A DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT

Abstract

A DLFM signal parameter estimation method based on the combined use of STFT and FRFT specifically includes the following steps: pulse width estimation is performed on the sorted DLFM single pulse radar intra-pulse signal data, followed by STFT. The instantaneous frequency curve is fitted using the least squares method to roughly estimate the center frequency and starting frequency. The signal is then classified as positive-negative DLFM or negative-positive DLFM based on these two parameters; FRFT is performed on the positive-negative DLFM data to estimate the frequency modulation slope and maximum instantaneous frequency, and calculate the center frequency, starting frequency, and bandwidth B; FRFT is performed on the negative-positive DLFM data to estimate the frequency modulation slope and minimum instantaneous frequency, and calculate the center frequency, starting frequency, and bandwidth B. The present invention comprehensively utilizes STFT and FRFT to perform signal feature extraction, waveform discrimination, and parameter estimation, and can accurately perform DLFM signal waveform discrimination and parameter estimation under conditions of 0dB or even below 0dB.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT. Background Art

[0002] Radar countermeasure reconnaissance systems analyze radar signals in three main aspects: signal interception, modulation recognition, and parameter estimation. With the development of radar technology, radar intra-pulse modulation patterns have become increasingly complex and diverse, posing a severe challenge to radar signal parameter estimation.

[0003] Currently, radar signal parameter estimation methods primarily fall into the following categories: time-domain-based methods, frequency-domain-based methods, time-frequency analysis-based methods, and wavelet transform-based methods. Frequency-modulated and phase-modulated signals in modern radars are typical non-stationary signals, and analysis of these non-stationary signals from both the time and frequency domains has significant limitations. Time-frequency analysis methods can simultaneously extract information from both the time and frequency domains of radar signals, obtaining frequency domain information that varies over time and extracting relatively complete signal information. Therefore, they can effectively analyze and process non-stationary signals.

[0004] Widely used time-frequency analysis methods include the short-time Fourier transform (STFT), fractional Fourier transform (FRFT), Wigner-Ville distribution (WVD), Wigner-Hough transform (WHTransform, WHT), Radon-Wigner transform (RWTransform, RWT), and wavelet transform (WT). A prominent problem with time-frequency analysis methods for radar signal parameter estimation is that a single time-frequency analysis method is limited in its applicability to a limited number of radar signal types, and under non-cooperative conditions, it is difficult to select the appropriate time-frequency analysis method in real time based on detected information.

[0005] Double Linear Frequency Modulation (DLFM) is an important modulation scheme in radar. It is a pulse compression signal with a large time-bandwidth product, crucial for achieving high resolution and strong anti-interference capabilities. To address the problem of DLFM signal parameter estimation under non-cooperative conditions, this paper proposes a DLFM signal parameter estimation method based on the combined application of STFT and FRFT. By integrating STFT, FRFT, time-frequency curve fitting, feature extraction, and discrimination, this method effectively achieves parameter estimation of DLFM signals under low signal-to-noise ratio conditions. Summary of the Invention

[0006] The purpose of the present invention is to propose a DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT, which can distinguish different waveform patterns of DLFM signals as low as 0dB and estimate the signal's starting frequency, center frequency, frequency modulation slope and bandwidth parameters.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT, comprising:

[0009] S1. Estimating the pulse width of the sorted DLFM single pulse radar intra-pulse signal data;

[0010] S2. Then perform STFT and use the least squares method to fit the instantaneous frequency curve to roughly estimate the center frequency f stftc and the starting frequency f stfts ;

[0011] S3. According to the center frequency f stftc and the starting frequency f stfts The relationship between the two determines the type of DLFM signal, and classifies the signal into positive-negative DLFM or negative-positive DLFM;

[0012] Positive-negative DLFM means that the frequency modulation slope of the signal in a pulse is positive in the first half of the pulse width, and the instantaneous frequency increases; the frequency modulation slope is negative in the second half of the pulse width, and the instantaneous frequency decreases.

