Evaluating CNN-Based Classification Models Combined with the Smoothed Pseudo Wigner-Ville Distribution to Identify Low Probability of Interception Radar Signals

Abstract

Fundamental in defense, Radar Electronic Warfare (REW) requires adaptation to current threats. Automatic recognition algorithms for intrapulse modulations (ATR) of Low Probability of Interception (LPI) radar signals are essential in REW. Existing LPI signal ATR methods combine the Choi-Williams Distribution (CWD) pre-processing technique with Convolutional Neural Networks (CNN). This work proposes two new ATR combinations, based on SqueezeNet and GoogLeNet CNN. Both used the Smoothed Pseudo-Wigner-Ville distribution (SPWVD) pre-processing technique as an alternative to CWD. Replacing CWD by SPWVD was based on the hypothesis that the latter usually provides higher resolutions than the former. The proposed ATR overcame the SOTA ATR, achieving a 99.06% accuracy, under noisy environments and providing evidence to the hypothesis raised. Experiments involved two datasets with 13 types of modulations and 806,000 samples each.

1 Introduction

Currently, Radar Electronic Warfare (REW)¹ has assumed a fundamental role in defense of countries around the world. Increasingly, REW Support Measures (ESM) have become essential to improve detection, identification, and protection processes against enemy equipment such as missiles, for instance. In the context of missile detection, efforts have been made to incorporate Electronic Intelligence systems (ELINT) into ESM equipment aimed at identifying Low Probability of Interception (LPI) radar signals [5]. Due to the use of robust automatic recognition algorithms of intrapulse modulations (ATR - Automatic Target Recognition) of LPI radar signals, ELINT systems have good performance, even in environments with low signal-to-noise ratio (SNR) [6]. For text simplification purposes, in this article, the acronym ATR will be used as the expression ATR model.

In recent years, several ATR systems for Low Probability of Intercept (LPI) radar signals have been developed using different classification algorithms, such as classical Artificial Neural Networks (ANN) [9], Decision Trees (DT) [10], and Convolutional Neural Networks (CNN) [6], among others [5]. To apply these ATR systems, the signals need to be pre-processed using Time-Frequency Analysis (TFA) techniques². The main TFA techniques employed in LPI radar signal ATR include the Choi-Williams Distribution (CWD) [6], Short-Time Fourier Transform (STFT) [13], and variations of the Wigner-Ville Distribution (WVD) [14, 15], such as the Smoothed Pseudo-Wigner-Ville (SPWVD). The SPWVD is one of the most effective TFA techniques for estimating various temporal and spectral parameters of LPI radar signals, especially in noisy environments [7]. Notably, literature works that have combined the TFA-CWD³ technique with CNN have achieved the best performances in identifying LPI radar signals [3, 5, 6].

When analyzing these studies, it becomes evident that although they all employed different Time-Frequency Analysis (TFA) techniques for signal pre-processing, there was no initiative to optimize the CNN’s hyperparameters according to the pre-processing technique. Efforts to optimize hyperparameters in Machine Learning applications are justified because, in general, classification model performance varies based on the data and the pre-processing applied to it [2]. Nevertheless, all the mentioned studies relied on the default parameterization of the CNN implementations.

In light of the above mentioned, this study raises the following hypothesis: Using a CNN with hyperparameters optimized accordingly to the TFA technique used in the pre-processing of LPI radar signals can lead to better performance when combining TFA+CNN⁴. Moreover, when comparing TFA+CNN with SPWVD as the TFA technique to cases where CWD is used, the former technique can lead to superior results.

