A Radar Anti-Main Lobe Spoofing Jamming Method Based on Radar Pattern

Abstract

This invention discloses a pattern-based EPC-MIMO radar anti-main lobe deception interference method, mainly addressing the problem that existing technologies cannot suppress main lobe deception interference under DOA error background. The implementation scheme is as follows: at the transmitting end, the transmitted signal is subjected to array element pulse coding; at the receiving end, the echo signal is subjected to matched filtering and decoding. Using the eigenvalue decomposition of the covariance matrix of the decoded echo signal, the equivalent receiving angle of the transmitted and received spatial frequencies of the false target is estimated, and multiple null regions are preset around the estimation results. Constraints are applied to the beam response around the false target in the transmit-receive spatial frequency domain. An optimization problem is constructed using an iterative weight vector control method, and the optimal weight vector is obtained by solving the optimization problem. The optimal beam is then used to suppress main lobe deception interference under DOA error background. This invention deepens the null depth, widens the null region of the pattern, improves the output signal-to-interference-plus-noise ratio and interference suppression performance, and can be used for target detection.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and further relates to a radar anti-main lobe deception jamming method, which can be used for target detection. Background Technology

[0002] In complex electromagnetic environments, deceptive jamming signals originating from the radar's main lobe direction can impair its target detection and tracking capabilities. EPC-MIMO radar, by simultaneously performing phase coding in the array elements and the slow time dimension, can control the main lobe direction of the transmitted pulse, resulting in pulse echoes from different range ambiguity regions possessing different transmission steering vectors. Based on this characteristic, by designing appropriate coding coefficients, EPC-MIMO radar can use non-adaptive beamforming techniques to extract signals from a specific range ambiguity region while suppressing interference signals from other range ambiguity regions. However, when there are errors in the direction of arrival (DOA), the performance of non-adaptive beamforming will be severely compromised.

[0003] Patent application CN202011131418.8 discloses a method for suppressing deception interference in array element-pulse code MIMO radar. The implementation scheme considers that false targets are delayed by several pulses compared to real targets and that real and false targets are located in different range ambiguity intervals. By designing the coding coefficients and compensation vectors of the EPC-MIMO radar, pre-compensation is performed on the transmit steering vector, and matched filtering is applied at the receiver to separate the transmit waveforms, ensuring that the false target is located precisely at the zero point of the radiation pattern and is effectively suppressed. Finally, the identification of real and false targets is achieved in the transmit and receive spatial frequencies and the three-dimensional pulse domain, and main lobe deception interference is suppressed by beam nulling. However, this method fails to suppress main lobe deception interference under the background of DOA error because it does not consider the problem of main lobe interference when DOA error exists. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the prior art by proposing a pattern-based EPC-MIMO radar anti-main lobe deception jamming method to effectively suppress main lobe deception jamming under DOA error background.

[0005] The key technologies of this invention are: using the eigenvalue decomposition of the echo signal sample covariance matrix to estimate the equivalent receiving angle in the transmission and reception spatial frequency domains of the main lobe spoofing interference; using the iterative weight vector control (IWC) method to constrain the beam response around the main lobe interference in the transmission-reception spatial frequency domain; iteratively updating the weight vector for beamforming until the beam response reaches the desired value, thus achieving optimal beamforming to suppress the main lobe spoofing interference. The implementation steps include the following:

[0006] (1) Construct a co-located MIMO radar system comprising M transmitting elements and N receiving elements. Set the system to transmit K pulses within the coherent processing time and perform pulse-element encoding on each transmitted pulse signal to obtain the k-th pulse signal s transmitted by the m-th transmitting element. m,k (t);

[0007] (2) Calculate the common propagation delay based on the distance and angle of the point target, calculate the Doppler frequency based on the velocity, and then calculate the k-th transmitted pulse signal s. m,k (t) The echo signal x of the point target is obtained after a time delay. n,k (t);

[0008] (3) Perform matched filtering on the echo signal at the receiving end, and decode it in the slow time dimension according to the output of the matched filtering of N receiving array elements to obtain the decoded echo signal.

[0009] (4) Perform eigenvalue decomposition of the covariance matrix on the decoded echo signal, and estimate the equivalent angle of the main lobe interference in the two-dimensional space-frequency plane of the transmit and receive space to obtain the estimation result of the q-th main lobe interference.