[0013] The frequency modulation slope and instantaneous frequency variation of the negative-positive DLFM are opposite to those of the positive-negative DLFM.

[0014] S4. Perform FRFT on the intra-pulse signal data of positive and negative DLFM radar pulses to estimate the frequency modulation slope K frft and the maximum instantaneous frequency f frfte , calculate the center frequency f frftc , starting frequency f frfts and bandwidth B;

[0015] S5. Perform FRFT on the intra-pulse signal data of the negative and positive DLFM radar pulse to estimate the frequency modulation slope K frft and the minimum instantaneous frequency f frftm , calculate the center frequency f frftc , starting frequency f frfts and bandwidth B.

[0016] The step of performing pulse width estimation on the sorted DLFM single pulse radar intra-pulse signal data in step S1 is:

[0017] The intercepted signal is sorted to obtain a signal pulse sequence containing intra-pulse modulation information. For any pulse, it is expressed as x(k), k = 1, 2, ..., K, K is the number of sampling points, and the sampling frequency is f s , perform amplitude normalization on x(k), and the processed signal sequence is expressed as

[0018] against Pulse width estimation is performed using a radar pulse repetition interval estimation method based on blind source separation, and the estimated pulse width is expressed as pw.

[0019] The data processed in step S1 is subjected to STFT, and the instantaneous frequency curve is fitted using the least squares method to roughly estimate the center frequency f stftc and the starting frequency f stfts The specific approach is:

[0020] against Perform STFT and use the least squares method to fit the instantaneous frequency curve. The fitting order is at least 2. The rough estimate of the starting frequency of the fitted frequency curve is expressed as f stfts , this value is the first value of the vertical axis of the frequency curve obtained by fitting, and the rough estimate of the center frequency is expressed as f stftc , this value is the midpoint of the vertical axis of the fitted frequency curve.

[0021] The step of determining the type of DLFM signal is: if f stfts <f stftc , then the DLFM signal is positive and negative DLFM, if f stfts >f stftc , then the DLFM signal is negative-positive.

[0022] The steps of performing FRFT on the positive and negative DLFM radar pulse intra-pulse signal data are as follows:

[0023] Perform FRFT on the signal x(t) to get X p (u), whose expression is as follows:

[0024]

[0025] Where K p (u,t)=A α exp[jπ(u 2 cotα-2utcscα+t 2 cotα)] is FRFTX p (u) is the kernel function, where α=pπ / 2, where p and α represent the order of FRFT and the rotation angle respectively;

[0026] Perform dimension normalization on the time domain and frequency domain of the linear frequency modulation signal, and convert both the time domain and the frequency domain of the linear frequency modulation signal into dimensionless domains;

[0027] After the dimension normalization operation, the representation of the center frequency of the linear frequency modulation changes from f0 to f′0. At the same time, the frequency modulation slope of the linear frequency modulation signal changes from μ to μ′. The relationship before and after the change is as follows:

[0028]

[0029] When α=-arccot(μ), X p (u)=AA α exp(jπu 2 cotα), X p (u) is an impulse function in the fractional Fourier domain. When f0 = ucscα, X p (u) obtains the maximum impact. Based on this feature, the parameters p, u and A can be estimated. The expression is:

[0030]

[0031] According to formula (3), the center frequency f0 and the linear frequency modulation slope μ of the linear frequency modulation signal can be estimated:

[0032]

[0033] Since the time of LFM signal cannot be in negative time space, the original time interval must be is changed to t∈[0,T]; in the time interval t∈[0,T] of processing LFM signal, the physical meaning of the center frequency f0 will change, where f0 represents the starting frequency;

[0034] After performing FRFT on the LFM signal, we can get X p When the parameters of the LFM signal are estimated according to formula (4), f0 needs to be processed. Through the processing, the parameters originally representing the center frequency estimation are changed to the parameters representing the starting frequency estimation. After the correction, the parameter estimation formula is as follows:

[0035]

[0036] The calculation method of bandwidth B is: B = pw × |K frft |;

[0037] Starting frequency f frfts The calculation method is: ffrfts =f frftmax -B / 2;

[0038] Center frequency f frftc The calculation method is: f frftc =f frftmax -B / 4;

[0039] When t∈[0,T / 2), the estimated frequency modulation slope = |K frft |; When When the estimated frequency modulation slope = -|K frft |.

