Low Probability of Intercept Radar Signal Recognition Based on Semi-Supervised Support Vector Machine

Abstract

Low probability of intercept (LPI) radar signal recognition under low signal-to-noise ratio (SNR) is a challenging task within electronic reconnaissance systems, particularly when faced with scarce labeled data and limited resources. In this paper, we introduce an LPI radar signal recognition method based on a semi-supervised Support Vector Machine (SVM). First, we utilize the Multi-Synchrosqueezing Transform (MSST) to obtain the time–frequency images of radar signals and undergo the necessary preprocessing operations. Then, the image features are extracted via Discrete Wavelet Transform (DWT), and the feature dimension is reduced by the principal component analysis (PCA). Finally, the dimensionality reduction features are input into the semi-supervised SVM to complete the classification and recognition of LPI radar signals. The experimental results demonstrate that the proposed method achieves high recognition accuracy at low SNR. When the SNR is −6 dB, its recognition accuracy reaches almost 100%.

1. Introduction

Electronic reconnaissance is a critical component of electronic warfare [1], and low probability of intercept (LPI) [2,3] radar signal recognition is a significant research issue in electronic reconnaissance. In the modern battlefield, the accurate recognition of LPI radar signals can effectively obtain enemy intelligence, thereby substantially enhancing the efficiency of reconnaissance. With the continuous enhancement of radar systems and the escalating complexity of electronic warfare technology, the capability to quickly and accurately recognize radar signals is becoming more and more important. However, in the increasingly complex electromagnetic environment, LPI radar signal recognition faces significant challenges. Traditional template matching methods [4] rely on comparing received signals with the template database for recognition. These methods cannot complete accurate recognition when the received signals have not integrated prior information. Therefore, exploring more effective methods for LPI radar signal recognition is crucial, particularly in the absence of prior information.

In recent years, machine learning techniques have been increasingly employed for radar signal recognition, giving rise to a large amount of research work [5]. Currently, machine learning-based approaches for radar signal recognition are primarily divided into two categories: unsupervised and supervised [6]. The former typically utilizes unsupervised algorithms such as K-Means clustering, principal component analysis (PCA), and t-SNE clustering, to learn from unlabeled samples by exploring similarities or approximate characteristics among different samples for signal clustering. Yang et al. [7] utilize a rough k-means classifier and relevance vector machine (RVM) for the recognition and selection of radar signals. Zhang et al. [8] employ density clustering algorithms to sort signal pulse descriptors, thereby achieving radar signal recognition. Wang et al. [9] identify unknown radar emitter signals using Affinity Propagation (AP) clustering methods and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithms. These methods complete signal recognition without the need for prior label information, which is both an advantage and a limitation of unsupervised learning. Due to the lack of prior information and the uncertainty in the number of output categories, these methods typically exhibit lower accuracy and stability.

Moreover, supervised methods for radar signal recognition generally treat radar signal recognition as a classification task, which typically requires a large amount of labeled data for training. Li et al. [10] employ an entropy theory-based radar transmission signal recognition algorithm using a neural network classifier to categorize the entropy characteristics of radar signals. Shieh et al. [11] use a three-layer Vector Neural Network (VNN) for radar signal recognition and classification. Huang et al. [12] replace traditional signal features with randomly projected compressed signals and then employ a robust Sparse Classification (SC) method for radar signal recognition. Jin et al. [13] use a dual Convolutional Neural Network (CNN) architecture to achieve classification and recognition of nine common types of radar signals, achieving over 95% accuracy in signal recognition at 0 dB. Li et al. [14] extract high-order spectral features of signals and use an SVM to classify and recognize radar signals, achieving over 90% accuracy in recognizing different signals at −8 dB. Supervised methods require substantial prior information and rely on complex neural network structures. However, the acquisition of extensive labeled samples within real-world scenarios is both challenging and resource-intensive, thereby constraining the widespread implementation of supervised recognition methods in practical applications, particularly in resource-constrained electromagnetic environments. To address the challenges, some semi-supervised methods have been proposed [15]. Yu et al. [16] apply a semi-supervised clustering algorithm to process and label a small number of signals captured on the battlefield, while Bai et al. [17] utilize a semi-supervised CNN to identify unknown signal sources. However, due to the characteristics of LPI radar signals such as high detectability, low interceptability, long pulse duration, strong interference, and the increasingly complex battlefield electromagnetic environment, as well as continuous advancements in radar technology, these methods are no longer able to meet the recognition requirements of LPI radar signals. A detailed comparison of the related work discussed above is provided in

Table 1. Comparison of data-driven methods for radar signal recognition.

