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RETRACTED ARTICLE: Recognition method of radar intra-pulse modulation type based on signal square spectrum bandwidth ratio

This article was retracted on 12 September 2022

This article has been updated


The twenty-first century is the era of electronic warfare and information warfare. The focus is of the battle between all parties. CEEMD can link the time domain and frequency domain, describe the two-dimensional time–frequency characteristics of the signal, and draw the time–frequency diagram of the signal, so as to reduce the noise signal and improve the signal-to-noise ratio of the signal. The purpose of this paper was to study how to adjust the signal square spectrum bandwidth ratio in the subject of identifying the intra-pulse modulation of radar, so as to solve the problem of identifying the type of radar intra-pulse modulation. The experimental results in this paper show that the decomposition result of EEMD is incomplete and the signal reconstruction error is larger. Compared with the previous two methods, not only the CEEMD method can effectively suppress modal aliasing, but also the decomposition result is complete; the signal reconstruction error is very small, and the decomposition results close to ideal value. The interleaving filter with a bandwidth ratio of 1:2 can divide the 100 GHz channel spacing into asymmetric output spectra with bandwidths greater than 60 GHz and 30 GHz, which effectively improves the current mix of 10 Gb/s and 40 Gb/s The bandwidth utilization of the system illustrates the success of the simulation experiment.

1 Introduction

With the rapid development of electronic technology and radar technology, more and more new advanced radar systems are making progress. The traditional five-parameter analysis can no longer meet the needs of modern electronic identification [1]. It is necessary to extract some more stable and surprise features in the pulse [2]. To meet the needs of investigation and analysis, the purpose of intra-pulse analysis is to evaluate the intra-pulse modulation parameters and determine the intra-pulse modulation method. The selection of configuration methods and configuration parameters is closely related to the operation and purpose of the radar. Therefore, its configuration parameters determine the interference radar signal. Effective evaluation can evaluate radar accurately and efficiently, which is very important. The electromagnetic environment of modern electronic battlefields is becoming increasingly complex. Electronic identification equipment is very dense. The electromagnetic signal is complex and dense, so that the signal blocked by the receiver is often the overlapping or overlapping mixed signal of many different radar sources. For estimation of configuration parameters, Multi-component radar signals are generally difficult to distinguish directly from only the time domain or the frequency domain. The time–frequency analysis method is mainly used to derive time–frequency characteristics, realize separation and parameter estimation. How to effectively separate and extract the parameters of multi-component radar signals is a difficult problem worth studying.

With the continuous development of modern communication technology, people pay more and more attention to the information security of the communication system [3]. As the fastest growing wireless communication system in recent years, because its signal is transmitted through an open channel, it is impossible to shield the physical signal like a wired communication system, so that the signal is transmitted in a closed state to prevent the signal. The middle is illegal. Intercepting and decrypting, so leaks are commonplace, and cybercrimes are also emerging in endlessly. The popularity of smartphones puts forward higher requirements for the security of wireless communication systems. PwC's global information security research report shows that global industry and market managers are steadily increasing their investment in information security. Research data shows that the losses caused by wireless security issues continue to increase, which makes more and more people fully aware of the importance of wireless security. Therefore, it is particularly important to add an information encryption module to the communication system to protect the information, especially how to prevent the information from leaking into the wireless channel.

At the beginning of the twentieth century, Chen T discovered chaos when studying the three-body problem and believed that the solutions of deterministic nonlinear differential equations were unpredictable. However, his research did not contribute to signal science, which has limitations of the times [4]. Experts in the field of machine learning such as Fan X introduced a deep neural network model inspired by the learning model of the human brain on Science in 2006, and pointed out that the multi-layer network structure has more excellent feature learning capabilities. And the difficulty of training can be overcome by layer-by-layer initialization', but his research did not propose how the specific algorithm should be simplified and modified [5]. Peng et al. did a systematic research on the recognition of the modulation type of radar signals, but their research was unable to extract the instantaneous autocorrelation characteristics of the signal from the instantaneous autocorrelation function, so it is not suitable for the current environment [6].