[0040] The steps of performing FRFT on the intra-pulse signal data of the negative-positive DLFM radar pulse are as follows:

[0041] The calculation method of bandwidth B is: B = pw × |K frft |;

[0042] Starting frequency f frfts The calculation method is: f frfts =f frftmin +B / 2;

[0043] Center frequency f frftc The calculation method is: f frftc =f frftmin +B / 4;

[0044] When t∈[0,T / 2), the estimated frequency modulation slope = -|K frft |; When When the estimated frequency modulation slope = |K frft |.

[0045] Due to the adoption of the above-mentioned technical solution, the present invention has the following advantages:

[0046] The present invention provides a DLFM signal parameter estimation method based on the combined use of STFT and FRFT. Compared with the existing technology, the present invention can distinguish different waveform patterns of DLFM signals under the condition of 0dB or lower signal-to-noise ratio, and estimate the signal's starting frequency, center frequency, frequency modulation slope and bandwidth parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the process of the present invention.

[0048] Figure 2 This is a waveform diagram of the signal time domain and spectrum when the signal-to-noise ratio is -2dB in Example 1.

[0049] Figure 3 This is the STFT time-frequency distribution diagram of the signal when the signal-to-noise ratio is -2dB in Example 1.

[0050] Figure 4 This is a frequency curve diagram obtained by fitting the signal after STFT transformation when the signal-to-noise ratio is -2dB in Example 1.

[0051] Figure 5 This is a waveform diagram of the signal time domain and spectrum when the signal-to-noise ratio is -2dB in Example 2.

[0052] Figure 6 This is the STFT time-frequency distribution diagram of the signal when the signal-to-noise ratio is -2dB in Example 2.

[0053] Figure 7 This is a frequency curve diagram obtained by fitting the signal after STFT transformation when the signal-to-noise ratio is -2dB in Example 2. DETAILED DESCRIPTION

[0054] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0055] See also Figure 1 The present invention provides a DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT, comprising:

[0056] S1. Estimating the pulse width of the sorted DLFM single pulse radar intra-pulse signal data;

[0057] S2. Then perform STFT and use the least squares method to fit the instantaneous frequency curve to roughly estimate the center frequency f stftc and the starting frequency f stfts ;

[0058] S3. According to the center frequency f stftc and the starting frequency f stfts The relationship between the two determines the type of DLFM signal, and classifies the signal into positive-negative DLFM or negative-positive DLFM;

[0059] Positive-negative DLFM means that the frequency modulation slope of the signal in a pulse is positive in the first half of the pulse width, and the instantaneous frequency increases; the frequency modulation slope is negative in the second half of the pulse width, and the instantaneous frequency decreases.

[0060] The frequency modulation slope and instantaneous frequency variation of the negative-positive DLFM are opposite to those of the positive-negative DLFM.

[0061] S4. Perform FRFT on the intra-pulse signal data of positive and negative DLFM radar pulses to estimate the frequency modulation slope K frft and the maximum instantaneous frequency f frfte , calculate the center frequency f frftc , starting frequency f frfts and bandwidth B;

[0062] S5. Perform FRFT on the intra-pulse signal data of the negative and positive DLFM radar pulse to estimate the frequency modulation slope K frft and the minimum instantaneous frequency f frftm , calculate the center frequency f frftx , starting frequency f frfts and bandwidth B.

