A single-channel radar signal blind source separation method under time-frequency aliasing

Abstract

The application discloses a radar signal single-channel blind source separation method under time-frequency aliasing, which comprises the following steps: firstly, Fourier transform is conducted on the received single-channel time-frequency aliasing radar signal, time-domain signals are converted into frequency-domain signals, and frequency band division is conducted; then, inverse Fourier transform is conducted on the frequency-domain signals after the frequency band division, a virtual multi-channel time-domain signal is constructed, eigenvalue decomposition is conducted on the covariance matrix of the virtual multi-channel time-domain signal, and a whitening matrix required in a whitening process is calculated; a blind source separation matrix is initialized, the blind source separation matrix is used, and source estimation is conducted; then, Fourier transform is conducted on the separated signals, frequency-domain signals are obtained after amplitude normalization, a frequency band division factor is set, and an optimal frequency band division factor is calculated; finally, the optimal frequency band division factor is used for frequency band division, and a final blind source separation result is obtained. The application has the advantages of simple method, high radar signal separation efficiency and good separation performance.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and in particular, it is a method for separating blind sources of single-channel radar signals under time-frequency aliasing. Background Technology

[0002] Radar signal simulation is one of the key technologies in electronic warfare threat environment simulation. The complex electromagnetic battlefield environment in modern warfare, characterized by severe spectral aliasing and spatial interweaving, poses a serious obstacle to modern information warfare. Isolating key source signals from numerous observed aliased signals can provide a competitive advantage in modern electronic warfare.

[0003] Radar signal separation refers to extracting the echo signal of the desired target from the received radar signal, that is, separating various radar clutter signals from the target echo signal to achieve clutter suppression. Since multiple radar signals received by a single channel often overlap in the time and frequency domains, traditional time-domain or frequency-domain filtering methods cannot separate such signals. Currently, the mainstream single-channel radar signal separation methods can be broadly categorized into three types: transform domain filtering methods, sparse decomposition representation methods, and single-channel to multi-channel conversion methods, followed by multi-channel blind source separation methods for solving the problem. The single-channel to multi-channel conversion can be broadly divided into empirical mode decomposition and wavelet or wavelet packet decomposition.

[0004] Although significant progress has been made in single-channel blind source separation technology using wavelet multi-scale decomposition in recent years, certain bottlenecks remain in single-channel radar signal blind source separation under time-frequency aliasing. These bottlenecks stem from the reliance on appropriate wavelet basis selection and empirically determined wavelet center frequencies, with the center frequency position being highly dependent on the separation algorithm's performance. Therefore, overcoming the limitations of limited prior conditions and achieving accurate and efficient radar signal separation is a key challenge to be addressed in single-channel radar signal blind source separation. Summary of the Invention

[0005] The purpose of this invention is to provide a radar signal blind source separation method that overcomes various interferences and quickly and accurately separates various radar signals under time-frequency aliasing.

[0006] The technical solution to achieve the purpose of this invention is: a method for separating blind sources of single-channel radar signals under time-frequency aliasing, comprising the following steps:

[0007] Step 1: Receive single-channel time-frequency aliased radar signal, and perform Fourier transform on the received single-channel time-frequency aliased radar signal to convert the time domain signal into a frequency domain signal.

[0008] Step 2: Divide the frequency domain signal into frequency bands;

[0009] Step 3: Perform inverse Fourier transform on the frequency domain signal after frequency band division to construct a virtual multi-channel time domain signal;

[0010] Step 4: Perform eigenvalue decomposition on the covariance matrix of the virtual multi-channel time-domain signal;

[0011] Step 5: Calculate the whitening matrix required for the whitening process;

[0012] Step 6: Initialize the blind source separation matrix and use it to estimate the information sources;

[0013] Step 7: Perform Fourier transform on the separated signal obtained in Step 6, and then normalize the amplitude to obtain the frequency domain signal.

[0014] Step 8: Set the frequency band allocation factor and calculate the optimal frequency band allocation factor;

[0015] Step 9: Use the optimal frequency band division factor to divide the frequency band, and repeat steps 3 to 6 to obtain the final blind source separation result.