Methods	Feature Extractor	Classifier	Unsupervised	Supervised	Semi-Supervised
Yang et al. [7]	/	K-means and RVM	√	-	-
Zhang et al. [8]	/	DBSCAN	√	-	-
Wang et al. [9]	/	AP Clustering and DBSCAN	√	-	-
Li et al. [10]	Entropy features	Neural Network	-	√	-
Shieh et al. [11]	Frequency, pulse width, and pulse repetition interval	VNN	-	√	-
Huang et al. [12]	Randomly projected compressed signals	SC	-	√	-
Jin et al. [13]	/	Dual CNN	-	√	-
Li et al. [14]	GLCM and Symmetric Hölder coefficients	SVM	-	√	-
Yu et al. [16]	/	Clustering	-	-	√
Bai et al. [17]	/	CNN	-	-	√
our	DWT	SVM	-	-	√

.

This paper introduces an alternative method for LPI radar signal recognition based on a semi-supervised SVM. The proposed method first employs the Multi-Synchrosqueezing Transform (MSST) to obtain time–frequency representations of LPI radar signals, ensuring the aggregation of the time–frequency spectrum and enhancing the resolution of the time–frequency images. Then, Discrete Wavelet Transform (DWT) is utilized to extract features from preprocessed time–frequency images, maximally distilling distinctive signal characteristics. Ultimately, the signal features that have been extracted are inputted into a semi-supervised SVM classifier to perform the recognition task. The experimental results demonstrate that this approach overcomes the limitations of unsupervised and supervised methods in LPI radar signal recognition and achieves high accuracy in recognizing nine types of signals under low SNR conditions. This work’s primary contributions can be outlined as follows:

• We introduce a novel method for recognizing LPI radar signals by utilizing semi-supervised SVM, which effectively improves the generalization ability of the model and saves labeling costs.
• The effective noise reduction achieved by combining the high time–frequency aggregation of MSST with DWT achieves high recognition accuracy at low SNR and improves the robustness of the radar signal recognition.
• Through extensive experiments on nine types of typical LPI radar signals, the proposed approach has shown superior performance compared to other methods, achieving impressive recognition accuracy even in low SNR situations.

The following sections of this paper are structured as follows: Section 2 outlines the proposed method, Section 3 details the comprehensive experiments conducted to validate its effectiveness, and Section 4 offers the conclusions drawn from the study. For all the acronyms involved in this paper, please refer to Appendix A.

2. The Proposed Method

This section delineates our method for recognizing LPI radar signals based on semi-supervised SVM. The proposed method primarily includes time–frequency transformation, image preprocessing, feature extraction, and semi-supervised classification. First, we convert the radar signals to time–frequency images utilizing MSST transformation. Then, we perform a series of preprocessing operations on obtained time–frequency images, including filtering, denoising, and interpolation. These operations aim to reduce redundancy and mitigate noise, thereby minimizing data computation while highlighting signal contours. Moreover, we exploited the DWT feature extractor to generate features from the preprocessed time–frequency images and reduced the high-dimensional features using the PCA method [18]. Finally, we feed the reduced dimensionality features into a semi-supervised SVM to accomplish the recognition of LPI radar signals. The overall architecture of the proposed method is shown in Figure 1.

2.1. MSST Time–Frequency Transformation

In order to enhance the energy concentration of characteristic signal components within the time–frequency distribution of LPI radar signals, simplify the signal processing workflow, and increase the computational efficiency, we employ the MSST for time–frequency transformations on the LPI radar signals. MSST is a classical time–frequency reassignment algorithm within the field of time–frequency analysis, which optimizes energy distribution through multiple iterative compressions of the time–frequency representations generated by the Short-Time Fourier Transform (STFT). This process concentrates the dispersed energy around the true frequencies into the central frequency, thus enhancing the aggregation of the signal’s time–frequency spectrum. As a linear time–frequency tool [19], MSST exhibits certain advantages over alternative time–frequency analysis techniques like Continuous Wavelet Decomposition (CWD) and Empirical Mode Decomposition (EMD) by reducing the impact of cross-terms and mode mixing. Next, we provide a formal introduction to the STFT and MSST time–frequency transformations.