[0063] The parameter estimation method is specifically as follows:

[0064] The intercepted signal is sorted to obtain a signal pulse sequence containing intra-pulse modulation information. For any pulse, it is expressed as x(k), k = 1, 2, ..., K, K is the number of sampling points, and the sampling frequency is f s , perform amplitude normalization on x(k), and the processed signal sequence is expressed as In the formula, |·| means taking the absolute value, and this symbol has the same meaning in the following steps;

[0065] against Pulse width estimation is performed using a radar pulse repetition interval estimation method based on blind source separation, and the estimated pulse width is expressed as pw.

[0066] against Perform STFT and use the least squares method to fit the instantaneous frequency curve. The fitting order is at least 2. The rough estimate of the starting frequency of the fitted frequency curve is expressed as f stfts , this value is the first value of the vertical axis of the frequency curve obtained by fitting, and the rough estimate of the center frequency is expressed as f stftc , this value is the midpoint of the vertical axis of the fitted frequency curve.

[0067] According to f stfts and f stftc Determine the type of DLFM signal.

[0068] If f stfts <f stftc , then the DLFM signal is positive-negative DLFM;

[0069] If f stfts >f stftc , then the DLFM signal is negative-positive.

[0070] Perform FRFT on positive and negative DLFM, and extract the frequency modulation slope K according to the transformed time-frequency waveform. frft and the maximum instantaneous frequency f frftmax , calculate the center frequency f frftc , starting frequency f frfts and bandwidth B.

[0071] The following is an explanation of the FRFT of a signal. For a signal x(t), we perform FRFT on it and get X p (u), whose expression is as follows:

[0072]

[0073] Where K p (u,t)=A p exp[jπ(u 2 cotα-2utcscα+t 2 cotα)] is FRFTX p (u) is the kernel function, where α=pπ / 2, where p and α represent the order of FRFT and the rotation angle, respectively.

[0074] After defining the FRFT, we can use it to estimate parameters of Linear Frequency Modulation (LFM) signals in both the time and frequency domains. Since the time and frequency domain dimensions of a signal are completely different, directly performing the FRFT on an LFM signal will not yield true parameters. Therefore, prior to parameter estimation, we must first normalize the LFM signal in both the time and frequency domains, converting them into dimensionless domains.

[0075] Before the dimension normalization operation, the time domain dimension of the LFM signal is The frequency domain dimension is Where T is the pulse width of the LFM signal, f s Is the sampling frequency of the signal. Before the normalization operation, the coordinate system of the time-frequency characteristics of the signal is (t, f). After the transformation, the new coordinate system of the time-frequency characteristics is (u, v), where the definition is is the scale factor of this transformation. After the coordinate system transformation, the time domain and frequency domain representation intervals of the LFM signal are and At this point, the dimension normalization of the LFM signal in the time domain and frequency domain has been completed. After normalization, the representation of the LFM center frequency changes from f0 to f′0. At the same time, the representation of the LFM signal's frequency modulation slope also changes from μ to μ′. The relationship before and after the change is as follows:

[0076]

[0077] When α=-arccot(μ), X p (u)=AA α exp(jπu 2 cotα), X p (u) is an impulse function in the fractional Fourier domain. When f0 = ucscα, X p (u) obtains the maximum impact. Based on this feature, the parameters p, u and A can be estimated. The expression is:

[0078]

[0079] According to formula (3), the center frequency f0 and the frequency modulation slope μ of the LFM signal can be estimated:

[0080]

[0081] Since the time of LFM signal cannot be in negative time space, the original time interval must be Change to t∈[0,T]. In the time interval t∈[0,T] of processing LFM signal, the physical meaning of center frequency f0 will change. Here f0 represents the starting frequency. After performing FRFT on LFM signal, we can get X p When the parameters of the LFM signal are estimated according to formula (4), f0 needs to be processed. Through the processing, the parameters that originally represent the center frequency estimation are changed to the parameters that represent the starting frequency estimation. After the correction, the parameter estimation formula is as follows:

[0082]

[0083] On the basis of the above-mentioned LFM signal parameter estimation, certain transformation processing must be performed to realize the parameter estimation of the DLFM signal.