To gather pieces of evidence that support the hypothesis raised above, this study aimed to analyze the results produced by the following combinations: $SPWVD$ $+$ $SqueezeNet_{opt}$; $CWD\!+\!SqueezeNet_{opt}$; $SPWVD\!+\!GoogLeNet_{opt}$; and $CWD\!+\!GoogLeNet_{opt}$. All these combinations were tested using 13 types of intrapulse modulations in LPI radar signals. The following combinations, $SPWVD\!+\!SqueezeNet_{opt}$, $CWD\!+\!SqueezeNet_{opt}$, $SPWVD\!+\!GoogLeNet_{opt}$ and $CWD\!+\!GoogLeNet_{opt}$, refer to versions of the CNN SqueezeNet and CNN GoogLeNet with optimized hyperparameters, trained after applying TFA-

SPWVD and TFA-CWD to the data, respectively. The 13 tested modulations were generated by considering a range of random values for their respective parameters, resulting in two Time-Frequency Image (TFI) databases: one derived from the application of TFA-SPWVD (SPWVD-TFI) and the other from the application of TFA-CWD (CWD-TFI). Each of these databases contains 403,000 TFI. Remarkably, the $SPWVD\!+\!GoogLeNet_{opt}$ combination achieved an average classification accuracy of 99.06% at $0dB$ SNR, surpassing both previous related works and the results obtained by the $CWD\!+\!GoogLeNet_{opt}$ combination, thus confirming the considered hypothesis.

The present text is structured into five sections. Section 2 introduces the Time-Frequency Analysis (TFA) techniques used to generate the Time-Frequency Images (TFI) employed in the experiments. Section 3 discusses state-of-the-art studies in LPI radar signal identification. Section 4 outlines the experimental methodology, including TFI creation and the structure of classifiers based on SqueezeNet and GoogLeNet. Section 5 describes the obtained results and compares them with those from related works. Finally, Sect. 6 presents the research reflections, highlighting the main contributions and suggesting avenues for future investigations.

2 Fundamental Theory

Various pre-processing techniques for Low Probability of Intercept (LPI) radar signals have been developed. Among these, we can highlight TFA methods such as the WVD, its variations, and the CWD. These techniques play a crucial role in enhancing ATR performance.

The WVD allows optimal time-frequency concentration compared to other TFA methods [11]. However, it introduces Cross-Terms (CT)⁵. To mitigate the influence of CT, the Pseudo-Wigner-Ville Distribution (PWVD) was introduced, incorporating a sliding analysis window along the frequency axis [11]. Subsequently, as an enhancement of the PWVD, the CWD was developed to reduce the CT influence both in frequency and time domains. The CWD is defined based on the Fourier transform X($\omega$) of x(t), as indicated in Eq. 1. Here, $t$ represents the time variable, $\omega$ is the angular frequency variable, $*$ denotes complex conjugation, and $\sigma = 1$ serves as a scale factor, critical for CT suppression by smoothing the CWD distribution. The kernel $\phi$ acts as a low-pass filter for processing the two-dimensional Fourier Transform into a Cohen class ambiguity function [11]. Typically, an exponential kernel $\phi (\xi ,\tau )=e^{-\xi ^2\tau ^2/\sigma }$ is adopted in this distribution [1].

$$\begin{aligned} \begin{aligned} CWD_x(t,\omega )=&\frac{1}{2\pi }\int _{\xi =-\infty }^{\infty }e^{-j\xi {t}}\int _{\mu =-\infty }^{\infty }\sqrt{\frac{\sigma }{4\pi \xi ^2}}e^{\frac{(\mu -\omega )^2}{4\xi ^2/\sigma }}x(\mu +\frac{\xi }{2})x^*(\mu -\frac{\xi }{2})d\mu {d\xi } \end{aligned} \end{aligned}$$

(1)

Another approach proposed to mitigate the interference caused by CT in the WVD is the creation of the SPWVD. The SPWVD introduces smoothing windows both in the time and frequency domains. Mathematically, the SPWVD is defined by Eq. 2 [7]. In this equation, h($\tau$) and g($\nu$) represent the time and frequency window functions, respectively. The signal x(t) corresponds to the analytic signal of r(t), and $*$ denotes complex conjugation. Specifically, the analytic signal x(t) follows the Equation $x(t) = r(t) + jH[r(t)]$, where $H[r(t)]$ represents the Hilbert transform of the real signal r(t).

