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Present radar signal emitter recognition approaches suffer from a dependency on prior information. Moreover, modern emitter recognition must meet the challenges associated with low probability of intercept technology and other obscuration methodologies based on complex signal modulation and must simultaneously provide a relatively strong ability for extracting weak signals under low SNR values. Therefore, the present article proposes an emitter recognition approach that combines ensemble empirical mode decomposition (EEMD) with the generalized S-transform (GST) for promoting enhanced recognition ability for radar signals with complex modulation under low signal-to-noise ratios in the absence of prior information. The results of Monte Carlo simulations conducted using various mixed signals with additive Gaussian white noise are reported. The results verify that EEMD suppresses the occurrence of mode mixing commonly observed using standard empirical mode decomposition. In addition, EEMD is shown to extract meaningful signal features even under low SNR values, which demonstrates its ability to suppress noise. Finally, EEMD-GST is demonstrated to provide an obviously better time-frequency focusing property than that of either the standard S-transform or the short-time Fourier transform.

RADAR signal emitter recognition is an important aspect of electronic warfare reconnaissance systems that seeks to identify individual radar emitters through an analysis of the electromagnetic signals and thereby determine vital information regarding the technical level, performance, position, and deployment conditions of enemy radar systems for supporting decision making regarding enemy weapon systems and targets [

The radar signal emitter recognition problem has been the subject of intensive investigation, and substantial development has been achieved. For example, an improved evidence modeling method that sought to fuse multisensor information was proposed to improve the accuracy of radar emitter recognition [

As discussed, the development of LPI technology has become an increasing challenge for electronic reconnaissance because LPI reduces the probability of signal interception by the passive reconnaissance equipment of an opposing party by controlling the transmitted power, signal bandwidth, signal parameters, and modulation patter. In addition, modern radar emitter signals adopt various modulation types to reduce the probability of being intercepted, making it difficult for radar interception receivers to effectively recognize signal features within a single dimension of time or frequency. Therefore, the development of emitter recognition methods must meet the challenges associated with the present and future development of LPI technology and other obscuration methodologies. Simultaneously, the prevalence of electromagnetic signals in electromagnetic space has undergone a sharp increase in modern times, which leads to both intentional and unintentional interference effects. Although the intensity of intentional interference is low, its effect is precisely calculated. Meanwhile, the sources and intensities of unintentional interference vary greatly, and this has the effect of decreasing the signal-to-noise ratio (SNR), which correspondingly increases the difficulty of signal detection. Therefore, modern radar reconnaissance interception receivers are required to provide a relatively strong ability for extracting weak signals under low SNR values.

From the above analysis of past work and existing challenges, we note that present radar emitter recognition approaches suffer most profoundly from subjective intervention and a severe dependency on prior information. Therefore, the present study eliminates this dependency on prior information by combining ensemble empirical mode decomposition (EEMD) with the generalized S-transform (GST) to realize the recognition of radar signal emitters. EEMD can be used to conduct adaptive extraction of intrinsic mode functions (IMFs) on each scale component of emitter signals from high frequency to low frequency with good local transient characteristic representation capacity and good noise suppression. The GST is then applied to the IMFs obtained by decomposition, and the time-frequency planar features of signals are characterized and extracted using the good time-frequency focusing property of GST for realizing effective radar signal emitter recognition. These advantages of the proposed EEMD-GST approach are verified by Monte Carlo simulations conducted using various mixed signals with additive Gaussian white noise.

Empirical mode decomposition (EMD) decomposes a signal

The specific sifting process by which

Basic process flow of empirical mode decomposition (EMD).

Determine all extrema of_{1}, and the first component_{1} of

Decomposition is further conducted by treating_{1} as if it were_{i} meets the two conditions of an IMF.

The first IMF obtained from_{1}. This IMF is then separated from

Decomposition is further conducted by treating_{1} as if it were

The full EMD representation of

According to the sifting process, each IMF component_{j} represents different periodic modes from high to low. Moreover, the instantaneous frequency of IMF at different moments changes along with changes in the signal itself.

