EPC-MIMO radar main lobe deception jamming resisting method based on directional diagram

Abstract

The invention discloses an EPC-MIMO radar main lobe deception jamming resisting method based on a directional diagram, and mainly solves the problem that main lobe deception jamming cannot be restrained under the DOA error background in the prior art. According to the implementation scheme, array element pulse coding is carried out on a transmitted signal at a transmitting end, and matched filtering and decoding are carried out on an echo signal at a receiving end; estimating an equivalent receiving angle of transmitting and receiving spatial frequencies of a false target by utilizing characteristic decomposition of a covariance matrix of the decoded echo signal, and presetting a plurality of null regions around an estimation result; the method comprises the steps of applying constraint to wave beam response around a false target in a transmitting-receiving spatial frequency domain, constructing an optimization problem by using an iterative weight vector control method, solving the optimization problem to obtain an optimal weight vector, and completing suppression of main lobe deception interference under the DOA error background by using an optimal wave beam. According to the method, the null depth is deepened, the null area of the directional diagram is widened, the output signal to interference plus noise ratio and the interference suppression performance are improved, and the method can be used for target detection.

Description

Technical Field

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

[0002] In a complex electromagnetic environment, deceptive interference signals from the radar main lobe direction will damage the radar's ability to detect and track targets. EPC-MIMO radar can control the main lobe direction of the transmitted pulse by performing phase encoding in the array element and slow time dimensions at the same time. Pulse echoes in different range ambiguity zones have different transmission steering vectors. Based on this feature, by designing appropriate coding coefficients, EPC-MIMO radar can use non-adaptive beamforming technology to extract signals in a certain range ambiguity zone and suppress interference signals in other range ambiguity zones. However, in the case of errors in the signal direction of arrival (DOA), the performance of non-adaptive beamforming will be severely compromised.

[0003] Patent document with application number CN202011131418.8 discloses a method for suppressing deceptive interference of an element-pulse coded MIMO radar, and its implementation scheme is as follows: considering that the false target is delayed by several pulses compared to the real target and the true and false targets are located in different distance ambiguity intervals, the coding coefficients and compensation vectors of the EPC-MIMO radar are designed, and the transmit steering vector is pre-compensated and the receiving end matched filtered to separate the transmit waveforms, so that the false target is located exactly at the zero point of the radiation pattern and is effectively suppressed; finally, the true and false targets are identified in the three-dimensional domain of the transmit and receive spatial frequencies and pulses, and the main lobe deceptive interference is suppressed by beam zeroing. Since this method does not consider the problem of main lobe interference when the DOA error exists, it cannot suppress the main lobe deceptive interference under the background of DOA error. Summary of the invention

[0004] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a directional pattern-based EPC-MIMO radar anti-mainlobe deception interference method to effectively suppress the mainlobe deception interference under the DOA error background.

[0005] The technical key of the present invention is: using the eigendecomposition of the echo signal sample covariance matrix to estimate the equivalent receiving angles in the transmitting and receiving spatial frequency domains of the main lobe deceptive interference; using the iterative weight vector control IWC method to impose constraints on the beam response around the main lobe interference in the transmitting-receiving spatial frequency domain; iteratively updating the weight vector to perform beam forming until the beam response reaches the expected value, and realizing the optimal beam to suppress the main lobe deceptive interference. The implementation steps include the following:

[0006] (1) A co-located MIMO radar system with M transmitting elements and N receiving elements is constructed. K pulses are transmitted within the coherent processing time of the system, and pulse-element encoding is performed on each transmitted pulse signal to obtain the kth pulse signal s transmitted by the mth 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 speed, and calculate the kth transmitted pulse signal s m,k (t) Time delay to get the echo signal x of the point target n,k (t);

[0008] (3) Performing matched filtering on the echo signal at the receiving end, decoding in the slow time dimension based on the outputs of the matched filtering of the N receiving array elements, and obtaining a decoded echo signal;

[0009] (4) Perform eigendecomposition of the covariance matrix of the decoded echo signal and estimate the equivalent angle of the main lobe interference in the two-dimensional plane of the transmit and receive spatial frequencies to obtain the qth main lobe interference estimation result.

