BPSK signal parameter estimation method based on comprehensive use of FRFT and wavelet transform

Abstract

A BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform, comprising pulse width estimation on BPSK single radar pulse intra-pulse data; FRFT is carried out to estimate the signal carrier frequency; the signal is subjected to continuous wavelet transform, and the wavelet coefficients are filtered and denoised through phase space reconstruction and singular value decomposition; the wavelet ridge is extracted through phase difference method; according to the estimated signal carrier frequency, a threshold is set to find the maximum value of the wavelet ridge and the corresponding abscissa position; according to the maximum value point, difference operation and sorting processing are carried out to calculate the symbol width, symbol number and bandwidth parameters; the estimated BPSK signal carrier frequency, bandwidth, symbol width and symbol number are outputted; the present application can accurately perform BPSK signal parameter estimation work under the condition of as low as 0 dB through feature mining and parameter estimation of the signal by FRFT and wavelet transform.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of signal processing, and particularly relates to a BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform. BACKGROUND

[0002] The analysis of radar signals by a radar countermeasure reconnaissance system mainly includes three aspects: signal interception, modulation identification and parameter estimation. With the development of radar technology, the intra-pulse modulation patterns of radars are becoming more and more complex and diverse, which brings severe challenges to the parameter estimation of radar signals.

[0003] At present, the parameter estimation methods of radar signals mainly include the following types: time-domain-based method, frequency-domain-based method, time-frequency analysis-based method, wavelet transform-based method and the like. The frequency modulation signals and phase modulation signals of modern radars are typical non-stationary signals, and the analysis of the non-stationary signals from the time domain or the frequency domain has obvious defects. The time-frequency analysis method can simultaneously extract the two-dimensional information of the time domain and the frequency domain of a radar signal, obtain the frequency domain information changing with time, and extract relatively complete signal information, so that the non-stationary signals can be effectively analyzed and processed. The time-frequency analysis methods that have been widely applied include fractional Fourier transform (FRFT) and wavelet transform (WT).

[0004] Phase-coded signals have the characteristics of large time-width and large bandwidth, which are obtained through nonlinear phase modulation, that is, the transmitted waveform is modulated in phase. Since the phase-coded signals can well solve the contradiction between the action distance and the resolution, have the advantages of waveform agility, coding flexibility, strong anti-interference ability, high tracking precision and easy engineering implementation, and the like, the phase-coded signals are widely applied in radar systems. Accordingly, the parameter estimation of the phase-coded signals has become one of the important tasks of radar countermeasure reconnaissance, and has very important research significance. The binary phase shift keying (BPSK) signal is a common pattern in phase coding, and at present, there is still a big challenge in the accurate estimation of the parameters of the BPSK signal, which is an urgent research topic. SUMMARY

[0005] The application aims to provide a BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform, which can accurately estimate the carrier frequency, bandwidth, symbol width and symbol number parameters of the BPSK signal with a high probability of more than 0 dB.

[0006] To achieve the above object, the application provides the following technical scheme.

[0007] A BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform, comprising the following steps:

[0008] S1. Pulse width estimation is performed on the BPSK single pulse radar intra-pulse signal data identified by sorting and modulation;

[0009] The intercepted signal is sorted and identified to obtain a BPSK signal pulse sequence containing intra-pulse modulation information, and for any one pulse, it is represented as x(t), t = 1, 2, …, T, T is the number of sampling points, and the sampling frequency is f s The x(t) is subjected to amplitude normalization processing, and the processed signal sequence is represented as In the formula, |·| represents taking an absolute value, and the meaning of this symbol is the same in the following steps;

[0010] The is subjected to pulse width estimation, and the estimation method adopts a radar pulse repetition interval estimation method based on blind source separation, and the estimated pulse width is represented as PW1, PW2, …, PW N , wherein 1, 2, …, N represent pulse numbers, and the is intercepted as a single pulse width signal sequence, represented as , wherein 1, 2, …, N represent pulse numbers, and the length of each pulse is a pulse width.

[0011] S2. FRFT is performed on the single pulse signal, and the signal carrier frequency is estimated;

[0012] The is subjected to FRFT, and according to the transformed waveform, the signal carrier frequency is estimated, and the estimated value is represented as f ce .

