LPI radar signal parameter estimation method under non-Gaussian noise

Abstract

The invention belongs to the technical field of radar signals, and particularly relates to an LPI radar signal parameter estimation method under non-Gaussian noise, which is based on a non-Gaussian noise hypothesis and is more in line with actual scene application requirements. For impulse noise interference obeying alpha stable distribution, a deep learning technology is adopted to carry out de-noising processing on a received signal, non-Gaussian noise is effectively suppressed by learning a mapping relation between a time-frequency spectrum and a residual spectrum of a noisy signal, an enhanced time-domain signal is reconstructed, the signal-to-noise ratio is improved, and high-precision parameter estimation is carried out.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signals, and particularly relates to a LPI radar signal parameter estimation method under non-Gaussian noise. BACKGROUND

[0002] The core content of radar countermeasure includes radar reconnaissance and defense. Radar reconnaissance aims to intercept, modulation identification, parameter estimation and positioning analysis of radar signals transmitted by non-cooperative parties through special equipment, so as to obtain key information such as radar technical parameters, deployment position and system type. In the current development of radar technology, the low probability of intercept (LPI) radar has become an important technical system of new radar equipment because it can significantly improve the survivability of the system. Correspondingly, the research on modulation identification and parameter estimation of LPI radar signals is becoming a frontier topic in the field of radar reconnaissance and reconnaissance. Effective identification and accurate parameter estimation are the key to decision-making and analysis of the target radar signal.

[0003] In the process of signal collection and transmission, noise interference is difficult to avoid, so it is of great significance to study the LPI radar signal detection and parameter estimation method in the noise environment. The traditional parameter estimation method is usually based on the assumption of Gaussian noise, but the burst interference in the actual scene often presents non-Gaussian characteristics, which leads to the fact that the parameter estimation method based on Gaussian assumption cannot meet the actual demand. As a typical non-Gaussian noise, impulse noise has the characteristics of large amplitude, short duration and sharp peak, which poses a serious challenge to the signal processing system. Therefore, studying the LPI radar signal detection and parameter estimation method under non-Gaussian noise and improving the anti-interference ability of the system have important theoretical value and practical application significance in the fields of radar, sonar and underwater acoustic communication. The shortcomings of the prior art mainly include: first, most of the existing methods are based on the assumption of Gaussian distribution noise, but the burst interference in the actual scene often presents non-Gaussian characteristics, which leads to the fact that the parameter estimation method based on Gaussian assumption cannot meet the actual demand; second, the high precision and effectiveness of the existing parameter estimation method are for a certain or certain type of LPI radar signal, which has certain limitations and generally poor generalization ability. SUMMARY

[0004] Unlike the traditional parameter estimation method based on Gaussian noise assumption, the present invention is based on non-Gaussian noise assumption, which is more in line with the actual scene application demand. For alpha stable distribution noise interference, deep learning technology is used to denoise the received signal, the mapping relationship between the noisy signal frequency spectrum and the residual spectrum is learned, the non-Gaussian noise is effectively suppressed, the enhanced time domain signal is reconstructed, the signal-to-noise ratio is improved, and high-precision parameter estimation is performed.

[0005] The technical scheme is as follows:

[0006] A method for estimating LPI radar signal parameters under non-Gaussian noise, comprising the following steps:

[0007] S1. Simulate and construct LPI radar pure signal and its noisy signal data pairs;

[0008] S2. Perform time-frequency transformation on the above two signals, and extract signal real and imaginary parts;

[0009] S3. Establish a full convolution denoising network to complete the mapping of the noisy signal STFT spectrum to the difference between the pure signal STFT spectrum, and obtain the estimated residual spectrum;

[0010] S4. Complete signal denoising, and perform inverse transformation on the denoised time-frequency spectrum to obtain the reconstructed enhanced time-domain signal;

[0011] S5. Estimate the LPI radar signal parameters.

