# Deep Feature Autoextraction Method for Intrapulse Data of Radar Emitter Signal

Authors: Shiqiang Wang; Caiyun Gao; Chang Luo; Huiyong Zeng; Guimei Zheng; Qin Zhang; Juan Bai; Binfeng Zong
Journal: Mobile Information Systems
 (2021)

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## Abstract

Concerned with the problems that the extracted features are the absence of objectivity for radar emitter signal intrapulse data because of relying on priori knowledge, a novel method is proposed. First, this method gets the sparse autoencoder by adding certain restrain to the autoencoder. Second, by optimizing the sparse autoencoder and confirming the training scheme, intrapulse deep features are autoextracted with encoder layer parameters. The method extracts the eigenvectors of six typical radar emitter signals and uses them as inputs to a support vector machine classifier. The experimental results show that the method has higher accuracy in the case of large signal-to-noise ratio. The simulation verifies that the extracted features are feasible.


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## Body

## 1. Introduction

The key to sorting and identification of radar signals effectively is to extract the features that can reflect the nature of the signal. In recent years, scholars have constructed features or proposed feature extraction methods for sorting and identification signal, such as features extracted via fractional Fourier transform (FRT) [1], scale-invariant feature transform (SIFT) features [2], low probability of sorting (LPS) features [3], fusion image feature [4], compressed sensing mask (CS-mask) feature [5], feature extraction algorithm using probability moment and ApEn [6], Manhattan distance-based features [7], and other features. Design features are a good way to sort or identify radar signals with exploit human wisdom and prior knowledge.The autoencoder (AE) under the deep learning theory aims to reconstruct the original input signal at the output layer. When extracting the distributed features of the data, the AE does not require additional supervisory information, and also, it can avoid the subjectivity when designing features. The research of AE has been a hot topic of concern in recent years, and many variation and application of the autoencoder has been developed [8–12]. Hinton improved the structure of the AE prototype and obtained the deep autoencoder (DAE) [13].Also, the different deep structure and the optimization of the cost function are constructed. In [14], Bengio develops the AE depth and proposes the sparse autoencoder (SAE), which divides the hidden structure by adding sparseness constraints to the hidden layer nodes.With different sparse punitive functions [15], different numbers of nodes in hidden layers [16], and preprocessing methods [17], SAE has different performance. The use of sparse encoders can not only carry out deep feature extraction [18] but also can complete the defect detection, classification, and blind source separation work [17].With development of modern radar toward multifunctional, multipurpose, and multisystem, the design of signal waveform is increasingly complex, and the signal regularity has also been damaged severely. So, relying on experience to design features is not enough to be competent for the task of radar signal in pulse feature extraction in the current electromagnetic environment. Therefore, if we use SAE to complete this task, it is expected to break through the shackles of the conventional method by extracting the inherent features of pulse signals.By studying the SAE framework, this study proposed a method of extracting the deep pulse features of the radar signal using SAE. First, the SAE frame is analyzed and obtained by applying the specific sparse constraint. Second, by optimizing the SAE and determining the training program, the radar signal deep pulse features are extracted automatically from coding layer parameters. Finally, the validity of the extracted features is proved by experiments.


## 2. Sparse Autoencoder Mechanism

The AE is a deep learning architecture that includes coding and decoding (the architecture as shown in Figure1).Figure 1
Autoencoder frame.The coding refers to get the representation of the middle layer with the original data as the network input and to get the code of the hidden layer. The decoding means that the intermediate layer features are decoded by the hidden layer, and the original input is rebuilt via the output layer. Through the encoding and decoding mechanism, the encoder makes the reconstructed error of the reconstructed signal small. Since it reconstructs the original input at the output layer as the target and no additional supervisory information is needed, the data feature can be learned from the original data automatically.