The innovations of this article are: (1) Radar intra-pulse modulation type identification method designed in this article can adjust the bandwidth ratio to meet the needs of different data traffic transmission. (2) This article uses time–frequency analysis to express the law of signal spectrum changes over time, effectively processing a large number of non-stationary signals involved in this article. (3) This paper designs a comparison between different methods, and uses a comparative experiment method to intuitively illustrate the advantages of the method designed in this paper from the aspects of noise reduction, output, and flow.

2 Recognition method of radar intra-pulse modulation type based on signal square spectrum bandwidth ratio

2.1 Introduction to chaotic communication system

With the increase in the density of radar signals in space and the increase in modulation types, the complexity of the modern electromagnetic environment is also increasing. As an emerging topic in the field of information security, chaotic communication systems have received extensive attention in the past 30 years [7]. The wide frequency spectrum and random-like characteristics of chaotic signals are important factors that can be used for information encryption in the communication field [8]. However, due to the late development of the chaotic communication system, the theoretical research is not yet mature. The existing research results mostly use the pseudo-random characteristics of the chaotic sequence to encrypt the baseband signal [9]. The chaotic concealment model in chaotic modulation based on analog signals is to additively modulate the information to be transmitted with the chaotic signal to hide the target signal [10]. The chaotic signal in the chaotic concealment model is not a carrier signal, but as a carrier to make the transmitted signal float on it for concealment [11]. Because the existing chaotic signal has a wide spectrum and the power spectrum is not concentrated, the chaotic mask can only transmit signals with less energy [12]. Since the transmitted signal is generally more regular and the power spectrum distribution is concentrated, if a signal with a larger energy is transmitted, it is easier to have a convex peak on the chaotic signal carrier spectrum, and it is easy to be found to be intercepted and reduce the confidentiality [13]. Therefore, when designing a chaotic signal, it is necessary to consider its power spectrum distribution characteristics according to different communication systems [14]. Due to the unsatisfactory distribution of the chaotic power spectrum, it is impossible to use the chaotic signal as the communication carrier to realize the wireless transmission of the signal, which is also an important factor restricting the application of the chaotic signal in the wireless communication field [15]. The chaotic-based broadband communication provides a brand-new method, which can play an important role in solving many contradictions and defects of the existing communication system [16].

The chaotic signal is the basis of the chaotic communication system, and its characteristics, especially the power spectral density distribution, will affect the performance of the system [17]. Because different chaotic communication systems have different requirements for their signal power spectral density distribution, for example, chaotic signals in a chaotic spread spectrum communication system need to have a wider spectrum distribution, which is just the opposite of a chaotic spread spectrum communication system [18], chaotic microwave communication The medium chaotic signal needs to have a relatively narrow spectrum distribution, while the chaotic signal in the chaotic frequency modulation radar needs to have a smooth power spectrum distribution. Therefore, the influencing factors of the chaotic signal power spectrum distribution are studied and the corresponding method of restricting the signal power spectrum distribution is found [19], it can provide chaotic signals with specific power spectrum distribution, and solve the needs of different chaotic signal characteristics of different chaotic communication systems [20]. Especially in modern wireless electronic countermeasures, chaotic signal spectrum can be used as protection [21], which can effectively prevent information from being tracked or intercepted by the enemy, which is of great significance for improving the confidentiality of chaotic communication systems [22]. The carrier signal used by the radio frequency stage in the wireless communication system is mostly a sinusoidal signal, and a third party can easily track the signal and intercept information [23]. The introduction of chaotic carrier signals in the radio frequency range for security protection is of great significance to wireless communication systems using open channels [24]. At present, in the design process of chaotic communication systems, it is very difficult to find chaotic signals with required, especially it is difficult to find signals with specific frequency spectrum required in current wireless communication. Therefore, designers often need to check when designing a chaotic communication system. A large number of existing chaotic signal models are used to select chaotic signals that conform to the characteristics of the system, which greatly increases the workload and brings unnecessary difficulties to the system design [25]. In the existing chaotic model, there may not be a chaotic signal that matches the chaotic system designed by the designer. At this time, the designer needs to spend a lot of time and energy to design the chaotic signal with a specific power spectrum distribution. Therefore, the influencing factors of the power spectrum distribution of the chaotic signal are studied and a method to restrict the power spectrum distribution of the signal is designed, which can provide different chaotic signals with different requirements for different chaotic communication systems. Enrich the types of chaotic signals and reduce the chaotic communication system Design difficulty. The research results of this subject can be applied to communication systems with high security requirements. As a wireless chaotic communication carrier, it can effectively protect data, reduce the probability of being intercepted and cracked, and promote the development of chaotic secure communication systems in practicing. [26].

