Coherent self-adaptive beam forming method based on co-prime array interpolation

Abstract

The invention discloses a coherent source adaptive beam forming method based on co-prime array interpolation, which belongs to the technical field of radar anti-interference, and comprises two stages, namely a first stage of de-coherence covariance matrix reconstruction and a second stage of adaptive beam former construction. In the first stage, received signal interpolation is carried out by constructing a sensor position model of a co-prime array, a mathematical model of signal receiving, description of signals and interference and definition of a steering vector, and effective separation of coherent source interference and target signals is realized by utilizing a diagonal matrix to carry out decoherence and a Vandermonde decomposition property of a Teraplitz matrix; in the second stage, an adaptive beam former is designed by reconstructing an interference and noise covariance matrix, and finally high-precision detection and extraction of a target signal in a complex environment are achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar anti-interference, and in particular relates to a coherent source adaptive beamforming method based on coprime array interpolation. Background Art

[0002] Adaptive beamforming is a widely used technique in array signal processing, with applications in radar, sonar, wireless communications, and medical fields. It uses the received data to dynamically adjust weights to isolate the signal of interest and minimize interference and noise. Minimum variance distortionless response is a powerful adaptive beamforming technique that relies on precise knowledge of the desired signal and array configuration to provide high resolution and anti-interference performance. However, its performance degrades significantly when there is a mismatch in the steering vector of the signal of interest due to non-ideal factors such as viewing direction error and wavefront distortion. In addition, the performance degrades dramatically if the received data contains information about the SOI, which is inevitable in practical scenarios. Enhancing the robustness of adaptive beamformers has been the focus of extensive research over the past few decades.

[0003] In adaptive beamforming of coherent sources, multiple signal sources may generate the same or similar signals during transmission, which is particularly common in fields such as radar, sonar, and wireless communications. The signal similarity brought by coherent sources makes it difficult for traditional beamforming methods to distinguish these signals, thus affecting the accuracy and performance of signal processing. Therefore, the research on adaptive beamforming technology of coherent sources is particularly important. It can improve the system's resolution and anti-interference capabilities in environments with significant multipath effects or dense signal sources, and ensure reliable signal reception and processing. This is of great significance for improving the target recognition capability of radar systems, the underwater target detection capability of sonar systems, and the signal transmission quality of wireless communication systems. Therefore, the research on adaptive beamforming technology in coherent source environments can not only overcome the limitations of traditional methods, but also further expand its application scope in complex signal environments.

[0004] The existing adaptive beamforming algorithm cannot effectively solve the problem of coherent interference sources: (1) Diagonal loading method: By adding constants to the diagonal of the covariance matrix to improve the stability and robustness of the beamforming algorithm. However, in the coherent source environment, the loaded diagonal terms may not be sufficient to separate the coherent signals, resulting in performance degradation. This is because diagonal loading cannot effectively distinguish multiple coherent signals, and thus cannot completely eliminate the interference between coherent sources. (2) Eigenstructure-based method: The eigendecomposition information of the covariance matrix is ​​used to enhance the performance of beamforming and suppress interference. In the face of coherent sources, eigenvalue decomposition may fail because coherent sources make the eigenvalue spectrum of the covariance matrix difficult to distinguish, making it impossible for the algorithm to accurately extract and separate the characteristic information of the coherent signal. (3) Uncertainty set-based method: Consider array errors and uncertainties in the beamforming process, and improve the robustness of the algorithm by optimizing the uncertainty set. However, for coherent sources, the error and uncertainty models are difficult to accurately describe the signal characteristics because the high correlation between coherent signals will cause the uncertainty model to fail, thus affecting the effect of beamforming. (4) Method based on covariance matrix reconstruction: The estimation error and noise influence are reduced by reconstructing the covariance matrix to enhance the accuracy of beamforming. However, coherent sources will make the reconstruction of the covariance matrix inaccurate, because the coherent signal will cause strong correlation in the matrix, making it difficult to effectively separate and suppress the coherent signal during the reconstruction process. Faced with the challenge of coherent sources, existing adaptive beamforming methods may encounter significant performance degradation in practical applications. In order to overcome these problems, further research and development of new beamforming technologies that can effectively process coherent signals is needed.