$$\begin{aligned} \begin{aligned} & SPWVD_x(t,f) = \int \int {x}(t-\nu +\tau /2){x^*}(t-\nu -\tau /2)h(\tau )g(\nu )e^{-j2\pi {f\tau }}d\nu {d\tau } \end{aligned} \end{aligned}$$

(2)

The visual effect of interference resulting from CT in the time-frequency domain can be observed in the examples shown in Fig. 1. These examples depict the results of applying different TFA techniques to an LPI radar signal. The resulting TFI from the WVD Fig. 1a and the PWVD Fig. 1b exhibit pronounced CT values (visible as highlighted vertical bars). In contrast, the TFI produced by the CWD Fig. 1c and the SPWVD Fig. 1d show reduced CT effects. Notably, although the TFI appears similar, the image in Fig. 1d seems to have a slightly higher resolution than that in Fig. 1c, suggesting a potential advantage of using SPWVD over CWD. More details about each TFA can be obtained in [11].

Fig. 1.

LPI Costas-4 Signal Pre-processed by Different TFA

3 Related Work

Currently, the state-of-the-art studies in the field of LPI radar signal classification, specifically regarding modulation type, include those by [3, 5, 6]. Table 1 presents main characteristics of these works compared to the present proposal. Notably, among these studies, only [3] explored different TFA techniques and compared results across classification models. However, unlike the current proposal, the three LPINet CNN evaluated in [3] experiments were generated using default hyperparameter values, regardless of the TFA technique used for signal pre-processing. Additionally, our proposal uniquely assessed and compared the effects of employing TFA-SPWVD and TFA-CWD on the same signals. This strategic choice was based on the expectation that even minor resolution differences, as illustrated in Figures 1d and 1c, could lead to improved classification results with TFA-SPWVD compared to TFA-CWD.

Table 1. Main Characteristics of Related Works and This Proposal

4 Proposed Methodology

To validate the hypothesis proposed in this study, we employed the methodology depicted in Fig. 2. This methodology comprises the following steps: Creation of LPI Radar Signal Instances Base, generated by adding Additive White Gaussian Noise (AWGN) and simulated channel loss to the noise-free LPI radar signal; Signal Pre-processing, generating the SPWVD-TFI and CWD-TFI bases by pre-processing the signals using SPWVD and CWD TFA techniques, respectively; Model training, validating and testing, where the classification models were trained, validated and tested based on the LPI modulation type using the pre-processed signals; and Evaluation of Results, where the performance of our proposed approach is evaluated. Notably, our method considered both TFA-SPWVD and TFA-CWD on the same signals, aiming to leverage their distinct characteristics for improved classification results. The next paragraphs detail each of these steps.

Fig. 2.

Flowchart of the Methodology Adopted in the Experiments

To create the Base of LPI Radar Signal Instances, we modeled the receiver of a radar system. We considered that the complex sample of an intercepted LPI radar signal is perturbed by Additive White Gaussian Noise (AWGN) and channel loss, as indicated by the equation: $y(k) = x(k) {\circledast } h(k) + n(k)$. In this equation: $x(k)$ represents the signal generated during the Signal Generation step, which is noise-free; $h(k)$ corresponds to the channel interference resulting from the Channel Loss Generation step; $n(k)$ characterizes the noise introduced during the AWGN Generation step; $k$ denotes the sample index for each $T_s$ (sampling period), considering a sampling frequency $f_s$.

Table 2. TFI Databases Generated in This Work

It’s important to emphasize that this study aimed to employ a data creation mechanism identical to that used in related works. To achieve this, we utilized the source code for generating LPI radar signals provided by the authors of [6] after corresponding via email. Additionally, we created the database using the same intrapulse modulations and parameter ranges specified in Table 1. Consequently, we generated 13 different types of LPI radar signal modulations, including linear frequency modulation (LFM), unmodulated (rectangular) signals, Costas modulation (Frequency Shift Key - FSK), binary Barker coding, five polyphase codes (Frank, P1, P2, P3, and P4), and four polytemporal codes (T1, T2, T3, and T4). Similar to [3], we introduced noise during the AWGN Generation step, varying the SNR from –20 dB to +10 dB with a 1.0 dB increment. In the same way, channel loss interference was modeled, using Rayleigh fading during the Channel Loss Generation step. The different signal instances constituting the LPI Signal Base were created by randomly varying the specific parameters for each intrapulse modulation, following the specifications outlined in [3] and detailed in Fig. 3.