We note from the above process that EMD can be applied to any signal, requires no prior information or assumptions, and can decompose signals into different modes adaptively according to the signal features itself. However, the application of EMD to a signal whose time scale changes rapidly can induce mode mixing, where a signal feature operative over widely different time scales is decomposed into a single IMF, or a signal feature operative over very similar time scales can be included in different IMFs. However, mode mixing limits the performance of EMD severely [

The mode mixing problem associated with EMD has been addressed by EEMD. In EEMD, an IMF is defined as the average IMF obtained over an ensemble of

Basic process flow of ensemble EMD (EEMD).

The following are the abbreviated implementation steps of the proposed algorithm.

Initialize the number of evaluations

Set evaluation index

Add white noise_{i}(

Decompose_{i}(_{i}(

Repeat steps 3 and 4

Based on the principle that the statistical average of uncorrelated sequences is zero, the mean values of the ensemble IMFs in (

The final result of EEMD decomposition is

The decomposition times of EEMD are different due to different signals, noise intensity, and the number of layers. However, for the final result of EEMD decomposition, most of them only have a set of maximum and minimum values, so an attempt can be made to determine the decomposition layers of EEMD [

The S-transform adopts the Fourier kernel and a frequency dependent window function of variable window length to obtain higher frequency resolution at lower frequencies and better time localization at higher frequencies [

Presently, primary airborne battle radar mainly adopts the X-band to obtain better high-frequency resolution, so as to realize effective detection in passive reconnaissance activities. Therefore, to enhance the time-frequency resolution capacity of the S-transform and thus improve its time-frequency focusing property, the GST applies a regulation coefficient

Accordingly, the determination of

For an arbitrary

Apply normalization processing to the GST.

Select

Repeat steps 1, 2, and 3 until obtaining the optimal value of_{opt}, that provides a minimum

Finally, an intelligent search algorithm can be employed in the optimization process, and the optimum GST is obtained by substituting_{opt} into (

At present, the radar is developing toward LPI. By controlling its transmitting power, signal bandwidth, signal parameters, and modulation styles, it can realize effective detection while reducing the probability of being intercepted by the enemy’s passive detection equipment, thus improving the ability of radar to perform tasks. Therefore, the development of LPI technology has become an urgent challenge for electronic reconnaissance.

In order to improve the recognition efficiency of radar signals without prior information under strong noise interference, based on the discussion in the previous section, this paper constructs the radar signal recognition process based on EEMD-GST. It is mainly divided into three parts, namely, signal preprocessing, system parameter adjustment, and signal recognition. The specific steps involved in the proposed EEMD-GST radar signal emitter recognition approach are given as follows.

Although it is assumed that the received radar signal is in the X-band, the X-band has a bandwidth of 4G, and the modulation style and amplitude of the signal are completely unknown. If the received signal is processed directly, the result of processing is likely not ideal under many unknown conditions, and the parameter interpretation is likely to be inaccurate. Therefore, in this paper, the signal is first obtained and interpreted through the EEMD-GST detection process.

The specific steps are as follows.

Discrete the signals obtained by the reconnaissance interception receiver, and input them into the EEMD-GST signal processing system.

Apply EEMD to decompose the time series signals, and obtain the IMFs.

Apply Particle Swarm Optimization algorithm to obtain the optimal GSTs of IMFs.

Analyze the time-frequency distribution figure obtained to evaluate the features of intercepted signals.

Combine signal characteristics based on the analysis of GSTs for each IMF to realize radar signal emitter recognition.

Parameterize the signal according to the signal recognition results, and simulate the detection signal approximately, namely, the signal to be detected and SNR to be estimated.