[0010]

[0011] Among them, h q is the qth largest eigenvector of the eigendecomposition of the covariance matrix of the decoded echo signal, u(θ R ,θ T ) represents the angle pair (θ R ,θ T ) is a two-dimensional joint steering vector for transmission and reception, q ranges from 1 to Q, Q represents the number of main lobe interferences, and the symbol H represents conjugate transpose;

[0012] (5) constructing a plurality of null regions with a preset response of ρ around the false target in the two-dimensional plane of the transmitting and receiving 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 ) indicates that when the weight vector is w, the angle (θ R ,θ T ) at the directional pattern response;

[0015] (6) Based on the false target angle estimation result and the preset multiple null areas, an optimization problem of the directional pattern weight vector is constructed, and the optimal weight vector is obtained by solving the optimization problem to obtain a directional pattern that meets the preset requirements, and the optimal weight vector w is obtained. * , and use this vector to eliminate the DOA error and suppress the main lobe interference.

[0016] Since the present invention imposes constraints on the preset null area around the false target in each round of iteration and solves the optimization problem to obtain the optimal weight vector, compared with the existing beamforming method, the DOA error can be effectively eliminated and the main lobe interference can be suppressed. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the implementation of the present invention;

[0018] Figure 2 It is a schematic diagram of the preset null sink area in the present invention;

[0019] Figure 3 The two-dimensional radiation patterns of transmitting and receiving in the spatial frequency domain are designed by the present invention and the existing beam forming method respectively;

[0020] Figure 4 It is a cross-sectional comparison diagram of the directional diagrams of the present invention and the existing beamforming method;

[0021] Figure 5 is a curve diagram showing the maximum amplitude response of the interference area according to the present invention changing with the number of iterations;

[0022] Figure 6 It is a comparison diagram of the output signal-to-interference-plus-noise ratio curve versus the input signal-to-noise ratio curve of the present invention and the prior art respectively. DETAILED DESCRIPTION

[0023] The following is a further detailed description of the implementation examples and effects of the present invention in conjunction with the accompanying drawings.

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

[0025] Step 1: construct a transmit signal model and perform pulse-element encoding on each transmit pulse signal.

[0026] 1.1) Set up M transmitting array elements and N receiving array elements, and use them to co-locate as a MIMO radar system;

[0027] 1.2) It is set to transmit K pulses within the coherent processing time of the system, and perform pulse-element encoding on each transmitted pulse signal to obtain the kth pulse signal s transmitted by the mth transmitting array element m,k (t):

[0028] (1.2.1) Encode the kth pulse transmitted by the mth transmitting element as:

[0029]

[0030] Among them, γ represents the coding coefficient;

[0031] (1.2.2) The orthogonal baseband waveform φ of the mth transmitting array element m (t), expressed as:

[0032]

[0033] Where m′ is the m′th transmitting array element, and τ represents an arbitrary delay;

[0034] (1.2.3) According to the results of (1.2.1) and (1.2.2), the k-th pulse signal emitted by the m-th transmitting array element is:

[0035]

[0036] Among them, E represents the transmission power and f0 represents the carrier frequency.

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

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

[0039]

[0040] Where d represents the array element spacing, and c represents the speed of light;

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

[0042]

[0043] Where λ0 represents the wavelength;

[0044] 2.3) Let the target pulse delay number in the range ambiguity region be p s According to the results of step 2.1) and step 2.2), the echo signal x of the kth pulse received by the nth receiving element is obtained. n,k (t):

[0045]

[0046] Among them, β sis the complex scattering coefficient of the point target, T r Indicates the pulse repetition time.