[0013] S3. Continuous wavelet transform is performed on the single pulse signal, and the wavelet coefficients are filtered and denoised through phase space reconstruction and singular value decomposition, and the wavelet ridge line is extracted through phase difference method;

[0014] The is subjected to wavelet transform, represented as cwt is a continuous wavelet transform function, 1 represents the scale of wavelet transform, and cmor2-1 represents the name of the wavelet basis function;

[0015] For y1, filtering processing is performed through phase space reconstruction and singular value decomposition, the number of rows of reconstruction is M, which can be set according to the number of points of y1, and the number of columns is , that is, The sampling point number is, the sampling interval is 1; the reconstructed and filtered signal is taken as an absolute value, denoted as yy1; the phase of yy1 is calculated, the phase difference is calculated by a phase difference method, and a wavelet ridge line F(t, f) is obtained, the abscissa is a sampling point, and the ordinate is a frequency value.

[0016] S4. The wavelet ridge line is shaped, a threshold value is set according to an estimated signal carrier frequency, a maximum value of the wavelet ridge line and a corresponding abscissa position are found, and the abscissa position is also a time when the maximum value is taken;

[0017] Let F max =max(F(t, f)), F min =min(F(t, f)), when F max -f ce ≥f ce - F min , the shaped wavelet ridge line F'(t, f)=F(t, f); when F max -f ce <f ce -F min , the shaped wavelet ridge line F'(t, f)=f ce +F max -F(t, f);

[0018] For the wavelet ridge line F'(t, f), a threshold value C is set according to the signal carrier frequency estimation value f ce , C=1.4*f ce , the wavelet ridge line value points with a wavelet ridge line ordinate value greater than C are found, all local maximum values and corresponding abscissa positions of the wavelet ridge line value points are found, and the abscissa positions correspond to sampling point positions or sampling time. The local maximum value sequence is represented as:

[0019] pks1, pks2,..., pks m ;

[0020] The abscissa position sequence corresponding to the local maximum value is represented as:

[0021] locs1, locs2,..., locs m ;

[0022] Wherein, m is the number of local maximum values.

[0023] S5. According to the maximum value points, difference operation and sorting processing are performed, and the symbol width, the symbol number and the bandwidth parameter are calculated;

[0024] The local maximum value corresponding abscissa position sequence is calculated by difference, and the interval of the local maximum value sequence abscissa position is obtained, and the difference method is:

[0025] Let i = 1:m-1, Δ i = locs(i+1)-locs(i);

[0026] The interval sequence Δ1, Δ2, …, Δ m-1 is arranged in ascending order, i.e. arranged from small to large, and the arranged interval sequence is represented as Δ'1, Δ'2, …, Δ' m-1 ; the initial value of the symbol width is represented as Δ'1×1 / f s , and the unit is s;

[0027] When m = 2, the estimated value of the symbol width is , and the unit is s. Directly go to step S53 to estimate the BPSK signal bandwidth and the number of symbols;

[0028] When m > 2, the parameter estimation is performed according to the following steps;

[0029] S51. Calculate the ratio of the next value to the previous value for the arranged interval sequence Δ'1, Δ'2, …, Δ' m-1 , and round off according to the rounding method. The ratio is calculated as follows:

[0030] Let j = 1:m-2,

[0031] S52. Estimate the symbol width value. The estimated value of the symbol width is τ e :

[0032]

[0033] The unit of τ e is s.

[0034] S53. Estimate the BPSK signal bandwidth and the number of symbols;

[0035] The estimated value of the bandwidth is , and the unit is Hz;

[0036] The estimated value of the number of symbols is , wherein PW is the BPSK pulse width estimated by step S1.

[0037] S6. Output the estimated BPSK signal carrier frequency, bandwidth, symbol width and number of symbols.

[0038] Due to the technical scheme as described above, the present application has the following advantages:

[0039] The application provides a BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform, compared with the prior art, the BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform avoids the defects of a single method in parameter estimation by comprehensively mining the respective advantages of the two time-frequency analysis methods of FRFT and wavelet transform, and accurately estimates the BPSK signal carrier frequency, symbol width, symbol number and bandwidth parameter under the condition of a low signal-to-noise ratio of 0 dB. BRIEF DESCRIPTION OF DRAWINGS

[0040] BRIEF DESCRIPTION OF DRAWINGS Figure 1 A BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform. DETAILED DESCRIPTION

[0041] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the application.

