A main lobe reconnaissance signal separation method based on multi-stage processing
Through a multi-stage processing method, the covariance matrix feature decomposition and time-domain cancellation technology are used to solve the problem that the existing technology is difficult to separate the close-range electromagnetic signals, and efficient signal separation and reconnaissance performance are achieved.
Patent Information
- Application Number
- CN202210877800.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-07-25
- Publication Date
- 2025-03-21
- Estimated Expiration
- 2042-07-25
AI Technical Summary
When the existing main lobe signal separation method processes electromagnetic signals with low spatial resolution, it is difficult to effectively separate the close-range signals, resulting in limited signal measurement and identification performance of the reconnaissance system.
Using a multi-stage processing method, by obtaining the received signal of the antenna array and calculating its covariance matrix, feature decomposition is performed to select the signal subspace, and searching for spectral peaks in combination with the multi-signal classification method, obtaining the incoming wave direction of the signal, and separating the signal through the time domain cancellation method.
This method does not require prior information of known signals, is insensitive to direction finding errors, can effectively separate the main lobe reconnaissance signal, improve signal recognition and parameter measurement performance, and does not affect subsequent beam formation.
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Figure CN115407292B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of signal processing, and in particular to a main lobe reconnaissance signal separation method based on multi-stage processing. Background Art
[0002] As a special military means of obtaining enemy military intelligence, electronic reconnaissance uses electronic equipment to collect weak electromagnetic signals in space, and after amplification and processing, identifies the characteristics of these signals. Electronic reconnaissance is divided into two aspects: communication electronic reconnaissance and radar electronic reconnaissance. The purpose of communication electronic reconnaissance is to obtain communication intelligence, understand the opponent's military intentions and the technical level of radio equipment, analyze the working frequency, modulation mode and modulation parameters of the enemy's communication signals based on the intercepted signals, locate the equipment, and guide the jammer to interfere with the communication equipment of key nodes; the purpose of radar electronic reconnaissance is to intercept useful information from the enemy radar transmission signal, obtain intelligence such as radar deployment, function, performance and modulation parameters in hot spots, send out jamming signals as needed to compress the enemy radar warning range, and guide lethal weapons to carry out fire strikes when necessary.
[0003] Whether it is communication electronic reconnaissance or radar electronic reconnaissance, it is necessary to measure and analyze the parameters of the radiation source signal to identify parameters such as signal power, bandwidth, carrier frequency, and modulation mode. Due to the large number of electromagnetic signals in space, the reconnaissance receiver receives more than one type of electromagnetic signal, and these signals are often inseparable in the time and frequency domains. It is necessary to separate the signals by the direction of the incoming wave. Electronic reconnaissance generally uses a wide beam to detect electromagnetic signals in space, and the spatial resolution is low. When two signals are close to each other in the airspace, it is difficult to separate the two types of signals through conventional airspace processing methods, which affects the subsequent reconnaissance system's measurement and identification of the reconnaissance signal. Therefore, signal separation is required before processing the reconnaissance signal to avoid mutual interference between the reconnaissance signals.
[0004] The existing main lobe signal separation methods are mainly divided into four categories: the first category is a processing method based on a blocking matrix. This method constructs a blocking matrix by obtaining the incoming wave direction of the main lobe signal to remove one of the main lobe signals, which will cause the loss of antenna freedom; the second category is a processing method based on feature projection. This method constructs the feature vector corresponding to the main lobe signal, performs feature projection matrix preprocessing, and eliminates one of the main lobe signals. This method is sensitive to errors, and feature estimation deviation will cause a sharp decline in interference suppression performance. The third category is a processing method based on blind source separation. This method uses the statistical characteristics between signals and uses independent component analysis to separate each signal. This method requires that there can only be one signal that obeys the Gaussian distribution in the mixed signal, and has high requirements on the statistical characteristics of the signal, which limits its practical application. The fourth category is a processing method based on polarization processing. This method starts from the angle domain and polarization domain of the signal and performs signal recognition by extracting the polarization feature differences of each signal in the main lobe. Electronic reconnaissance is a non-cooperative signal reception method. It is difficult to identify the polarization mode of the mixed signal, and the antenna distribution needs to meet certain requirements. Therefore, it is necessary to adopt new technical means to study the separation method of the main lobe reconnaissance signal and improve the signal recognition and parameter measurement performance of the electronic reconnaissance system. Summary of the invention
[0005] The object of the present invention is to overcome the above-mentioned defects and provide a main lobe reconnaissance signal separation method based on multi-stage processing.