[0005] The present invention is a coherent source adaptive beamforming method based on coprime array interpolation, which is applicable to interference source scenarios. The method utilizes the decoherence of a diagonal matrix and the Vandermonde decomposition property of the Teplitz matrix to effectively separate the coherent source interference and the target signal, and at the same time improves the robustness of the method by reconstructing the interference and noise covariance matrix. The method can effectively solve the problem of target signal energy leakage caused by coherent source interference, and also has high practical value for applications such as wireless signal reception. Summary of the invention

[0006] The present invention aims to solve the technical problem that in actual scenarios, coherent signal source interference causes energy leakage in the reception of target signals, and aims to provide a coherent source adaptive beamforming method based on coprime array interpolation.

[0007] In order to solve the technical problem, the technical solution of the present invention is:

[0008] A coherent source adaptive beamforming method based on coprime array interpolation, the method comprising:

[0009] The first stage is dealcoherence covariance matrix reconstruction and the second stage is adaptive beamformer construction;

[0010] In the first stage, the sensor position model of the coprime array, the mathematical model of signal reception, the description of the signal and interference, and the definition of the steering vector are constructed to interpolate the received signal. The coherence of the diagonal matrix and the Vandermonde decomposition property of the Teplitz matrix are used to achieve effective separation of the coherent source interference and the target signal. In the second stage, an adaptive beamformer is designed by reconstructing the interference and noise covariance matrix, ultimately achieving high-precision detection and extraction of target signals in complex environments.

[0011] Furthermore, the first stage includes:

[0012] Received signal interpolation: Using the sensor positions of the coprime array, a virtual array is constructed by interpolation and an observation vector model is established to obtain the observation vector of the virtual ULA;

[0013] Derivation of decorrelation covariance matrix: Calculate the covariance matrix by interpolating the observed vector, reconstruct the covariance matrix through matrix operations, and finally construct a new matrix so that the interference signal is decorrelated;

[0014] Teplitz-type matrix construction: The reconstructed covariance matrix is ​​expressed by constructing a Hermitian Teplitz matrix, which is further processed to obtain a more accurate modeling of the interference;

[0015] Atomic norm recovery covariance matrix: Using the atomic norm theory, the atomic l0 norm is relaxed to the atomic l1 norm. Through optimization solution, the required covariance matrix is ​​reconstructed and restored, and finally the pseudo covariance matrix is ​​obtained for subsequent beamforming.

[0016] Furthermore, the second stage includes:

[0017] Orthogonal projection matrix construction: Construct a quasi-covariance matrix and invert it to obtain the projection matrix C, which is used to eliminate the information of the desired signal while retaining interference and noise;

[0018] INCM matrix reconstruction: Use the projection matrix to process the covariance matrix and reconstruct the INCM matrix, which retains the interference and noise information;

[0019] Calculate the weight vector: Finally, the weight vector is calculated based on the MVDR criterion, and the optimal weight vector is solved using the reconstructed INCM matrix to achieve adaptive beamforming of the target signal.

[0020] Furthermore, the sensor position model of the coprime array, the mathematical model of signal reception, the description of signals and interference, and the definition of the steering vector specifically include:

[0021] The sensor locations for a coprime array are:

[0022]

[0023] Where M and N are coprime numbers, the array aperture is (2M-1)Nd, d = λ / 2, λ is the carrier wavelength;

[0024] There is a narrowband SOI and L far-field narrowband interferers coherent with the SOI; the DOAs of the signal and the interferer come from different directions θ0, θ1, …, θ L , the observation vector of the array is expressed as:

[0025]

[0026] Where t is the time measurement of the signal, s0(t), s l (t) are the waveforms of signal and interference respectively, where s l (t) = γ l s0(t), is a non-zero complex number, is independent and identically distributed (iid) additive Gaussian white noise, is the steering vector related to the incoming wave direction;

[0027] The steering vector for a coprime array is:

[0028]

[0029] in,

[0030] Further, the received signal interpolation specifically includes:

[0031] The augmented array construction interpolation array manifold is expressed as:

[0032]

[0033] in, Represents the remaining elements in set U after removing the elements in set S;

[0034] The observation vector of the virtual ULA is:

[0035]

[0036] Among them, γ0=1, denote the steering matrix and noise vector of the virtual ULA respectively.