[0010]

[0011] Among them, h q It is the q-th largest eigenvector of the eigenvalue decomposition of the covariance matrix of the decoded echo signal, u(θ). R ,θ T ) represents the angle pair (θ) R ,θ T The relevant two-dimensional joint steering vector for transmission and reception, q takes values ​​from 1 to Q, where Q represents the number of main lobe interferences, and the symbol H represents the conjugate transpose;

[0012] (5) Construct multiple null regions with a preset response of ρ around the dummy target in the two-dimensional plane of the transmission and reception spatial frequencies;

[0013] L w (θ R ,θ T ) = w H u(θ R ,θ T )=ρ

[0014] Among them, L w (θ R ,θ T ) represents the angle pair (θ) when the weight vector is w. R ,θ T The directional pattern response at point ()

[0015] (6) Based on the spurious target angle estimation results and multiple preset null regions, an optimization problem for the radiation pattern weight vector is constructed. Solving the optimization problem yields the optimal weight vector, which constitutes the radiation pattern that meets the preset requirements, and the optimal weight vector w is obtained. * This vector is used to eliminate the direction of arrival (DOA) error, thereby suppressing the main lobe interference.

[0016] This invention applies constraints to a pre-defined null region around the dummy target in each iteration, and solves the optimization problem to obtain the optimal weight vector. Therefore, compared with existing beamforming methods, it can effectively eliminate the direction of arrival (DOA) error and suppress main lobe interference. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0018] Figure 2 This is a schematic diagram of the preset zero-depression region in this invention;

[0019] Figure 3 These are two-dimensional transmission-reception spatial frequency domain radiation patterns designed using the present invention and existing beamforming methods, respectively.

[0020] Figure 4 This is a cross-sectional view comparing the radiation pattern of the present invention with that of existing beamforming methods;

[0021] Figure 5 This is a graph showing the maximum amplitude response in the interference region of this invention as a function of the number of iterations;

[0022] Figure 6 This is a comparison chart of the output signal-to-interference-plus-noise ratio (SINR) versus the input SINR of the present invention and existing technologies, respectively. Detailed Implementation

[0023] The embodiments and effects of the present invention will be further described in detail below with reference to the accompanying drawings.

[0024] Reference Figure 1 The implementation steps of this example include the following:

[0025] Step 1: Construct the transmitted signal model and perform pulse-array encoding on each transmitted pulse signal.

[0026] 1.1) Set up M transmitting array elements and N receiving array elements, and use them together to form a MIMO radar system;

[0027] 1.2) Set the system to transmit K pulses within the coherent processing time, and perform pulse-element encoding on each transmitted pulse signal to obtain the k-th pulse signal s transmitted by the m-th transmitting element. m,k (t):

[0028] (1.2.1) Encode the k-th pulse emitted by the m-th transmitting element as:

[0029]

[0030] Where γ represents the coding coefficient;

[0031] (1.2.2) The orthogonal baseband waveform φ of the m-th transmitting element m (t), represented as:

[0032]

[0033] Where m′ is the m′-th transmitting element, and τ represents any time delay;

[0034] (1.2.3) Based on the results of (1.2.1) and (1.2.2), the k-th pulse signal transmitted by the m-th transmitting element is:

[0035]

[0036] Where E represents the transmit power and f0 represents the carrier frequency.

[0037] Step 2: Construct an echo signal model based on the location of the point target.

[0038] 2.1) Assume there is a point target in the far field, with an angle of θ0 and a distance of R0, respectively. Then the common propagation delay τ of this point target from the m-th array element to the n-th array element is... m,n for:

[0039]

[0040] Where d represents the spacing between array elements and c represents the speed of light;

[0041] 2.2) Considering a point target moving with velocity v0, the Doppler frequency f of this point target is... d0 :

[0042]

[0043] Where λ0 represents the wavelength;

[0044] 2.3) Let p be the target pulse delay number in the range ambiguity region. s Based on the results of steps 2.1) and 2.2), the echo signal x of the k-th pulse received by the n-th receiving element is obtained. n,k (t):

[0045]

[0046] Where, β sLet T be the complex scattering coefficient of the point target. r This indicates the pulse repetition time.

[0047] Step 3: Perform matched filtering on the echo signal.

[0048] 3.1) Construct M sets of matched filters, where the m-th matched filter h m (t) is represented as:

[0049] h m (t)=φ m * (-t)

[0050] The symbol * indicates conjugation;

[0051] 3.2) Use M sets of matched filters to separate each transmitted waveform to obtain the output x of the m-th matched filter. n,m,k (t) is:

[0052]

[0053] in, λ represents the complex scattering coefficient, λ0 represents the wavelength, d represents the element spacing, θ0 represents the target incident angle, and the symbol × represents convolution.