2.2 Basis of spatial spectrum estimation

In the field of signal processing, it mainly includes four stages of sampling, compression, coding transmission, and decompression [27]. First, the received signal is sampled, then the received data is transformed, compressed and encoded, and then the encoded signal is received, and finally the signal is post-processed, which can be understood as the inverse process. This encoding and decoding method is restricted by the Nyquist theorem. In order to improve the technical indicators, the sampling rate should be greatly increased when using traditional sampling methods. This will inevitably bring a greater burden to the performance and functions of the data processing system and the real-time system. It is also difficult to reach a high technical level [28]. The generally adopted process is shown in Fig. 1.

Fig. 1
figure 1

Process flowchart

In the field of signal processing, if there is a signal itself or most of the elements are zero and some elements are not zero in a given change area, then this kind of signal is called a sparse signal. For example, audio and video signals become sparse signals after waveform transformation, and the impact noise in the communication system is also sparse signals. Taking into account the different forms of expression from general signals, it can provide a new way of thinking for sampling and coding, making information conversion faster and more efficient.

Unlike the procedure described in Fig. 1, compression detection, which has developed rapidly in recent years, can perform both signal sampling and signal compression. It is sparse to the signal itself or after the conversion process. On the basis of matrix operations, it first uses a transformation basis matrix to represent the original signal as a dilution signal in another domain, and then selects an observation matrix that has nothing to do with the transformation basis matrix. Perform theoretical synchronization and compression to reduce the dimension of the original signal after the operation to the ideal level, and finally solve the constraint optimization problem, and complete the signal reconstruction and parameter extraction in the sense of probability. The main body of compressed sensation theory includes the following three steps, and the main processing flow is shown in the following Fig. 2.

Fig. 2
figure 2

Compressed sensing theory process flow

2.3 Frequency method

Under normal circumstances, the time domain analysis of the signal can only reflect the waveform characteristics of the signal, and the frequency domain analysis can only reflect the frequency spectrum and energy distribution characteristics of the signal. Neither of these two methods can reflect the characteristics of the signal frequency components changing over time; the time–frequency analysis can be used to express the law of the signal spectrum changing with time, and finally establish a distribution, which can reflect the form of the signal energy or intensity in the two-dimensional space of time–frequency. Time–frequency analysis the method is a very effective way to analyze and process non-stationary signals.

Fourier Transform (Fourier Transform, FT) is the most common classical method for processing and analyzing stationary signals. As shown in formula 1:

$$P\left( {t,f} \right) = aP_{1} \left( {t,f} \right) + bP_{2} \left( {t,f} \right)$$

Time domain describes the relationship of mathematical functions or physical signals to time. To study the characteristics of a signal at a certain time t in the time domain of a signal to be analyzed, the STFT change of the signal can be defined as:

$${\text{STFT}}\left( {t,f} \right) = \int_{ - \varpi }^{ + \infty } {x\left( t \right)\omega \left( {\tau - t} \right)\exp \left( { - j2\pi f\tau } \right)} \,{\text{d}}\tau$$

The continuous WT in the time domain is defined as:

$${\text{CWT}}\left( {a,b} \right) = \frac{1}{\sqrt a }\int_{ - \infty }^{ + \infty } {h\left( t \right)w} \left( {\frac{t - a}{a}} \right)\,{\text{d}}t$$

The S transformation of the function h(t) can be expressed as:

$${\text{ST}}\left( {t,f} \right) = \int_{ - \infty }^{ + \infty } {h\left( \tau \right)w\left( {\tau - t} \right)\exp \left( { - j2\pi f\tau } \right)} \,{\text{d}}\tau$$


$$w\left( t \right) = \frac{1}{{\sigma \sqrt {2\pi } }}\exp \left( { - \frac{{t^{2} }}{{2\sigma^{2} }}} \right),\;\sigma \left( f \right) = \frac{1}{\left| f \right|}$$