We assume that the LPI radar signal $s\left(t\right)$ intercepted by the electronic reconnaissance receiver consists of a modulated signal $x\left(t\right)$ and Gaussian white noise $v\left(t\right)$ [20]. The LPI radar signal $s\left(t\right)$ can be represented as follows:

$$s\left(t\right)=x\left(t\right)+v\left(t\right)=A\left(t\right)Rect\left(t,T\right)e^{j\phi \left(f,t\right)}+v\left(t\right)$$

(1)

where $A\left(t\right)$ and $\phi \left(·\right)$, respectively, denote the amplitude and phase of the signal, and $T$ represents pulse width.

For signal $s\left(t\right)$, the STFT representation under the action of the window function $g\left(t\right)$ and synchronous compression expression are as follows:

$$G\left(t,w\right)={{\displaystyle \int }}_{-\infty }^{+\infty }g\left(u-t\right)s\left(u\right)e^{-jw\left(u-t\right)}$$

(2)

$$T_s\left(t,\eta \right)={{\displaystyle \int }}_{-\infty }^{+\infty }G\left(t,w\right)\delta (\eta -\widehat{w}\left(t,w\right))dw$$

(3)

where $\delta \left(·\right)$ represents the impulse function. By synchronously compressing $G\left(t,w\right)$, the STFT time–frequency spectrum is compressed along the frequency axis, enhancing the aggregation of signal energy. Subsequently, the time–frequency plot undergoes multiple SST iterative transformations [21]:

$$\begin{gathered} T_s^{\left[2\right]}\left(t,\eta \right)={{\displaystyle \int }}_{-\infty }^{+\infty }{T}_s^{\left[1\right]}\left(t,w\right)\delta (\eta -\widehat{w}\left(t,w\right))dw \\ {T}_s^{\left[3\right]}\left(t,\eta \right)={{\displaystyle \int }}_{-\infty }^{+\infty }{T}_s^{\left[2\right]}\left(t,w\right)\delta (\eta -\widehat{w}\left(t,w\right))dw \\ \dots \\ {T}_s^{\left[N\right]}\left(t,\eta \right)={{\displaystyle \int }}_{-\infty }^{+\infty }{T}_s^{\left[N-1\right]}\left(t,w\right)\delta (\eta -\widehat{w}\left(t,w\right))dw \end{gathered}$$

(4)

where ${T_s}^{\left[1\right]}\left(t,w\right)$ is equivalent to $T_s\left(t,w\right)$, which is the result of the SST calculation and $N$ represents the number of iterations $\left(N\ge 2\right)$; that is, the number of SST operations performed. From the iterative process described by Equation (4), it is evident that after $N$ iterations of the SST, the energy of the signal’s time–frequency spectrum is substantially concentrated around the central frequency, effectively compressing the signal’s instantaneous frequency. The time–frequency representations of 9 standard radar signals acquired using simulation analysis utilizing the MSST transform are shown in Figure 2.

2.2. Preprocessing of Time–Frequency Images

To better minimize noise interference in the time–frequency domain images and thereby extract effective features from these images, a series of preprocessing steps must be applied to the time–frequency images obtained through MSST. The image processing steps in this paper primarily include image grayscaling, image cropping, and Wiener filtering. Firstly, the images are converted to grayscale, followed by cropping to reduce the image size. Subsequently, the cropped images undergo Wiener filtering to suppress noise within the grayscale images. Finally, morphological gradient processing is performed by subtracting the eroded image from the dilated image to obtain the morphological gradient, which highlights areas of significant grayscale changes, thus accentuating the signal’s morphology and obtaining the image’s morphological gradient. The preprocessing workflow is illustrated in Figure 3.

2.3. DWT Feature Extraction

To facilitate enhanced recognition and interpretation of features within time–frequency images, and to eliminate irrelevant information, we employ the Discrete Wavelet Transform (DWT) [22] for feature extraction. DWT is a spectral analysis tool that discretizes the scale and translation of basic wavelets. It can not only examine the frequency-domain characteristics of local time-domain processes but also examine the time-domain characteristics of local frequency-domain processes. Thus, it is suitable for processing non-stationary signals, offering enhanced resolution and representation capability in both the time and frequency domains.