[0054] Step 4: Organize the matched filtering results and decode them in the slow time dimension.

[0055] 4.1) Organize the outputs of the matched filters from the N receiving channels, and combine the results from the matched filter of the k-th pulse. express:

[0056]

[0057] Where, x n,m,k (t) represents the matched filtering result of the k-th pulse transmitted by the m-th transmitting element and received by the n-th receiving element, and the symbol T represents transpose;

[0058] 4.2) The matched filtering result of the kth pulse In slow-time dimension decoding, the result after decoding the k-th pulse is obtained.

[0059] (4.2.1) The decoding vector g of the k-th pulse k Represented as:

[0060]

[0061] Among them, 1 N Represents an N-dimensional column vector whose elements are all 1s. This represents the code of the k-th pulse transmitted by the m-th transmitting element. This represents the code of the k-th pulse transmitted by the M-th transmitting element. Indicates the Kronecker product;

[0062] (4.2.2) Decode the k-th pulse to obtain the decoding result.

[0063]

[0064] Here, diag represents a diagonal matrix, and the symbol H represents the conjugate transpose.

[0065] Step 5: Organize the decoding results of K pulses to obtain the decoding result Y(t) of the total echo signal.

[0066] 5.1) Based on the launch guidance vector a(f) of the real target T0 ), receiving guide vector b(f) R0 ) and the Doppler vector c(f d0 The decoding results of K pulses are rewritten into the decoding result Y of the real target signal. s (t):

[0067]

[0068] in, Indicates the received spatial frequency. Indicates the transmission space frequency;

[0069] 5.2) In the presence of DOA error, based on the launch guidance vector a(f) of the false target Tq ), receiving guide vector b(f) Rq ) and the Doppler vector c(f dq Organize the decoding results of K pulses, and represent the decoding result of the q-th false target signal as Y. q (t):

[0070]

[0071] in, The complex scattering coefficients of the dummy target are denoted as . Indicates the received spatial frequency of the dummy target. θ represents the spatial frequency of the dummy target's emission. q The incident angle of the false target is represented by Δθ; Δθ represents the angular offset, assumed to be distributed within the allowable DOA error [-θ]. L ,θ H In the diagram, p′ represents the impulse delay number of the dummy target, and f dq Indicates the Doppler frequency of the false target;

[0072] 5.3) Based on the results of steps 5.1) and 5.2), the decoding result Y(t) of the total echo signal is obtained:

[0073]

[0074] Where N(t) represents the decoding result of the noise signal.

[0075] Step 6: Solve for the decoded echo signal covariance matrix R x And decompose its features.

[0076] 6.1) Obtain the covariance matrix R from the decoded echo signal. x :

[0077]

[0078] 6.2) Perform the following eigenvalue decomposition on the covariance matrix:

[0079] R x =UΛU H

[0080] Where U is a matrix composed of eigenvectors, and Λ is a diagonal matrix composed of eigenvalues.

[0081] Step 7: Estimate the angle of the false target and pre-determine multiple null regions around the estimation result, such as... Figure 2 As shown.

[0082] 7.1) Calculation of angle pair (θ) R ,θ T The related two-dimensional joint steering vector u(θ) for transmitting and receiving R ,θ T ):

[0083]

[0084] Where, θ R θ represents the equivalent angle of the received spatial frequency. T The equivalent angle representing the transmission spatial frequency;

[0085] 7.2) Based on the transmit / receive two-dimensional joint steering vector u(θ) R ,θ T The equivalent angle of the spatial frequency of the dummy target's transmission and reception is estimated, and the estimation result is obtained.

[0086]

[0087] Among them, h q It is the q-th largest eigenvector of the eigenvalue decomposition of the covariance matrix of the decoded echo signal. The angle θ represents the maximum value of the function. R and θ T ;

[0088] 7.3) Angle estimation of dummy targets in the two-dimensional plane of transmission and reception spatial frequencies Construct multiple null regions with a preset response of ρ around the perimeter:

[0089] L w (θ R ,θ T ) = w H u(θ R ,θ T )=ρ

[0090] Among them, L w (θ R ,θ T ) represents the angle pair (θ) when the weight vector is w. R ,θ T The directional pattern response at ().