[0016] Further, in step 1, the received single-channel time-frequency aliased radar signal is subjected to a Fourier transform to convert the time-domain signal into a frequency-domain signal, as detailed below:

[0017] Step 1.1: Define the mixed signal received by the radar receiver as x(t), t∈N, where N represents the time range for receiving the mixed signal;

[0018] Step 1.2: Perform Fourier transform on the received single-channel time-frequency aliased radar signal to obtain the frequency domain signal X(w), thus converting the radar signal from a time domain signal to a frequency domain signal.

[0019] Furthermore, the frequency band division of the frequency domain signal described in step 2 is as follows:

[0020] Based on the single-channel signal receiving frequency band L1≤f≤L2, where L1 is the lower cutoff frequency, L2 is the upper cutoff frequency, and f is the frequency of the received signal, the frequency domain signal X(w) is divided into M segments within the receiving frequency band, resulting in the segmented frequency domain signals X1(w), X2(w)...X M (w), its frequency band range is F1, F2…F M ;

[0021] Frequency band allocation is as shown in equation (1):

[0022]

[0023] In the formula, L3 is the bandwidth of each segment of the frequency domain signal after it is uniformly divided.

[0024] Furthermore, step 3 involves performing an inverse Fourier transform on the frequency domain signal after frequency band division to construct a virtual multi-channel time domain signal, as detailed below:

[0025] For the segmented frequency domain signals X1(w), X2(w)...X M (w) Perform N-point inverse Fourier transforms respectively to obtain x1(t), x2(t), ..., x M Given M time-domain signals (t), construct a virtual multi-channel time-domain signal X = [x1(t), x2(t), ... x2(t)]. M (t)] T Where x1(t), x2(t), ..., x M The length of signal x(t) should be consistent with the length of the mixed signal x(t).

[0026] Furthermore, the eigenvalue decomposition of the covariance matrix of the virtual multi-channel time-domain signal described in step 4 is as follows:

[0027] For the constructed M virtual multi-channel time-domain signals X=[x1(t),x2(t),…,x M (t)] T covariance matrix R x Perform eigenvalue decomposition:

[0028] R x =E{XX H}=UΛU H (2)

[0029] Where U is the eigenvector and Λ is the eigenvalue matrix.

[0030] Furthermore, the whitening matrix required for the whitening process described in step 5 is as follows:

[0031] The whitening matrix Z required for the whitening process is calculated. After whitening, the matrix has uncorrelated characteristics among its components and has unit variance. The formula is as follows:

[0032] Z = Λ -1 / 2 U H X (3)

[0033] Furthermore, the initialization of the blind source separation matrix described in step 6, and the use of the blind source separation matrix to estimate the information source, are detailed as follows:

[0034] Step 6.1: Use the FastICA algorithm to perform blind source separation and extract the original independent signals from the mixed data;

[0035] Initialize the separation matrix W H =I M IM Given an M×M identity matrix, the separation matrix W H The column vectors w1, w2, ... w in M According to w1 to w M The sequence is updated using the iterative formula of w, and the separation matrix W is obtained. H The iterative formula for each column vector w is shown in equation (4):

[0036]

[0037] Where Z is the whitening matrix calculated in step 5, E{·} denotes the expectation, g:R→R is a nonlinear function, and g=y 3 ;

[0038] Step 6.2: Use the separation matrix W obtained in step 6.1 H To estimate the information source Y=W H X.

[0039] Furthermore, step 7 involves performing a Fourier transform on the separated signal obtained in step 6, followed by amplitude normalization to obtain the frequency domain signal, as detailed below:

[0040] The separated signal Y = [y1(t), y2(t), ..., y2(t)] obtained in step 6 is used to separate the signal. M (t)] T After performing a Fourier transform and amplitude normalization, the frequency domain signal [Y1(w), Y2(w)..., Y] is obtained. M (w)] T .