### 2.1. Autoencoder (AE) Theory

The basic theory of the AE can be summarized as follows: supposing an unlabelled training is set tox = {x(1), x(2), x(3),…}, wherexi∈ℜn. As a neural network, the AE uses back propagation for unsupervised learning. The learning task is to make the output value equal to the original input, that means y(i) = x(i). Prototype of AE is shown in Figure 2:Figure 2
Prototype autoencoder.According to the meaning of an autoencoder, by learning knowledge, the functionhW,bx≈x would be captured. If the training set contains m samples, training the special neural network AE shown in Figure 2 using the gradient descent method, we get the loss function for a single training sample (x, y):(1)JW,b;x,y=12hW,bx−y2.The loss function of the entire network (training set) is expressed as follows:(2)JW,b=1m∑i=1mJW,b;xi,yi+λ2∑l=1nl−1∑i=1sl∑l=1sl+1Wjil2=1m∑i=1m12hW,bxi−yi2+λ2∑l=1nl−1∑i=1sl∑l=1sl+1Wjil2.In formula (2), the first item is the sum squared error term and the second item is the regularization term (also known as the weight decay term), which tends to reduce the weight and help prevent overfitting. The weight decay parameter λ dominates the relative importance of these two items. Also, the slightly overloaded symbols should be noted: formula (1) is the error cost squared for a single example, and formula (2) is the total cost function, including the weight decay item. Also, in formula (2), the symbol Wjil represents the relevance of parameters between unit j in layer l and unit i in layer l + 1. The symbol b denotes the bias, hW,bx is the encoder output and is the function of the activation value, connection parameter W, and bias term. Via the encoder formula (2), we could achieve the minimum value using W and b as the parameters. If the activation value could reconstruct its original input properly, it is assumed that it retains most of the information contained in the original data.If we simply keep the radar pulse modulation information, it is not enough to get useful features from the encoder. That is, an autoencoder (AE) with the same input and output dimensions only needs to learn a simple constant function for achieving the perfect reconstruction of the data. But, in fact, it is expected that an AE can learn a more complex nonlinear function. So, it is necessary to give the AE a certain constraint to learn a better feature representation.


### 2.2. Analysis of Sparse Autoencoder

Consider two cases. One is that if the nodes of the input layer are more than the hidden ones, then the network must learn the compressed representation of input, which means to give the hidden layer node activation value as a vector element. It needs to reconstruct the larger dimension input with the vector. The other one is that if the nodes of the hidden layer are more, even more than the input ones, then it is necessary to impose some constraints on the network so as to find the structure of the original input. Here, the hidden nodes work with sparseness constraints.Sparseness constraint is an important type of constraint that makes the learned expression more meaningful. Such an AE is called deep sparse autoencoders (DSAE), SAE in short.The implementation of SAE mainly includes three important aspects, namely, the application of specific sparseness constraints, optimization of SAE structure, and determination of the DAE training schemes. Therefore, when optimizing the deep SAE for extracting the features of the pulse data, it is necessary to add the sparse constraint, and then, the hidden layers and neurons are increased, the distribution of hidden layer nodes is adjusted, and the sharing method of weight values is changed. Through these operations, the basic framework of DAE is optimized. Finally, according to the different requirements, the appropriate cost function, optimization strategy [19], hidden layer quality factor, and parameter optimization performance index are selected to determine the training scheme of DAE.Assuming that the activation value of the hidden layer nodej is denoted as aj2x when the input is x, formula ρ^j=1/m∑i=1maj2xi indicates the average activation of the hidden layer node j [20]. The specific sparse constraint ρ^j=ρ is added, where ρ denotes the sparse parameter and usually is close to 0 (e.g., ρ = 0.05). That means, if this constraint is satisfied, the activation of the hidden layer node must be approximate to zero [21]. To reach this purpose, when optimizing the objective function, ρ^j with a large deviation from the sparse parameters ρ is needed to be punished. Usually, we use KL distances as a penalty item:(3)KLρρ^j=ρlogρρ^j+1−ρlog1−ρ1−ρ^j.According to the loss function of the autoencoder and the sparseness requirement, the SAE loss function expression is(4)JsparseW,b=JW,b+β∑j=1s2KLρρ^j.In formula (4), s2 denotes the hidden neurons numbers, and β is used as the parameter to control the proportion of the sparse penalty term [21].Next, the functionJW,b would be solved, and the minimum value would be seeked out under different W and b.For the purpose of solving the neural network, the parameters ofWjil and bil should be initialized to an initial random number close to zero. Then, the optimization algorithm similar to the bulk gradient descent method is used for the objective function, and finally, the parameter matrix of the whole network is obtained.In order to restrict all connection parametersW and bias items to a specific data space, the SAE should be pretrained.Through this step, the reduction of the quality factor randomly initialized for the hidden layer is prevented and for the purpose of facilitating to optimize these parameters of the whole neural network systematically. When pretraining the SAE, it is very important to initialize the SAE input and hidden layers in an unsupervised way and then to train each hidden layer as an autocorrelator with the greedy layer-wise pretraining algorithm to reconstruct the input data [22].