[0091] Step 8: Construct the optimization problem of the direction pattern weight vector.

[0092] 8.1) Estimation based on the angle of the dummy target Obtain the distribution of the equivalent angles of the dummy target at the transmission and reception spatial frequencies. and

[0093]

[0094]

[0095] Where, -θ L θ represents the lower limit of the allowable DOA error. U This indicates the upper limit of the allowable DOA error. These represent the equivalent angles of the receiving and transmitting spatial frequencies of the first dummy target, respectively. Let represent the equivalent angles of the received and transmitted spatial frequencies of the Q-th dummy target, respectively, and let ∪ denote the union;

[0096] 8.2) Based on the sampling angle, (θ) α ,θ β The transmit / receive joint two-dimensional steering vector u(θ) α ,θ β Construct the Hermitian conjugate matrix Ω:

[0097]

[0098] in, These represent the sampling points in the receiving space dimension and the transmitting space dimension, respectively, and U represents the total number of samples;

[0099] 8.3) Find the angle pair with the largest deviation between the amplitude response of the radiation pattern and the preset response ρ in the i-th iteration.

[0100]

[0101] in, The equivalent angle representing the received spatial frequency. The equivalent angle representing the transmission spatial frequency. The angle θ represents the maximum value of the function. R and θ T ;

[0102] 8.4) Based on the results of steps 8.2) and 8.3), set constraints. Under these constraints, solve for the minimum value of the 2-norm of the weight vector, thus obtaining the following optimization problem for iterating over the weight vector.

[0103]

[0104] Where w represents the weight vector to be determined, w (i) Let u(θ0,θ0) represent the static weight vector in the i-th iteration, and let u(θ0,θ0) represent the transmit / receive guidance vector of the real target, which is used as the initial weight vector w. (0) η is the preset null response, min represents finding the minimum value, |||| 2 Represents the 2-norm;

[0105] 8.5) Further optimize the constraints:

[0106] (8.5.1) The Hermitian conjugate matrix Ω is decomposed as follows:

[0107]

[0108] Where V = [v1,...,v] P ,...,v MN ] is a matrix composed of eigenvectors. It is a diagonal matrix composed of eigenvalues, where P represents the rank of Ω and v1 represents the first eigenvalue. The corresponding feature vector, v P Represents the Pth eigenvalue The corresponding feature vector, v MN Represents the MNth eigenvalue The corresponding feature vector;

[0109] (8.5.2) Based on the properties of the Hermitian conjugate matrix, use Vs =[u1,,...,u r ] Approximate V, where u1 represents the eigenvector corresponding to the largest eigenvalue of Ω, u r Let P represent the eigenvector corresponding to the r-th largest eigenvalue of Ω, where r = 1, ..., P;

[0110] (8.5.3) To obtain a deeper zero trap, the optimization problem is modified according to the approximate substitution in (8.5.2). Transform into

[0111]

[0112] (8.5.4) Combine the constraints in (8.5.3) and let e = [1, 0] T This leads to a new optimization problem.

[0113]

[0114] in, Describe the complex space of MN×(2+P) dimensions. Let represent the (2+P)×1 dimensional real space.

[0115] Step 9: Solve the optimization problem to obtain the optimal weight vector.

[0116] 9.1) Expanding a new optimization problem using Lagrange multipliers We obtain the Lagrange expansion L (i) (w):

[0117]

[0118] Where w represents the weight vector to be determined, w (i) Let λ represent the static weight vector in the i-th iteration, and let λ represent the Lagrange multiplier vector. Represents a set of constraints;

[0119] 9.2)L (i) (w) find the gradient with respect to w And order The following expression is obtained:

[0120]

[0121] Solving this equation yields Where 2η=λ;

[0122] 9.3) Substitute the solution from step 9.2) into the constraint conditions. In this process, the closed-form solution of the weight vector in the i-th round of optimization is obtained.

[0123]

[0124] 9.4) Let ε be a preset termination value. In the i-th iteration, when the termination condition... When this condition is met, the preset requirements of the orientation pattern are satisfied. At this point, the iterative update stops, and the optimal weight vector is obtained, denoted as w. * .

[0125] Step 10: Suppress main lobe spoofing interference under the background of DOA error using the optimal weight vector, that is, use the decoding result Y(t) of the total echo signal and the optimal weight vector w * Multiplication yields the anti-interference result.

