduces the Wasserstein distance on the basis of GAN, improves the quality of sample generation to some extent. At a sample expansion of 90 and a JNR of 10 dB, its recognition rate reaches 85.47%, an improvement of approximately 3.5% over the GAN network. DCGAN, which replaces fully connected layers with convolutional layers to capture local features in images, produces higher-quality samples than the fully connected layer-only GAN model. The figures show that recognition rates after sample augmentation are about 8% higher compared to GAN and WGAN models. The proposed algorithm, WDCGAN-SA, achieves the highest recognition rates across different sample sizes, about 5% higher than DCGAN. This demonstrates that the data augmentation methods designed in this study effectively improve the accuracy of recognizing communication interference signals under small sample conditions.

6. Conclusions

Addressing the issue of low recognition rates due to the difficulty in obtaining communication jamming signal data samples, this paper proposes a WDCGAN-SA model embedded with an attention mechanism to augment and expand the time–frequency plots of communication jamming signals. Subsequently, a classification model based on C-ResNet was constructed to achieve recognition of communication jamming signals under small sample conditions. The experimental results indicate:

(1)

The WDCGAN-SA generative model addresses the problem of training gradient vanishing caused by the original GAN model’s use of JS divergence to measure the distribution distance between real and generated data by introducing the Wasserstein distance and gradient penalty term. Additionally, by incorporating attention modules into the generative model, the ability to learn signal features from the time–frequency plots of communication jamming signals is enhanced. As a result, experiment 5.2 demonstrates that, compared to the traditional DCGAN network, the WDCGAN-SA model significantly improves the quality of generated samples.

(2)

To enhance the feature extraction capability of the classification model and thereby improve recognition accuracy, this paper integrates the Convolutional Block Attention Module (CBAM) into a deep residual network. CBAM extracts features by combining spatial and channel information, allowing for a greater focus on key features in the time–frequency plots of communication jamming signals, thereby improving the classification accuracy of the residual network. Experiment 5.3 shows that the recognition rate of the C-ResNet classification model is 4.23% higher than that of the traditional CNN model.

(3)

Experiments 5.4 and 5.5 indicate that compared to traditional models such as GAN, WGAN, and DCGAN, the proposed WDCGAN-SA-based method for recognizing communication jamming signals with small samples achieves higher recognition rates across datasets with varying amounts of time–frequency plots. This method meets the requirements for accurate classification under conditions of scarce communication jamming signal data. Additionally, the experiments conducted in this study validate the effectiveness of the proposed method, providing theoretical support and insights for the recognition of communication jamming signals with small samples.