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

[0048] 3.1) Construct M groups of matched filters, where the mth group of matched filters h m (t) is expressed as:

[0049] h m (t) = φ m * (-t)

[0050] Among them, the symbol * represents conjugation;

[0051] 3.2) Use M groups of matched filters to separate the transmitted waveforms and obtain the output x of the mth group of matched filters. n,m,k (t) is:

[0052]

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

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

[0055] 4.1) Arrange the outputs of the matched filters of the N receiving channels and convert the result of the matched filter from the kth pulse express:

[0056]

[0057] Among them, x n,m,k (t) represents the matched filtering result of the kth pulse transmitted by the mth transmitting element and received by the nth receiving element, and the symbol T represents transposition;

[0058] 4.2) Match the k-th pulse to the filter result Decode in the slow time dimension and get the result after decoding the kth pulse

[0059] (4.2.1) The decoding vector g of the kth pulse k It is expressed as:

[0060]

[0061] Among them, 1 N represents an N-dimensional column vector whose elements are all 1, represents the kth pulse code transmitted by the mth transmitting array element, represents the kth pulse code transmitted by the Mth transmitting array element, represents the Kronecker product;

[0062] (4.2.2) Decode the kth pulse and get the decoding result

[0063]

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

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

[0066] 5.1) According to the launch guidance vector a(f T0 ), receiving the steering vector b(f R0 ) and the Doppler vector c(f d0 ), rewrite the decoding result of K pulses into the decoding result Y of the real target signal s (t):

[0067]

[0068] in, represents the received spatial frequency, represents the emission spatial frequency;

[0069] 5.2) In the presence of DOA error, according to the launch guidance vector a(f Tq ), receiving the steering vector b(f Rq ) and the Doppler vector c(f dq ), sort out the decoding results of K pulses, and express the decoding result of the qth false target signal as Y q (t):

[0070]

[0071] in, is the complex scattering coefficient of the false target, Indicates the receiving spatial frequency of the false target, represents the false target emission spatial frequency, θ q represents the incident angle of the false target; Δθ represents the angle offset, which is assumed to be distributed within the allowable DOA error [-θ L ,θ H ], p′ represents the pulse delay number of the false target, f dq Indicates the Doppler frequency of the false target;

[0072] 5.3) According to the results of step 5.1) and step 5.2), the decoding result Y(t) of the total echo signal is obtained:

[0073]

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

[0075] Step 6: Solve the decoded echo signal The 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 eigendecomposition on the covariance matrix:

[0079] R x =UΛU H

[0080] Among them, U is a matrix consisting of eigenvectors, and Λ is a diagonal matrix consisting of eigenvalues.

[0081] Step 7, estimate the false target angle and preset multiple null regions around the estimated result, such as Figure 2 shown.

[0082] 7.1) Calculate the angle pair (θ R ,θ T ) related to the two-dimensional joint steering vector u(θ R ,θ T ):

[0083]

[0084] Among them, θ R Represents the equivalent angle of receiving spatial frequency, θ T The equivalent angle representing the transmitted spatial frequency;

[0085] 7.2) According to the two-dimensional joint steering vector u(θ R ,θ T ) Estimate the equivalent angle of the false target's transmitting and receiving spatial frequency, and obtain the estimated result

[0086]

[0087] Among them, h q is the qth largest eigenvector of the eigendecomposition 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) Estimated angle of false target in the two-dimensional plane of transmitting and receiving spatial frequencies Construct multiple null regions with preset response ρ around:

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

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

[0091] Step 8: construct the optimization problem of the directional pattern weight vector.

[0092] 8.1) Angle estimation based on false targets Get the distribution of equivalent angles of false targets at the transmitting spatial frequency and the receiving spatial frequency and

[0093]

[0094]

[0095] Among them, -θ L Indicates the lower limit of the allowable DOA error, θ U Indicates the upper limit of the allowed DOA error, Respectively represent the equivalent angles of the receiving and transmitting spatial frequencies of the first false target, They represent the equivalent angles of the receiving and transmitting spatial frequencies of the Qth false target, respectively, and the symbol ∪ represents the union;

[0096] 8.2) According to the sampling angle (θ α ,θ β ) of the joint two-dimensional steering vector u(θ α ,θ β ) constructs the Hermitian conjugate matrix Ω:

[0097]

[0098] in, They 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 directional pattern and the preset response ρ in the i-th iteration

[0100]

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

[0102] 8.4) According to the results of step 8.2) and step 8.3), set the constraint conditions. Under this constraint condition, solve the minimum value of the 2-norm of the weight vector, that is, obtain the following optimization problem for iterating the weight vector:

[0103]

[0104] Among them, w represents the weight vector to be calculated, w (i) represents the static weight vector in the i-th iteration, u(θ0,θ0) represents the real target's send and receive steering vector and is used as the initial weight vector w (0) , η is the preset zero-sink response, min means to find the minimum value, |||| 2 represents the 2-norm;

[0105] 8.5) Further optimize the constraints:

[0106] (8.5.1) Perform the following eigendecomposition on the Hermitian conjugate matrix Ω:

[0107]

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

[0109] (8.5.2) According to the characteristics of Hermitian conjugate matrices, use Vs =[u1,,...,u r ] is approximately substituted for V, where u1 represents the eigenvector corresponding to the maximum eigenvalue of Ω, and u r represents the eigenvector corresponding to the rth largest eigenvalue of Ω, r = 1, ...P;

[0110] (8.5.3) In order to obtain a deeper null, according to the approximate substitution in (8.5.2), the optimization problem is replaced by Convert to

[0111]

[0112] (8.5.4) Combining the constraints in (8.5.3), let e=[1,0] T , we get a new optimization problem

[0113]

[0114] in, represents the MN×(2+P)-dimensional complex space, Represents the (2+P)×1-dimensional real number space.

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

[0116] 9.1) Use Lagrange multipliers to develop new optimization problems Get the Lagrangian expansion L (i) (w):

[0117]

[0118] Among them, w represents the weight vector to be calculated, w (i) represents the static weight vector in the i-th iteration, λ represents the Lagrange multiplier vector, Represents a set of constraints;

[0119] 9.2)L (i) (w) Find the gradient of w And order The following expression is obtained:

[0120]

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

[0122] 9.3) Substitute the solution from step 9.2) into the constraints The closed-form solution of the weight vector for the i-th round of optimization is obtained

[0123]

[0124] 9.4) Let ε be the preset termination value. In the i-th iteration, when the termination condition When it is reached, the preset requirements of the directional graph are met, and the iterative update is stopped at this time, and the optimal weight vector is recorded as w * .

[0125] Step 10: Use the optimal weight vector to suppress the main lobe deception interference under the DOA error background, that is, the decoding result Y(t) of the total echo signal is compared with the optimal weight vector w * Multiply to get the anti-interference result

[0126]

[0127] The effect of the present invention can be further illustrated by the following simulation experiment:

[0128] 1. Simulation parameters

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

[0130] Table 1 EPC-MIMO radar system simulation parameters

[0131]

[0132] Table 2 Target parameters

[0133]

[0134] 2. Simulation Content

[0135] Simulation 1: Based on the EPC-MIMO radar, the present invention and the three existing beamforming methods QCSS, LCSS, and PDNBB are used to form the directional pattern under the above simulation parameters. The results are as follows: Figure 3 .in, Figure 3 (a) is a directional pattern formed using the present invention, Figure 3 (b) is the directional pattern formed using the QCSS method. Figure 3 (c) is the directional pattern formed using the LCSS method, Figure 3 (d) is the directional pattern formed using the PDNBB method. Figure 3 It can be seen that the directional pattern of the present invention forms a deeper null area in the preset area under the DOA error background, while the directional pattern of the existing method does not form a null or the null is shallow under the DOA error background, and cannot suppress the main lobe interference.

[0136] Simulation 2, based on EPC-MIMO radar, uses the present invention and the three existing beamforming methods QCSS, LCSS, and PDNBB to form the directional pattern, and observes the profile of the directional pattern. The results are as follows: Figure 4 .Depend on Figure 4 It can be seen that although the existing beamforming technology forms a wide null, the null depth is shallow, and the main lobe interference suppression effect under the DOA error background is poor. The present invention forms a wide null at the interference position and the null depth reaches -50dB, which can effectively suppress the main lobe interference under the DOA error background.