And the window function needs to meet:

$$\int_{ - \infty }^{ + \infty } {w\left( {\tau - t,f} \right)} \,{\text{d}}t = 1$$

ST meets:

$$\int_{ - \infty }^{ + \infty } {{\text{ST}}\left( {\tau ,f} \right)} \,{\text{d}}\tau = H\left( f \right)$$


$$h\left( t \right) = \int_{ - \infty }^{ + \infty } {\left\{ {\int_{ - \infty }^{ + \infty } {{\text{ST}}\left( {\tau ,f} \right){\text{d}}\tau = H\left( f \right)} } \right\}} \,\exp \left( { - j2\pi ft} \right)\,{\text{d}}f$$

Considering at the time-shifting level, there are:

$$h\left( {t - r} \right) \Leftrightarrow {\text{ST}}\left( {\tau - r,f} \right)\exp \left( { - j2\pi fr} \right)$$

Due to the lossless reversibility, using the generalized window function to replace the Gaussian window in the ST definition, we get:

$$S\left( {\tau ,f,p} \right) = \int_{ - \infty }^{ + \infty } {h\left( t \right)w\left( {\tau - t,f,p} \right)} \exp \left( { - j2\pi fr} \right)$$

In the nonlinear time–frequency transformation, there are:

$$p\left( {t,f} \right) = \left| a \right|^{2} P_{1} \left( {t,f} \right) + \left| b \right|^{2} P_{2} \left( {t,f} \right) + 2R\left[ {abP_{12} \left( {t,f} \right)} \right]$$

The WVD of the signal x(t) can be expressed as:

$${\text{WVD}}\left( {t,f} \right) = \int_{ - \infty }^{ + \infty } {h\left( {t + \frac{\tau }{2}} \right)h^{*} \left( {t + \frac{\tau }{2}} \right)\exp \left( { - j2\pi f\tau } \right)} \,{\text{d}}\tau$$

Because there is no window function in the formula, the problem of mutual restriction of time and frequency like in STFT or WT will not arise.

In case:

$$h\left( t \right) = h_{1} \left( t \right) + h_{1} \left( t \right)$$

Then there are:

$${\text{WVD}}\left( {t,f} \right) = {\text{WVD}}_{1} \left( {t,f} \right) + {\text{WVD}}_{2} \left( {t,f} \right) + 2{\text{Re}} \left\{ {{\text{WVD}}_{12} \left( {t,f} \right)} \right\}$$
$${\text{WVD}}_{{{12}}} \left( {t,f} \right) = \int_{ - \infty }^{ + \infty } {h_{1} \left( {t + \frac{\tau }{2}} \right)h_{2}^{*} \left( {t + \frac{\tau }{2}} \right)\exp \left( { - j2\pi f\tau } \right)} \,{\text{d}}\tau$$

In summary, the algorithm part has been introduced, and the experiment is ready to begin.

3 Methods/experimental section

3.1 Suppression effect of CEEMD decomposition on modal aliasing caused by noise

The experimental object is EEMD to suppress the influence of modal aliasing caused by noise. Analyze the effect of EEMD decomposition on the suppression of modal aliasing caused by noise, without considering the modal aliasing caused by intermittent signals, only analyze the effect of EEMD in suppressing modal aliasing caused by noise, and use multi-component radar without intermittent signals The signal is simulated and analyzed, and the simulation conditions are set as follows: SNR = 10 dB, the multi-component radar signal is decomposed by EMD and EEMD respectively, and the waveform diagram of the radar signal after down-conversion is shown in Fig. 3.

Fig. 3
figure 3

Radar signal grpdelay

The time domain waveform diagram of the radar signal after down-conversion is shown in Fig. 4.

Fig. 4
figure 4

Radar signal time domain waveform

MATLAB is a commercial mathematics software produced by MathWorks in the United States. It is used in data analysis, wireless communication, deep learning, image processing and computer vision, signal processing, quantitative finance and risk management, robotics, control systems and other fields. Comparing the simulation of the effect of EEMD in suppressing modal aliasing caused by noise, IMF1 to IMF3 represent single-component signals, single-component radar signals are decomposed into IMF4, and single-component radar signals are decomposed into IMF5 and IMF6, and three single-component radars are decomposed into IMF5 and IMF6. The signals are basically separated, and there is no phenomenon that the components belonging to different single-component signals are mixed in the same mode. Therefore, CEEMD effectively separates each IMF. The mode aliasing caused by noise is the same as EEMD. There is a good suppression effect. The purpose of Fig. 5 is to show that the mode aliasing caused by noise is compared with EEMD. Figure 5 shows the reconstruction error of EEMD.