[0041] Furthermore, step 8, which involves setting the frequency band allocation factor and calculating the optimal frequency band allocation factor, is detailed as follows:

[0042] Step 8.1: Set the frequency band division factor a, with a ranging from 0 to 1 in increments of 0.05;

[0043] Step 8.2: Substitute the frequency band division factor a into the frequency band division formula (1) to obtain:

[0044]

[0045] Step 8.3: For each frequency band partitioning factor a, calculate the variance of the maximum amplitude of the frequency domain signal in each channel and the amplitude of the signal in the received frequency band range L1≤f≤L2, to obtain [D1{Y1(w)},D2{Y2(w)}…,D M {Y M (w)}], where D n {Y n(w)},n∈[1,M] represents the variance of the nth channel, and then the average variance of the virtual multi-channel corresponding to each frequency band partitioning factor is calculated as D=D1+D2+…D M / M;

[0046] Step 8.4: Change the frequency band division factor a in steps of 0.05, compare the average variance D calculated by different frequency band factors a, and take the frequency band division factor a1 corresponding to the minimum value as the optimal frequency band division factor.

[0047] Furthermore, step 9 involves using the optimal frequency band allocation factor to perform frequency band allocation, and repeating steps 3 to 6 to obtain the final blind source separation result, as detailed below:

[0048] The frequency band is divided using the optimal frequency band division factor a1. Then, steps 3 to 6 are repeated to perform inverse Fourier transform on the frequency domain signal after the frequency band division, construct a virtual multi-channel time domain signal, and perform eigenvalue decomposition on the covariance matrix of the virtual multi-channel time domain signal to calculate the whitening matrix required for the whitening process. Then, the blind source separation matrix is ​​initialized, and the source is estimated using the blind source separation matrix to obtain the final blind source separation result.

[0049] Compared with the prior art, the present invention has the following significant advantages: (1) It uses frequency band division to construct virtual multi-channel, which is simple in structure and improves the efficiency of radar signal separation; (2) It adapts to frequency band division based on the results, without relying on empirical values ​​to set parameters, thus improving the performance of radar signal separation. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the blind source separation method for single-channel radar signals under time-frequency aliasing according to the present invention.

[0051] Figure 2a This is a comparison chart of the QPSK signal similarity coefficients of the separation results under different signal-to-noise ratios when using the method of this invention and when using traditional wavelet transform to construct virtual multi-channel blind source separation.

[0052] Figure 2b This is a comparison chart of the BPSK signal similarity coefficients of the separation results under different signal-to-noise ratios when using the method of this invention and when using traditional wavelet transform to construct virtual multi-channel blind source separation.

[0053] Figure 3a This is a comparison chart of the QPSK signal similarity coefficients of the separation results under different carrier frequency intervals using the method of this invention and the traditional wavelet transform to construct virtual multi-channel blind source separation in this embodiment of the invention.

[0054] Figure 3bThis is a comparison chart of the BPSK signal similarity coefficients of the separation results under different carrier frequency intervals using the method of this invention and the traditional wavelet transform to construct virtual multi-channel blind source separation in this embodiment of the invention. Detailed Implementation

[0055] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0056] Combination Figure 1 The present invention provides a method for blind source separation of single-channel radar signals under time-frequency aliasing, comprising the following steps:

[0057] Step 1: Receive the single-channel time-frequency aliased radar signal, and perform a Fourier transform on the received single-channel time-frequency aliased radar signal to convert the time-domain signal into a frequency-domain signal, as follows:

[0058] Step 1.1: Define the mixed signal received by the radar receiver as x(t), t∈N, where N represents the time range for receiving the mixed signal;

[0059] Step 1.2: Perform Fourier transform on the received single-channel time-frequency aliased radar signal to obtain the frequency domain signal X(w), thus converting the radar signal from a time domain signal to a frequency domain signal.

[0060] Step 2: Divide the frequency domain signal into frequency bands, as follows:

[0061] Based on the single-channel signal receiving frequency band L1≤f≤L2, where L1 is the lower cutoff frequency, L2 is the upper cutoff frequency, and f is the frequency of the received signal, the frequency domain signal X(w) is divided into M segments within the receiving frequency band, resulting in the segmented frequency domain signals X1(w), X2(w)...X M (w), its frequency band range is F1, F2…F M ;

[0062] Frequency band allocation is as shown in equation (1):

[0063]

[0064] In the formula, L3 is the bandwidth of each segment of the frequency domain signal after it is uniformly divided.

