Time-Frequency Analysis and Target Recognition of HRRP Based on CN-LSGAN, STFT, and CNN

Key Laboratory of Jiangxi Province for Image Processing and Pattern Recognition, School of Information Engineering, Nanchang Hangkong University, Nanchang 330063, China National Engineering Laboratory for Video Technology, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China Henan Aerospace Hydraulic Pneumatic Technology Company Limited, China Aerospace Science and Industry Corporation Limited, Zhengzhou 451191, China


Introduction
HRRP is the vector sum of all scatters electromagnetic echoes, which can reflect the geometric structure, scatters point distribution, and other characteristics of the target. Also, it is easy to be obtained and processed, so the radar target recognition of HRRP has become a research hotspot that has attracted much attention in the academic community [1][2][3][4][5][6][7][8][9][10][11]. In recent years, with the large-scale rise of deep neural networks, deep learning provides new ideas for the research of radar automatic target recognition (RATR) of HRRP. Compared to the traditional recognition method, the HRRP target recognition method of deep learning can avoid the excessive use of manual rules to extract the target features and acquire high-order features. e recognition rate of the Deep Belief Network (DBN) reached 92.8% [12]; the CNN was also applied to RATR [13,14], and the recognition rate was greatly improved; the Recurrent Neural Network (RNN) [15] and LSTM [16] had both achieved good recognition rates. However, in these actual application scenarios, HRRP acquired contain noise, which affects the amplitude of HRRP. When the signal-to-noise ratio of the data is low, the amplitude of these data differs greatly from the amplitude of the real data, and when the features are extracted, the extracted features also differ greatly from the features of the real data, thus interfering with the recognition results. So, HRRP needs to be enhanced in order to improve the signal-to-noise ratio. e GAN is a deep-learning model widely applied to data augmentation, and it was used for image blind denoising [17] and speech augmentation [18,19]. But, it has not been applied to HRRP augmentation. HRRP is denoised only by an Auto Encoder (AE) [20].
To solve the problem of radar target recognition of HRRP under low signal-to-noise ratio circumstances, we proposed a new kind of generative model, called the CN-LSGAN. e CN-LSGAN can generate data similar to the real data with low signal-to-noise data as input, thus improving the signal-to-noise ratio of the data. In addition, in order to simulate the noisy HRRP data in actual application scenarios, we added different degrees of Gaussian white noise to the real data and then used the CN-LSGAN to enhance the data to improve the SNR. en, we used the obtained data for target recognition. In order to improve the recognition effect as much as possible, time-frequency analysis is performed on the data before the recognition, and the data are converted from one-dimensional data to twodimensional data. e obtained time-frequency data contain more features. In the target recognition task, the more the data features, the better the recognition effect is generally. Finally, the obtained time-frequency data are recognized by the CNN, and the recognition result is obtained. In this paper, the following contributions have been achieved: (1) Improve the LSGAN to solve the model collapse problem (2) Improve the signal-to-noise ratio of HRRP data by the CN-LSGAN (3) Use the combination of STFT time-frequency analysis and shallow network CNN architecture to test the recognition rate of the enhanced data by CN-LSGAN e rest of this paper is organized as follows: e second part introduces the proposed method in detail, mainly including the illustration of the CN-LSGAN, STFT, and CNN; the third part chiefly focuses on the experimental results and analysis; and the fourth part concludes the paper.

Time-Frequency Analysis and Target
Recognition of HRRP Based on the CN-LSGAN, STFT, and CNN

Design of the CN-LSGAN.
e GAN is a generative model designed by Goodfellow [21]. e model consists of a generator (G) and a discriminator (D), as shown in Figure 1.
e input of D is real data or G(z), and the output of D is 1 or 0. e adversarial training is carried out between D and G, so that G(z) approaches the real data. When D cannot determine the source of the input after continuous adversarial training and iterative optimization, it is considered that G has learned the real data distribution. e loss function of the GAN is where E is the expectation of the distribution function,P data is the real data distribution, and P z is the noise distribution. e real data are the clean HRRP, and the input of G is the noisy HRRP, as is shown in Figure 2.
rough the adversarial training, the data generated by G are similar to the clean HRRP, and then, the denoise purpose is achieved. e LSGAN [22] is used instead of the GAN in this paper, and the loss function of the LSGAN is shown as follows: Compared to the GAN, the LSGAN uses least-squares loss in place of cross-entropy loss, which effectively solves the gradient disappearance problem during the model training stage. However, the LSGAN also has shortcomings; the LSGAN has a large output freedom degree and is prone to model collapse. ese problems will lead to poor quality and low diversity of generated samples. In terms of these problems, a constraint item is, respectively, added to the loss function of the LSGAN's D and G, and the two constraint items are shown as follows: rough the improvement of the LSGAN, formula (2) can be rewritten as follows: 2 Complexity In formula (5), λ 1 and λ 2 represent the adjustment weights, which adjust ξ(D) and ξ(G), respectively. ξ(D) can solve the model collapse, and ξ(G) can reduce the output freedom degree of G. e LSGAN with the abovementioned constraint items is called the CN-LSGAN.
Both G and D of the CN-LSGAN adopt the fully connected network structure, as shown in Figures 3 and 4 .