[0006] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:
[0007] A main lobe reconnaissance signal separation method based on multi-stage processing, comprising:
[0008] Obtaining a received signal S of an antenna array and calculating a covariance matrix R of the received signal S, wherein the number of array elements of the antenna array is M; the received signal includes a plurality of reconnaissance signals;
[0009] Performing eigendecomposition on the covariance matrix R to obtain a diagonal matrix Λ constructed by M eigenvalues and a matrix U composed of M eigenvectors; the eigenvalues in the diagonal matrix Λ decrease from the upper left to the lower right;
[0010] Select the eigenvectors corresponding to the first P eigenvalues as the signal subspace U P , the first P eigenvalues are the P eigenvalues selected in sequence from the upper left in the diagonal matrix Λ;
[0011] The spectrum peak is searched in the main lobe range by using the multiple signal classification method to obtain the incoming wave direction θ of each reconnaissance signal in the main lobe D , take the incoming direction of one of the signals θ P As the incoming wave direction of the interference signal and construct the guiding vector a of the interference signalP , take the incoming direction of another signal θ T As the incoming wave direction of the target signal and construct the guidance vector a of the target signal T ;
[0012] The received signal s of the first array element 1 Multiplying the interference signal's steering vector to obtain the sample values of interference in the 2nd to Mth array elements The interference signal in the received signal of each array element is eliminated in turn by using the time domain cancellation method to obtain the cancellation results of the 2nd to Mth antenna array elements. For the first array element, the product of the received signal of the second array element and the conjugate of the interference signal steering vector is used as the interference sample for cancellation, and the cancellation result is obtained.
[0013] Directing vector a with target signal T and interference signal steering vector a P The difference between the two is taken as the new steering vector a N , the target signal s to be detected is obtained through beam forming.
[0014] Repeat the above process to change the incoming directions of the interference signal and the target signal, separate the received signal, and obtain various reconnaissance signals.
[0015] Preferably, the calculation formula of the covariance matrix R of the received signal S is as follows:
[0016] R = E[S(t)S H (t)]
[0017] Where S(t) = [s 1 (t) s 2 (t) … s M (t)],s 1 (t) s 2 (t) …s M (t) respectively represent the received signals of the 1st, 2nd, …, Mth array element at time t, () H To find the conjugate transpose operation.
[0018] Preferably, the calculation formula for eigendecomposition of the covariance matrix R is as follows:
[0019]
[0020] where λ m is the mth eigenvalue, m=1,2,…,P,u m is the eigenvector corresponding to the mth eigenvalue, is the nth eigenvalue, n=P+1,…,M,u nis the eigenvector corresponding to the nth eigenvalue.
[0021] Preferably, the signal subspace U P It is expressed as:
[0022] U P =[u 1 ,u 2 ,…,u P ]
[0023] where u 1 ,u 2 ,…,u P is the eigenvector corresponding to the 1st, 2nd,…,Pth eigenvalue.
[0024] Preferably, the method of searching for spectral peaks is as follows:
[0025] The spatial spectrum function P(θ) at the incoming wave direction θ satisfies
[0026]
[0027] where a(θ) is the steering vector of the antenna array, m is the index of the antenna element, m = 1, 2, ..., M, d is the distance between adjacent elements, λ is the signal wavelength, j is the imaginary unit, and I is an M × M unit matrix;
[0028] All incoming wave directions are traversed to obtain the maximum value of the spatial spectrum function, where the maximum value of the spatial spectrum function is the spectrum peak.