Specifically, DWT involves the application of low-pass and high-pass filters to individual rows and columns of the time–frequency image, resulting in the derivation of approximate and detail coefficients for each segment. The results are subsequently downsampled, halving the image size. In this paper, we employ the Mallat algorithm [23] to perform the two-dimensional DWT. The steps of this fast algorithm are presented as follows:

$$\begin{gathered} W_{LL}^j\left(n_1,n_2\right)={\displaystyle \sum }_{i_1=0}^{k-1} {\displaystyle \sum }_{{\dot{l}}_2=0}^{K-1}g\left(i_1\right)g\left(i_2\right)W_{LL}^{j-1}\left(2_{n1}-i_1\right)\left(2_{n2}-i_1\right) \\ {W}_{LH}^j\left(n_1,n_2\right)={\displaystyle \sum }_{i_1=0}^{k-1} {\displaystyle \sum }_{{\dot{l}}_2=0}^{K-1}g\left(i_1\right)h\left(i_2\right)W_{LL}^{j-1}\left(2_{n1}-i_1\right)\left(2_{n2}-i_1\right) \\ {W}_{HL}^j\left(n_1,n_2\right)={\displaystyle \sum }_{i_1=0}^{k-1} {\displaystyle \sum }_{{\dot{l}}_2=0}^{K-1}h\left(i_1\right)g\left(i_2\right)W_{LL}^{j-1}\left(2_{n1}-i_1\right)\left(2_{n2}-i_1\right) \\ {W}_{HH}^j\left(n_1,n_2\right)={\displaystyle \sum }_{i_1=0}^{k-1} {\displaystyle \sum }_{{\dot{l}}_2=0}^{K-1}h\left(i_1\right)h\left(i_2\right)W_{LL}^{j-1}\left(2_{n1}-i_1\right)\left(2_{n2}-i_1\right) \\ j=1 , 2 , \dots , n \end{gathered}$$

(5)

where $g$ and $h$ represent the low-pass filter and high-pass filter used for the decomposition, respectively. The time–frequency image of the radar signal after preprocessing is denoted as $W_{LL}^0$. $W_{LL}^j\left(n_1,n_2\right)$ denotes the low-frequency sub-band where energy is concentrated. $W_{LH}^j\left(n_1,n_2\right)$ is the horizontal low-frequency and vertical high-frequency sub-band. $W_{HL}^j\left(n_1,n_2\right)$ represents the horizontal high-frequency and vertical low-frequency sub-band. $W_{HH}^j\left(n_1,n_2\right)$ is the horizontal high-frequency and vertical high-frequency sub-band. $j$ indicates the transformation level, $n\le {log}_{2}N$. The data flow of the image decomposition is illustrated in Figure 4.

In this figure, ↓2 indicates downsampling by a factor of 2, meaning that the output contains only half the number of input samples. For an image of size $N\times N$, the image is first decomposed into low-frequency and high-frequency components through horizontal filtering. These components are then further decomposed through vertical filtering, resulting in four sub-band images. This process completes one level of transformation. The low-frequency component $LL$ obtained after the transformation is further decomposed, while the high-frequency components $HL$, $LH$, and $HH$, can be directly output. By repeating this process iteratively, the wavelet transform is ultimately completed.

In this paper, we use the “db4” wavelet basis function to perform a two-level decomposition of the time–frequency images to obtain its decomposition coefficients, which form a 154,559-dimensional vector. Due to the large data volume, this significantly reduces the efficiency of radar signal recognition. Therefore, we employ PCA for dimensionality reduction, resulting in an 1800-dimensional vector as image features for semi-supervised SVM recognition.

2.4. Semi-Supervised SVM for Recognition

To realize the recognition task of LPI radar signals, we introduce a semi-supervised SVM model based on a self-training mechanism [24] for radar signal recognition. Semi-supervised SVM provides a machine learning method that combines approaches from both supervised and unsupervised learning to address classification problems. In traditional supervised learning SVM, all training samples are labeled, meaning each sample is associated with a corresponding output category. However, in practice, acquiring a large number of labeled samples can be prohibitively expensive or difficult. Semi-supervised learning methods enhance the performance and generalizability of the model by utilizing a combination of partially labeled samples and a substantial quantity of unlabeled samples. The basic idea of this algorithm is to first train a base model on a small amount of labeled data. Then, use this model to predict unlabeled data and treat these predictions as pseudo-labels. These pseudo-labels are combined with the labeled data for further model training. In this way, information from unlabeled data is indirectly transferred to the model through pseudo-labels, thereby improving model performance. Figure 5 depicts the structure of the algorithm.