[0065] Step 3: Perform an inverse Fourier transform on the frequency domain signal after frequency band division to construct a virtual multi-channel time domain signal, as follows:

[0066] For the segmented frequency domain signals X1(w), X2(w)...X M (w) Perform N-point inverse Fourier transforms respectively to obtain x1(t), x2(t), ..., x MGiven M time-domain signals (t), construct a virtual multi-channel time-domain signal X = [x1(t), x2(t), ... x2(t)]. M (t)] T Where x1(t), x2(t), ..., x M The length of signal x(t) should be consistent with the length of the mixed signal x(t).

[0067] Step 4: Perform eigenvalue decomposition on the covariance matrix of the virtual multi-channel time-domain signal, as follows:

[0068] For the constructed M virtual multi-channel time-domain signals X=[x1(t),x2(t),…,x M (t)] T covariance matrix R x Perform eigenvalue decomposition:

[0069] R x =E{XX H}=UΛU H (2)

[0070] Where U is the eigenvector and Λ is the eigenvalue matrix.

[0071] Step 5: Calculate the whitening matrix required for the whitening process, as follows:

[0072] The whitening matrix Z required for the whitening process is calculated. After whitening, the matrix has uncorrelated characteristics among its components and has unit variance. The formula is as follows:

[0073] Z = Λ -1 / 2 U H X (3)

[0074] Step 6: Initialize the blind source separation matrix. Use the blind source separation matrix to estimate the information sources, as follows:

[0075] Step 6.1: Use the FastICA algorithm to perform blind source separation and extract the original independent signals from the mixed data;

[0076] Initialize the separation matrix W H =I M I M Given an M×M identity matrix, the separation matrix W H The column vectors w1, w2, ... w in M According to w1 to w M The sequence is updated using the iterative formula of w, and the separation matrix W is obtained. H The iterative formula for each column vector w is shown in equation (4):

[0077]

[0078] Where Z is the whitening matrix calculated in step 5, E{·} denotes the expectation, g:R→R is a nonlinear function, and g=y 3 ;

[0079] Step 6.2: Use the separation matrix W obtained in step 6.1 H To estimate the information source Y=W H X.

[0080] Step 7: Perform a Fourier transform on the separated signal obtained in Step 6, and then normalize the amplitude to obtain the frequency domain signal, as follows:

[0081] The separated signal Y = [y1(t), y2(t), ..., y2(t)] obtained in step 6 is used to separate the signal. M (t)] T After performing a Fourier transform and amplitude normalization, the frequency domain signal [Y1(w), Y2(w)..., Y] is obtained. M (w)] T .

[0082] Step 8: Set the frequency band allocation factor and calculate the optimal frequency band allocation factor, as follows:

[0083] Step 8.1: Set the frequency band division factor a, with a ranging from 0 to 1 in increments of 0.05;

[0084] Step 8.2: Substituting the frequency band division factor a into the frequency band division formula (1), we can obtain:

[0085]

[0086] Step 8.3: For each frequency band partitioning factor a, calculate the variance of the maximum amplitude of the frequency domain signal in each channel and the amplitude of the signal in the received frequency band range L1≤f≤L2, to obtain [D1{Y1(w)},D2{Y2(w)}…,D M {Y M (w)}], where D n {Y n (w)},n∈[1,M] represents the variance of the nth channel, and then the average variance of the virtual multi-channel corresponding to each frequency band partitioning factor is calculated as D=D1+D2+…D M / M;

[0087] Step 8.4: Change the frequency band division factor a in steps of 0.05, compare the average variance D calculated by different frequency band factors a, and take the frequency band division factor a1 corresponding to the minimum value as the optimal frequency band division factor.

[0088] Step 9: Using the optimal frequency band allocation factor, perform frequency band allocation, and repeat steps 3 to 6 to obtain the final blind source separation result, as follows:

[0089] The frequency band is divided using the optimal frequency band division factor a1. Then, steps 3 to 6 are repeated to perform inverse Fourier transform on the frequency domain signal after the frequency band division, construct a virtual multi-channel time domain signal, and perform eigenvalue decomposition on the covariance matrix of the virtual multi-channel time domain signal to calculate the whitening matrix required for the whitening process. Then, the blind source separation matrix is ​​initialized, and the source is estimated using the blind source separation matrix to obtain the final blind source separation result.