Fig. 3.

Parameter Ranges Used in Generating LPI Signal Instances [3]

As specified in [3], to generate the CWD-TFI and SPWVD-TFI bases, we initially pre-processed each LPI radar signal using the SPWVD and CWD techniques. During this step, we applied Kaiser filters with a size of $63$ samples and a shape factor of $0.5$ to smooth the time and frequency windows. Subsequently, we obtained the corresponding TFI, capturing images with $256$ grayscale levels and dimensions of (50 $\times$ 50) pixels using bicubic interpolation for resizing. Figure 4 illustrates examples of TFI obtained from TFA-SPWVD with an SNR of +10 dB.

Fig. 4.

TFI examples from the SPWVD-TFI base

As indicated in Table 2, two databases were generated, each containing $403.000$ TFI ($31$ SNR levels * $13$ LPI signals * $1000$ LPI Signal Instances).

During the Data Partitioning step, each TFI base was sorted into five disjoint sets to facilitate cross-validation. In each cross-validation round, the data was stratified into training, validation, and test datasets in a 70-15-15 ratio, following a process and proportion similar to that used by [3].

The ATR proposed in this work was evaluated using classifiers based on two CNN models: SqueezeNet and GoogLeNet. Each of these CNN models was selected for distinct reasons.

SqueezeNet⁶ was chosen primarily because it delivers strong performance comparable to AlexNet in image classification tasks, yet with $50$ times fewer parameters and a model size $510$ times smaller. This compactness makes SqueezeNet suitable for memory-constrained devices [4]. Additionally, as indicated in Table 1, SqueezeNet falls within a medium-sized network category compared to other CNN used in related works. Its topological architecture features unique Fire Modules, comprising squeeze layers with 1 $\times$ 1 convolution filters and expand layers with 1 $\times$ 1 and 3 $\times$ 3 convolution filters. You can visualize this architecture in Fig. 5. In this work, we have chosen version 1.1 of the SqueezeNet network because it requires 2.4 times fewer computations than version 1.0 while maintaining the same accuracy⁷.

Fig. 5.

SqueezeNet CNN [4]

GoogLeNet⁸ was chosen primarily for its performance, which approaches the SOTA in classification [12]. This network architecture consists of 27 deep layers, formed by stacking 9 inception modules linearly, as illustrated in Fig. 6. These modules utilize 1 $\times$ 1, 3 $\times$ 3, and 5 $\times$ 5 convolution filters, along with maximum pooling layers. This structure enables image identification and categorization, even when limited information is available [12].

Fig. 6.

Inception module [12]

The fine-tuning of the SqueezeNet and the GoogLeNet was made through a MATLAB app known as Deep Designer⁹. The optimization process of the hyperparameter values of the SqueezeNet was made for the CWD-TFI ($CWD\!+\!SqueezeNet_{opt}$) and for the SPWVD-TFI ($SPWVD\!+\!SqueezeNet_{opt}$). In the same way, the optimization process of the hyperparameter values of the GoogLeNet was made for the CWD-TFI ($CWD\!+\!GoogLeNet_{opt}$) and for the SPWVD-TFI ($SPWVD\!+\!GoogLeNet_{opt}$). These optimization processes were possible due to the use of the MATLAB app known as Experiment Manager¹⁰ using Bayesian searches. These searches employed stochastic gradient descent with momentum (SGDm) as the optimizer. The optimal hyperparameter values and their corresponding search ranges during training are summarized in Table 3. Additionally, a minibatch size of 128 was used for all models.