[0029] Preferably, the incoming direction θ of the reconnaissance signal in the main lobe is D The calculation formula is as follows:
[0030]
[0031] Preferably, the interference signal steering vector a P The construction formula is as follows:
[0032]
[0033] Where d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
[0034] Preferably, the steering vector a of the target signal T The construction formula is as follows:
[0035]
[0036] Where d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
[0037] Preferably, the interference signal sample value in the mth array element cancellation at time t is The calculation formula is as follows:
[0038]
[0039] where s 1 (t) is the received signal of the first array element at time t, d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
[0040] Preferably, the cancellation result of the mth array element at time t is satisfy:
[0041]
[0042] where s m (t) is the received signal of the mth array element at time t, [] -1 To perform the inverse operation.
[0043] Preferably, the interference signal sample value in the first array element cancellation at time t is The calculation formula is as follows:
[0044]
[0045] where s 2 (t) is the received signal of the second array element at time t, d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
[0046] Preferably, the calculation formula of the target signal s to be detected is as follows:
[0047]
[0048] Compared with the prior art, the present invention has the following beneficial effects:
[0049] (1) The method proposed in the present invention utilizes two-stage space-time processing, does not require prior information of known signals, is insensitive to direction finding errors, and can effectively separate the main lobe reconnaissance signal.
[0050] (2) The present invention uses a time domain cancellation method to perform time domain cancellation on the array element level signal by finding the direction of the signal, which does not affect the subsequent beam forming and can ensure that the energy of the received signal is not affected.
[0051] (3) The present invention reconstructs part of the reconnaissance signal in the spatial domain through array element signals and angle measurement results, which greatly improves the efficiency of obtaining signal samples and has stronger applicability.
[0052] (4) The present invention adopts the time domain adaptive cancellation method to cancel interference to a great extent, reduce the cancellation residual, and improve the parameter acquisition performance of the reconnaissance signal. BRIEF DESCRIPTION OF THE DRAWINGS
[0053] Figure 1 This is a flow chart of a main lobe reconnaissance signal separation method based on multi-stage processing of the present invention;
[0054] Figure 2 Schematic diagram of the first reconnaissance signal of the present invention, wherein (a) is a signal waveform diagram, (b) is a signal spectrum diagram, and (c) is a signal constellation diagram;
[0055] Figure 3 Schematic diagram of the second reconnaissance signal of the present invention, wherein (a) is a signal waveform diagram, (b) is a signal spectrum diagram, and (c) is a signal constellation diagram;
[0056] Figure 4 Schematic diagram of a signal obtained by a reconnaissance system after mixing the first and second reconnaissance signals of the present invention, wherein (a) is a signal waveform diagram, (b) is a signal spectrum diagram, and (c) is a signal constellation diagram;
[0057] Figure 5 The spectrum peak search result using the multiple signal classification method within the main lobe range of the present invention;
[0058] Figure 6 Schematic diagram of the first reconnaissance signal obtained after signal separation of the present invention, wherein (a) is a signal waveform diagram, (b) is a signal spectrum diagram, and (c) is a signal constellation diagram;
[0059] Figure 7 Schematic diagram of the second reconnaissance signal obtained after signal separation of the present invention, wherein (a) is a signal waveform diagram, (b) is a signal spectrum diagram, and (c) is a signal constellation diagram. DETAILED DESCRIPTION
[0060] The following detailed description of the present invention will make the features and advantages of the present invention more clear and explicit.