Time-Frequency Analysis Based on STFT.
Time-domain analysis of HRRP only characterizes the amplitude of the signal, which only provides limited information for feature learning. In contrast, the spectral feature is a two-dimensional (time and frequency) representation of HRRP, which includes the frequency-domain characteristics of the target and reflects the phase information. STFT is used for the

Design of the CNN.
e dimension of the time-frequency data obtained by the time-frequency analysis for HRRP is (2,64), and the CNN is designed according to the dimension. e model consists of two convolutional layers, a pooling layer, two fully connected layers, and a SoftMax classifier, and the sizes of the convolutional kernel of two convolutional layers are 3 * 3, as shown in Figure 5.

Experimental Data.
e clean HRRP are gained by the electromagnetic simulation technology, which has simulated five kinds of aircraft (Su27, F16, M2000, J8II, and J6). ere are 18,000 samples for each aircraft, so there are a total of 90,000 samples. In order to verify the effectiveness of the denoise method based on the CN-LSGAN, Gaussian white noise is added to the clean HRRP, and six kinds of noisy HRRP data with signal-to-noise ratios of 0 dB, 5 dB, 10 dB, 15 dB, 20 dB, and 25 dB are obtained, where, the clean HRRP is called dataset A, the noisy HRRP is called dataset B, and the HRRP generated by the generative model is called dataset C; these three datasets are divided into a training set and test set at a ratio of 9:1. Figure 6 shows four samples of dataset A, and Figure 7 shows four samples of dataset B with a signal-to-noise ratio of 10 dB.  Table 1. When cosine similarity is equal to 1 or the MSE is equal to 0, it means that the data samples in a certain dataset are very similar, which means that model collapse has occurred. From Table 1, it can be seen that the cosine similarity of the data generated by the GAN and LSGAN is both 1.0 and the MSE is equal to or very close to 0, which means that the data e measured data are shown between four kinds of data and the clean HRRP, as shown in Table 2.

HRRP Denoise.
When the PCC is equal to 1 or the GRA is equal to 1, the generated data are the same as the clean data, which means that the quality of the generated data and the denoise performance are great. e PCC value of the CN-LSGAN is slightly lower than the PCC value of the LSGAN, but is higher than the PCC value of the GAN. Also, the GRA value of the CN-LSGAN is much larger than that of the other two networks. From Tables 1 and 2, it can be seen that the    CN-LSGAN not only effectively solved the model collapse problem but also generated higher data quality and better denoise performance than the GAN and LSGAN.

Time-Frequency Analysis.
STFT is used for the HRRP time-frequency analysis. When the window length is large, the time resolution is poor and the frequency resolution is high. e situation is the opposite when the window length is narrow. According to the sample characteristics, the Hanning windows with window lengths of 32, 16, and 4 are used, and the obtained time-frequency data are shown in Figure 11.
Data set A performed STFT under the Hanning windows of four window lengths, and the obtained time-frequency data are recognized by the CNN; the result is shown in Figure 12.
When the window length of the window function is 4, the recognition rate of the obtained time-frequency analysis results can reach 99.8%, so the optimal STFT window function length is 4.

Target Recognition.
e enhanced data by the CN-LSGAN are transformed into two-dimensional data by STFT and then recognized by the CNN. A variety of methods are used to recognize the noisy HRRP data (dataset B), and these recognition rates are shown in Figure 13. ese recognition rates of three methods are compared to the proposed method. e first method is the one-dimensional CNN method, the second method is the LSTM method, and the third method is the STFT-CNN method, that is, STFT is combined with the two-dimensional CNN. It can be seen that the proposed method based on the CN-LSGAN, STFT, and CNN has a better recognition performance than the other three recognition methods. Also, the other three recognition methods are greatly affected by the signal-to-noise ratio, and when the Recognition rate (%) 5 1 0 1 5 2 0 2 5 0 SNR (dB) Figure 13: Recognition rate curves of four different recognition methods. e recognition rate curves showed the change trend of the recognition rate with the data signal-to-noise ratio. 8 Complexity data signal-to-noise ratio is low, these recognition rates are low. By comparing the recognition rate curve of the first method to the curve of the third method, the recognition rate of the third method is slightly lower than that of the first method when the signal-to-noise ratio is 0 dB, while under other signal-to-noise ratios, the recognition rates are higher than the those of the first method. It shows that the third method can improve the recognition performance by combining STFT with the twodimensional CNN.

Conclusions
is paper described an HRRP target recognition method based on the CN-LSGAN, STFT, and CNN, which effectively solves the recognition problem under low signal-to-noise ratio conditions. Among them, the CN-LSGAN is obtained through adding a constraint item to D and G of the LSGAN, respectively. e CN-LSGAN not only solves the problems of excessive freedom degrees of GAN output, poor quality of generated data, and insignificant denoise performance but also solves the model collapse problem of the GAN and LSGAN. By the means of STFT which analyzes the time-frequency characteristics of HRRP, the frequency-domain features and phase features of the target are introduced, and more features are helpful in the feature extraction and target recognition for the CNN. ese experimental results show that the method based on STFT and the CNN has better recognition performance compared to the method of one-dimensional CNN and the method of LSTM. e proposed target recognition method has achieved a high recognition performance based on low signal-to-noise ratio HRRP, but there are still some problems. For example, CN-LSGAN training is unstable, and it is difficult to achieve the trade-off between the time resolution and the frequency resolution by STFT. In future research, the network structure and parameter adjustment of the CN-LSGAN will be further optimized and the Deep Convolution Generative Adversarial Network (DCGAN) will be tried to be combined with the CN-LSGAN. Also, other time-frequency analysis methods such as wavelet transform will be utilized for HRRP.

Data Availability
Experimental data are provided in supplementary materials.

Conflicts of Interest
e authors state that there are no conflicts of interest in the publication of this article.