Fig. 5
figure 5

EEMD method

Figure 6 is the reconstruction error of the CEEMD method.

Fig. 6
figure 6

CEEMD method

It can be seen that the decomposition result of EEMD is incomplete and the signal reconstruction error is larger; compared with the previous two methods, the CEEMD method not only can effectively suppress modal aliasing, but also the decomposition result is complete, the signal reconstruction error is very small, and the decomposition result is close to ideal value. Therefore, the CEEMD method can be selected for experiment in this article.

3.2 Introduction to the basic configuration of radar signals and performance analysis of algorithms

Pulse repetition frequency (PRF) is one of the most important characteristic parameters of pulsed radar signals. Pulse repetition frequency jitter can be considered as a kind of random jitter. It is an electronic protection technology used to counter synchronous jammers. With the development of radar technology, signal parameters are changeable and there are phenomena such as serious signal overlap. The radar signal has the characteristics of large instantaneous bandwidth, complex modulation method, and flexible frequency, which make it difficult to monitor the signal. The following are the basic configuration and technical parameters of Radarsat-2 as the simulation diagram of this article, as shown in Table 1.

Table 1 Radarsat-2 spaceborne SAR technical parameters

Introduce the technical parameters of F-SAR as shown in Table 2.

Table 2 F-SAR technical parameters

The classification performance of the ensemble learning methods used by the two satellites is compared with the results obtained by SVM classification. The values in the columns of the different methods indicate the classification accuracy of different data sets. The experimental results are shown in Table 3.

Table 3 Algorithm performance comparison based on different data sets

For the listed standard data sets, the classification accuracy of the integrated deep learning method in this chapter is generally higher than that of the general SVM classification method. This is because the ensemble learning combines the results of multiple different deep model learning to obtain a better classification effect. dB is a ratio, a numerical value, and a pure counting method without any unit indication. It has different names in different fields, so it also represents different practical meanings.

The simulation results made by the MN method are shown in Table 4.

Table 4 MN method detection rate simulation effect

The simulation results made by the frequency domain MN method are shown in Table 5.

Table 5 Frequency domain MN method detection rate simulation results

When the signal-to-noise ratio is higher than − 4 dB, the MN method can detect the pulse 100%; when the signal-to-noise ratio is − 4, − 5 dB, due to the increase of noise power, part of the noise is mistakenly detected as a pulse; the signal-to-noise ratio is at − 6 dB, the noise power is too large and the amplitude exceeds the threshold. Therefore, each frame is judged to have a signal, and the entire signal sequence is considered to be a pulse, which can be regarded as a false alarm all the time. When the signal-to-noise ratio is higher than − 10 dB, the frequency domain MN method can detect the pulse 100%; when the signal-to-noise ratio is − 10, − 11 dB, due to the increase of noise power, a small part of the noise is also mistakenly detected as a pulse. But it can still reach a detection rate of more than 60%; when the signal-to-noise ratio is lowered, the performance has been severely deteriorated and can no longer be used. However, even when the signal-to-noise ratio is as low as − 13 dB, there are no false alarms. It can be seen that the frequency domain MN method has a significant improvement in anti-noise performance compared to the MN method.

3.3 Related experimental content and analysis of square spectrum bandwidth ratio

According to the simulation results of the MZI and microring hybrid structure interleaving filter in the previous analysis and demonstration, it can be known that the power distribution ratio of the three TMIs has a great influence on the output spectrum, so it is necessary to discuss its influence in detail. Discuss the change trend of the output spectrum while fixing the power distribution ratio of two TMIs and changing the power distribution ratio of one of the TMIs. Table 6 shows the simulation results of different TMI splitting ratios.

