In electronic warfare systems, detecting low-probability-of-intercept (LPI) radar signals poses a significant challenge due to the signal power being lower than the noise power. Techniques using statistical or deep learning models have been proposed for detecting low-power signals. However, as these methods overlook the inherent characteristics of radar signals, they possess limitations in radar signal detection performance. We introduce a deep learning-based detection model that capitalizes on the periodicity characteristic of radar signals. The periodic autocorrelation function (PACF) is an effective time-series data analysis method to capture the pulse repetition characteristic in the intercepted signal. Our detection model extracts radar signal features from PACF and then detects the signal using a neural network employing long short-term memory to effectively process time-series features. The simulation results show that our detection model outperforms existing deep learning-based models that use conventional autocorrelation function or spectrogram as an input. Furthermore, the robust feature extraction technique allows our proposed model to achieve high performance even with a shallow neural network architecture and provides a lighter model than existing models.
Keywords: electronic warfare; low-probability-of-intercept; signal detection; deep learning; time-series analysis
With the increasing complexity of electronic warfare, the superiority of friendly forces is considerably influenced by the electronic warfare support (ES) system capabilities. These ES systems are tasked with detecting, identifying, and locating the sources of radiated emissions from adversaries, thereby recognizing threats and influencing contemporary warfare strategies [[
Over the past several decades, considerable effort has been expended in research to detect radar signals. This includes techniques using energy as a test statistic for signal detection [[
Recently, deep learning algorithms based on convolutional neural networks (CNNs) or recurrent neural networks (RNNs) have demonstrated considerable potential in signal processing. Deep learning algorithms are also being applied in radar signal processing. Moreover, deep learning-based signal detection techniques have shown superior detection performance compared to conventional methods [[
While existing deep learning-based algorithms have shown effective performance in signal detection, these methods rely on feature extraction techniques that do not consider the unique characteristics of radar signals, leading to performance limitations in radar signal detection. These existing methods often struggle to adapt to the dynamic and complex characteristics of radar signals, making it a challenge to achieve optimal detection performance. Therefore, using feature extraction techniques tailored for radar signals allows for overcoming the limitations in detection performance. This adaptation enables the extraction of more relevant and distinct features, enhancing the detection accuracy and efficiency. We propose a robust detection method by leveraging feature extraction techniques that utilize the periodicity characteristic of radar signals. Considering the pulse repetition characteristic of radar signals, we utilized the periodic autocorrelation function (PACF) to capture and analyze periodic signals and provide richer information. Additionally, our model employs radar signal detection neural networks structured with long short-term memory (LSTM), demonstrating high efficacy in processing time-series features. The primary objective of this study is to contribute to ES system advancement by introducing a robust method for LPI radar signal detection. This paper demonstrates that integrating PACF and deep learning approaches can substantially enhance the detection capabilities of ES systems compared to existing algorithms and solve the challenges raised by LPI radar signals.
The remainder of this paper is organized as follows. In Section 2, we introduce the LPI radar signals received by the ES system and present previous studies related to signal detection. Section 3 provides a detailed explanation of the proposed LPI radar signal detection method. In Section 4, we present the simulation environment and performance analysis results. In addition, we highlight the detection capabilities of our proposed method by comparing it with existing deep learning-based detection algorithms. Finally, the discussions and future research directions are presented in Section 5, and the conclusions are summarized in Section 6.
The signal detection algorithm is central in the ES system and allows a quick understanding of the enemy's location, activities, and tactics. However, inaccurate detections can result in strategic warfare setbacks, emphasizing the demand for rapid and precise signal detection algorithm development. In this section, we discuss the LPI radar signals received by the ES system and the methods for detecting these signals.
Signals intercepted by the ES system include the transmitted radar signals
(
where n is the sample index increasing every
The primary focus of this study is to determine whether a signal exists in the intercepted signal
(
Here, the null hypothesis
(
Extensive research has been conducted on generating test statistics that can effectively detect signals. Among these developed techniques, the energy detection method has been widely employed to detect the signal by employing the energy of the received signal as the test statistic [[
Recently, deep learning techniques have gained significant attention as powerful tools in signal processing. Particularly, their application to signal detection techniques has demonstrated remarkable performance improvements. Recent techniques for signal detection use short-time Fourier transform (STFT) and CNN [[
Although existing signal detection techniques have contributed significantly to the advancement of signal detection, the demand for methods that offer improved accuracy, inference speed, and generalization capabilities persists. This section introduces a novel deep learning-based signal detection method that utilizes the inherent periodicity of radar signals and leverages periodicity analysis to achieve superior signal detection performance compared to conventional methods. Furthermore, by exploiting the periodicity feature of signals for signal detection, our approach exhibits generalization capabilities, allowing accurate detection of signals not included in the training dataset. In addition, the proposed model applies preprocessing steps that compress the data size while minimizing performance degradation for rapid signal detection. The overall block diagram of the proposed model is shown in Figure 1.