[0084] The calculation method of bandwidth B is: B = pw × |K frft |;

[0085] Starting frequency f ftfts The calculation method is: f frfts =f frftmax -B / 2;

[0086] Center frequency f frftc The calculation method is: f frftc =f frftmax -B / 4;

[0087] When t∈[0,T / 2), the estimated frequency modulation slope = |Kfrft |; When When the estimated frequency modulation slope = -|K frft |.

[0088] Perform FRFT on the negative-positive DLFM and extract the frequency modulation slope K according to the transformed time-frequency waveform. frft and the minimum instantaneous frequency f frftmin , calculate the center frequency f frftc , starting frequency f frfts and bandwidth B. The estimation of these parameters also needs to be based on the LFM signal parameter estimation method introduced in S5.

[0089] The calculation method of bandwidth B is: B = pw × |K frft |;

[0090] Starting frequency f frfts The calculation method is: f frfts =f frftmin +B / 2;

[0091] Center frequency f frftc The calculation method is: f frftc =f frftmin +B / 4;

[0092] When t∈[0,T / 2), the estimated frequency modulation slope = -|K frft |; When When the estimated frequency modulation slope = |K frft |.

[0093] In order to further verify the technical solution of the present invention, the present invention is further described below in conjunction with experimental test diagrams.

[0094] The experimental verification of the present invention is carried out under computer simulation conditions, and the simulation software adopts MATLAB R 2010a. In order to verify the effectiveness of the present invention, two groups of experimental tests are carried out.

[0095] Example 1:

[0096] The DLFM signal is positive and negative, with a signal amplitude of 5V and a starting frequency of f st =20MHz, bandwidth B s =20MHz, pulse width pw s = 20μs, and the simulation duration is one pulse width. Under different signal-to-noise ratios and sampling frequencies, the waveform identification and parameter estimation results of the signal using this patented solution are shown in Table 1.

[0097] Table 1. Results of positive and negative DLFM signal waveform classification and signal parameter estimation

[0098]

[0099] Example 2:

[0100] The DLFM signal is negative-positive, with a signal amplitude of 5V and a starting frequency of f st =30MHz, bandwidth B s =20MHz, pulse width pw s =15μs, and the simulation duration is one pulse width. Under different signal-to-noise ratios and sampling frequencies, the waveform identification and parameter estimation results of the signal using this patented solution are shown in Table 2.

[0101] Table 2 Negative-positive DLFM signal waveform classification and signal parameter estimation results

[0102]

[0103] The above experimental results show that the present invention can accurately perform waveform analysis and parameter estimation on DLFM signals under the condition of 0 dB or below 0 dB.