[0061] The present invention first obtains the echo signal received by the antenna array and calculates the covariance matrix of the received signal. Then, the covariance matrix of the received signal is subjected to eigendecomposition, and the number of information sources is judged according to the eigenvalues obtained by the eigendecomposition. Then, according to the distribution of the eigenvalues, the eigenvector corresponding to the large eigenvalue is selected as the signal subspace, and the spectrum peak is searched within the main lobe range of the beam using a multiple signal classification method to obtain the wave direction of the main lobe reconnaissance signal, and the wave direction of one of the signals is taken as the wave direction of the interference signal and the steering vector of the interference signal is constructed, and the wave direction of the other signal is taken as the wave direction of the target signal and the steering vector of the target signal is constructed. Then, the product of the received signal of the first array element and the steering vector of the interference signal is used as the sample value of the interference, and the interference signal in the received signal of each array element is eliminated in turn by using the method of time domain cancellation. For the first array element, the product of the received signal of the second array element and the conjugate of the steering vector of the interference signal is used as the sample value of the interference for cancellation. Then, the difference between the steering vector of the target signal and the steering vector of the interference signal is used as the new steering vector, and the reconnaissance signal is obtained by beamforming, and the separation of the reconnaissance signals can be realized in turn. The present invention can effectively identify and separate the main lobe reconnaissance signal.
[0062] like Figure 1 As shown, the specific steps of the present invention are as follows:
[0063] (1) Obtaining a received signal S of the antenna array and calculating a covariance matrix R of the received signal S; the received signal includes a variety of reconnaissance signals;
[0064] (2) Performing eigendecomposition on the covariance matrix of the received signal S to obtain the eigenvalue diagonal matrix Λ and the eigenvector matrix U;
[0065] (3) According to the distribution of eigenvalues, select the eigenvectors corresponding to the first P larger eigenvalues in the diagonal matrix as the signal subspace U P ;
[0066] (4) Using the multiple signal classification method to search for spectrum peaks within the main lobe, the incoming direction θ of each reconnaissance signal within the main lobe is obtained. D , take the direction of arrival of one of the signals as the direction of arrival of the interference signal and construct the steering vector a of the interference signal P , take the wave direction of another signal as the wave direction of the target signal and construct the steering vector a of the target signal T ;
[0067] (5) The received signal s of the first array element 1 Multiply the interference sample values in the 2nd to Mth array elements by the steering vector of the interference signal The interference signal in each array element is eliminated in turn using the time domain cancellation method. For the first array element, the product of the received signal of the second array element and the conjugate of the interference signal steering vector is used as the interference sample for cancellation;
[0068] (6) Using the target signal to guide vector a T and interference signal steering vector a P The difference between the two is taken as the new steering vector a N , the target signal s to be detected is obtained through beam forming. Other detection signals can be obtained through multiple processing.
[0069] In step (1), at time t, the covariance matrix of the received signal is calculated as follows:
[0070] R = E[S(t)S H (t)]
[0071] Where S(t)=[s 1 (t) s 2 (t) … s M (t)],s 1 (t) s 2 (t) … s M (t) respectively represent the received signals of the 1st, 2nd, …, Mth array element at time t, () H To find the conjugate transpose operation.
[0072] In step (2), the calculation formula for eigendecomposition of the covariance matrix R is as follows:
[0073]
[0074] where λ m is the mth eigenvalue, m=1,2,…,P,u m is the eigenvector corresponding to the mth eigenvalue, is the nth eigenvalue, n=P+1,…,M,u n is the eigenvector corresponding to the nth eigenvalue.
[0075] In step (3), select the eigenvectors corresponding to the first P larger eigenvalues in the diagonal matrix as the signal subspace U P , which can be expressed as:
[0076] U P =[u 1 ,u 2 ,…,u P ]
[0077] In step (4), the spatial spectrum function P(θ) at the incoming wave direction θ satisfies
[0078]
[0079] where a(θ) is the steering vector of the antenna array, m is the index of the antenna element, m = 1, 2, ..., M, d is the distance between adjacent elements, λ is the signal wavelength, j is the imaginary unit, and I is an M × M unit matrix;
[0080] All incoming wave directions are traversed to obtain the maximum value of the spatial spectrum function, where the maximum value of the spatial spectrum function is the spectrum peak.
[0081] In step (4), the direction of arrival of each reconnaissance signal in the main lobe is θ D The calculation formula is as follows:
[0082]
[0083] In step (4), the interference signal's steering vector a P The construction formula is as follows:
[0084]
[0085] Where d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
[0086] In step (4), the steering vector a of the target signal T The construction formula is as follows:
[0087]
[0088] Where d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
[0089] In step (4), the interference signal sample value in the mth array element cancellation at time t is The calculation formula is as follows:
[0090]
[0091] where s 1 (t) is the received signal of the first array element at time t.