[0126]

[0127] The effects of this invention can be further illustrated by the following simulation experiments:

[0128] I. Simulation Parameters

[0129] The simulation parameters include the simulation parameters of the EPC-MIMO radar system and the target parameters, as shown in Table 1 and Table 2, respectively.

[0130] Table 1 Simulation parameters of EPC-MIMO radar system

[0131]

[0132] Table 2 Target Parameters

[0133]

[0134] II. Simulation Content

[0135] Simulation 1: Under the above simulation parameters, based on the EPC-MIMO radar, radiation pattern formation was performed using the present invention and three existing beamforming methods: QCSS, LCSS, and PDNBB. The results are as follows: Figure 3 .in, Figure 3 (a) is a radiation pattern formed using the present invention. Figure 3 (b) is a direction map generated using the QCSS method. Figure 3 (c) is the direction map generated using the LCSS method. Figure 3 (d) is the radiation pattern generated using the PDNBB method. Figure 3 As can be seen, the radiation pattern of the present invention forms a deep null region in the preset area under the background of DOA error, while the radiation pattern of the prior art does not form a null or the null is shallow under the background of DOA error, and cannot suppress the main lobe interference.

[0136] Simulation 2: Based on EPC-MIMO radar, radiation pattern formation was performed using the present invention and three existing beamforming methods: QCSS, LCSS, and PDNBB. The cross-section of the radiation pattern was observed, and the results are as follows. Figure 4 .Depend on Figure 4 It is evident that while existing beamforming techniques create wide nulls, the null depth is relatively shallow, resulting in poor suppression of main lobe interference under DOA error conditions. In contrast, this invention creates wide nulls at the interference location with a null depth of -50dB, effectively suppressing main lobe interference under DOA error conditions.

[0137] Simulation 3: Using this invention, the maximum amplitude response curve of the interference region changes with the number of iterations. The results are as follows: Figure 5 .Depend on Figure 5 As can be seen, with continuous iteration and optimization of the weight vector, the maximum amplitude response in the interference region is continuously reduced, and after the 68th iteration, the maximum amplitude response is reduced to -50dB, which satisfies the iteration stopping condition and the iteration stops, indicating that the present invention can converge quickly.

[0138] Simulation 4 simulates the performance of false target interference suppression using the present invention and three existing beamforming methods: QCSS, LCSS, and PDNBB. The results are as follows: Figure 6 .from Figure 6 It can be seen that the output signal-to-interference-plus-noise ratio (SIR) of several methods increases with the increase of the SIR. However, when the input SIR is greater than 15dB, the output SIR of existing beamforming methods gradually flattens out. When the input SIR is greater than 40dB, the output SIR of existing beamforming methods decreases due to signal cancellation. In contrast, the output SIR of the present invention shows an increasing trend, and has a higher output SIR than existing beamforming methods, exhibiting better main lobe spoofing interference suppression performance.

[0139] The existing methods used in the simulation are sourced as follows:

[0140] QCSS, quadratic constraint sector suppressed. A.Amar and MADoron, "Alinearly constrained minimum variance beamformer with a pre-specifiedsuppression level over a pre-defined broad null sector," Signal Process., vol.109, pp.165-171, 2015.

[0141] LCSS, linear constraint sector suppressed. A.Amar and MADoron, "Alinearly constrained minimum variance beamformer with a pre-specifiedsuppression level over a pre-defined broad null sector," Signal Process., vol.109, pp.165-171, 2015.

[0142] PDNBB, projection and diagonal loading null broadening beamforming. X.Mai, W.Li, and Y.Li, "Robust adaptive beamforming against signal steeringvector mismatch and jammer motion," Int.J.Antennas Propag., vol.2015, pp.1–12, Jul.2015

[0143] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

[0144] It should be noted that the step numbers in the specification and claims of this invention are only for the purpose of clearly describing the embodiments of this invention and facilitating understanding, and their order is not limited.