[0042] BRIEF DESCRIPTION OF DRAWINGS Figure 1 The application provides a BPSK signal parameter estimation method based on comprehensive application of FRFT and wavelet transform, and the scheme specifically comprises the following steps:

[0043] S1. Pulse width estimation is performed on the BPSK single pulse radar intra-pulse signal data identified through sorting and modulation identification;

[0044] The intercepted signal is sorted and identified to obtain a BPSK signal pulse sequence containing intra-pulse modulation information, and for any one pulse, the pulse is represented as x(t), t=1, 2, …, T, T is the number of sampling points, and the sampling frequency is f s The amplitude of x(t) is normalized, and the signal sequence after processing is represented as In the formula, |·| represents taking an absolute value, and the meaning of the symbol is the same in the following steps;

[0045] The pulse width estimation is performed on The pulse repetition interval estimation method based on blind source separation is used as the estimation method, and the estimated pulse width is represented as PW1, PW2, …, PW N Where 1, 2, …, N represent pulse numbers, and The signal sequence is intercepted as a single pulse width, and is represented as Where 1, 2, …, N represent pulse numbers, and the time length of each pulse is a pulse width.

[0046] S2. Perform FRFT on a single pulse signal to estimate the signal carrier frequency;

[0047] right Perform FRFT to estimate the signal carrier frequency based on the transformed waveform. The estimated value is expressed as f. ce .

[0048] S3. Perform continuous wavelet transform on a single pulse signal, and filter and reduce noise in the wavelet coefficients through phase space reconstruction and singular value decomposition. Extract wavelet ridges using the phase difference method.

[0049] right Perform wavelet transform, denoted as cwt is the continuous wavelet transform function, 1 represents the scale of the wavelet transform, and cmor2-1 represents the name of the wavelet basis function;

[0050] For y1, filtering is performed through phase space reconstruction and singular value decomposition. The number of rows in the reconstruction is M, which can be set according to the number of points in y1, and the number of columns is... Right now The number of sampling points is given, and the sampling interval τ = 1. The absolute value of the reconstructed and filtered signal is taken and represented as yy1. For yy1, its phase is calculated, and the phase difference is calculated by the phase difference method to obtain the wavelet ridge F(t,f), whose horizontal axis is the sampling point and the vertical axis is the frequency value.

[0051] S4. Shape the wavelet ridge line. Based on the estimated signal carrier frequency, set a threshold and find the maximum value of the wavelet ridge line and its corresponding horizontal coordinate position. The horizontal coordinate position is also the moment when the maximum value is taken.

[0052] Let F max =max(F(t,f)), F min =min(F(t,f)), when F max -f ce ≥f ce - F min When, the shaped wavelet ridge F′(t,f)=F(t,f); when F max -f ce <f ce -F min At that time, the ridge line of the shaped wavelet F′(t,f)=f ce +F max -F(t,f);

[0053] For the wavelet ridge F′(t,f), based on the signal carrier frequency estimate f ce Set a threshold C, C = 1.4 × f ceFor the wavelet ridge line with the value of the wavelet ridge line longitudinal coordinate greater than C, find all local maximum values and their corresponding horizontal coordinate positions, which correspond to the sampling point positions or sampling time. The local maximum value sequence is represented as:

[0054] pks1, pks2, …, pks m ;

[0055] The horizontal coordinate position sequence corresponding to the local maximum value is represented as:

[0056] locs1, locs2, …, locs m ;

[0057] Wherein, m is the number of local maximum values.

[0058] S5. According to the maximum value point, perform difference operation and sorting processing to calculate the symbol width, symbol number and bandwidth parameters;

[0059] Sort the maximum values from small to large, and then further perform difference operation on the position sequence to obtain the sampling point interval between each adjacent position in the position sequence. The smallest maximum value interval corresponds to the initial value of the symbol width to be estimated;

[0060] Calculate the ratio of the next sampling point interval to the previous sampling point interval and take the integer to obtain a ratio sequence. According to the initial value of the symbol width, the sampling point interval sorted from small to large, and the ratio sequence, calculate the final symbol width estimation value;

[0061] According to the relationship between the symbol width and the bandwidth, calculate the BPSK signal bandwidth;

[0062] According to the BPSK signal pulse width and the symbol width, calculate the symbol number.

[0063] Perform difference calculation on the horizontal coordinate position sequence corresponding to the local maximum value to obtain the interval of the local maximum value sequence horizontal coordinate position. The difference method is:

[0064] Let i = 1:m-1, Δ i = locs(i+1)-locs(i);

[0065] Sort the interval sequence Δ1, Δ2, …, Δ m-1 in ascending order, that is, arrange the values from small to large. The sorted interval sequence is represented as Δ′1, Δ′2, …, Δ′ m-1 ; The initial value of the symbol width is represented as Δ′1×1 / f s , whose unit is s;

[0066] When m = 2, the estimation value of the symbol width is The unit is s. The step S53 is directly entered to estimate the BPSK signal bandwidth and the symbol number;

[0067] When m>2, the parameter estimation is performed according to the following steps;

[0068] S51. The interval sequence Δ'1, Δ'2, …, Δ'm-1 after sorting is obtained. m-1 The ratio of the latter value to the former value is calculated, and rounding is performed. The ratio is calculated as follows:

[0069] Let j=1:m-2,

[0070] S52. The symbol width value is estimated. The symbol width estimation value is τ e :

[0071]

[0072] The unit of τ e is s.