[0012] Preferably, the noisy signal is composed of pulse noise (satisfying Levy alpha stable distribution) and pure LPI radar signal; as a non-Gaussian distribution, its probability density function does not have a unified and closed analytical expression, and the definition of alpha stable distribution is given by its characteristic function. A random variable ψ is said to have a stable distribution if there exist parameters: 0 < α ≤ 2, -1 ≤ β ≤ 1, γ > 0, and δ is a real number, satisfying the following function form:

[0013]

[0014] In the formula, the parameters of the alpha stable distribution include characteristic exponent α, skewness parameter β, dispersion coefficient γ, and location parameter δ; α determines the thickness of the probability density function tail, and the smaller α is, the thicker the tail is, and the stronger the impact is; β determines the skewness of the distribution: when β = 0, the distribution is symmetric, when β < 0, it is right-skewed, and when β > 0, it is left-skewed; γ determines the deviation of the distribution from the mean; and δ determines the position of the probability density function on the x-axis.

[0015] Preferably, in step S1, the noisy signal x(t) can be represented as,

[0016] x(t) = s(t) + n(t);

[0017] In the formula, s(t) represents the pure signal, and n(t) represents the random pulse noise, which satisfies the alpha stable distribution.

[0018] Preferably, in step S2, short-time Fourier transform is performed on the pure signal and the noisy signal to obtain their two-dimensional time-frequency images and time-frequency matrices, which are shown as follows:

[0019]

[0020] where s(t) is the input signal, which is either the pure signal or the noisy signal; w(t) is the selected window function, w * (t) is the conjugate function of the window function, j is the imaginary unit; STFT(t, f) is the short-time Fourier transform result. 1024 frequency points are saved, and a 1024x1024x1 three-dimensional STFT complex feature can be obtained. The real and imaginary parts of the STFT spectrum are extracted and normalized as the input of the network; when the simulation data is generated, the time-frequency domain features of the pure signal are reserved.

[0021] Preferably, in step S3, the full convolutional network constructed adopts a modified VGG network architecture, which is suitable for image denoising. The network has a total of 15 layers, each of the first 14 layers contains a convolutional layer and a ReLU nonlinear activation layer, and the last layer only contains a convolutional layer. The convolution kernel size is set to 3x3, and the pooling layer is deleted. The network model input features have a total of two channels, which are the real part X r and the imaginary part X i of the received signal STFT spectrum X respectively; the model output is the residual (including the real part and the imaginary part ) of the received signal and the pure signal. The model is trained using the residual learning and batch normalization strategy until the loss function converges.

[0022] Preferably, in step S3, the loss function of the network is:

[0023]

[0024] In the formula, B is the number of batch samples, M and K represent the total number of time frames and frequency points in the STFT spectrum respectively; V(m, k) represents the value of the true residual at time-frequency point (m, k); and represents the value of the network predicted residual at time-frequency point (m, k).

[0025] Preferably, in steps S3 and S4, the denoised signal time-frequency spectrum is the original noisy signal X minus the network predicted output residual

[0026]

[0027] The inverse transform of can reconstruct the time-domain sequence after removing the impulse noise Subsequently, high-precision signal parameter estimation can be performed,

[0028]

[0029] Preferably, in step S5, according to the characteristics of different LPI radar signals, the corresponding signal parameters are estimated:

[0030] Parameters estimable for LFM signal include frequency, pulse number, pulse width, repetition period, duty cycle, frequency modulation slope;

[0031] Parameters estimable for phase shift keying signal include symbol rate, bit rate, symbol width, symbol rate.