## 2.1. Autoencoder (AE) Theory

The basic theory of the AE can be summarized as follows: supposing an unlabelled training is set tox = {x(1), x(2), x(3),…}, wherexi∈ℜn. As a neural network, the AE uses back propagation for unsupervised learning. The learning task is to make the output value equal to the original input, that means y(i) = x(i). Prototype of AE is shown in Figure 2:Figure 2
Prototype autoencoder.According to the meaning of an autoencoder, by learning knowledge, the functionhW,bx≈x would be captured. If the training set contains m samples, training the special neural network AE shown in Figure 2 using the gradient descent method, we get the loss function for a single training sample (x, y):(1)JW,b;x,y=12hW,bx−y2.The loss function of the entire network (training set) is expressed as follows:(2)JW,b=1m∑i=1mJW,b;xi,yi+λ2∑l=1nl−1∑i=1sl∑l=1sl+1Wjil2=1m∑i=1m12hW,bxi−yi2+λ2∑l=1nl−1∑i=1sl∑l=1sl+1Wjil2.In formula (2), the first item is the sum squared error term and the second item is the regularization term (also known as the weight decay term), which tends to reduce the weight and help prevent overfitting. The weight decay parameter λ dominates the relative importance of these two items. Also, the slightly overloaded symbols should be noted: formula (1) is the error cost squared for a single example, and formula (2) is the total cost function, including the weight decay item. Also, in formula (2), the symbol Wjil represents the relevance of parameters between unit j in layer l and unit i in layer l + 1. The symbol b denotes the bias, hW,bx is the encoder output and is the function of the activation value, connection parameter W, and bias term. Via the encoder formula (2), we could achieve the minimum value using W and b as the parameters. If the activation value could reconstruct its original input properly, it is assumed that it retains most of the information contained in the original data.If we simply keep the radar pulse modulation information, it is not enough to get useful features from the encoder. That is, an autoencoder (AE) with the same input and output dimensions only needs to learn a simple constant function for achieving the perfect reconstruction of the data. But, in fact, it is expected that an AE can learn a more complex nonlinear function. So, it is necessary to give the AE a certain constraint to learn a better feature representation.