[0104] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT, characterized in that: The steps include: S1. Estimating the pulse width of the sorted DLFM single pulse radar intra-pulse signal data; S2. The data processed in step S1 is then subjected to STFT, and the instantaneous frequency curve is fitted using the least squares method to roughly estimate the center frequency f stftc and the starting frequency f stfts ; S3. According to f in step S2 stfts and f stftc Determine the type of DLFM signal and classify the signal as positive-negative DLFM or negative-positive DLFM; S4. Perform FRFT on the positive and negative DLFM radar pulse intra-pulse signal data to estimate the frequency modulation slope K frft and the maximum instantaneous frequency f frfte , calculate the center frequency f frftc , starting frequency f frfts and bandwidth B; the steps of performing FRFT on the positive and negative DLFM radar pulse intra-pulse signal data are as follows: Perform FRFT on the signal x(t) to get X p (u), whose expression is as follows: Where K p (u, t) = A α exp[jπ(u 2 cota-2utcscα+t 2 cotα)] is FRFTX p (u) is the kernel function, where α=pπ / 2, where p and α represent the order of FRFT and the rotation angle respectively; Perform dimension normalization on the time domain and frequency domain of the linear frequency modulation signal, and convert both the time domain and the frequency domain of the linear frequency modulation signal into dimensionless domains; After the dimension normalization operation, the representation of the center frequency of the linear frequency modulation changes from f0 to f′0. At the same time, the frequency modulation slope of the linear frequency modulation signal changes from μ to μ′. The relationship before and after the change is as follows: When α=-arccot(μ), X p (u)=AA α exp(jπu 2 cotα), X p (u) is an impulse function in the fractional Fourier domain. When f0 = ucscα, X p (u) obtains the maximum impact. Based on this feature, the parameters p, u and A can be estimated. The expression is: According to formula (3), the center frequency f0 and the linear frequency modulation slope μ of the linear frequency modulation signal can be estimated: Since the time of LFM signal cannot be in negative time space, the original time interval must be is changed to t∈[0, T]; in the time interval t∈[0, T] of processing the LFM signal, the physical meaning of the center frequency f0 will change, where f0 represents the starting frequency; After performing FRFT on the LFM signal, we can get X p When the parameters of the LFM signal are estimated according to formula (4), f0 needs to be processed. Through the processing, the parameters originally representing the center frequency estimation are changed to the parameters representing the starting frequency estimation. After the correction, the parameter estimation formula is as follows: The calculation method of bandwidth B is: B = pw × |K frft |; Starting frequency f frfts The calculation method is: f frfts =f frftmax -B / 2; Center frequency f frftc The calculation method is: f frftc =f frftmax -B / 4; When t∈[0, T / 2), the estimated frequency modulation slope = |K frft |; When When the estimated frequency modulation slope = -|k frft |; S5. Perform FRFT on the intra-pulse signal data of the negative and positive DLFM radar pulse to estimate the frequency modulation slope K frft and the minimum instantaneous frequency f frftm , calculate the center frequency f frftc , starting frequency f frfts and bandwidth B.

2. The DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT according to claim 1 is characterized in that: The step of performing pulse width estimation on the sorted DLFM single pulse radar intra-pulse signal data in step S1 is: The intercepted signal is sorted to obtain a signal pulse sequence containing intra-pulse modulation information. For any pulse, it is expressed as x(k), k = 1, 2, ..., K, K is the number of sampling points, and the sampling frequency is f s , perform amplitude normalization on x(k), and the processed signal sequence is expressed as against Pulse width estimation is performed using a radar pulse repetition interval estimation method based on blind source separation, and the estimated pulse width is expressed as pw.

3. The DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT according to claim 1 is characterized in that: The data processed in step S1 is subjected to STFT, and the instantaneous frequency curve is fitted using the least squares method to roughly estimate the center frequency f stftc and the starting frequency f stfts The specific approach is: against Perform STFT and use the least squares method to fit the instantaneous frequency curve. The fitting order is at least 2. The rough estimate of the starting frequency of the fitted frequency curve is expressed as f stfts , this value is the first value of the vertical axis of the frequency curve obtained by fitting, and the rough estimate of the center frequency is expressed as f stftc , this value is the midpoint of the vertical axis of the fitted frequency curve.

4. The DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT according to claim 1, characterized in that: The step of determining the type of DLFM signal is: if f stfts <f stftc , then the DLFM signal is positive and negative DLFM, if f stfts >f stftc , then the DLFM signal is negative-positive.

5. The DLFM signal parameter estimation method based on the comprehensive application of STFT and FRFT according to claim 1 is characterized in that: The steps of performing FRFT on the intra-pulse signal data of the negative-positive DLFM radar pulse are as follows: The calculation method of bandwidth B is: B = pw × |k frft |; Starting frequency f frfts The calculation method is: f frfts =f frftmin +B / 2; Center frequency f frftc The calculation method is: f frftc =f frftmin +B / 4; When t∈[0, T / 2), the estimated frequency modulation slope = -|K frft |; When When the estimated frequency modulation slope = |K frft |.

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