As shown in Figure 1, the proposed detection technique consists of the following steps: (
In this subsection, we introduce the ACFs used to generate the data input for the neural network employed for signal detection. Because the signals intercepted by the ES system are time-series data, these received signals can be used directly as input for the neural network. However, ES systems utilize a very high sampling frequency to receive signals, resulting in many samples in the intercepted signals. Hence, using the received signals directly as input data for the neural network can increase the computational demand for signal detection. Therefore, rather than using the received data directly as neural network input, extracting the features from the received signal and using them as the input proves effective for neural network training. Therefore, we introduce ACF, traditionally used for periodicity analysis, and PACF, which effectively captures the inherent periodicity features of the intercepted radar signals, in our proposed method.
Time-series data shows that the current state's value is closely related to past and future values. Such time-series data is said to have autocorrelation. ACF represents the degree of correlation over time and assesses the correlation between signals
(
Figure 2a is an example of an LFM signal used to examine ACF. The simulated signal is a periodic signal with SNR of 0 dB with a signal acquisition time (T) of 120
In time-series data, the current state's value is closely related to past and future values. In particular, when considering radar signals received by ES systems, they exhibit a distinct pulse repetition interval, representing a periodic signal where pulses repeat. For such radar signals, ACF depicts the degree of correlation over time. However, with increasing delay, there is a corresponding decrease in correlation, as shown in Figure 2b. The signal perfectly matches itself at
We utilize a modified ACF to overcome the issue of decreasing correlation with increasing delay. The modified ACF uses the received signal repetitively when calculating the correlation. We utilize an extended signal
(
Using the extended signal, we compute PACF
(
Figure 2c shows the results of calculating PACF using simulated signals from Figure 2a. Compared to the ACF results in Figure 2b, the correlations at ±40
Using PACF, we can accurately observe the periodic characteristics of radar signals, even in weak signal environments. To efficiently train the neural network and reduce computational load, we introduce a data preprocessing step before using PACF results in the neural networks. The data preprocessing consists of three steps: a unit conversion step, negative delay value removal step, and data compression step. The unit conversion step involves converting the PACF data, which has a linear scale, into a decibel scale to increase the learning efficiency of the deep learning model. Figure 3a shows the result of converting the PACF from Figure 2c. The peaks due to correlations are observed when examining the effects in Figure 2c with a linear scale. However, by converting the results into a decibel scale as shown in Figure 3a, we can observe the peaks caused by correlations and assess the sidelobe levels generated by the signal and noise.
The second data preprocessing step involves removing data related to negative delays and eliminating unnecessary data to reduce the computational load of the neural network model. PACF used for time-series analysis has a symmetric property around zero delay, as described by the following equation:
(
Negative delay values are redundant to perform signal detection with the data corresponding to positive delays. Therefore, when inputting PACF data into the neural network model, unnecessary negative delay values can be removed. This helps reduce the computational load of the neural network. Figure 3b shows the result of retaining only the data corresponding to positive delays from the PACF data in Figure 3a.
The final step in the preprocessing stage involves compressing the data using fixed-length max pooling. Max pooling is a commonly used technique in deep learning models to reduce data size [[
In this subsection, we introduce LSTM, a type of RNN used in our proposed method to detect signals from the extracted PACF feature data. Unlike basic artificial neural networks (ANNs), RNN has a loop structure and contains hidden states within the network. The loop structure allows RNN to store information from past input data in hidden states and utilizes it for current and future data to improve the performance of neural networks. Due to these characteristics, RNN is known to be more efficient than traditional ANN in solving problems related to time-series data, such as natural language processing, video analysis, and signal classification [[
A common issue with traditional RNN structures is the lack of long-term dependencies. In other words, these networks primarily rely on recent input data, and data from a distant past have limited influence on the processing of current input data. LSTM [[
The cell state is updated from the previous cell state value
(
where
Our proposed signal detection technique employs a fully-connected network to determine the presence of a signal based on the extracted feature vectors from LSTM. The fully-connected network consists of an input and output layer. The input layer is composed of input nodes, each with a length equal to the number of hidden units in the LSTM. The output layer has two output nodes to calculate the probabilities associated with the presence or absence of a signal. Subsequently, the detection model applies the softmax function [[
For training the detection neural network, we generated a training dataset consisting of three modulation schemes with various modulation parameters for each scheme. The parameters for the training dataset are summarized in Table 2.