In the process of EEMD processing, the total average number

In the GST transformation process, the adjustment factor

Therefore, this section builds an adaptive optimization process with two parameters, which is shown in Figure

Construct the simulated signal_{0}(

Set the average number

Decompose the mixed signal by EEMD to obtain the_{r}(

Calculate the peak signal-to-noise ratio (PSNR) and noise intensity_{r}(_{max}) of_{0}(

Determine whether the current PSNR is greater than 0.9_{max}, which is to judge whether most of the characteristics of the signal are retained. If the conditions are met, proceed to the next step. Otherwise, adjust the parameter

Set the adjustment factor

Conduct GST to the reconstructed signal to obtain the time-frequency distribution diagram. Calculate the time-frequency distribution diagram of the simulated signal_{0}(

Determine whether SSIM is greater than 0.9, which is to find whether the signals before and after processing are similar and whether the details are well retained. When SSIM is greater than 0.9, most information of the signal is considered to be retained and we can proceed to

Complete the parameter setting of the system.

In the above process, calculating the PSNR and SSIM can be completed by directly calling MATLAB function package, which is easy to implement. Next we will introduce the way to adjust_{max}, which will be used as the error feedback.

The control method of parameter

Many parameters are similar to (

To sum up, the system parameters can be adjusted dynamically and adaptively according to different signal parameters and modulation styles, so as to achieve the approximate matching between system parameters and the signal to be detected.

By constructing the approximated parameter matching system and inputting the signal to be detected to the processing flow in Figure

Radar signal emitter recognition process based on EEMD and the generalized S-transform (GST).

Processing flow of algorithm parameters adjustment.

As there is no a priori information of the signal to be detected, if the system parameter is fixed during the detection procedure, the generality of test may be poor and the result may not be ideal. Therefore, the proposed flow preprocesses the detection signal to obtain approximated prior information. A negative feedback mechanism and a corresponding control law are designed, and the system parameters are dynamically adjusted to match the signals to be detected as much as possible. Finally, the signal to be detected is input into the processing flow with adjusted parameters to realize identification, thereby greatly improving the accuracy of signal recognition. The applicability and universality of the algorithm are stronger, and the performance is further improved

Monte Carlo simulation analyses were conducted to demonstrate the advantages of the proposed EEMD-GST radar signal emitter recognition approach from three different perspectives. Firstly, EMD and EEMD were applied to decompose a mixed signal formed as a linear superposition of a high-frequency intermittent signal and a simple continuous signal, and the decomposition results were compared to demonstrate that EEMD can effectively suppress mode mixing. Secondly, EEMD was applied to decompose mixed signals composed of a standard linear frequency modulated (LFM) signal and additive Gaussian white noise of different amplitudes. Then, the ability of EEMD to extract meaningful signal features was evaluated under different SNR values to demonstrate the ability of the algorithm to suppress noise. Thirdly, EEMD-GST processing was applied to a mixed signal involving the linear superposition of several typical radar signals with additive white Gaussian noise, and the analysis results obtained were compared with the corresponding results obtained using the standard S-transform (ST) and the short-time Fourier transform (STFT) to verify the effectiveness of the proposed approach. The simulations employed 5 sets of Lenovo personal computers in parallel with Core™ i7-3770 CPUs operating under a clock frequency of 3.40 GHz and 4 GB of memory.

Electronic reconnaissance is highly covert. Often using optical camouflage, rarely moving and with ground clutter coverage, passive detection equipment is extremely difficult to detect by opposing radar. At the same time, the electronic reconnaissance party itself is passive, and it is impossible for the enemy passive detection equipment to detect our passive reconnaissance equipment. Similar to how many sound sources can be detected in a dark environment, it is difficult to tell how many listeners there are. As a result, it is impossible to determine how many passive reconnaissance devices are in the battlefield, and it is more difficult to determine the location of equipment and other information. As a result, it is impossible to conduct precise spoofing interference on passive equipment. The interference faced by passive equipment is mainly strong noise. Therefore, in order to be closer to the reality, the signal-to-noise ratio is set lower in the subsequent simulation verification to reflect the applicability of the method.