The specific steps of the algorithm are as follows. First, we train an initial SVM model as SVM1 using a small amount of labeled data. Then, we use the trained model SVM1 to predict unlabeled samples, generating pseudo-labels P1. The generated pseudo-labels are combined with the labeled data to form an augmented training dataset, we retrain the SVM model as SVM2 with the augmented training dataset. Next, we use SVM2 to predict unlabeled data again, obtaining predicted labels P2. For an unlabeled sample, if its pseudo-label in P1 is consistent with the predicted label in P2, then the pseudo-label is used as its true label for output. Repeat this process until the labels for all unlabeled nodes have been predicted.

This approach expands the labeled dataset with predictions from unlabeled data and greatly enhances the model’s performance and generalization on test data through iterative training, while effectively reducing the cost of labeled data.

3. Experiments

To assess the efficacy of the proposed approach, we conduct simulation experiments on 9 kinds of typical LPI radar signals. We analyze experimental results from various perspectives, including performance comparison with baselines, performance analysis of every signal, algorithm robustness, ablation analysis, and semi-physical simulation experiments.

3.1. Dataset Description

In our experiments, we selected nine typical LPI radar signals, including CW, LFM, NLFM, 4FSK, BPSK, QPSK, BPSK/LFM, FSK/LFM, and FSK/BPSK, for experiments. To ensure the generality of the experimental SNR range, we chose an SNR range from −14 dB to 10 dB, with a step size of 2 dB. For each SNR, 600 samples are generated for each signal type. Among these, 400 samples constitute the training set, comprising 200 labeled samples and 200 unlabeled samples, while the remaining 200 samples are for testing. Consequently, there are a total of 3600 training samples and 1800 test samples for the nine types of signals at each SNR. The simulation parameter setting of every radar signal is shown in

Table 2. Simulation parameter settings.

Radar Waveform	Simulation Parameter	Range
All	Sample frequency (fs)	200 MHz
	Carrier frequency	20 MHz
	Pulse Width	6 μs
LFM	Bandwidth	40 MHz
4FSK	Frequency point	15,30,50,80 MHz
	Code length	[0,0,1,0,0,1,1,1]
BPSK	Code length	[1,1,1,0,0,1,0]
QPSK	Code length	[0,1,0,0,1,0,1,1]

.

3.2. Performance Comparison

To assess the effectiveness of the proposed method in this paper, we first compare it with other baseline methods, including MSST + HOG + SVM [25], MSST + Dual Channel + SVM [26], CWT + CNN [27], LPI-Net [28], and GLGCM + SVM [29]. MSST + HOG + SVM utilizes MSST for time–frequency transformation. Histogram of Oriented Gradients (HOG) is employed for feature extraction, which computes histograms of oriented gradients in local regions of the image to describe local structure and shape information. Finally, supervised SVM is used for radar signal recognition. MSST + Dual Channel + SVM involves the use of MSST for time–frequency transformation. It employs a dual-channel feature extraction method combining the Gray-Level Co-occurrence Matrix (GLCM) and Local Binary Pattern Variance (LBPV). GLCM describes the spatial relationships between pixel gray levels in images, while LBPV focuses on describing local texture features of the image. Finally, a supervised SVM classifier is used for classification. CWT + CNN treats Continuous Wavelet Transform (CWT) coefficients as image features and processes them for classification using CNN. LPI-Net employs CWD for time–frequency analysis and introduces a CNN called LPI-Net. It includes multi-level cascaded processing modules to learn highly discriminative features across multiple scales. GLGCM + SVM utilizes Choi–Williams Distribution (CWD) and Ambiguity Function (AF) for the time–frequency transformation of radar signals. It then extracts fused texture features from time–frequency images using the Gray Level-Gradient Co-occurrence Matrix (GLGCM) and performs radar signal recognition using supervised SVM. We separately tested the recognition accuracy of the method proposed in this paper and the five methods mentioned above, as well as the average runtime. The experimental results on the variation of recognition accuracy of different algorithms with varying SNR are illustrated in Figure 6. The average runtime of different algorithms within the range of −14 dB to −10 dB is shown in

Table 3. Comparison of computational efficiency for different algorithms.

Recognition Method	Recognition Duration (s)
LPI-Net	787.7
GLGCM + SVM	111.6
CWT + CNN	2023.4
MSST + Dual Channel + SVM	167
MSST + HOG + SVM	185.4
Proposed method	86.4

.