The generated training dataset consists of 60,000 signals, which includes 30,000 signals with additive white Gaussian noise and 30,000 white Gaussian noise signals used for generating noisy signals. The 60,000 signals for the training dataset are transformed into input data using ACFs and the data preprocessing steps introduced in Section 3. Within the preprocessing steps, the ACFs generated from the signals are compressed to a length of 256 through fixed-length max pooling. The number of hidden units in the LSTM layer of the proposed detection model is 32. During the neural network training using the generated training dataset, the Adam optimization algorithm [[
We analyze the comparative performance between the proposed detection model and existing signal detection methods. Within the realm of non-neural network detection methods, we considered an entropy detector, which uses the entropy of the received signal as a test statistic [[
The test dataset used for performance comparison was constructed by generating 500 signals for each modulation scheme at a single SNR. The modulation parameters used to generate test signals were the same as those used in the training dataset, as shown in Table 2, with a fixed duty cycle of 50%. Figure 5 shows the detection probabilities of a detector with a false alarm probability of 0.1 for different SNRs across various pulse widths. All detectors demonstrated similar detection performance across all modulation schemes, and the results shown in Figure 5 represent the average detection probabilities for simulated signals with three different modulation schemes.
The detection performance analysis reveals that the proposed technique exhibits superior signal detection performance. Among the techniques considered, the STFT-CNN model exhibited the best performance, followed by the ACF-1DCNN model and non-neural network detection methods. Moreover, we confirmed that our proposed technique outperforms existing deep learning-based algorithms in weak signal detection performance. In the comparative analysis between the STFT-CNN, distinguished for its superior detection capability among existing methods, and our proposed model, it was found that the performance deviation was insubstantial at a pulse width of 10
We proposed a deep learning-based radar signal detection model that utilizes LSTM and PACF for periodicity analysis. Our model employed PACF as a time-series data analysis method, which provides rich information such as periodicity and sidelobe levels. The detection model used an LSTM to detect signals from feature data converted with various preprocessing steps applied to the computation results of PACF. Performance analysis using various modulation schemes revealed that the proposed model has remarkable detection capabilities. The analysis results demonstrated that the proposed detection method outperforms existing deep learning-based models. Furthermore, the proposed technique exhibited the best detection performance and achieved the lightest model compared to existing deep learning-based models. These results could be attributed to the powerful time-series data analysis technique employing PACF and preprocessing methods. Our proposed model achieved high performance even with considerably fewer neural network layers by extracting distinct and feature-rich input data with reduced size from intercepted signals. Therefore, the proposed method is a promising candidate for practical detection algorithms in ES systems requiring accurate and fast signal detection techniques. However, the proposed method presents a challenge for real-time implementation as it requires a sufficient signal acquisition time. Therefore, in the future, we plan to research on detection model that can be implemented in real-time using time-series analysis with PACF.
We introduced a model for detecting radar signals that exploit deep learning techniques and PACF for periodicity analysis. The model outperformed existing deep learning models in terms of detection probability and computational complexity. Therefore, we expect our proposed detection method to be effectively applied to ES systems. We plan to further research and develop a real-time detection model using time-series analysis with PACF.
DIAGRAM: Figure 1 Block diagram of the proposed signal detection method.
Graph: Figure 2 Examples of simulated radar signals and corresponding computed autocorrelation functions (ACFs). (a) Simulated LFM radar signal, (b) Computed ACF, (c) Computed PACF.
Graph: Figure 3 Results of the preprocessing steps. (a) decibel scale conversion process results, (b) negative delay removal process results, (c) fixed-length max pooling results.
Graph: Figure 4 Architecture of the LSTM network.
Graph: Figure 5 Detection probabilities of the detectors at various SNRs. Pulse width of (a) 10 μ s, (b) 20 μ s, and (c) 30 μ s.
Table 1 Frequency and phase modulation functions for three modulation schemes.
Modulation Scheme (Hz) (rad) LFM constant Costas code constant Barker code constant 0 or
Table 2 Parameters for training dataset generation.
Modulation Scheme Parameter Value Sampling frequency 50 MHz SNR dB All Pulse width s Duty cycle Signal acquisition time LFM Center frequency MHz Modulation bandwidth MHz Fundamental frequency MHz Costas code Number of frequency hops Frequency spacing MHz Center frequency MHz Barker code Barker code length Cycles per phase code
Table 3 Hyperparameter used for training proposed signal detection model.
Hyperparameter Value Initial learn rate Learning rate reduction 3% per epoch Epochs 30 Mini batch size 64 Input data length 256 Number of hidden units 32
Conceptualization, D.-H.P.; methodology, D.-H.P.; software, D.-H.P.; validation, D.-H.P., M.-W.J. and D.-M.S.; formal analysis, D.-H.P.; investigation, D.-H.P., M.-W.J. and D.-M.S.; resources, D.-H.P.; data curation, D.-H.P.; writing—original draft preparation, D.-H.P.; writing—review and editing, D.-H.P., M.-W.J. and H.-N.K.; visualization, D.-H.P.; supervision, H.-N.K.; project administration, H.-N.K. All authors have read and agreed to the published version of the manuscript.
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The authors declare no conflict of interest.
By Do-Hyun Park; Min-Wook Jeon; Da-Min Shin and Hyoung-Nam Kim
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