Claims

1. A method for resisting main lobe deception jamming in EPC-MIMO radar based on radiation pattern, characterized in that, Includes the following steps: (1) Construct a co-located MIMO radar system with M transmitting elements and N receiving elements. Set the system to transmit K pulses within the coherent processing time and perform pulse-element encoding on each transmitted pulse signal to obtain the k-th pulse signal transmitted by the m-th transmitting element. ; (2) Calculate the common two-way propagation delay based on the distance and angle of the point target, and apply it to the k-th transmitted pulse signal. The time delay yields the echo signal from the point target. ; (3) Perform matched filtering on the echo signal at the receiving end, and decode it in the slow time dimension according to the output of the matched filtering of N receiving array elements to obtain the decoded echo signal. (4) Perform eigenvalue decomposition of the covariance matrix on the decoded echo signal, and estimate the equivalent angle of the false target in the two-dimensional plane of the transmission and reception space frequency to obtain the estimation result of the qth false target. ; ； in, It is the q-th largest eigenvector of the eigenvalue decomposition of the covariance matrix of the decoded echo signal. Representation and angle pair The relevant two-dimensional joint guidance vector for transmitting and receiving has a value of q from 1 to Q, where Q represents the number of false targets and the symbol H represents the conjugate transpose. (5) Construct multiple null regions with a preset response of ρ around the dummy target in the two-dimensional plane of the transmission and reception spatial frequencies; ； in, Indicates when the weight vector is Time angle The directional response at that location; (6) Based on the false target angle estimation results and multiple preset null regions, construct an optimization problem for the radiation pattern weight vector, solve the optimization problem to obtain the optimal weight vector to construct a radiation pattern that meets the preset requirements, and obtain the optimal weight vector. This vector is used to eliminate the direction of arrival (DOA) error, thereby suppressing the main lobe interference.

2. The method according to claim 1, characterized in that, Step (1): Perform pulse-element encoding on each transmitted pulse signal to obtain the pulse signal transmitted by the transmitting element. The steps include the following: (1a) Encode the k-th pulse emitted by the m-th transmitting element as: ； in, Represents the coding coefficients; (1b) The orthogonal baseband waveform of the m-th transmitting element , is represented as: ； in, For the first Each launch array element Indicates arbitrary time delay; (1c) Based on the results of steps (1a) and (1b), the k-th pulse signal transmitted by the m-th transmitting element is obtained as follows: ； in, Indicates the transmission power. Indicates the carrier frequency.

3. The method according to claim 2, characterized in that, Step (2) Calculate the propagation delay based on the location of the point target to obtain the echo signal of the point target. The steps include the following: (2a) Assume there is a point target in the far field, and the target's angle and distance are respectively and Then the common propagation delay of the target point from the m-th array element to the n-th array element is... for: ； Where d represents the spacing between array elements and c represents the speed of light; (2b) Consider the point target as having a velocity of For a moving point target, the Doppler frequency of that point target is... : ； in, Indicates wavelength; (2c) Let the target pulse delay number in the range ambiguity region be... Based on the results of steps 2.1) and 2.2), the first... The first receiving element received the first echo signal of each pulse : ； in, Let be the complex scattering coefficient of the point target. Indicates the pulse repetition time. .

4. The method according to claim 3, characterized in that, In step (3), matched filtering is performed on the echo signal at the receiving end. The steps include the following: (3a) Construction Group matched filters, where the first Group matched filter Represented as: ； The symbol * indicates conjugation; (3b) Use The matched filter group separates each transmitted waveform to obtain the first... Output of group matched filter for: ； in, For complex scattering coefficients, Indicates wavelength. Indicates the spacing between array elements. Indicates the angle of incidence of the target. Indicates the pulse repetition time, symbol This represents convolution.

5. The method according to claim 4, characterized in that, In step (3), decoding is performed in the slow time dimension based on the output of the matched filtering of N receiving array elements. The steps include the following: (3c) Organizing The output of the matched filter of the receiving channel will come from the first channel. The result of pulse matched filtering express: ； in, This represents the matched filtering result of the k-th pulse transmitted by the m-th transmitting element and received by the n-th receiving element, with the symbol T indicating transpose; (3d) will be the first Decoding vector of each pulse Represented as: ； in, Indicates that all elements are 1 dimensional column vector, This represents the code of the k-th pulse transmitted by the m-th transmitting element. This represents the code of the k-th pulse transmitted by the M-th transmitting element. , Indicates the Kronecker product; (3e) Match filter result of the kth pulse Decoding in slow time dimension yields the first... The result of pulse decoding : ； Where diag represents a diagonal matrix; (3f) Organize The decoding results of each pulse yield the decoding result of the true target signal. : ； in, Indicates the receiving guide vector. Indicates the received spatial frequency. Indicates the launch steering vector. Indicates the transmission space frequency. Represents the Doppler vector. Indicates the pulse repetition time; (3g) Sorting in the presence of DOA error The decoding results of each pulse are used to obtain the decoding result of the q-th false target signal. : ； in, The complex scattering coefficients of the dummy target are denoted as . Indicates the received spatial frequency of the dummy target. Indicates the spatial frequency of the dummy target's emission. Indicates the angle of incidence of the decoy target; This represents the angular offset, assuming it is distributed within the allowable DOA error. middle, This represents the pulse delay number of the dummy target. Indicates the Doppler frequency of the false target; (3h) Based on the results of steps (3d) and (3e), the decoding result of the total echo signal is obtained. : ； in, This indicates the decoding result of the noise signal.