[0037] Furthermore, the derivation of the decorrelation covariance matrix and the construction of the Teplitz type matrix specifically include:

[0038] Derivation of the decorrelation covariance matrix:

[0039] Actual ULA receiving signal Assume that:

[0040]

[0041] The steering vector of the real ULA is defined as:

[0042]

[0043] The covariance matrix of is:

[0044]

[0045] Among them, the vector γ is the reason for the rank reduction in the part of the covariance matrix related to SOI and interference;

[0046] Consider the steering vectors for coprime arrays Interpolation results in There is a value of 0, and then use The calculated covariance matrix has all zero columns; construct a selection matrix B for After removing all zero columns, we get:

[0047]

[0048] in, is the covariance matrix after the target signal is filtered out in orthogonal space, e i is a column vector, except for the i-th position which is 1, all elements are 0;

[0049] Rephrased as:

[0050]

[0051] in:

[0052]

[0053] At this time, all the prior information of the signal and interference is contained in In the formula, it is expressed as R S ,for:

[0054]

[0055] By constructing a new matrix for decoherence, it is:

[0056]

[0057] Due to the existence of coherent source interference, ZZ H It is not a diagonal matrix. Keep its diagonal part and get a new matrix:

[0058]

[0059] in,

[0060] Teplitz-type matrix construction:

[0061] The Hermitian-Teplitz matrix can be restated as Rewritten as:

[0062]

[0063] The Teplitz matrix is ​​expressed as:

[0064]

[0065] Further, the construction of the atomic norm recovery covariance matrix specifically includes:

[0066] According to the atomic norm theory, the steering vectors of SOI and coherent interference in the received signal are separated by selecting off-grid atomic sets. The atomic set is defined as:

[0067]

[0068] The l0 norm is very effective in finding the optimal sparse feature term, so the atomic l0 norm is used as a constraint condition, which can be expressed as:

[0069]

[0070] In the l0-norm constraint problem, the convex hull of the l1-norm completely contains the convex hull of the l0-norm, that is, the l1-norm is the tightest convex relaxation of the l0-norm. Relaxing the atomic l0-norm to the atomic l1-norm is:

[0071]

[0072] calculate The SCM is:

[0073]

[0074] Based on the above derivation and the prior conditions of the Hermitian-Teplitz matrix, the optimization problem is established to obtain the required pseudo-covariance matrix R S , described as:

[0075]

[0076] Among them, Π is a S The number of non-zero known elements and zero unknown elements in Binary matrices;

[0077] Introducing the ANM problem, we get:

[0078]

[0079] Among them, μ is a regularization parameter;

[0080] Minimization of the atomic norm can be equivalent to the following SDP problem:

[0081]

[0082] in, is a Hermitian matrix.

[0083] Furthermore, the orthogonal projection matrix construction specifically includes:

[0084] Construct a class covariance matrix as:

[0085]

[0086] Among them, I is the unit matrix, and the value of α affects the orthogonality between the constructed matrix and the expected signal, so a larger value should be taken;

[0087] C is expressed in the form of eigenvalues ​​and eigenvectors, eigenvalue μ i Arrange in descending order:

[0088]

[0089] μ is the eigenvalue in descending order, and μ1=M,μ i =1.ξ i and μ are the corresponding eigenvectors and eigenvalues;

[0090] The inverse matrix of the constructed class covariance matrix C is expressed as:

[0091]

[0092] based on is satisfied and α>>1, C is approximately:

[0093]

[0094] C -1 As the projection matrix B, it is:

[0095]

[0096] Furthermore, the INCM matrix reconstruction specifically includes:

[0097] The covariance matrix after projection matrix processing, in which the SOI information is eliminated and the interference and noise information is retained, is:

[0098]

[0099] The INCM matrix is ​​reconstructed by the corresponding eigenvalues ​​and eigenvectors:

[0100]

[0101] in, for The minimum eigenvalue of .