[0073] S53. The BPSK signal bandwidth and the symbol number are estimated.

[0074] The bandwidth estimation value is The unit is Hz;

[0075] The estimation value of the symbol number is Wherein, PW is the BPSK pulse width estimated by the step S1.

[0076] S6. The estimated BPSK signal carrier frequency, bandwidth, symbol width and symbol number are output.

[0077] In order to further verify the technical scheme of the present application, the present application will be further described in combination with the experimental test diagram.

[0078] The experimental verification of the present application is performed under the computer simulation condition, and the simulation software adopts MATLAB R2010a. In order to verify the effectiveness of the present application, two groups of experimental tests are performed.

[0079] Embodiment 1:

[0080] The BPSK signal amplitude is 1V, the carrier frequency is f c =10MHz, the symbol width is 1μs, the signal bandwidth is 1MHz, the encoding mode is thirteen-bit Barker code [1,1,1,1,1,0,0,1,1,0,1,0,1], and the sampling frequency is f s= 100MHz, the simulation time is one pulse width. Set different signal-to-noise ratios, and perform Monte Carlo simulation 500 times at each signal-to-noise ratio. When the difference between the estimated symbol width and the actual symbol width is not greater than 1 / 10 of the actual symbol width, it is considered that the symbol width estimation is accurate. When the difference between the estimated bandwidth and the actual bandwidth of the signal is not greater than 1 / 10 of the actual bandwidth, it is considered that the bandwidth estimation is accurate. When the estimated symbol number is equal to the actual symbol number, it is considered that the symbol number estimation is accurate. Through the patent scheme, the parameter estimation accuracy of the signal is shown in Table 1.

[0081] Table 1 Parameter accuracy rate of thirteen-bit Barker code BPSK signal

[0082]

[0083]

[0084] Embodiment 2:

[0085] The BPSK signal amplitude is 1V, and the carrier frequency is f c = 10MHz, the symbol width is 1μs, the signal bandwidth is 1MHz, the encoding mode is eleven-bit Barker code [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0], and the sampling frequency is f s = 120MHz, the simulation time is one pulse width. Set different signal-to-noise ratios, and perform Monte Carlo simulation 500 times at each signal-to-noise ratio. When the difference between the estimated symbol width and the actual symbol width is not greater than 1 / 10 of the actual symbol width, it is considered that the symbol width estimation is accurate. When the difference between the estimated bandwidth and the actual bandwidth of the signal is not greater than 1 / 10 of the actual bandwidth, it is considered that the bandwidth estimation is accurate. When the estimated symbol number is equal to the actual symbol number, it is considered that the symbol number estimation is accurate. Through the patent scheme, the parameter estimation accuracy of the signal is shown in Table 2.

[0086] Table 2 Parameter accuracy rate of eleven-bit Barker code BPSK signal

[0087]

[0088] It can be known from the analysis of Embodiment 1 that when the signal signal-to-noise ratio is 0dB, the symbol width estimation, bandwidth estimation and symbol number estimation accuracy rates all reach more than 85%, and with the increase of the signal-to-noise ratio, the three parameter estimation accuracy rates also increase, and when the signal-to-noise ratio is more than 2dB, the estimation accuracy rates of the three parameters can reach 100%. For Embodiment 2, when the signal signal-to-noise ratio is 0dB, the symbol width estimation, bandwidth estimation and symbol number estimation accuracy rates all reach more than 99%, and with the increase of the signal-to-noise ratio, the three parameter estimation accuracy rates also increase. The above experimental results show that the present application can estimate the parameters of the BPSK signal with a very high probability under the condition of as low as 0dB.