[0032] Preferably, the estimation of specific parameters is as follows:

[0033] Estimation of frequency: Fourier transform is performed on the signal to obtain a frequency spectrum, and the point corresponding to the spectrum peak is the center frequency point;

[0034] Estimation of pulse number: according to the reconstructed time sequence signal after noise reduction, a certain threshold is set according to the signal envelope, and the rising edge and falling edge of the pulse are detected; the rising and falling edges can obtain the pulse number;

[0035] Estimation of pulse width: the ratio of the difference between adjacent rising edge and falling edge to the sampling rate is the pulse width;

[0036] Estimation of repetition period: the difference between the rising edge and the sampling rate is the repetition period;

[0037] Estimation of duty cycle: the ratio of the pulse width to the repetition period is the duty cycle;

[0038] Frequency modulation slope: the ratio of the bandwidth to the pulse width is the frequency modulation slope;

[0039] Estimation of symbol rate: the symbol rate of the modulated signal is estimated by using cyclic autocorrelation; the autocorrelation function of the signal is calculated, the cyclic autocorrelation values corresponding to different time delays are obtained by Fourier transform, the cyclic autocorrelation amplitudes corresponding to different time delays are accumulated, and the position where the symbol rate is proportional to the nonlinear filtering result will appear discrete spectrum line, and the symbol rate can be quickly estimated by detecting the position of the discrete spectrum line;

[0040] Estimation of symbol width: the symbol width is obtained by using the autocorrelation function and the autocorrelation peak value;

[0041] Estimation of symbol rate: the inverse of the symbol width.

[0042] Compared with the prior art, the present application has the following beneficial effects:

[0043] In view of the problems that the signal is susceptible to external interference and the parameter dimension is various, the LPI radar signal parameter estimation method under alpha stable distribution noise interference is researched and explored, the advantages of deep learning in image processing and feature extraction are fully utilized, and the present application provides an LPI radar signal parameter estimation method under non-Gaussian noise.

[0044] Different from the traditional parameter estimation based on Gaussian noise assumption, the patent is based on the non-Gaussian noise assumption (subject to alpha stable distribution), which is more in line with the actual scene application requirements. First, five kinds of LPI radar signal models are constructed, and alpha stable distribution noise is added to generate samples under different generalized signal-to-noise ratios. For radar pulse interference, deep learning technology is used to denoise the received signal. A fully convolutional denoising network is constructed to convert the time domain signal to the time-frequency domain. The network effectively suppresses non-Gaussian noise by learning the mapping relationship between the noisy signal time-frequency spectrum and the residual spectrum. Then, the denoised time-frequency spectrum is inverse transformed to reconstruct the enhanced time domain signal and improve the signal-to-noise ratio. Finally, while maintaining high accuracy, the simultaneous estimation of multiple signal parameters is realized. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 The technical solution flowchart of the present application is as follows:

[0046] Figure 2 The flowchart of the fully convolutional denoising network is as follows. DETAILED DESCRIPTION

[0047] The technical solution of the present application will be described in detail below through specific examples and drawings. It should be understood that the specific features in the examples and the examples of the present application are detailed descriptions of the technical solution of the present application, rather than limitations of the technical solution of the present application, and the specific technical features can be combined with each other.

[0048] A LPI radar signal parameter estimation method under non-Gaussian noise, comprising the following steps:

[0049] (1) Constructing a noisy signal and pure signal data pair

[0050] In actual engineering practice, pulse noise mainly manifests as short-time large-amplitude irregular signals with significant pulse peak characteristics. The alpha stable distribution model meets the generalized central limit theorem and can well fit the pulse noise. As a non-Gaussian distribution, its probability density function does not have a unified, closed analytical expression, therefore, the definition of alpha stable distribution is generally given by its characteristic function. A random variable ψ is said to have a stable distribution if there exist parameters: 0 < α ≤ 2, -1 ≤ β ≤ 1, γ > 0, δ is a real number, and satisfy the following function form,

[0051]

[0052] The parameters of the alpha stable distribution include a characteristic exponent a, a skewness parameter b, a dispersion coefficient g, and a location parameter d. a determines the thickness of the tail of the probability density function, the smaller a is, the thicker the tail is, and the more impulsive it is. b determines the skewness of the distribution. When b = 0, the distribution is symmetric, when b < 0, it is right-skewed, and when b > 0, it is left-skewed. g determines the degree of deviation of the distribution from the mean, similar to the variance of the Gaussian distribution. d determines the position of the probability density function on the x-axis.