## 2.2. Analysis of Sparse Autoencoder

Consider two cases. One is that if the nodes of the input layer are more than the hidden ones, then the network must learn the compressed representation of input, which means to give the hidden layer node activation value as a vector element. It needs to reconstruct the larger dimension input with the vector. The other one is that if the nodes of the hidden layer are more, even more than the input ones, then it is necessary to impose some constraints on the network so as to find the structure of the original input. Here, the hidden nodes work with sparseness constraints.Sparseness constraint is an important type of constraint that makes the learned expression more meaningful. Such an AE is called deep sparse autoencoders (DSAE), SAE in short.The implementation of SAE mainly includes three important aspects, namely, the application of specific sparseness constraints, optimization of SAE structure, and determination of the DAE training schemes. Therefore, when optimizing the deep SAE for extracting the features of the pulse data, it is necessary to add the sparse constraint, and then, the hidden layers and neurons are increased, the distribution of hidden layer nodes is adjusted, and the sharing method of weight values is changed. Through these operations, the basic framework of DAE is optimized. Finally, according to the different requirements, the appropriate cost function, optimization strategy [19], hidden layer quality factor, and parameter optimization performance index are selected to determine the training scheme of DAE.Assuming that the activation value of the hidden layer nodej is denoted as aj2x when the input is x, formula ρ^j=1/m∑i=1maj2xi indicates the average activation of the hidden layer node j [20]. The specific sparse constraint ρ^j=ρ is added, where ρ denotes the sparse parameter and usually is close to 0 (e.g., ρ = 0.05). That means, if this constraint is satisfied, the activation of the hidden layer node must be approximate to zero [21]. To reach this purpose, when optimizing the objective function, ρ^j with a large deviation from the sparse parameters ρ is needed to be punished. Usually, we use KL distances as a penalty item:(3)KLρρ^j=ρlogρρ^j+1−ρlog1−ρ1−ρ^j.According to the loss function of the autoencoder and the sparseness requirement, the SAE loss function expression is(4)JsparseW,b=JW,b+β∑j=1s2KLρρ^j.In formula (4), s2 denotes the hidden neurons numbers, and β is used as the parameter to control the proportion of the sparse penalty term [21].Next, the functionJW,b would be solved, and the minimum value would be seeked out under different W and b.For the purpose of solving the neural network, the parameters ofWjil and bil should be initialized to an initial random number close to zero. Then, the optimization algorithm similar to the bulk gradient descent method is used for the objective function, and finally, the parameter matrix of the whole network is obtained.In order to restrict all connection parametersW and bias items to a specific data space, the SAE should be pretrained.Through this step, the reduction of the quality factor randomly initialized for the hidden layer is prevented and for the purpose of facilitating to optimize these parameters of the whole neural network systematically. When pretraining the SAE, it is very important to initialize the SAE input and hidden layers in an unsupervised way and then to train each hidden layer as an autocorrelator with the greedy layer-wise pretraining algorithm to reconstruct the input data [22].


## 3. Deep Feature Extraction of Radar Signal with SAE

Different radar emitter signals have different intrapulse features. The sparse autoencoder (SAE) is used for feature extraction, and there is no need to define features in advance. When the intrapulse data are input into the network, the network will automatically learn to obtain the various levels of the input radar emitter signal, that means the feature expression.As a deep learning framework, SAE builds a multilayer network layer by layer, so that the machine can learn the relationship reflected in the data automatically. SAE learns features with better generalization and expressiveness ability in this way. In other words, the SAE combines low-level features to achieve implicit data feature expression, thus forming more abstract high-level features or expressions.


### 3.1. Deep Intrapulse Feature Extraction Framework

For the radar emitter signal pulse sequence entering the reconnaissance and receiving system, because of their approximate short-term stability, it is considered that the adjacent continuous multiframe short-time samples are concatenated to obtain long-term samples, which constitute the original input of the network. Considering that it is necessary to describe the complex data of the radar signal and the training requirement of the subsequent sorting model for the extracted deep intrapulse feature, the intermediate coding layer uses the Gaussian-type node. The remaining hidden layer adopts the Bernoulli-type node. Based on optimization of SAE, the radar signal deep intrapulse feature extraction framework is shown in Figure3.Figure 3
Deep intrapulse feature extraction frame.For Gaussian-type nodes, the output is a linear combination of inputs that satisfies(5)yil=fxil=∑jwijyil−1+bil.For Bernoulli-type nodes, the output is the sigmoid map for the input that satisfies(6)yil=σxil=σ∑jwijyil−1+bil=11+exp−∑jwijyil−1−bil,where xil and yil represent the node i of the first layer for source input and output, respectively, bil represents the offset of the node, wij represents the connection weight between i and the next node, and yil−1 represents the output value of the next node.SAE uses the minimum error between the reconstructed input and the original input as the objective function and then adjusts the network parameters using the back-propogation (BP) algorithm. The objective function is written as(7)Jθ=1mx−fdecfencx,where θ denotes the network parameter, m denotes the training sample amount, x denotes the original input of the network, fenc(x) is the middle layer coding output of the network, and fdecfencx is the middle layer input coding result reconstructed by the decoding network.