Table 3. Search Ranges and Optimal Values Found for SqueezeNet and GoogLeNet hyperparameters during Cross-Validation process

Finally, the Evaluation of Results step was made by comparing the performance of the $SPWVD\!+\!SqueezeNet_{opt}$, $CWD\!+\!SqueezeNet_{opt}$, $SPWVD\!+\!GoogLeNet_{opt}$, and $CWD\!+\!GoogLeNet_{opt}$ combinations with each other and with the results reported by state-of-the-art studies.

All experiments were conducted on a hardware platform with an Intel® Core™ i5-12500H 12th Gen CPU running at 2.50 GHz, 16 GB of RAM, and a single NVIDIA GeForce RTX 3070 Ti GPU with 8 GB of memo

5 Results

To obtain evidence supporting the validity of the hypothesis raised in this study, three analyses were conducted based on the evaluation of the obtained results.

The first analysis was conducted in two stages. In the first stage, the results of the $CWD\!+\!SqueezeNet_{opt}$ and $SPWVD\!+\!SqueezeNet_{opt}$ combinations obtained during the cross-validation process were compared. In the second stage, the results of the $CWD\!+\!GoogLeNet_{opt}$ and $SPWVD\!+\!GoogLeNet_{opt}$ combinations, also obtained during cross-validation, were compared. Both stages present precision values for each tested combination considering the 13 LPI signal types and varying SNR between –20 dB and 10 dB. Notably, regardless of the combination used, precision approaches 100% for higher SNR values (above 0 dB) across all LPI signal types.

The results of the first analysis using SqueezeNet can be visualized in Fig. 7. Comparing Fig. 7a and Fig. 7b, it can be noticed that, at –20 dB, the Barker signal achieved 97.4% precision with $CWD\!+\!SqueezeNet_{opt}$ and 93.2% precision with $SPWVD\!+\!SqueezeNet_{opt}$. Conversely, at the same SNR, the T2 signal achieved 31.2% precision with $CWD\!+\!SqueezeNet_{opt}$ and 55.5% with $SPWVD\!+\!SqueezeNet_{opt}$. Another important observation is the favorable results for signals T1 to T4 when using $SPWVD\!+\!SqueezeNet_{opt}$, especially at negative SNR values, compared to results obtained with $CWD\!+\!SqueezeNet_{opt}$. However, at –15 dB SNR, $CWD\!+\!SqueezeNet_{opt}$ outperformed $SPWVD\!+\!SqueezeNet_{opt}$ for the Costas and LFM signals.

Fig. 7.

Comparison of classification precision tested by SqueezeNet_opt

The results of the first analysis using the GoogLeNet are presented in Fig. 8. Comparing Fig. 8a and Fig. 8b, it can be noticed that, at –20 dB, the Barker signal achieved 97.1% precision with $CWD\!+\!GoogLeNet_{opt}$ and 95.2% precision with $SPWVD\!+\!GoogLeNet_{opt}$. Similarly, at the same SNR, the T1 signal achieved 66.7% precision with the $SPWVD\!+\!GoogLeNet_{opt}$ against 27.6% with the $CWD\!+\!GoogLeNet_{opt}$. Another notable result is the good performance of the LFM signal, using the $SPWVD\!+\!GoogLeNet_{opt}$, and the Costas signal, with the $CWD\!+\!GoogLeNet_{opt}$.

Fig. 8.

Comparison of classification precision tested by GoogLeNet_opt

In summary, based on the results obtained in the first analysis, it is clear that both combinations yielded comparable outcomes. Specifically, each combination performed better for certain LPI radar signal types and worse for others. Consequently, there is no single combination that outperforms the other across all 13 LPI radar signal types and the entire SNR range.

The second analysis aimed to compare the average accuracy results obtained by considering all 13 LPI radar signal types together, across the 5 rounds of cross-validation adopted, and the four types of ATR combinations. Accordingly, the average accuracy value was calculated for each combination across the entire SNR range, as illustrated in Fig. 9. It can be noticed in Fig. 9 that the combinations using the CNN GoogLeNet_opt achieved higher accuracy.