[0090] Example 1

[0091] like Figure 1 As shown, the single-channel radar signal blind source separation method under time-frequency aliasing of the present invention includes the following steps:

[0092] Step 1: Receive the single-channel time-frequency aliased radar signal, and perform a Fourier transform on the received single-channel time-frequency aliased radar signal to convert the time-domain signal into a frequency-domain signal, as follows:

[0093] Step 1.1: For the time-frequency aliased time-domain radar signal x(t), t∈N, obtained by mixing the received QPSK quadrature phase shift keying signal and BPSK binary phase shift keying signal with a 1:1 mixing coefficient, N represents the time range of receiving the mixed signal. The carrier frequency of the QPSK signal is 8.5MHz, the carrier frequency of the BPSK signal is 8MHz, the code rate of the two signals is 0.6Mbps, and the sampling rate is 99MHz.

[0094] Step 1.2: Perform a Fourier transform on the mixed signal to obtain the frequency domain signal X(w), where w represents the frequency, thus converting the time domain signal into a frequency domain signal.

[0095] Step 2: Divide the frequency domain signal into frequency bands, as follows:

[0096] Based on the single-channel signal receiving frequency band of 7MHz≤f≤9MHz, where f is the frequency of the received signal, the frequency domain signal X(w) is divided into two segments within the receiving frequency band, resulting in the segmented frequency domain signal X1(w) with a frequency band range of 7MHz≤f≤8MHz; and the frequency domain signal X2(w) with a frequency band range of 8MHz≤f≤9MHz.

[0097] Step 3: Perform an inverse Fourier transform on the frequency domain signal after frequency band division to construct a virtual multi-channel time domain signal, as follows:

[0098] Perform N-point inverse Fourier transforms on the segmented frequency domain signals X1(w) and X2(w) respectively to obtain two time domain signals, x1(t) and x2(t), and construct a virtual multi-channel X = [x1(t), x2(t)]. TThe lengths of the x1(t) and x2(t) signals should be consistent with the length of the mixed signal x(t).

[0099] Step 4: Perform eigenvalue decomposition on the covariance matrix of the virtual multi-channel time-domain signal, as follows:

[0100] The two constructed virtual multi-channel time-domain signals are X = [x1(t), x2(t)]. T For its covariance matrix R x Perform eigenvalue decomposition:

[0101] R x =E{XX H}=UΛU H (2)

[0102] U is the eigenvector, and Λ is the eigenvalue matrix.

[0103] Step 5: Calculate the whitening matrix required for the whitening process, as follows:

[0104] The whitening matrix Z required for the whitening process is calculated. After whitening, the matrix has uncorrelated characteristics of each component and has unit variance, as shown in equation (3):

[0105] Z = Λ -1 / 2 U H X (3)

[0106] Step 6: Initialize the blind source separation matrix. Use the blind source separation matrix to estimate the information sources, as follows:

[0107] Step 6.1: Use the FastICA algorithm to perform blind source separation and extract the original independent signals from the mixed data;

[0108] Initialize the separation matrix W H =I 2×2 I 2×2 Given a 2×2 identity matrix, the separation matrix W H Each column vector w1, w2 in the matrix is ​​updated using the iterative formula for w in the order from w1 to w2, resulting in the separation matrix W. H The iterative formula for each column vector w is shown in equation (4):

[0109]

[0110] Where Z is the whitening matrix calculated in step 5, E{·} represents the expectation, and g:R→R is a nonlinear function that can be chosen in different ways. In this formula, g=y 3 ;

[0111] Step 6.2: Use the separation matrix W obtained in step 6.1 HEstimating the source Y=W H X.