It can be seen from Figure 6 that with the increase in signal-to-noise ratio (SNR), the recognition accuracy of each algorithm exhibits an upward trend. Notably, the algorithm proposed in this paper demonstrates an overall recognition rate higher than that of other algorithms, with a recognition accuracy approaching 100% at −6 dB. Furthermore, compared to the deep learning-based algorithms CWT + CNN and LPI-Net, the proposed approach in this paper not only maintains high accuracy but also significantly reduces computational time, thus improving efficiency. Additionally, the proposed algorithm outperforms MSST + HOG + SVM, MSST + Dual Channel + SVM, and LPI-Net noticeably when the SNR is below 0 dB. Moreover, compared to GLGCM + SVM, the algorithm presented in this paper effectively mitigates the drawback of significant fluctuations in recognition accuracy caused by large fluctuations in features extracted by the ambiguous function.

We also compare the computational complexity of the proposed approach with baselines. As shown in Table 3, the method proposed in this paper demonstrates a significant speed advantage over the other algorithms. This indicates that the proposed algorithm excels in computational complexity and execution efficiency, enabling rapid data processing. Moreover, the shorter running time implies that the algorithm has lower computational resource requirements, allowing more efficient utilization of CPU and memory resources. This also suggests good scalability, maintaining high performance with larger datasets or more complex applications.

3.3. Performance Analysis

We analyze the recognition performance of the proposed model for 9 types of LPI radar signals. The experimental results are shown in Figure 7. It can be observed that its recognition accuracy generally increases as the SNR rises. Under low SNR conditions, our method exhibits high recognition precision, particularly for signal waveforms such as NLFM, 2FSK, LFM/FSK, and LFM/BPSK. Even at −10 dB, its recognition accuracy reaches approximately 100%. Moreover, when the SNR is no lower than −10 dB, its overall recognition accuracy of the signals remains above 93%. This is because their time–frequency features extracted by DWT are more distinguishable compared to other signals. Additionally, it can be seen that when the SNR is −10 dB, the recognition accuracy of LFM and BPSK signals is below 50%, indicating poor recognition performance for them. In contrast, the recognition accuracy of the QPSK signal approaches 100% at −14 dB. Overall, the proposed method can effectively recognize these 9 types of signals.

Finally, we conducted a comprehensive analysis of the recognition accuracy across specific SNR levels using the confusion matrix, as illustrated in Figure 8. As demonstrated in Figure 8a, the recognition accuracy for BPSK and CW signals does not surpass 70% at −12 dB. A segment of these signals exhibits mutual confusion, attributed to the diminished phase position features of BPSK at lower SNRs, leading to morphological similarities between them. Additionally, LFM is susceptible to confusion with LFM/BPSK due to their similar spectral shapes, stemming from the linear frequency variation over time characteristic shared by both modulation techniques in low SNR environments. As the SNR decreases, the effectiveness of DWT in extracting distinguishing features diminishes, subsequently reducing the recognition accuracy. Nevertheless, as the SNR increases, the accuracy of classifying all nine standard radar signals can be significantly improved. As shown in Figure 8b, when the SNR is elevated to −6 dB, the identification accuracy for all nine radar types exceeds 95%.

3.4. Algorithmic Robustness

To further validate the robustness of the algorithm, we assess the recognition accuracy of signals under varying SNRs and mixed SNR conditions. For different SNRs, training sets are constructed with samples at −14 dB, −6 dB, 10 dB, and 6 dB, while testing sets are comprised of samples at −8 dB, 2 dB, 8 dB, and 0 dB. Mixed SNRs are selected within the range of −14 dB to −10 dB, with a step size of 2 dB for both training and test sets. For each SNR, 400 samples are selected for the training and 200 samples for the testing. The experimental results are presented in

Table 4. Overall accuracy on training set and test set under different SNRs.

Training Set SNR/dB	Test Set SNR/dB	Overall Accuracy/%
−14	−6	91.788
−6	2	100
10	4	100
6	0	100
−14~−10	−14~−10	83.76

.

It can be observed from this table that the overall recognition rates of the proposed model exceed 90% under various SNRs, with three groups achieving a recognition accuracy of up to 100%. For mixed SNRs, even under relatively low SNRs, its recognition accuracy for nine types of radar signals reached 83.76%. Therefore, our approach demonstrates excellent robustness.