[0053] LPI radars usually use complex modulated spread spectrum signals with large time-bandwidth product, which can achieve large detection range and high low probability of intercept (LPI) performance at the same time. There are many kinds of LPI radar signals, and they are still developing. In this paper, several classical LPI radar signals are studied, including linear frequency modulation (LFM) signal, nonlinear frequency modulation (NLFM) signal, binary phase shift keying (BPSK) signal, quaternary phase shift keying (QPSK) signal, and binary frequency shift keying (BFSK) signal. In this section, the signal model will be established, and the alpha stable distribution noise will be added to generate samples under different generalized signal-to-noise ratios (GSNRs) for training the model. The specific parameter settings are shown in Table 1.

[0054] Table 1 Parameter settings of simulation signal dataset

[0055]

[0056] Assume that x(t) is a noisy signal, which can be represented as:

[0057] x(t) = s(t) + n(t);

[0058] In the formula, s(t) represents a pure signal, and n(t) represents random impulse noise, which is subject to an alpha stable distribution.

[0059] (2) Data preprocessing

[0060] Short-time Fourier transform (STFT) is performed on the pure LPI radar signal and the noisy signal to obtain their two-dimensional time-frequency images and time-frequency matrices,

[0061]

[0062] where s(t) is the input signal, i.e., the pure signal or the noisy signal; w(t) is the selected window function, w * (t) is the conjugate function of the window function, and STFT(t, f) is the short-time Fourier transform result. 1024 frequency points are saved, and 1024x1024x1 three-dimensional STFT complex features can be obtained. The real and imaginary parts of the STFT spectrum are extracted and normalized as the input of the network. When generating simulation data, the time-frequency domain features of the pure signal are preserved.

[0063] (3) Model construction

[0064] Residual learning in convolutional neural networks was originally proposed to address the performance degradation problem, and network models are easier to learn residual mappings than identity mappings. Strategies for predicting residual images have been used for visual problems, and residual mapping strategies often show better convergence and denoising robustness in practice. Inspired by this, the present invention proposes an end-to-end trainable deep CNN for signal denoising. Compared with existing discriminant models that learn explicit image priors, the network does not directly output the denoised image, but outputs the predicted residual image, i.e. uses the residual learning strategy to remove the underlying clean image from the noisy signal.

[0065] First, according to the generated noisy signal and pure signal data pair, the signal is subjected to time-frequency transformation, and the signal real and imaginary parts are extracted, and then a full convolution denoising network is established to complete the mapping from the noisy signal STFT spectrum to the difference between its pure signal STFT spectrum, to obtain the estimated residual spectrum, effectively suppressing non-Gaussian noise, as shown in Figure 2 The denoised time-frequency spectrum is then inverse transformed to obtain the reconstructed enhanced time-domain signal.

[0066] The impulse signal denoising network uses a full convolution structure, and the present invention modifies the VGG network architecture to make it suitable for image denoising. The network parameter settings are shown in Table 2, the convolution kernel size is set to 3x3, the pooling layer is deleted, and the network is set according to the effective patch size used in the most advanced denoising method. The depth is 15 layers, the first 14 layers each contain a convolution layer and a ReLU nonlinear activation layer, and the last layer only contains a convolution layer. Except for the last layer, the network input features have a total of two channels, which are the real part X r and the imaginary part X i of the received signal STFT spectrum X, and the model output is the residual including the real part and the imaginary part of the received signal and the pure signal amplitude spectrum. The received signal and the pure signal amplitude spectrum are used as the output of the denoising network. For model training, the residual learning formula is used, and it is combined with batch normalization until the loss function converges, to achieve fast training and improved denoising performance.