### 3.2. Deep Intrapulse Features Automatic Extraction

After training the deep SAE, fine-tuning is needed for the network, and it is a necessary step to optimize the deep SAE, where the BP algorithm is used to complete this task. When fine-tuning, the input layer, output layer, and all hidden layers are taken as a whole, and then, the supervised learning method is used to adjust the pretrained neural network [23]. Then, the ownership and bias are optimized after several iterations at last. Through this process, we can complete the radar emitter signal hierarchical feature extraction. The steps of feature automatic extraction are as follows:Step 1: initialize the network by assigning weight values and thresholdsStep 2: select the class data samples randomly with the algorithm for training the SAE and then calculate the output of each layerStep 3: find the reconstruction error of each layer which is used for adjusting weight values and deviationsStep 4: determine whether the reconstruction error satisfies designing demands and repeat steps 2 and 3 if the requirements are not met until the entire SAE output meets designing demandsStep 5: use the encoding layer parameters to map the original input to get new features, that meansy=fx;θencodeIn Step 5, x denotes the original radar signal data input,θencode denotes the network parameter of the encoding part, and y denotes the intermediate layer feature vector based on deep intrapulse features extraction.By using SAE to extract the pulse features automatically, we can extract the deep interpretation factor of the dense radar signal sample. Also, we can keep the original input nonzero feature, increase the algorithm robustness, and enhance the linear separability of the pulse signal, so that the classification boundary becomes clearer, the scale of the variable can be control to a certain extent, the structure of the given input data can be changed, and the original information can be enriched. Finally, the comprehensiveness and accuracy of the information expression can be improved.


## 3.1. Deep Intrapulse Feature Extraction Framework

For the radar emitter signal pulse sequence entering the reconnaissance and receiving system, because of their approximate short-term stability, it is considered that the adjacent continuous multiframe short-time samples are concatenated to obtain long-term samples, which constitute the original input of the network. Considering that it is necessary to describe the complex data of the radar signal and the training requirement of the subsequent sorting model for the extracted deep intrapulse feature, the intermediate coding layer uses the Gaussian-type node. The remaining hidden layer adopts the Bernoulli-type node. Based on optimization of SAE, the radar signal deep intrapulse feature extraction framework is shown in Figure3.Figure 3
Deep intrapulse feature extraction frame.For Gaussian-type nodes, the output is a linear combination of inputs that satisfies(5)yil=fxil=∑jwijyil−1+bil.For Bernoulli-type nodes, the output is the sigmoid map for the input that satisfies(6)yil=σxil=σ∑jwijyil−1+bil=11+exp−∑jwijyil−1−bil,where xil and yil represent the node i of the first layer for source input and output, respectively, bil represents the offset of the node, wij represents the connection weight between i and the next node, and yil−1 represents the output value of the next node.SAE uses the minimum error between the reconstructed input and the original input as the objective function and then adjusts the network parameters using the back-propogation (BP) algorithm. The objective function is written as(7)Jθ=1mx−fdecfencx,where θ denotes the network parameter, m denotes the training sample amount, x denotes the original input of the network, fenc(x) is the middle layer coding output of the network, and fdecfencx is the middle layer input coding result reconstructed by the decoding network.


## 3.2. Deep Intrapulse Features Automatic Extraction

After training the deep SAE, fine-tuning is needed for the network, and it is a necessary step to optimize the deep SAE, where the BP algorithm is used to complete this task. When fine-tuning, the input layer, output layer, and all hidden layers are taken as a whole, and then, the supervised learning method is used to adjust the pretrained neural network [23]. Then, the ownership and bias are optimized after several iterations at last. Through this process, we can complete the radar emitter signal hierarchical feature extraction. The steps of feature automatic extraction are as follows:Step 1: initialize the network by assigning weight values and thresholdsStep 2: select the class data samples randomly with the algorithm for training the SAE and then calculate the output of each layerStep 3: find the reconstruction error of each layer which is used for adjusting weight values and deviationsStep 4: determine whether the reconstruction error satisfies designing demands and repeat steps 2 and 3 if the requirements are not met until the entire SAE output meets designing demandsStep 5: use the encoding layer parameters to map the original input to get new features, that meansy=fx;θencodeIn Step 5, x denotes the original radar signal data input,θencode denotes the network parameter of the encoding part, and y denotes the intermediate layer feature vector based on deep intrapulse features extraction.By using SAE to extract the pulse features automatically, we can extract the deep interpretation factor of the dense radar signal sample. Also, we can keep the original input nonzero feature, increase the algorithm robustness, and enhance the linear separability of the pulse signal, so that the classification boundary becomes clearer, the scale of the variable can be control to a certain extent, the structure of the given input data can be changed, and the original information can be enriched. Finally, the comprehensiveness and accuracy of the information expression can be improved.