[0092] In step (5), the cancellation result of the mth array element at time t is satisfy:
[0093]
[0094] Where i represents the array element index, [] -1 To find the inverse operation. m (t) is the received signal of the i-th array element at time t.
[0095] In step (5), the interference signal sample value in the first element cancellation at time t is The calculation formula is as follows:
[0096]
[0097] where s 2 (t) is the received signal of the second array element at time t.
[0098] In step (6), the calculation formula of the useful signal s at time t is as follows:
[0099]
[0100] Spectrum is the abbreviation of frequency spectrum density, which is the distribution curve of frequency. Searching for the target signal in the frequency band is called signal detection. If there is no signal in the frequency band, the spectrum is relatively flat; if there is a signal in the frequency band, the spectrum will have large fluctuations at the signal position. From the above analysis, it can be seen that if the spectrum fluctuates greatly at the signal position in the frequency band, it is considered that there is a signal in the frequency band.
[0101] From the above analysis, it can be seen that within a specific frequency band, if the waveform, bandwidth and constellation diagram of the target signal are inconsistent with the original signal, it means that the signal received by the reconnaissance is impure and the signal parameter identification and modulation type identification cannot be performed. If the signal waveform, bandwidth and constellation diagram obtained after signal separation are consistent with the original signal, the subsequent signal parameter identification and modulation type identification can be performed, which shows the effectiveness of the proposed method. The spectrum of the signal under different conditions is analyzed below, and a brief description is as follows.
[0102] Figure 2 The waveform, spectrum and constellation diagram of the 16QAM signal to be detected. It can be seen that the spectrum has large fluctuations at the signal position. Figure 3 The waveform, spectrum and constellation diagram of the QPSK signal to be detected. It can be seen that the spectrum has large fluctuations at the signal position. Figure 4 The waveform, spectrum and constellation diagram of the mixed signal are obtained by detecting the main lobe of the antenna beam of the electronic reconnaissance system. From the results in the figure, it can be seen that the waveform, spectrum and constellation diagram of the mixed signal are different from those of the 16QAM signal and the QPSK signal because the signal separation is not performed.
[0103] Figure 5 This is the result obtained by searching the spectrum peak in the main lobe of the beam using the multiple signal classification method. From the result, two obvious peaks can be seen, corresponding to the incoming directions of the 16QAM signal and the QPSK signal respectively. The result shows that the method of the present invention can realize interference direction finding.
[0104] Figure 6The signal waveform, spectrum and constellation diagram obtained by post-processing the main lobe signal separation using the method proposed by the present invention. Figure 2 By comparison, the obtained signal waveform, spectrum and constellation diagram are basically the same as the original 16QAM signal. However, there are differences in amplitude due to the influence of antenna beam reception and noise.
[0105] Figure 7 The signal waveform, spectrum and constellation diagram obtained by post-processing the main lobe signal separation using the method proposed by the present invention. Figure 2 By comparison, the obtained signal waveform, spectrum and constellation diagram are basically the same as the original QPSK signal. However, there are differences in amplitude due to the influence of antenna beam reception and noise.
[0106] The above results show that the method proposed in the present invention can effectively separate the reconnaissance signals within the main lobe range of the antenna beam.
[0107] The present invention has been described in detail above in conjunction with specific implementations and exemplary examples, but these descriptions cannot be understood as limiting the present invention. Those skilled in the art understand that, without departing from the spirit and scope of the present invention, a variety of equivalent substitutions, modifications or improvements may be made to the technical solution of the present invention and its implementation methods, all of which fall within the scope of the present invention. The scope of protection of the present invention shall be subject to the attached claims.
[0108] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.