Another conclusion drawn from the results presented in Fig. 9 is that networks composed of the SPWVD-TFI datasets, specifically $SPWVD\!+$

$SqueezeNet_{opt}$ and $SPWVD\!+\!GoogLeNet_{opt}$, exhibited superior average accuracy across the entire SNR range when compared to combinations using the CWD-TFI datasets ($CWD\!+\!SqueezeNet_{opt}$ and $CWD\!+\!GoogLeNet_{opt}$). Additionally, it is noteworthy that for high SNR values, average accuracy approaches 100%, regardless of the combination used. For instance, at 0 dB, $SPWVD\!+\!SqueezeNet_{opt}$ achieved an accuracy of 97.83%, while $SPWVD\!+\!GoogLeNet_{opt}$ reached 99.06%. Another noteworthy aspect from the curves in Fig. 9 that reflects the superior performance of $SPWVD\!+\!SqueezeNet_{opt}$ combination compared to $CWD\!+\!SqueezeNet_{opt}$ occurred at an SNR of –15 dB. At this point, $SPWVD\!+\!SqueezeNet_{opt}$ outperforms $CWD\!+\!SqueezeNet_{opt}$ by 4.4 p.p. Similarly, the optimal performance point for the $SPWVD\!+\!GoogLeNet_{opt}$ combination, comparing with $CWD\!+\!GoogLeNet_{opt}$, occurs at an SNR of –16 dB, with a margin of 2.7 p.p above $CWD\!+\!GoogLeNet_{opt}$. Ultimately, the SPWVD-TFI based combinations consistently achieve more prominent accuracy results when compared to the CWD-TFI based combinations, mainly at negative SNR values.

Fig. 9.

Average accuracy obtained with the four proposed ATR combinations

Table 4 provides the mean, minimum, and maximum accuracy values and the standard deviation obtained by each ATR combination. It also shows the p-values and the results of the Wilcoxon Signed Rank Test applied to the ATR combination pairs ($CWD+SqueezeNet$, $SPWVD+SqueezeNet$) and ($CWD+GoogLeNet$, $SPWVD+GoogLeNet$) with significance level $\alpha = 0.05$ and null hypothesis $H_0$ stating that the means are statistically identical for each pair of ATR combinations. The Wilcoxon test was run in MATLAB with the Statistics and Machine Learning Toolbox.

Table 4. Accuracy Values and Results of Wilcoxon Signed Rank Test

The results obtained, shown by Table 4, suggest a slight superiority of SPWVD-TFI over CWD-TFI when combined with an optimized CNN for classification. On average, the worst result of $SPWVD\!+\!SqueezeNet_{opt}$ $80.9\%$ outperformed the best result of $CWD\!+\!SqueezeNet_{opt}$ $80.25\%$. Similarly, the worst result of $SPWVD\!+\!GoogLeNet_{opt}$ $83.04\%$ surpassed the best result of $CWD\!+\!GoogLeNet_{opt}$ $82,8\%$. Additionally, its important to note that the standard deviation of mean accuracy for $SPWVD\!+\!SqueezeNet_{opt}$ $0.22$ was significantly lower than for $CWD\!+\!SqueezeNet_{opt}$ $0.34$, indicating more consistent accuracy distributions for the SPWVD-TFI-based combinations, while both $CWD\!+\!GoogLeNet_{opt}$ and $SPWVD\!+\!GoogLeNet_{opt}$ standard deviation of average accuracy’s have been similar and rather small values, $0.13$ and $0.17$ respectively. It is also important to highlight that the Wilcoxon test rejected the null hypothesis in both ATR combination pairs, indicating statistical evidence that SPWVD can lead to more accurate classification models than CWD.