[0089] Although the present application has been described in detail with reference to the foregoing embodiments, the technical solutions recorded in the foregoing embodiments can be modified or some technical features can be replaced by equivalent features by those skilled in the art, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0090] Note:

[0091] Radar pulse repetition interval estimation method based on blind source separation (application date: April 28, 2021, application number: 202110466533.9)

Claims

1. A method for estimating BPSK signal parameters based on the combined application of FRFT and wavelet transform, characterized in that: Includes the following steps: Pulse width estimation is performed on the BPSK single-pulse radar pulse signal data identified by sorting and modulation. The carrier frequency of a single pulse signal is estimated by performing FRFT on it. A continuous wavelet transform is performed on a single pulse signal, and the wavelet coefficients are filtered and denoised by phase space reconstruction and singular value decomposition. The wavelet ridge is extracted by the phase difference method. The wavelet ridge is shaped, and a threshold is set according to the estimated signal carrier frequency. The maximum value of the wavelet ridge and its corresponding abscissa position are found. The abscissa position is also the moment when the maximum value is obtained. Based on the maximum point, differential operation and sorting are performed to calculate the symbol width, number of symbols and bandwidth parameters; The maxima are sorted in ascending order of value, and then the position sequence is further differentially processed to obtain the sampling interval between adjacent positions in the position sequence. The smallest maxima interval corresponds to the initial value of the symbol width to be estimated. Then calculate the ratio of the next sampling point interval to the previous sampling point interval, and round it to obtain a ratio sequence. Based on the initial value of the symbol width, the sampling point intervals sorted from smallest to largest, and the ratio sequence, calculate the final estimated value of the symbol width. The bandwidth of the BPSK signal is calculated based on the relationship between symbol width and bandwidth. The number of symbols is calculated based on the pulse width and symbol width of the BPSK signal; Output the estimated BPSK signal carrier frequency, bandwidth, symbol width, and number of symbols.

2. The BPSK signal parameter estimation method based on the combined application of FRFT and wavelet transform according to claim 1, characterized in that: The specific method for pulse width estimation of the BPSK single-pulse radar intra-pulse signal data identified by sorting and modulation is as follows: The intercepted signal is sorted and identified to obtain a BPSK signal pulse sequence containing intra-pulse modulation information. For any pulse, it is represented as x(t), t = 1, 2, ..., T, where T is the number of sampling points and the sampling frequency is f. s After normalizing the amplitude of x(t), the processed signal sequence is represented as follows: right Pulse width estimation is performed using a radar pulse repetition interval estimation method based on blind source separation. The estimated pulse widths are denoted as PW1, PW2, ..., PW N Where 1, 2, ..., N represent pulse numbers, and... The signal sequence truncated to a single pulse width is represented as follows: Where 1, 2, ..., N represent pulse numbers, and the duration of each pulse is one pulse width.

3. The BPSK signal parameter estimation method based on the combined application of FRFT and wavelet transform according to claim 1, characterized in that: The specific method for estimating the carrier frequency of a single pulse signal by performing FRFT is as follows: right Perform FRFT to estimate the signal carrier frequency based on the transformed waveform. The estimated value is expressed as f. ce .

4. The BPSK signal parameter estimation method based on the combined application of FRFT and wavelet transform according to claim 1, characterized in that: The specific method for performing continuous wavelet transform on a single pulse signal, filtering and denoising the wavelet coefficients through phase space reconstruction and singular value decomposition, and extracting wavelet ridges using the phase difference method is as follows: right Perform wavelet transform, denoted as cwt is the continuous wavelet transform function, 1 represents the scale of the wavelet transform, and cmor2-1 represents the name of the wavelet basis function; For y1, filtering is performed through phase space reconstruction and singular value decomposition. The number of rows in the reconstruction is M, which can be set according to the number of points in y1, and the number of columns is... Right now The number of sampling points is given, and the sampling interval τ = 1. The absolute value of the reconstructed and filtered signal is taken and represented as yy1. For yy1, its phase is calculated, and the phase difference is calculated by the phase difference method to obtain the wavelet ridge F(t, f), whose horizontal axis is the sampling point and the vertical axis is the frequency value.

5. The BPSK signal parameter estimation method based on the combined application of FRFT and wavelet transform according to claim 1, characterized in that: The specific method for shaping the wavelet ridge line, setting a threshold based on the estimated signal carrier frequency, and finding the maxima of the wavelet ridge line and its corresponding abscissa position is as follows: Let F max =max(F(t, f)), F min =min(F(t, f)), when F max -f ce ≥f ce -F min When, the shaped wavelet ridge F′(t, f) = F(t, f); when F max -f ce <f ce -F min At that time, the ridge line of the shaped wavelet F′(t, f) = f ce +F max -F(t, f); For the wavelet ridge F′(t, f), based on the signal carrier frequency estimate f ce Set a threshold C, C = 1.4 × f ce For wavelet ridge points whose ordinate values ​​are greater than C, find all their local maxima and their corresponding abscissa positions, where the abscissa positions correspond to the sampling point positions or sampling times; the local maximum sequence is represented as: pks1, pks2,…, pks m ; The sequence of x-coordinate positions corresponding to local maxima is represented as follows: locs1,locs2,…,locs m ; Where m is the number of local maxima.

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