Standard radar signals generally represent a pulse pattern, particularly for airborne fire-control radar. As such, radar silence is generally maintained while approaching an objective, and radar is suddenly deployed only when within close proximity to an objective, resulting in signal patterns characterized by strong intermittency. Therefore, the decomposition results of EMD and EEMD were compared for the mixed signal shown in Figure

Linear superposition of a low-frequency cosine function signal with steady-state characteristics (signal 1) and a burst-type signal with high-frequency transient components (signal 2).

Comparison of the decomposition results of (a) EMD and (b) EEMD for the mixed signal given in Figure

EMD decomposition result

EEMD decomposition result

Comparing Figure

Therefore, to further quantify and measure algorithm performance, we adopted the similarity coefficient_{ij} of a source signal time series _{j}(

The value of_{ij} calculated between IMF5 obtained via EEMD and signal 1 was 0.9901, and that between IMF2 and signal 2 was 0.9476. However, the largest value of_{ij} calculated between any IMF obtained via EMD and signal 1 was 0.8533, and that with signal 2 was only 0.5279. Therefore, we can conclude that, compared with EMD, EEMD not only can suppress mode mixing to some extent, but also can obtain better decomposability, which contributes toward realizing the effective preprocessing of radar signals.

The antinoise capability of EEMD was evaluated in comparison to that of EMD when applied to a typical LFM signal with additive Gaussian white noise of different intensities. The assumed simulated signal is given as_{ij} using formula (_{ij} and MSE results are presented in Figures

Comparison of (a) the similarity coefficient and (b) mean squared error (MSE).

Comparison diagram of the highest similarity coefficient under different signal-to-noise ratios

Comparison diagram of the lowest MSE under different signal-to-noise ratios

We can directly note from Figure _{ij} for the IMFs obtained by EEMD are always greater than those obtained by EMD, and the IMFs obtained by EEMD maintain a largest_{ij} value of approximately 0.2 for an SNR of −20 dB. Therefore, EEMD provides a better processing effect than EMD under very low SNR. Moreover, the IMFs obtained by EEMD maintain a largest_{ij} value of approximately 0.5 at an SNR of −10 dB, which represents a good representation for signal recognition. In addition, we note from Figure

These results are a clear reflection of the processing conducted by EMD and EEMD, as discussed in Section _{ij} values obtained between the IMFs and the actual signal, thus suppressing the influence of noise.

The above simulation results and theoretical analysis demonstrate that EEMD can be applied for the extraction of weak signals under a strong noise background with good processing effect, and this can be expected to aid in the detection and analysis of LPI signals under low SNR values.

To verify the effectiveness of the proposed EEMD-GST approach, we constructed a linear superposition of the following four typical harmonic signals._{1} is an LFM signal,_{2} is a phase-modulated signal, and_{3} and_{4} are sinusoidal signals. As such, we defined the actual mixed signal as_{1}(_{2}(_{3}(_{4}(

First, the mixed signal_{1},_{2},_{3}, and_{4}. We can note directly from the figures that the simulation result obtained by EEMD-GST presents an obviously better time-frequency focusing property than that of either ST or STFT. Although the ST characterizes the features of the phase-modulated signal_{2} reasonably well, its resolution for sinusoidal signals_{3} and_{4} remains relatively poor. However, the STFT cannot clearly characterize the time-frequency characteristics of LFM signal_{1} and phase-modulated signal_{2}. As such, we can quantitatively conclude that EEMD-GST can provide the time-frequency characteristics required for emitter recognition.

Time-frequency analysis results.

EEMD-GST time-frequency transform diagram

ST time-frequency transform diagram

STFT time-frequency transform diagram

At the same time, in order to ensure that the signal may be of burst type, after intercepting a section of signal, the time-frequency analysis is carried out on it, and the results are shown in Figure

Next, we considered the actual mixed signal

Time-frequency analysis results obtained by (a) EEMD-GST, (b) ST, and (c) STFT under an SNR of −12 dB.