[0102] Further, the calculation of the weight vector specifically includes:

[0103] The weight vector based on the MVDR criterion is:

[0104]

[0105] Compared with the prior art, the advantages of the present invention are:

[0106] The present invention proposes an adaptive beamforming method based on coprime array interpolation and reconstruction of interference and noise covariance matrices, which is suitable for coherent interference signal sources and complex noise situations; it can accurately eliminate coherent interference and obtain a better output signal-to-noise ratio. It is suitable for interference source scenarios. The method utilizes the decoherence of the diagonal matrix and the Vandermonde decomposition property of the Teplitz matrix to effectively separate the coherent source interference and the target signal, and at the same time improves the robustness of the method through reconstruction of the interference and noise covariance matrix. The method can effectively solve the problem of target signal energy leakage caused by coherent source interference, and it also has high practical value for applications such as wireless signal reception. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 , a flow chart of the method of the present invention;

[0108] Figure 2 , DOA estimation after coprime array interpolation;

[0109] Figure 3 , DOA estimation in orthogonal projection space;

[0110] Figure 4 , beam pattern after reconstruction based on the interference plus noise covariance matrix. DETAILED DESCRIPTION

[0111] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0112] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0113] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0114] Embodiment 1:

[0115] like Figure 1 As shown, the coherent source adaptive beamforming method based on coprime array interpolation of the present invention includes two stages:

[0116] Stage 1: Decorrelation and covariance matrix reconstruction

[0117] The sensor locations for a coprime array are:

[0118]

[0119] Wherein, M and N are coprime numbers, the array aperture is (2M-1)Nd, d=λ / 2, and λ is the carrier wavelength.

[0120] There is a narrowband SOI and L far-field narrowband interferences coherent with the SOI. The DOAs of the signal and interference come from different directions θ0, θ1, …, θ L , the observation vector of the array can be expressed as:

[0121]

[0122] Where t is the time measurement of the signal. s0(t), s l (t) are the waveforms of signal and interference respectively, where s l (t) = γ l s0(t), is a non-zero complex number. is independent and identically distributed (iid) additive Gaussian white noise. is the steering vector related to the incoming wave direction.

[0123] The steering vector for a coprime array is:

[0124]

[0125] in,

[0126] Step 1: Receive signal interpolation

[0127] The augmented array construction interpolation array manifold can be expressed as:

[0128]

[0129] in, Represents the elements remaining after removing the elements in set S from set U.

[0130] The observation vector of the virtual ULA is:

[0131]

[0132] Among them, γ0=1, denote the steering matrix and noise vector of the virtual ULA respectively.

[0133] Step 2: Derivation of the decorrelation covariance matrix

[0134] Actual ULA receiving signal Assume that:

[0135]

[0136] The steering vector of the real ULA is defined as:

[0137]

[0138] The covariance matrix of is:

[0139]

[0140] The vector γ is responsible for the rank reduction in the covariance matrix for SOI and interference.

[0141] Since the steering vector of the coprime array Interpolation results in There is a value of 0, and then use The calculated covariance matrix contains all zero columns. Construct a selection matrix B for After removing all zero columns, we get:

[0142]

[0143] in, e i is a column vector with all elements zero except the i-th position which is 1.