3.5. Ablation Analysis

Based on the preceding discussion, our proposed method primarily comprises three modules: MSST, DWT, and semi-supervised SVM. To investigate the effectiveness of each module, we conduct ablation experiments, where specific modules or functionalities are removed or altered to study their impact on the overall performance of the model. We define three experimental setups:

(a)

CWT + DWT + semi-supervised SVM, the proposed model that replaces the MSST time–frequency transformation component with CWT.

(b)

MSST + HOG + semi-supervised SVM, the proposed model that omits the DWT feature extraction module.

(c)

MSST + DWT + SVM, where the proposed semi-supervised SVM model based on a self-training mechanism is replaced with supervised SVM.

From Figure 9, it can be observed that the recognition accuracy of the proposed algorithm is significantly higher than that of MSST + HOG + semi-supervised SVM. This indicates that MSST has a more pronounced effect on the time–frequency transformation of radar signals. Additionally, the recognition accuracy of the proposed algorithm is also notably higher than that of CWT + DWT + semi-supervised SVM. This suggests that DWT performs well in extracting features from radar images. Furthermore, at −12 dB and −10 dB, the recognition accuracy of the proposed algorithm is significantly higher than that of the MSST + DWT + SVM approach. This demonstrates that semi-supervised SVM can achieve comparable or slightly higher performance than fully supervised classifiers even with reduced labeled samples, further highlighting the superiority of the proposed method. However, at −14 dB, the recognition accuracy of the proposed algorithm is lower than that of MSST + DWT + SVM, possibly due to increased noise interference under SNR conditions.

3.6. Semi-Physical Simulation Experiment

To further validate the effectiveness and reliability of the proposed method, we conduct semi-physical simulation experiments to assess its performance in real-world environments. We conducted experiments using the semi-physical simulation platform in our laboratory [25], which consists primarily of three components: a simulation control computer, a signal simulator, and a signal collector, as shown in Figure 10. The basic parameters of this simulation platform are set as follows: maximum transmit and receive signal bandwidth: 200 MHz; waveform bit width for transmission and reception: 16 bits; sampling rate: 3GSa/s; and frequency band: C-band.

Its procedure is described as follows: Firstly, the simulation control computer generates nine types of radar signal waveforms with random characteristics, annotates each signal, and then sends them to the signal simulator at specified intervals. Next, the signal simulator performs analog-to-digital conversion, and frequency conversion to the C-band, and transmits the signals via the transmitting antenna into the air. Simultaneously, the receiving antenna captures echoes in the C-band, and the simulation control computer directs the signal collector to gather antenna signals. Subsequently, a series of operations including down-conversion, analog-to-digital conversion, and pulse extraction are performed on these signals to form the dataset for testing. Finally, the proposed algorithm in this paper is employed to identify the received real radar signals. The results of the semi-physical simulation experiment are compared with analog experiments, as shown in Figure 11.

Overall, the recognition accuracy of the semi-physical simulation experiment was lower than that of the simulated experiment. This discrepancy is attributed to increased noise, multipath effects, and fading in the electromagnetic propagation channels during the semi-simulation, resulting in fluctuating signals. Nevertheless, under lower SNR conditions, the semi-physical simulation experiment still achieved relatively high accuracy. Specifically, at −8 dB, the recognition accuracy reached 80%, and it approached nearly 100% at 0 dB. These findings indicate that our proposed method remains effective in real-world environments.

4. Conclusions

In this study, we introduce a semi-supervised SVM-based approach for LPI radar signal recognition. This technique employs MSST to derive a time–frequency representation of radar signals, significantly enhancing the concentration of signal energy and improving the distribution of energy, which aids in signal reconstruction. By leveraging the multi-resolution capability and local adaptability of DWT, it employs DWT to extract time–frequency features of the signal. We introduced a semi-supervised SVM model for signal recognition, which overcomes the challenges of low accuracy in unsupervised learning algorithms and the requirement for massive, labeled samples in supervised learning algorithms. The experimental results demonstrate that the proposed method achieves higher recognition accuracy for nine typical radar signals than other algorithms, even in low SNR situations, while also exhibiting good robustness.

In our future work, we will continue to optimize feature fusion methods and explore more effective strategies for feature combinations to address challenges in recognizing different signal interferences and complex electromagnetic environments. Furthermore, we will focus on advancements in technology, investigating how new deep learning algorithms and more advanced feature extraction techniques can be applied to enhance the performance and robustness of our models. These explorations not only aim to drive developments in our research field but also hold promise for providing more reliable solutions for practical applications.