EEMD-GST time-frequency transform diagram under -12 dB

ST time-frequency transform diagram under -12 dB

STFT time-frequency transform diagram under -12 dB

As can be seen intuitively from Figure

To quantitatively evaluate the relative performances of the three algorithms, we take Figure

PSNR represents the ratio between the maximum possible power of a signal and the power of destructive noise that affects its expression accuracy. It is commonly used as a measurement method for signal reconstruction quality in image compression and other fields. Structural similarity is an index to measure the similarity of two images. SSIM index describes structural information as independent of brightness and contrast from the perspective of image composition, which reflects the properties of object structure in the scene. It has become a widely used method to measure video quality in broadcast and cable TV.

In this paper, PSNR is used to measure the noise resistance of the algorithm, and SSIM is used to quantitatively describe the algorithm's noise suppression and image similarity after restoration. PSNR and SSIM are used to measure the antinoise performance of the algorithm.

To guarantee the credibility of our simulation results, simulation verification was conducted using the MATLAB source code written by Ronna Fattal. The PSNR and SSIM results obtained are given in Figures

Comparison of the (a) peak SNR (PSNR) and (b) structural similarity (SSIM).

PSNR comparison diagram under different signal-to-noise ratios

SSIM comparison diagrams under different signal-to-noise ratios

The simulation and theoretical analyses conducted in previous subsections demonstrate that EEMD has relatively strong antinoise performance. Therefore, the EEMD-GST approach can obtain more ideal data preprocessing under low SNR conditions. Meanwhile, compared to ST and STFT, the GST demonstrates a better time-frequency focusing property. Thus, radar signal characteristics are more clearly represented, and the EEMD-GST approach can be expected to be more effective for recognizing the specific modulation of radar signal emitters. However, the order of the computational complexity of the signal analyses considered is

In order to further reflect the performance of this method, literature [

Comparison of the structural similarity with other algorithms (SSIM).

It can be seen from Figure

To sum up, compared with the classical algorithm and the current mainstream improved algorithm, the algorithm in this paper has improved in efficiency, and the result is more intuitive. It is also more accurate and has good applicability for processing the signal with low signal-to-noise ratio.

Present radar signal emitter recognition approaches suffer most profoundly from a severe dependency on prior information. Moreover, the development of emitter recognition methods must meet the challenges associated with the present and future development of LPI technology and other obscuration methodologies based on complex signal modulation. Simultaneously, modern radar reconnaissance interception receivers are required to provide a relatively strong ability to extract weak signals under low SNR values. Therefore, the present study eliminated this dependency on prior information by combining EEMD with the GST to realize the robust recognition of radar signal emitters. The basic theories of EMD, EEMD, and GST were presented, and the procedure for conducting EEMD-GST was defined. Monte Carlo simulations were conducted to demonstrate the advantages of the proposed EEMD-GST approach from three different perspectives. Firstly, the decomposition results obtained with EMD and EEMD were compared when applied to a mixed signal formed as a linear superposition of a high-frequency intermittent signal and a simple continuous signal. Secondly, EMD and EEMD were applied to decompose mixed signals composed of a standard LFM signal and additive Gaussian white noise of different amplitudes. Thirdly, EEMD-GST processing was applied to a mixed signal involving the linear superposition of several typical radar signals with additive white Gaussian noise, and the analysis results obtained were compared with the corresponding results obtained using the standard ST and the STFT. The results of these simulations can be outlined as follows:

While the present work has provided an integrated and improved radar signal emitter recognition approach, the mathematical expression of the signal after conducting EEMD-GST remains to be researched in detail to enable the quantitative characterization of emitter recognition performance and provide a basis for further research.

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported in part by the National Natural Science Foundation of China under Grant 67103427, 61502522, 61472442, and 61472443 and Natural Science Foundation of Shaanxi Province under 2017JQ6035 and 2016JM6017.