[0067] Table 2 Denoising network parameter settings

[0068]

[0069] The loss function of the network is:

[0070]

[0071] In the formula, B is the number of batch samples, M and K represent the total number of time frames and frequency points in the STFT spectrogram, respectively; V(m, k) represents the value of the true residual at time-frequency point (m, k); V(m, k) represents the value of the residual predicted by the network at time-frequency point (m, k). This loss function is more robust to outliers than MSE (L2 loss) and is suitable for noise estimation tasks.

[0072] (4) Reconstruction of time-domain sequence

[0073] The time-frequency spectrum of the denoised signal is as follows:

[0074]

[0075] The inverse transform of can reconstruct the time-domain sequence after removing noise

[0076]

[0077] (5) High-precision estimation of LPI radar signal parameters

[0078] According to the characteristics of different LPI radar signals, the corresponding signal parameters are estimated. For example, the parameters that can be estimated for LFM signals include frequency, pulse number, pulse width, repetition period, duty cycle, and frequency modulation slope. The parameters that can be estimated for phase shift keying signals include symbol rate, bit rate, symbol width, and symbol rate. The following is the estimation method for specific parameters.

[0079] Frequency estimation: Fourier transform is performed on the signal to obtain the frequency spectrum, and the point corresponding to the spectrum peak is the center frequency point.

[0080] Pulse number estimation: According to the reconstructed time sequence signal after noise reduction, a certain threshold is set according to the signal envelope, and the rising edge and falling edge of the pulse are detected. The rising and falling edges can be used to obtain the pulse number.

[0081] Pulse width estimation: The ratio of the difference between adjacent rising and falling edges to the sampling rate is the pulse width.

[0082] Repetition period estimation: The rising edge is differentiated, and the ratio of the result to the sampling rate is the repetition period.

[0083] Duty cycle estimation: The ratio of the pulse width to the repetition period is the duty cycle.

[0084] Frequency modulation slope: The ratio of the bandwidth to the pulse width is the frequency modulation slope.

[0085] The symbol rate is estimated by using the cyclic autocorrelation. The autocorrelation function of the signal is calculated, and the cyclic autocorrelation values corresponding to different time delays are obtained by Fourier transform. The cyclic autocorrelation amplitudes corresponding to different time delays are accumulated, and the accumulated results are nonlinearly filtered. Discrete spectral lines appear at positions proportional to the symbol rate, and the symbol rate can be quickly estimated by detecting the positions of the discrete spectral lines.

[0086] The bit rate is estimated according to the modulation order and the symbol rate.

[0087] The symbol width is estimated by using the autocorrelation function and the autocorrelation peak value.

[0088] The symbol rate is estimated by using the cyclic autocorrelation. The autocorrelation function of the signal is calculated, and the cyclic autocorrelation values corresponding to different time delays are obtained by Fourier transform. The cyclic autocorrelation amplitudes corresponding to different time delays are accumulated, and the accumulated results are nonlinearly filtered. Discrete spectral lines appear at positions proportional to the symbol rate, and the symbol rate can be quickly estimated by detecting the positions of the discrete spectral lines.

[0089] The above only describes the preferred embodiments of the present application. It should be noted that those skilled in the art can make several improvements and modifications without departing from the technical principles of the present application, and these improvements and modifications should also be considered as falling within the protection scope of the present application.

Claims

1. A method for LPI radar signal parameter estimation under non-Gaussian noise, characterized in that, The method comprises the following steps: S1. Simulate the construction of LPI radar pure signal and its noisy signal data pair; S2. Perform time-frequency transformation on the above two signals, and extract signal real part and imaginary part; S3. Establish a full convolution denoising network to complete the mapping of the noisy signal STFT spectrum to the difference between the noisy signal STFT spectrum and the pure signal STFT spectrum, and obtain the estimated residual spectrum; S4. Complete signal denoising, and perform inverse transformation on the denoised time-frequency spectrum to obtain the reconstructed enhanced time-domain signal; S5. Estimate the LPI radar signal parameters.

2. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 1, characterized in that, The noisy signal is composed of random pulse noise and pure LPI radar signal; the pulse noise satisfies Levy alpha stable distribution.

3. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 1, characterized in that, In step S1, it is assumed that x(t) is a noisy signal, which can be expressed as: x(t) = s(t) + n(t); In the formula, s(t) represents a pure signal, and n(t) represents random pulse noise, which satisfies alpha stable distribution.

4. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 1, characterized in that, In step S2, short-time Fourier transform is performed on the pure signal and the noisy signal to obtain their two-dimensional time-frequency images and time-frequency matrices, which are shown as follows: where s(t) is the input signal, i.e. the pure signal or the noisy signal; w(t) is a selected window function, w * (t) is the conjugate function of the window function, j is the imaginary unit, and STFT(t,f) is the short-time Fourier transform result.

5. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 1, characterized in that, In step S3, the constructed full convolutional network adopts a modified VGG network architecture, which has a total of 15 layers, each of the first 14 layers contains a convolutional layer and a ReLU nonlinear activation layer, and the last layer only contains a convolutional layer; the convolution kernel size is set to 3x3, and the pooling layer is deleted; the network model input features have a total of two channels, which are the real part X r and the imaginary part X i of the received signal STFT spectrum X respectively; the model output is the residual of the received signal and the pure signal including the real part and the imaginary part The model is trained using the residual learning and batch normalization strategy until the loss function converges.

6. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 5, characterized in that, In step S3, the loss function of the network is: In the formula, B is the number of batch samples, M and K respectively represent the total number of time frames and frequency points in the STFT spectrogram; V(m, k) represents the value of the real residual at time-frequency point (m, k); V(m, k) represents the value of the residual of network prediction at time-frequency point (m, k).

7. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 6, characterized in that, In step S3 and step S4, the time-frequency spectrum of the denoised signal is the residual of the original noisy signal X minus the network prediction output right The time-domain sequence after removing impulse noise can be reconstructed by performing an inverse transform. High-precision signal parameter estimation can then be performed.

8. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 7, characterized in that, In step S5, according to the characteristics of different LPI radar signals, the corresponding signal parameters are estimated: The estimable parameters of the LFM signal include frequency, pulse number, pulse width, repetition period, duty cycle, and frequency modulation slope; The estimable parameters of the phase shift keying signal include symbol rate, bit rate, symbol width, and symbol rate.

9. The LPI radar signal parameter estimation method under non-Gaussian noise according to claim 8, characterized in that, The estimation of specific parameters is as follows: Estimation of frequency: Fourier transform is performed on the signal to obtain the frequency spectrum, and the point corresponding to the spectrum peak is the center frequency point; Estimation of pulse number: according to the threshold set according to the signal envelope, the rising edge and falling edge of the pulse are detected according to the denoised reconstructed time sequence signal; the pulse number can be obtained according to the rising and falling edges; Estimation of pulse width: the ratio of the difference between adjacent rising edges and falling edges to the sampling rate is the pulse width; Estimation of repetition period: the ratio of the differential of the rising edge to the sampling rate is the repetition period; Estimation of duty cycle: the ratio of the pulse width to the repetition period is the duty cycle; Estimation of frequency modulation slope: the ratio of the bandwidth to the pulse width is the frequency modulation slope; Estimation of symbol rate: the symbol rate of the modulated signal is estimated by using cyclic autocorrelation; the autocorrelation function of the signal is calculated, the cyclic autocorrelation values corresponding to different time delays are obtained by Fourier transform, the cyclic autocorrelation amplitude corresponding to different time delays is accumulated, and the position where the accumulated result is proportional to the symbol rate will appear discrete spectrum lines, the symbol rate can be estimated by detecting the position of the discrete spectrum lines and selecting the secondary peak value in the cyclic autocorrelation profile; Estimation of symbol width: the symbol width is obtained by using the autocorrelation function and the autocorrelation peak value; Estimation of symbol rate: the inverse of the symbol width.

Images