[0137] Simulation 3, using the present invention to simulate the curve of the maximum amplitude response of the interference area changing with the number of iterations, the results are as follows Figure 5 .Depend on Figure 5 It can be seen that with the continuous iterative optimization of the weight vector, the maximum amplitude response of the interference area is constantly decreasing, and after the 68th round of iteration, the maximum amplitude response is reduced to -50dB, meeting the iteration stop condition, and the iteration stops, indicating that the present invention can converge quickly.

[0138] Simulation 4 uses the present invention and the three existing beamforming methods QCSS, LCSS, and PDNBB to simulate the false target interference suppression performance. The results are as follows Figure 6 .from Figure 6 It can be seen that the output signal-to-noise ratios of several methods increase with the increase of the signal-to-noise ratio; when the input signal-to-noise ratio is greater than 15dB, the output signal-to-noise ratio of the existing beamforming method gradually tends to be flat; when the input signal-to-noise ratio is greater than 40dB, the output signal-to-noise ratio of the existing beamforming method decreases due to signal cancellation; and the output signal-to-noise ratio of the present invention shows an increasing trend, and has a higher output signal-to-noise ratio than the existing beamforming method, and has better main lobe deception interference suppression performance.

[0139] The existing methods used in the simulation are from:

[0140] QCSS, quadratic constraint sector suppressed. A.Amar and MADoron, "Alinearly constrained minimum variance beamformer with a pre-specified suppression 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-specified suppression 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 only a specific example of the present invention and does not constitute any limitation to the present invention. It is obvious that for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes in form and details without departing from the principles and structures 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 the present invention are only for a clear description of the implementation scheme of the present invention to facilitate understanding, and the sequence of the step numbers is not limited.

Claims

1. A method for anti-main lobe deception interference of EPC-MIMO radar based on directional pattern, characterized in that: The steps include: (1) A co-located MIMO radar system with M transmitting elements and N receiving elements is constructed. K pulses are transmitted within the coherent processing time of the system, and pulse-element encoding is performed on each transmitted pulse signal to obtain the kth pulse signal s transmitted by the mth transmitting element. m,k (t); (2) Calculate the common two-way propagation delay based on the distance and angle of the point target, and calculate the kth transmitted pulse signal s m,k (t) Time delay to get the echo signal x of the point target n,k (t); (3) Performing matched filtering on the echo signal at the receiving end, decoding in the slow time dimension based on the outputs of the matched filtering of the N receiving array elements, and obtaining a decoded echo signal; (4) Perform eigendecomposition of the covariance matrix of the decoded echo signal and estimate the equivalent angle of the false target in the two-dimensional plane of the transmitting and receiving spatial frequencies to obtain the qth false target estimation result. Among them, h q is the qth largest eigenvector of the eigendecomposition of the covariance matrix of the decoded echo signal, u(θ R ,θ T ) represents the angle pair (θ R ,θ T ) is a two-dimensional joint guidance vector for transmission and reception, q ranges from 1 to Q, Q represents the number of false targets, and the symbol H represents conjugate transpose; (5) constructing a plurality of null regions with a preset response of ρ around the false target in the two-dimensional plane of the transmitting and receiving spatial frequencies; L w (i R ,i T )=w H u(θ R ,i T )=ρ Among them, L w (θ R ,θ T ) indicates that when the weight vector is w, the angle (θ R ,θ T ) at the directional pattern response; (6) Based on the false target angle estimation result and the preset multiple null areas, an optimization problem of the directional pattern weight vector is constructed, and the optimal weight vector is obtained by solving the optimization problem to obtain a directional pattern that meets the preset requirements, and the optimal weight vector w is obtained. * , and use this vector to eliminate the DOA error and suppress the main lobe interference.