[0144] Rephrased as:

[0145]

[0146] in,

[0147]

[0148] At this time, all the prior information of the signal and interference is contained in In the formula, it is expressed as R S ,for:

[0149]

[0150] By constructing a new matrix for decoherence, it is:

[0151]

[0152] Due to the existence of coherent source interference, ZZ H It is not a diagonal matrix. Keep its diagonal part and get a new matrix:

[0153]

[0154] in,

[0155] Step 3: Construction of the Teplitz-type matrix

[0156] The Hermitian-Teplitz matrix can be restated as Rewrite as

[0157]

[0158] The Teplitz matrix is ​​expressed as:

[0159]

[0160] Step 4: Atomic norm restores the covariance matrix

[0161] According to the atomic norm theory, the off-grid atomic set is selected to achieve the steering vector separation of SOI and coherent interference in the received signal. The atomic set is defined as:

[0162]

[0163] The l0 norm is very effective in finding the optimal sparse feature term, so the atomic l0 norm is used as a constraint condition, which can be expressed as:

[0164]

[0165] In the l0-norm constraint problem, the convex hull of the l1-norm can completely contain the convex hull of the l0-norm, that is, the l1-norm is the tightest convex relaxation of the l0-norm. Relaxing the atomic l0-norm to the atomic l1-norm is:

[0166]

[0167] calculate The SCM is:

[0168]

[0169] Based on the above derivation and the optimization problem established based on the prior conditions of the Hermitian-Teplitz matrix, the required pseudo-covariance matrix R can be obtained. S , described as:

[0170]

[0171] Among them, ∏ is a character used to distinguish R S The number of non-zero known elements and zero unknown elements in Binary matrix.

[0172] Introducing the ANM problem, we get:

[0173]

[0174] Here, μ is a regularization parameter.

[0175] Minimization of the atomic norm can be equivalent to the following SDP problem:

[0176]

[0177] in, is a Hermitian matrix.

[0178] In the stage of constructing the adaptive beamformer, the pseudo-covariance matrix R S The signal feature matrix after eliminating coherent interference is provided, which becomes the basis for calculating the orthogonal projection matrix and INCM matrix. These matrices are then used to design the weight vector of the beamformer so that the beamformer can still accurately enhance the desired signal in the presence of coherent interference. Figure 2 As shown, it is the DOA estimation after coprime array interpolation, which can accurately estimate the DOA of the target signal and the three decorrelated coherent interference signals.

[0179] Phase 2: Adaptive Beamformer Construction

[0180] Step 1: Orthogonal projection matrix construction

[0181] Construct a class covariance matrix as:

[0182]

[0183] The value of α affects the orthogonality between the constructed matrix and the expected signal, and should be a larger value.

[0184] C can be expressed in the form of eigenvalues ​​and eigenvectors. The eigenvalue μ i Arrange in descending order:

[0185]

[0186] μ is the eigenvalue in descending order, and μ1=M,μ i =1.ξ i and μ are the corresponding eigenvectors and eigenvalues.

[0187] The inverse matrix of the constructed class covariance matrix C can be expressed as:

[0188]

[0189] based on is satisfied and α>>1, C can be approximated as:

[0190]

[0191] C -1 It can be used as the projection matrix B, as follows:

[0192]

[0193] Step 2: INCM matrix reconstruction

[0194] The covariance matrix after projection matrix processing, in which the SOI information is eliminated and the interference and noise information is retained, is:

[0195]

[0196] The INCM matrix is ​​reconstructed by the corresponding eigenvalues ​​and eigenvectors:

[0197] (89)

[0199] in, for The minimum eigenvalue of . Figure 3 As shown in FIG. 1 , the DOA estimation in the orthogonal projection space can accurately obtain the DOA of the three interference signals after filtering out the target signal.

[0200] Step 3: Calculate the weight vector

[0201] The weight vector based on the MVDR criterion is:

[0202]

[0203] Embodiment 2:

[0204] The interference suppression measured in multiple interference situations demonstrates the suppression effect of the present invention on the coherent signal source:

[0205] Set the working parameters: coprime array M = 3, N = 5, a total of 11 array elements, array element spacing is set to half a wavelength. Target wave direction 0°, coherent source wave direction -30°, 30°, 60°, SNR = 20dB, each array element receives the interference-to-noise ratio INR = 30dB, the number of snapshots is 100.