## 4. Experimentation and Analysis

In this study, 6 typical radar emitter signals are selected for simulation experiments. The 6 signals are conventional waveform (CW), linear frequency modulation (LFM), nonlinear frequency modulation (NLFM), binary phase-shift keying (BPSK), quaternary phase-shift keying (QPSK), and frequency-shift keying (FSK) signal. For these signals, the pulse width adopts 10.8 µs, the carrier frequency adopts 0.85 GHz, the sampling frequency adopts 2400 MHz, the modulation bandwidth of LFM adopts 0.045 GHz, the NLFM adopts sinusoidal frequency modulation, BPSK adopts 31 bit pseudorandom code, QPSK adopts Huffman code, and FSK adopts the Barker code. For each radar signal, there are 120 samples for every 5 dB in the range of 0–20 dB SNR, total samples number is 600, of which 200 samples are used as the training data of the classifier, and the other 400 data are used as test data for signal identification. Before training the classifier and testing signal classification recognition effect, all samples are extracted with deep intrapulse feature extraction. In order to reflect the feature distribution of each radiation source signal, this study selects 60 datasets of feature samples with typical SNR (15 dB) of each signal from these extracted eigenvectors. A total of 300 feature samples distribution are shown Figure4.Figure 4
Deep feature scattering of emitter signal.The conclusion can be drawn via Figure4 that these three-dimensional deep features of the two signal of CW and LFM are better. The deep features of NLFM, BPSK, and QPSK are clustering well, but between different signals, the features overlap partially. As to the FSK signal, it has poor intraclass feature clustering and overlap with NLFM. Figure 4 shows that with optimized SAE, we can extract different radar signal deep features of interclass separation and intraclass aggregation. For the purpose of verifying the validity of the extracted deep feature further, the SVM is used to classify and identify the radar emitter signals denoted by the deep feature vector.The correct classification recognition rate obtained by SVM with different SNRs is given Table1. The result adopts the mean value of 20 test results, and the average result is the mean value of each signal classification result between 0 and 20 dB SNR, where ARR represents the average recognition rate.Table 1
Comparison of recognition accuracy under different SNRs.
Signal typeClassification recognition rate (%)0 dB5 dB10 dB15 dB20 dBARR (%)CW96.0498.8710010010098.98LFM88.9210010010010097.78BPSK82.3184.5289.9296.6310090.68QPSK86.0291.6195.0998.5910094.26FSK77.4385.3789.1894.1698.5588.94NLFM81.1584.6293.6298.1310091.50It can be seen from Table1 that in a special range of SNR, we can classify and identify the radar emitter signal well using the SVM classifier with the extracted deep feature as the eigenvector. Each radar emitter signal can obtain the high correct recognition rate. The signal recognition rate relates to signal complexity. For relatively simple signal forms such as CW and LFM-modulated signals, the average correct recognition rate can be up to 98.98% and 97.78%; for more complex signal forms such as FSK modulated signal, the average correct recognition rate is 88.94%, which is related to poor clustering of the deep feature and the partial overlap of features, but this result is acceptable in engineering applications. In addition, the average correct recognition result of these 6 types of emitter signals reach to 93.69%, and the recognition performance is good.


## 5. Conclusions

The key to sort and identify the radar signal efficiently is to extract the features which can reflect the signal intrinsic features. Aiming at the problem of lack of objectivity due to dependence on a priori knowledge in the extraction of radar signal features, an automatic extraction method of the deep pulse feature is proposed. This method optimizes the sparse autoencoder at the beginning and then extracts the deep pulse feature of the radar signal using the coding layer parameters automatically. The support vector machine is used to classify and identify the typical radiation source signals characterized by deep pulse features. The results show that the satisfactory results can be obtained in a large scale of signal-to-noise ratio, and the method of features extracted automatically is verified to be valid in this study.



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