2. The method according to claim 1, characterized in that Step (1): pulse-element encoding is performed on each transmit pulse signal to obtain a pulse signal transmitted by the transmit element. The implementation steps include the following: (1a) Encode the kth pulse transmitted by the mth transmitting element as follows: Among them, γ represents the coding coefficient; (1b) The orthogonal baseband waveform φ of the mth transmitting array element m (t), expressed as: Where m′ is the m′th transmitting array element, and τ represents an arbitrary delay; (1c) According to the results of step (1a) and step (1b), the kth pulse signal emitted by the mth transmitting array element is: Among them, E represents the transmission power and f0 represents the carrier frequency.

3. The method according to claim 1, characterized in that: Step (2) calculates the propagation delay according to the position of the point target to obtain the echo signal of the point target, and the implementation steps include the following: (2a) Assume that there is a point target in the far field, and the angle and distance of the target are θ0 and R0 respectively. Then the common propagation delay τ of the point target from the mth array element to the nth array element is mn for: Where d represents the array element spacing, and c represents the speed of light; (2b) Consider a point target moving at a speed v0. Then the Doppler frequency f of the point target is d0 : Where λ0 represents the wavelength; (2c) Let the target pulse delay number in the range ambiguity region be p s According to the results of step 2.1) and step 2.2), the echo signal x of the kth pulse received by the nth receiving element is obtained. n,k (t): Among them, β s is the complex scattering coefficient of the point target, T r Represents the pulse repetition time, n=1,2,…,N.

4. The method according to claim 1, characterized in that In step (3), matched filtering is performed on the echo signal at the receiving end, and the implementation steps include the following: (3a) Construct M groups of matched filters, where the mth group of matched filters h m (t) is expressed as: h m (t)=φ m * (-t) Among them, the symbol * represents conjugation; (3b) Use M groups of matched filters to separate the transmitted waveforms, and obtain the output x of the mth group of matched filters. n,m,k (t) is: in, is the complex scattering coefficient, λ0 represents the wavelength, d represents the array element spacing, θ0 represents the target incident angle, T r represents the pulse repetition time, and the symbol × represents convolution.

5. The method according to claim 1, characterized in that In step (3), decoding is performed in the slow time dimension according to the output of the matched filtering of the N receiving array elements. The implementation steps include the following: (3c) Arrange the outputs of the matched filters of the N receiving channels and convert the result of the matched filter from the kth pulse express: Among them, x n,m,k (t) represents the matched filtering result of the kth pulse transmitted by the mth transmitting element and received by the nth receiving element, and the symbol T represents transposition; (3d) The decoding vector g of the kth pulse k It is expressed as: Among them, 1 N represents an N-dimensional column vector whose elements are all 1, represents the kth pulse code transmitted by the mth transmitting array element, represents the kth pulse code transmitted by the Mth transmitting array element, m = 1, 2, ..., M, represents the Kronecker product; (3e) The kth pulse matching filter result Decode in the slow time dimension and get the result after decoding the kth pulse Where diag represents a diagonal matrix; (3f) Arrange the decoding results of K pulses to obtain the real target signal decoding result Y s (t): in, represents the receive steering vector, represents the received spatial frequency, represents the launch steering vector, represents the transmitted spatial frequency, represents the Doppler vector, T r represents the pulse repetition time; (3g) In the presence of DOA error, the decoding results of K pulses are sorted to obtain the decoding result Y of the qth false target signal q (t): in, is the complex scattering coefficient of the false target, Indicates the receiving spatial frequency of the false target, represents the false target emission spatial frequency, θ q represents the incident angle of the false target; Δθ represents the angle offset, which is assumed to be distributed within the allowable DOA error [-θ L ,θ H ], p′ represents the pulse delay number of the false target, f dq Indicates the Doppler frequency of the false target; (3h) According to the results of step (3d) and step (3e), the decoding result Y(t) of the total echo signal is obtained: Wherein, N(t) represents the decoding result of the noise signal.