[0206] Specific process:

[0207] (1) Construct a coprime array model, M = 3, N = 5, 0, 3, 5, 6, 9, 10, 12, 15, 20, 25;

[0208] (2) constructing a regularization matrix B according to the actual sensor positions in the coprime array;

[0209] (3) Define atomic sets

[0210] (4) Constructing the atomic norm optimization problem;

[0211] (5) Solve the optimization problem to get the matrix

[0212] (6) constructing an orthogonal projection matrix in the SOI direction;

[0213] (7) Processing with orthogonal projection matrix

[0214] (8) Reconstruct INCM into R INCM ;

[0215] (9) Calculate the weight function using the MVDR criterion;

[0216] Effect comparison: Compared with the traditional adaptive beamforming algorithm, the present invention is suitable for coherent interference signal sources and complex noise situations; it can accurately eliminate coherent interference and obtain a better output signal-to-noise ratio. Figure 4 As shown, the power directional diagram obtained by the present invention can well receive the target signal and perform anti-interference processing on the directional area of ​​the interference signal, and the main-sidelobe ratio can reach 13.27dB.

[0217] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0218] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0219] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0220] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0221] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0222] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for adaptive beamforming of coherent sources based on coprime array interpolation, characterized in that: The method comprises: The first stage is deallocation covariance matrix reconstruction and the second stage is adaptive beamformer construction; In the first stage, the sensor position model of the coprime array, the mathematical model of signal reception, the description of the signal and interference, and the definition of the steering vector are constructed to interpolate the received signal. The coherence of the diagonal matrix and the Vandermonde decomposition property of the Teplitz matrix are used to achieve effective separation of the coherent source interference and the target signal. In the second stage, an adaptive beamformer is designed by reconstructing the interference and noise covariance matrix, ultimately achieving high-precision detection and extraction of target signals in complex environments.

2. The method of coherent source adaptive beamforming based on coprime array interpolation according to claim 1, characterized in that: The first phase includes: Received signal interpolation: Using the sensor positions of the coprime array, a virtual array is constructed by interpolation and an observation vector model is established to obtain the observation vector of the virtual ULA; Derivation of decorrelation covariance matrix: Calculate the covariance matrix by interpolating the observed vector, reconstruct the covariance matrix through matrix operations, and finally construct a new matrix so that the interference signal is decorrelated; Teplitz-type matrix construction: The reconstructed covariance matrix is ​​expressed by constructing a Hermitian Teplitz matrix, which is further processed to obtain a more accurate modeling of the interference; Atomic norm recovery covariance matrix: Using the atomic norm theory, the atomic l0 norm is relaxed to the atomic l1 norm. Through optimization solution, the required covariance matrix is ​​reconstructed and restored, and finally the pseudo covariance matrix is ​​obtained for subsequent beamforming.

3. The method for adaptive beamforming of coherent sources based on coprime array interpolation according to claim 1, characterized in that: The second phase includes: Orthogonal projection matrix construction: Construct a quasi-covariance matrix and invert it to obtain the projection matrix C, which is used to eliminate the information of the desired signal while retaining interference and noise; INCM matrix reconstruction: Use the projection matrix to process the covariance matrix and reconstruct the INCM matrix, which retains the interference and noise information; Calculate the weight vector: Finally, the weight vector is calculated based on the MVDR criterion, and the optimal weight vector is solved using the reconstructed INCM matrix to achieve adaptive beamforming of the target signal.

4. The method for adaptive beamforming of coherent sources based on coprime array interpolation according to claim 1, characterized in that: The sensor position model of the coprime array, the mathematical model of signal reception, the description of signals and interference, and the definition of steering vectors specifically include: The sensor locations for a coprime array are: Where M and N are coprime numbers, the array aperture is (2M-1)Nd, d = λ / 2, λ is the carrier wavelength; There is a narrowband SOI and L far-field narrowband interferers coherent with the SOI; the DOAs of the signal and the interferer come from different directions θ0, θ1, ..., θ L , the observation vector of the array is expressed as: Where t is the time measurement of the signal, s0(t), s l (t) are the waveforms of signal and interference respectively, where s l (t) = γ l s0(t), is a non-zero complex number, is independent and identically distributed (iid) additive Gaussian white noise, is the steering vector related to the incoming wave direction; The steering vector for a coprime array is: in, 5. The method of coherent source adaptive beamforming based on coprime array interpolation according to claim 2, characterized in that: The received signal interpolation specifically includes: The augmented array construction interpolation array manifold is expressed as: in, Represents the remaining elements in set U after removing the elements in set S; The observation vector of the virtual ULA is: Among them, γ0=1, denote the steering matrix and noise vector of the virtual ULA respectively.