[0112] Step 7: Perform a Fourier transform on the separated signal obtained in Step 6, and then normalize the amplitude to obtain the frequency domain signal, as follows:

[0113] The separated signal Y = [y1(t), y2(t)] obtained in step 6 T After performing a Fourier transform and amplitude normalization, the frequency domain signal [Y1(w), Y2(w)] is obtained. T .

[0114] Step 8: Set the frequency band allocation factor and calculate the optimal frequency band allocation factor, as follows:

[0115] Step 8.1: Set the frequency band division factor a, with a ranging from 0 to 1 in increments of 0.05;

[0116] Step 8.2: Substituting the frequency band allocation factor 'a' into the frequency band allocation formula yields:

[0117]

[0118] L3 represents the bandwidth of each frequency band after the frequency domain signal is uniformly divided, L1 = 7MHz, L2 = 9MHz, L4 represents the overlap between adjacent frequency bands after adding the frequency band division factor a; F1 and F2 represent the bandwidth of frequency domain signals Y1(w) and Y2(w), respectively.

[0119] Step 8.3: For each frequency band partitioning factor a, calculate the variance of the maximum amplitude of the frequency domain signal in each channel and the amplitude of the signal in the receiving frequency band range of 7MHz≤f≤9MHz, and obtain [D1{Y1(w)},D2{Y2(w)}] where D n {Y n (w)},n∈[1,2] represents the variance of the nth channel, and then the average variance of the virtual multi-channel corresponding to each frequency band division factor is calculated as D=D1+D2 / 2;

[0120] Step 8.4: Change the frequency band division factor a in steps of 0.05, and compare the average variance D calculated by different frequency band factors a. The minimum value of the average variance D corresponds to the frequency band division factor a1 = 0.5.

[0121] Step 9: Using the optimal frequency band allocation factor, perform frequency band allocation, and repeat steps 3 to 6 to obtain the final blind source separation result, as follows:

[0122] Frequency bands are divided using a band division factor a1 = 0.5. Then, steps 3 to 6 are repeated to perform inverse Fourier transform on the frequency domain signal after band division, constructing a virtual multi-channel time domain signal. Eigenvalue decomposition is performed on the covariance matrix of the virtual multi-channel time domain signal to calculate the whitening matrix required for the whitening process. Then, the blind source separation matrix is ​​initialized, and the source is estimated using the blind source separation matrix to obtain the final blind source separation result.

[0123] The results of traditional wavelet transform-based virtual multi-channel blind source separation and the separation results of this invention are as follows: Figure 2a , Figure 2b , Figure 3a , Figure 3b As shown, compared with the traditional wavelet transform method for constructing virtual multi-channel blind source separation, this invention has a simpler structure while significantly improving separation performance under time-frequency aliasing.

Claims

1. A method for blind source separation of single-channel radar signals under time-frequency aliasing, characterized in that, Includes the following steps: Step 1: Receive single-channel time-frequency aliased radar signal, and perform Fourier transform on the received single-channel time-frequency aliased radar signal to convert the time domain signal into a frequency domain signal. Step 2: Divide the frequency domain signal into frequency bands, as follows: Based on the single-channel signal receiving frequency band ,in To receive the lower cutoff frequency, The upper limit cutoff frequency for receiving signals. To determine the frequency of the received signal, the frequency domain signal is divided within the receiving frequency band. The frequency band is divided into M equal segments to obtain the segmented frequency domain signal. , … Its frequency band range is , … ; Frequency band allocation is as shown in equation (1): （1） In the formula This refers to the bandwidth corresponding to each segment of the frequency domain signal after it has been uniformly divided. Step 3: Perform inverse Fourier transform on the frequency domain signal after frequency band division to construct a virtual multi-channel time domain signal; Step 4: Perform eigenvalue decomposition on the covariance matrix of the virtual multi-channel time-domain signal; Step 5: Calculate the whitening matrix required for the whitening process; Step 6: Initialize the blind source separation matrix and use it to estimate the information sources; Step 7: Perform Fourier transform on the separated signal obtained in Step 6, and then normalize the amplitude to obtain the frequency domain signal. Step 8: Set the frequency band allocation factor and calculate the optimal frequency band allocation factor; Step 9: Use the optimal frequency band division factor to divide the frequency band, and repeat steps 3 to 6 to obtain the final blind source separation result.