6. The method according to claim 1, characterized in that In step (4), the decoded echo signal is subjected to characteristic decomposition of the covariance matrix, and the implementation steps include the following: (4a) The covariance matrix R of the decoded echo signal x It is expressed as: in, is the decoding result of the kth pulse; (4b) For the covariance matrix R x Perform the following feature decomposition: R x =UΛU H Among them, U is a matrix consisting of eigenvectors, and Λ is a diagonal matrix consisting of eigenvalues.

7. The method according to claim 1, characterized in that Step (5) constructs an optimization problem of the directional pattern weight vector based on the false target angle estimation result and the preset multiple null areas. The implementation steps include the following: (5a) Construct the Hermitian conjugate matrix Ω: in, They represent the sampling points in the receiving space dimension and the transmitting space dimension respectively, U represents the total number of samples, -θ L Indicates the lower limit of the allowable DOA error, θ U Indicates the upper limit of the allowed DOA error, Respectively represent the equivalent angles of the receiving and transmitting spatial frequencies of the first false target, They represent the equivalent angles of the receiving and transmitting spatial frequencies of the Qth false target, respectively, and the symbol ∪ represents the union; (5b) Find the angle pair with the largest deviation between the amplitude response of the directional pattern and the preset response ρ in the i-th iteration in, represents the equivalent angle of the received spatial frequency, represents the equivalent angle of the transmitted spatial frequency, The angle θ represents the maximum value of the function R and θ T ; (5c) According to the results of (5a) and (5b), constraints are set. Under these constraints, the minimum value of the 2-norm of the weight vector is solved, and the following optimization problem for iterating the weight vector is obtained: Among them, w represents the weight vector to be calculated, w (i) represents the static weight vector in the i-th iteration, u(θ0,θ0) represents the real target's sending and receiving steering vector, u(θ0,θ0) is set as the initial weight vector, η is the preset null sink response, min represents the minimum value, || || 2 represents the 2-norm; (5d) Perform eigendecomposition on the Hermitian conjugate matrix Ω and obtain: Where V = [v1,…,v P ,…,v MN ] is a matrix consisting of eigenvectors, is a diagonal matrix consisting of eigenvalues, P represents the rank of Ω, and v1 represents the first eigenvalue The corresponding eigenvector, v P represents the Pth eigenvalue The corresponding eigenvector, v MN Represents the MNth eigenvalue The corresponding eigenvector; (5e) According to the properties of Hermitian conjugate matrices, use V s =[u1,,…,u r ] is approximately substituted for V, where u1 represents the eigenvector corresponding to the maximum eigenvalue of Ω, and u r Represents the eigenvector corresponding to the rth largest eigenvalue of Ω, r=1,…P. (5f) In order to obtain a deeper null, the optimization problem is replaced by the approximate substitution in (5e). Convert to (5g) Combining the constraints in step (5f), we get the following new optimization problem: in, represents the MN×(2+P)-dimensional complex space, Represents the (2+P)×1-dimensional real number space.

8. The method according to claim 1, characterized in that In step (5), solving the optimization problem to obtain the optimal weight vector constitutes a directional diagram that meets the preset requirements, and the implementation steps include the following: (5h) Expand the optimization problem using Lagrange multipliers get: Among them, w represents the weight vector to be calculated, w (i) represents the static weight vector in the i-th iteration, || || 2 represents the 2-norm, λ represents the Lagrange multiplier vector, Represents a set of constraints; (5i)L (i) (w) Find the gradient of w And let The following expression is obtained: Solving this formula yields Where 2η = λ; (5g) Substitute the solution in (5i) into the constraints The closed-form solution of the weight vector for the i-th round of optimization is obtained (5k) Let ε be the preset termination value. In the i-th iteration, when the termination condition When , the preset requirements of the directional diagram are met, and the iterative update is stopped at this time, and the optimal weight vector is recorded as w ＊ .

9. The method according to claim 1, characterized in that: In step (5), the optimal weight vector w is used ＊ , to eliminate the DOA error, the formula is as follows: in, represents the result after interference suppression, and Y(t) is the decoding result Y(t) of the total echo signal.

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