Table 6 Simulation results of different TMI splitting ratios

The interleaving filter with a bandwidth ratio of 1:2 can divide the 100 GHz channel spacing into asymmetric output spectra with bandwidths greater than 60 GHz and 30 GHz, which effectively improves the current mix of 10 Gb/s and 40 Gb/s The bandwidth utilization of the system. However, with the explosive growth of signal transmission, the signal has also changed from 3 and 4G to 5G, because the interleaving filter with adjustable bandwidth ratio has also become a key part of the research. Table 7 introduces the design parameters of the power allocation ratio under three bandwidth ratios.

Table 7 Design parameters of three TMI power allocation ratios under different bandwidth ratios

4 Results and discussion section

4.1 Signal ratio

In this paper, for 5 single radar signals and 6 mixed radar signals with a signal-to-noise ratio of -5-10 dB, the PCA method is used for preprocessing and noise reduction. The noise reduction effects at different reconstruction levels of the signal are shown below. Table 8 shows the degree of improvement of a single signal.

Table 8 The signal-to-noise ratio of a single signal is improved after PCA noise reduction

Table 9 is the signal-to-noise ratio of the mixed signal.

Table 9 The signal-to-noise ratio of the mixed signal is improved after PCA noise reduction

The data in the table shows that whether it is a radar receiving signal containing 5 single signals or 6 mixed signals, the signal-to-noise ratio improved by the PCA method is different when the signal reduction degree is different. When the signal reconstruction degree is 90%, the signal-to-noise ratio is different. The noise ratio has improved the most. The reason is that the noise component occupies a certain proportion in the radar received signal. When the signal reconstruction degree is high, the noise content discarded by the PCA transformation is less, and the signal-to-noise ratio of the radar received signal is limited. When the degree is low, in addition to the noise, the components discarded by the PCA transform also include a large number of radar modulated signals, so the signal-to-noise ratio is increased instead of decreasing.

4.2 Multi-rate spectrum sensing technology

Although the wideband spectrum sensing method based on compressed sensing reduces the sampling rate, the computational complexity of the compressed sampling algorithm is relatively high, and the sensing method based on compressed sampling has high requirements for synchronization and is difficult to implement, so it is not practical. To solve this problem, some researchers have proposed a multi-rate broadband spectrum sensing method based on under-sampling. This method uses multiple signal sampling branches to under-sample the signal. The sampling rate of each sampling branch is different. The under-sampled data is processed accordingly, and then the spectrum of the signal is restored according to the processing results of each branch, and finally the occupancy of the signal is detected according to the restored spectrum. This method reduces the synchronization requirements of the spectrum sensing method based on compressed sensing, but it still needs to use compressed sensing to reconstruct the spectrum, and the computational complexity is relatively high. Most of the existing spectrum is sensing algorithms are proposed for stationary signals. If these algorithms are used to perform spectrum sensing on non-stationary signals, the sensing performance is not ideal. However, non-stationary signals such as chirp signals and frequency hopping signals are widely used in wireless communications. Therefore, it is necessary to study the narrow-band spectrum sensing methods of non-stationary signals.

4.3 Radar detection system

The radar detection system faces a complex electromagnetic environment and various threats. In the past 10 years, the environmental signal density has increased by an order of magnitude. New radar systems dominate, and anti-stealth and low-probability surveillance, broadband, and high bandwidth have become the development trend of radar design. The overlap of radar waveforms in time, space, and frequency is increasing. How to find useful information in the broadband complex electromagnetic environment has become a major challenge for radar detection systems. At the same time, another challenge facing the radar detection system is how to improve the real-time processing capability of the system. The modern battlefield is changing rapidly, and the reaction time on the battlefield is crucial. Some applications of military radar systems are armed precision systems, once the target enters the strike range, it can quickly capture the target and enter the working mode. The response speed of the recognition system is directly related to its own survival.