6. The method according to claim 5, characterized in that, In step (4), the eigenvalue decomposition of the covariance matrix of the decoded echo signal is performed. The steps include the following: (4a) The covariance matrix of the decoded echo signal Represented as: ； in, For the first Decoding results of each pulse; (4b) For the covariance matrix Perform the following eigenvalue decomposition: ； in, It is a matrix composed of eigenvectors. It is a diagonal matrix composed of eigenvalues.

7. The method according to claim 6, characterized in that, Step (5) Based on the spurious target angle estimation results and multiple pre-defined null regions, construct an optimization problem for the radiation pattern weight vector. The implementation steps include the following: (5a) Construct the Hermitian conjugate matrix : ； in, These represent the sampling points in the receiving space dimension and the transmitting space dimension, respectively, where U represents the total number of samples. , , This indicates the lower limit of the allowable DOA error. This indicates the upper limit of the allowable DOA error. , These represent the equivalent angles of the receiving and transmitting spatial frequencies of the first dummy target, respectively. , Represent the equivalent angles of the received and transmitted spatial frequencies of the Q-th dummy target, respectively, with symbols... Represents the union; (5b) Find the angle pair with the largest deviation between the amplitude response of the radiation pattern and the preset response ρ in the i-th iteration. : ； in, The equivalent angle representing the received spatial frequency. The equivalent angle representing the transmission spatial frequency. The angle representing the maximum value of the function. and ; (5c) Based on the results of (5a) and (5b), set constraints. Under these constraints, solve for the minimum value of the 2-norm of the weight vector, which gives the following optimization problem for iterating over the weight vector. : ； in, This represents the weight vector to be determined. This represents the static weight vector in the i-th iteration. The transmit / receive guidance vector representing the actual target is set. Let be the initial weight vector, η be the preset null response, and min denote the minimum value. Represents the 2-norm; (5d) Hermitian conjugate matrix Performing eigenvalue decomposition yields: ； in, It is a matrix composed of eigenvectors. It is a diagonal matrix composed of eigenvalues, and P represents... rank, Represents the first eigenvalue The corresponding feature vector, Represents the Pth eigenvalue The corresponding feature vector, Represents the MNth eigenvalue The corresponding feature vector; (5e) Based on the properties of Hermitian conjugate matrices, using Approximate substitution ,in express The eigenvector corresponding to the largest eigenvalue. express The eigenvector corresponding to the r-th largest eigenvalue. ; (5f) In order to obtain a deeper zero trap, the optimization problem is modified according to the approximate substitution in (5e). Transform into : ； (5g) Combining the constraints in step (5f), we obtain the following new optimization problem. : ； in, , express Complex space of dimension 1 express The real space of dimension .

8. The method according to claim 7, characterized in that, In step (5), solving the optimization problem yields the optimal weight vector, which forms the orientation pattern that meets the preset requirements. The implementation steps include the following: (5h) Optimization problem using Lagrange multipliers expansion get: ； in, This represents the weight vector to be determined. This represents the static weight vector in the i-th iteration. Describes the 2-norm. , Denotes the Lagrange multiplier vector. Represents a set of constraints; (5i) right Find the gradient and ordered to be This yields the following expression: ； Solving this equation yields ,in, ; (5g) Substitute the solution from (5i) into the constraint conditions. In this process, the closed-form solution of the weight vector in the i-th round of optimization is obtained. : ； (5k) Let The preset termination value is used in the i-th iteration when the termination condition is met. When the preset requirements of the radiation pattern are met, the iterative update stops, and the optimal weight vector is obtained, denoted as . .

9. The method according to claim 8, characterized in that, In step (5), the optimal weight vector is used. To eliminate the Direction of Arrival (DOA) error, the formula is as follows: ； in, This indicates the result after interference suppression. Decoding result of the total echo signal .

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