6. The method of coherent source adaptive beamforming based on coprime array interpolation according to claim 2, characterized in that: The derivation of the decorrelation covariance matrix and the construction of the Teplitz-type matrix include: Derivation of the decorrelation covariance matrix: Actual ULA receiving signal Assume that: The steering vector of the real ULA is defined as: The covariance matrix of is: Among them, the vector y is the reason for the rank reduction in the part of the covariance matrix related to SOI and interference; Consider the steering vectors for coprime arrays Interpolation results in There is a value of 0, and then use The calculated covariance matrix has all zero columns; construct a selection matrix B for After removing all zero columns, we get: in, is the covariance matrix after the target signal is filtered out in orthogonal space, e i is a column vector, except for the i-th position which is 1, all elements are 0; Rephrased as: in: At this time, all the prior information of the signal and interference is contained in In the formula, it is expressed as R S ,for: By constructing a new matrix for decoherence, it is: Considering the existence of coherent source interference, ZZ H It is not a diagonal matrix. Keep its diagonal part and get a new matrix: in, Teplitz-type matrix construction: The Hermitian-Teplitz matrix can be restated as Rewritten as: The Teplitz matrix is ​​expressed as:

7. The method of coherent source adaptive beamforming based on coprime array interpolation according to claim 2, characterized in that: The constructing of the atomic norm recovery covariance matrix specifically includes: According to the atomic norm theory, the steering vectors of SO1 and coherent interference in the received signal are separated by selecting off-grid atomic sets. The atomic set is defined as: The l0 norm is very effective in finding the optimal sparse feature term, so the atomic l0 norm is used as a constraint condition, which can be expressed as: In the l0-norm constraint problem, the convex hull of the 11-norm completely contains the convex hull of the l0-norm, that is, the 11-norm is the tightest convex relaxation of the l0-norm. Relaxing the atomic l0-norm to the atomic 11-norm is: calculate The SCM is: Based on the above derivation and the prior conditions of the Hermitian-Teplitz matrix, the optimization problem is established to obtain the required pseudo-covariance matrix R S , described as: Among them, Π is a S The number of non-zero known elements and zero unknown elements in Binary matrices; Introducing the ANM problem, we get: Among them, μ is a regularization parameter; Minimization of the atomic norm can be equivalent to the following SDP problem: in, is a Hermitian matrix.

8. The method for adaptive beamforming of coherent sources based on coprime array interpolation according to claim 3, characterized in that: The orthogonal projection matrix construction specifically includes: Construct a class covariance matrix as: Among them, I is the unit matrix, and the value of α affects the orthogonality between the constructed matrix and the expected signal, so a larger value should be taken; C is expressed in the form of eigenvalues ​​and eigenvectors, eigenvalue μ i Arrange in descending order: μ is the eigenvalue in descending order, and μ1=M, μ i =1,ξ i and μ are the corresponding eigenvectors and eigenvalues; The inverse matrix of the constructed class covariance matrix C is expressed as: based on is satisfied and α>>1, C is approximately: C -1 As the projection matrix B, it is:

9. The method of coherent source adaptive beamforming based on coprime array interpolation according to claim 3, characterized in that: The INCM matrix reconstruction specifically includes: The covariance matrix after projection matrix processing, in which the SOI information is eliminated and the interference and noise information is retained, is: The INCM matrix is ​​reconstructed by the corresponding eigenvalues ​​and eigenvectors: in, for The minimum eigenvalue of .

10. The method for adaptive beamforming of coherent sources based on coprime array interpolation according to claim 3, characterized in that: The calculation of the weight vector specifically includes: The weight vector based on the MVDR criterion is:

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