Claims
1. A main lobe reconnaissance signal separation method based on multi-stage processing, characterized in that: include: Obtain a received signal S of the antenna array, and calculate a covariance matrix R of the received signal S, where the number of array elements of the antenna array is M; The received signal includes a plurality of reconnaissance signals; Performing eigendecomposition on the covariance matrix R to obtain a diagonal matrix Λ constructed by M eigenvalues and a matrix U composed of M eigenvectors; the eigenvalues in the diagonal matrix Λ decrease from the upper left to the lower right; Select the eigenvectors corresponding to the first P eigenvalues as the signal subspace U P , the first P eigenvalues are the P eigenvalues selected in sequence from the upper left in the diagonal matrix Λ; The spectrum peak is searched in the main lobe range by using the multiple signal classification method to obtain the incoming wave direction θ of each reconnaissance signal in the main lobe D , take the incoming direction of one of the signals θ P As the incoming wave direction of the interference signal and construct the guiding vector a of the interference signal P , take the incoming direction of another signal θ T As the incoming wave direction of the target signal and construct the guidance vector a of the target signal T ; Multiply the received signal s1 of the first array element by the steering vector of the interference signal to obtain the sample values of the interference in the second to Mth array elements The interference signal in the received signal of each array element is eliminated in turn by using the time domain cancellation method to obtain the cancellation results of the 2nd to Mth antenna array elements. For the first array element, the product of the received signal of the second array element and the conjugate of the interference signal steering vector is used as the interference sample for cancellation, and the cancellation result is obtained. Directing vector a with target signal T and interference signal steering vector a P The difference between the two is taken as the new steering vector a N , the target signal s to be detected is obtained through beam forming; Repeat the above process to change the incoming directions of the interference signal and the target signal, separate the received signal, and obtain various reconnaissance signals.
2. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1 is characterized in that: The calculation formula of the covariance matrix R of the received signal S is as follows: R=E[S(t)S H (t)] where S(t)=[s1(t) s2(t) … s M (t)], s1(t) s2(t) … s M (t) respectively represent the received signals of the 1st, 2nd, …, Mth array element at time t, () H To find the conjugate transpose operation.
3. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1 is characterized in that: The calculation formula for eigendecomposition of the covariance matrix R is as follows: where λ m is the mth eigenvalue, m=1,2,…,P,u m is the eigenvector corresponding to the mth eigenvalue, is the nth eigenvalue, n=P+1,…,M,u n is the eigenvector corresponding to the nth eigenvalue.
4. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1, characterized in that: Signal subspace U P It is expressed as: U P =[u1,u2,…,u P ] where u1,u2,…,u P is the eigenvector corresponding to the 1st, 2nd,…,Pth eigenvalue.
5. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1, characterized in that: The way to search for peaks is as follows: The spatial spectrum function P(θ) at the incoming wave direction θ satisfies where a(θ) is the steering vector of the antenna array, m is the index of the antenna element, m = 1, 2, ..., M, d is the distance between adjacent elements, λ is the signal wavelength, j is the imaginary unit, and I is an M × M unit matrix; All incoming wave directions are traversed to obtain the maximum value of the spatial spectrum function, where the maximum value of the spatial spectrum function is the spectrum peak.
6. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 5, characterized in that: The direction of the reconnaissance signal in the main lobe is θ D The calculation formula is as follows: 。 7. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1, characterized in that: The steering vector a of the interference signal P The construction formula is as follows: Where d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
8. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1, characterized in that: The steering vector a of the target signal T The construction formula is as follows: Where d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
9. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1, characterized in that: The sample value of the interference signal in the mth array element cancellation at time t The calculation formula is as follows: Where s1(t) is the received signal of the first array element at time t, d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
10. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 9, characterized in that: The cancellation result of the mth array element at time t is satisfy: where s m (t) is the received signal of the mth array element at time t, [] -1 To perform the inverse operation.
11. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1, characterized in that: The interference signal sample value in the first array element cancellation at time t The calculation formula is as follows: Where s2(t) is the received signal of the second array element at time t, d is the distance between adjacent array elements, λ is the signal wavelength, and j is the imaginary unit.
12. The main lobe reconnaissance signal separation method based on multi-stage processing according to claim 1, characterized in that: The calculation formula of the target signal s to be detected is as follows:
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