In Fig. 10, we present the confusion matrices, at –8 dB SNR, for the two combinations that achieved the highest accuracy, considering their validation rounds, the $SPWVD\!+\!GoogLeNet_{opt}$ and $CWD\!+\!GoogLeNet_{opt}$. In both confusion matrices, certain modulation types are strongly confused with others. For instance, P1 signals are often misclassified as P4, while T1 signals are confused with T2. These misclassifications occur regardless of the TFA technique employed (i.e. CWD or SPWVD). However, a noticeable advantage lies in the classification capability of $SPWVD\!+\!GoogLeNet_{opt}$ over $CWD\!+\!GoogLeNet_{opt}$. This conclusion is based on two observations: The higher accuracy achieved by $SPWVD\!+\!GoogLeNet_{opt}$ $90.00\%$ compared to $CWD\!+\!GoogLeNet_{opt}$ $89.38\%$; and the better precision provided by $SPWVD\!+\!GoogLeNet_{opt}$, which outperformed $CWD\!+\!GoogLeNet_{opt}$ when classifying 5 LPI radar signal types (Barker, LFM, P3, P4, and T1), and losing only at classifying 3 LPI signal types (P1, T2, and T3). These findings underscore the effectiveness of SPWVD-TFI in enhancing radar waveform recognition, particularly in low SNR environments.

Fig. 10.

Confusion Matrices

The results observed in the first and second analyses provide evidence supporting the validity of the hypothesis proposed in this study. Specifically, the use of the SPWVD TFA technique, combined with SqueezeNet and GoogLeNet CNN trained with optimal hyperparameter values, appears to be a promising option for identifying the modulations of LPI radar signals.

Finally, the third analysis was conducted to ensure the promising performance of the ATR combinations proposed in this article compared with the related studies listed in Table 1. This comparison was feasible because all these studies evaluated their combinations using cross-validation, and the LPI radar signal instance base used in our study was generated following the same procedures and execution conditions as those adopted by the related works in their experiments.

The graph in Fig. 11 indicates the mean accuracy values obtained by our study and related works. From this figure, it is possible to note that the proposed combinations outperform all combinations from related studies across the entire tested SNR range. Notably, accuracy remains consistently high for SNR values above $0dB$. Considering the SNR range from –6 dB to 10 dB, the proposed combinations achieve an average accuracy of 97.41% with $SPWVD\!+\!SqueezeNet_{opt}$ and 98.05% with $SPWVD\!+\!GoogLeNet_{opt}$, while the combination proposed by [3] achieves 96.33%. Even at the lower end of the SNR spectrum (e.g., –18 dB), our approach achieves an accuracy of 39%, surpassing the 25% accuracy reported by [3]. This 14 p.p difference represents a 56% improvement, demonstrating robust performance even in noisy conditions. The gain achieved by the present work, especially under low SNR values, gives the ELINT, incorporated into an ESM system, a better capacity for an early reaction against threats that employ guidance technology based on LPI radars, such as, missiles. It should be noted that the radar signals transmitted by a missile equipped with an LPI radar have very low power and are immersed in noise. Therefore, the highest detection range of an ESM will be limited to the lowest SNR value at which that ESM is capable of correctly detecting an LPI signal.

Fig. 11.

Mean accuracy values of the proposed ATR and related works

Finally, given the results of the three above analyses, it is possible to observe the effectiveness of our proposed ATR combinations across different SNR levels.

6 Conclusions

In the context of automatic identification of LPI radar signals, this article presents the following contributions: (i) providing experimental evidence that employing the SPWVD TFA technique as a preprocessing step can lead to better classification model performance compared to models built using the CWD TFA technique, current state-of-the-art solution for this problem; (ii) proposing two new ATR combinations, where the pre-processing was based on SPWVD and the classifiers were based on CNN SqueezeNet and GoogLeNet. These ATR combinations outperform existing literature approaches across a wide SNR range from –18 dB to +10 dB, considering 13 distinct intrapulse modulations; (iii) providing two large image databases, each containing 403,000 samples, to be used in further experiments in this field.

As part of future work, in our quest for further evidence to validate the hypothesis proposed in this article and to enhance the state-of-the-art in LPI radar signal modulation detection, we intend to evaluate the performance of new ATR combinations and different signal types. For example, in the future, we intend to explore the use of STFT as the pre-processing TFA technique combined with different CNN models and with different signal input datasets, such as with acoustic signals.