The typical description of traditional radar signals is mainly based on five important characteristics: pulse time of arrival (TOA), pulse width (PW), pulse angle of arrival (DOA), carrier frequency (RF) and pulse power (P). In the complex and changeable signal environment, the method of sorting and identifying the common features of multiple parameters has attracted widespread attention. In addition to the five traditional parameters mentioned above, new feature parameters have attracted more and more attention, and signal intrusion features are one of them. The intra-pulse characteristics of radar signals, including pulse rise time, fall time, and modulation type, have been determined as the fingerprint characteristics of the signal. Radar pulse modulation analysis is the basic technology of modern radar response information processing. Through pulse modulation type analysis, you can observe the signal characteristics of amplitude modulation, frequency modulation, and modulation included in the signal. The changing law of the configuration mode provides a brand-new method for further classifying and identifying radar signals and broadening the scope of information analysis. Due to the particularity and sensitivity of research in this field, many pulse modulation analysis algorithms only introduce the basic principles, and seldom introduce the application background and engineering. Therefore, it is necessary to study the mechanics algorithm for the analysis of the radar modulation type within the pulse, which is of great significance to the actual realization of the electromagnetic identification system.

5 Conclusions

The experimental results show that the proposed method of radar intra-pulse modulation type recognition based on the signal square spectrum bandwidth ratio is better than traditional methods, the bandwidth ratio is adjustable, and the noise reduction processing accuracy is also very good. Through the research of this article, this topic has been successfully completed. CEEMD effectively separates each IMF. The mode aliasing caused by noise is the same as EEMD. There is a good suppression effect. This paper uses comparative experiment method and time–frequency analysis method to design a comparative experiment between CEEMD and EEMD. The experimental results show that the decomposition result of EEMD is incomplete and the signal reconstruction error is larger. Compared with the previous two methods, the CEEMD method not only can effectively suppress the modal is aliased, and the decomposition result is complete, the signal reconstruction error is very small, and the decomposition result is close to the ideal value. The interleaving filter with a bandwidth ratio of 1:2 can divide the 100 GHz channel spacing into asymmetric output spectra with bandwidths greater than 60 GHz and 30 GHz, which effectively improves the current mix of 10 Gb/s and 40 Gb/s The bandwidth utilization of the system. The shortcomings of this article are: (1) Designed bandwidth ratio adjustable CEEMD method cannot input any bandwidth ratio. This part of the content can be focused on in future research. (2) The experiments designed in this paper are all simulation experiments using matlab, which are more or less fundamentally different from actual radar monitoring. In the future, experiments with lower experimental accuracy and more scientific and effective can be designed.

Availability of data and materials

Data sharing does not apply to this article because no data set was generated or analyzed during the current research period.

Change history



Fourier transform


Empirical mode decomposition


Ensemble empirical mode decomposition


Complete ensemble empirical mode decomposition


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This work was supported by Liaoning Provincial Education Department's 2019 Scientific Research Funding Project (QL201911).

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Authors and Affiliations



DL, ZX: Writing—editing. LG, LZ: data analysis. All authors read and approved the final manuscript.

Authors’ Information

Dongmei Li lecturer in aircraft and aviation engineering, doctor of Chinese Academy of Sciences. She has been engaged in the research of airborne radar signal analysis and processing for more than ten years, participated in the development and improvement of active airborne radar reconnaissance equipment, published many professional articles on radar signal processing and analysis, and has rich practical experience.

Zhiyuan Xu was born in Liaoning,Changtu. P.R. China, in 1981. He received the Ph.D. from Dalian Maritime University, P.R. China. Now, he works in School of Navigation and Naval Architecture, Dalian Ocean University. His research interest include computational intelligence, maritime communication and big data analysis.

Lei Gu associate professor, major in Electronic Science and Technology, Ph.D., graduated from Changchun University of technology. It has won one third prize of provincial natural science academic achievements. 15 academic papers have been published in domestic and foreign journals, 3 of which are SCI searches and one monograph has been published. Participated in 2 provincial scientific research projects.

Lanxiang Zhu doctor of engineering, master tutor, founder of the fourth generation radar. It has won 1 second prize and 1 third prize of Jilin Natural Science Academic Achievement Award, 6 national invention patents, 2 monographs and 24 papers, including 1 SCI retrieval paper, 18 EI retrieval papers and 5 core journal papers. Participated in and completed 2 NSFC projects and more than 20 provincial scientific research projects.

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Correspondence to Zhiyuan Xu.

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Li, D., Xu, Z., Gu, L. et al. RETRACTED ARTICLE: Recognition method of radar intra-pulse modulation type based on signal square spectrum bandwidth ratio. EURASIP J. Adv. Signal Process. 2021, 107 (2021).

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