2. The method for separating blind sources of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 1 involves receiving a single-channel time-frequency aliased radar signal. The received single-channel time-frequency aliased radar signal is then subjected to a Fourier transform to convert the time-domain signal into a frequency-domain signal, as detailed below: Step 1.1: Set the mixed signal received by the radar receiver to be... ,in Indicates the time range for receiving mixed signals; Step 1.2: Perform a Fourier transform on the received single-channel time-frequency aliasing radar signal to obtain the frequency domain signal. This converts radar signals from time-domain signals to frequency-domain signals.

3. The method for separating blind sources of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 3 involves performing an inverse Fourier transform on the frequency domain signal after frequency band division to construct a virtual multi-channel time domain signal, as detailed below: For the segmented frequency domain signal , … Perform separately Point Fourier inverse transform yields , …、 A virtual multi-channel time domain signal is constructed from M time domain signals. ,in , …、 The signal length should be consistent with the mixed signal. The length remains consistent.

4. The method for separating blind sources of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 4 involves performing eigenvalue decomposition on the covariance matrix of the virtual multi-channel time-domain signal, as detailed below: For the constructed M virtual multi-channel time-domain signals covariance matrix Perform eigenvalue decomposition: （2） in For feature vectors, It is the eigenvalue matrix.

5. The method for separating blind sources of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 5 describes the calculation of the whitening matrix required for the whitening process, as follows: Calculate the whitening matrix required for the whitening process The whitened matrix has uncorrelated characteristics among its components and has unit variance, as shown in the formula: （3）。 6. The method for separating blind sources of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 6 involves initializing the blind source separation matrix and using it to estimate the information sources. Specifically: Step 6.1: Use the FastICA algorithm to perform blind source separation and extract the original independent signals from the mixed data; Initialize the separation matrix , for identity matrix, for the separation matrix Each column vector in According to arrive The order of application The iterative formula is updated to separate the matrix. Each column vector The iterative formula is as shown in equation (4): （4） in The whitening matrix obtained in step 5. Indicates the expectation. It is a nonlinear function, where ; Step 6.2: Use the separation matrix obtained in Step 6.1 To estimate the information source. .

7. The method for separating blind sources of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 7 describes performing a Fourier transform on the separated signal obtained in step 6, followed by amplitude normalization to obtain the frequency domain signal, as detailed below: The separation signal obtained in step 6 After performing a Fourier transform and amplitude normalization, the frequency domain signal is obtained. .

8. The method for separating blind sources of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 8, which involves setting the frequency band allocation factor and calculating the optimal frequency band allocation factor, is detailed below: Step 8.1: Set the frequency band allocation factor , The value ranges from 0 to 1 in increments of 0.

05. Step 8.2: Divide the frequency band into factors. Substituting into the frequency band allocation formula (1), we get: （5） Step 8.3: Divide each frequency band into factors. Calculate the maximum amplitude of the frequency domain signal for each channel and its receiving frequency band range. The variance of the signal amplitude is obtained. ,in Indicates the first The variance of each channel is calculated, and then the average variance of the virtual multi-channel corresponding to each frequency band partitioning factor is obtained. ; Step 8.4: Change the frequency band allocation factor in steps of 0.

05. Comparison of factors in different frequency bands The calculated average variance Take the frequency band allocation factor corresponding to its minimum value. , as the optimal frequency band allocation factor.

9. The method for blind source separation of single-channel radar signals under time-frequency aliasing according to claim 1, characterized in that, Step 9 involves using the optimal frequency band allocation factor to divide the frequency band, and repeating steps 3 to 6 to obtain the final blind source separation result, as detailed below: With the optimal frequency band allocation factor To perform frequency band division, repeat steps 3 to 6, perform inverse Fourier transform on the frequency domain signal after frequency band division, construct a virtual multi-channel time domain signal, perform eigenvalue decomposition on the covariance matrix of the virtual multi-channel time domain signal, calculate the whitening matrix required for the whitening process, initialize the blind source separation matrix, use the blind source separation matrix to estimate the source, and obtain the final blind source separation result.

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