Covariance matrix reconstruction and steering vector optimization interference suppression method based on projection transformation

Abstract

The invention relates to an interference suppression method for covariance matrix reconstruction and steering vector optimization based on projection transformation, and belongs to the field of array interference suppression. The method comprises the following steps: S1, constructing a received signal covariance matrix by using received data; s2, calculating a reconstructed interference and noise covariance matrix through integral reconstruction; s3, carrying out eigenvalue decomposition on the reconstructed interference and noise covariance matrix; s4, constructing a projection transformation matrix by using the noise subspace obtained by decomposition, and performing projection transformation on the interference and noise covariance matrix; s5, the interference and noise covariance matrix loaded with the optimal diagonal loading factor is adopted, and sharpening processing is carried out; s6, establishing a space containing all interference signal steering vectors; s7, optimizing a steering vector based on a maximized array output power criterion; and S8, calculating the weight of the beam former by using the optimized steering vector and the reconstructed interference and noise covariance matrix. According to the method and the device, the problem of main lobe offset caused by target steering vector mismatch in the adaptive beam forming technology is solved, the null width is widened, the problem that null and interference directions are inconsistent is solved, and interference is suppressed under the condition of interference signal incoming direction disturbance.

Description

Technical Field

[0001] The invention belongs to the field of array interference suppression, and relates to an interference suppression method based on covariance matrix reconstruction and steering vector optimization of projection transformation. Background Art

[0002] Adaptive beamforming technology effectively suppresses interference and noise and improves the output signal to interference and noise ratio (SINR) by forming nulls in the interference direction. It has been widely used in mobile communications, sonar, biomedicine and other fields, and has become a research hotspot in the field of array signal processing. Commonly used beamformers, such as minimum variance distortionless response beamformers, lack robustness to various system errors. When the array is in a non-ideal application environment, the anti-interference performance will drop sharply. In the real environment, there are array element position errors, channel amplitude phase errors, etc. in the actual working environment, which causes deviations in the target steering vector constraints. Theoretical studies have shown that when there is a constraint deviation in the target steering vector, problems such as main lobe offset may occur under low signal-to-noise ratio conditions, reducing the output SINR; when the interference direction is unstable or the antenna platform vibrates, the beam null and the interference direction will be inconsistent, so that the interference cannot be effectively suppressed. If the null is optimized and widened, the array antenna can effectively improve the ability to cope with the relative motion of the beam null and the interference, and improve the array's ability to suppress interference. Summary of the invention

[0003] In view of this, the present invention provides an interference suppression method based on covariance matrix reconstruction and steering vector optimization of projection transformation. In this method, the robustness of beamforming is improved in low snapshot, motion interference and steering vector mismatch scenarios.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] An interference suppression method based on covariance matrix reconstruction and steering vector optimization of projection transformation, characterized in that the method comprises the following steps:

[0006] S1: Construct the received signal covariance matrix R using the received data x ;

[0007] S2: Calculate the reconstructed interference plus noise covariance matrix by integral reconstruction;

[0008] S3: perform eigenvalue decomposition on the reconstructed interference plus noise covariance matrix;

[0009] S4: construct a projection transformation matrix using the noise subspace obtained by decomposition, and perform projection transformation on the interference plus noise covariance matrix;

[0010] S5: Use the interference plus noise covariance matrix with the optimal diagonal loading factor and perform sharpening processing;

[0011] S6: Establish a space containing all interference signal steering vectors;

[0012] S7: Optimize the steering vector based on the criterion of maximizing array output power;

[0013] S8: Calculate beamformer weights using the optimized steering vector and the reconstructed interference plus noise covariance matrix.

[0014] Further, in step S1, the received signal covariance matrix R is constructed using the received data x ;

[0015]

[0016] Where K is the number of snapshots, (·) H represents conjugate transpose, and x(k) is the array receiving the data vector.

[0017] Further, in step S2, the observation space is divided into a desired signal region θ and an undesired signal region In the area of ​​undesired signals Integrate and reconstruct the covariance matrix of the acquired array received signal:

[0018]

[0019] Where a(θ) is the steering vector of the uniform linear array angle θ, d is the interval between each array element, and λ is the wavelength.

[0020] Further, in step S3, the reconstructed interference plus noise covariance matrix R i+n Perform eigenvalue decomposition,

[0021]

[0022] In the formula, M represents the number of array elements, λ i Represents the matrix R i+n M eigenvalues ​​after eigenvalue decomposition, u i Represents λ i The corresponding eigenvector; Λ j and Λ n They represent the eigenvalue matrix of the interference signal subspace and the eigenvalue matrix of the noise subspace respectively; U j and U nThey represent the interference signal subspace and the noise subspace respectively, where the eigenvector corresponding to the noise subspace is U j =[v1,v2,…,v j ], (1,2,…,j) represents the number of interferences.

[0023] Further, in step S4, the steering vector of the interference signal can be estimated as:

[0024]

[0025] In the formula, ||·||2 represents the two-norm.

[0026] Constructing the projection transformation matrix using the estimated steering vector

[0027]

[0028] Then the interference plus noise covariance matrix R i+n Projecting to the projection transformation matrix, we get

[0029] R i+n =VR i+n V

[0030] Thereby, the interference component of the interference plus noise covariance matrix can be enhanced, thereby increasing the interference power.

[0031] Furthermore, in step S5, in order to improve the stability of the algorithm, R i+n To perform diagonal loading:

[0032] R i+n =R i+n +μI

[0033] Among them, μ represents the diagonal loading factor, and I represents the M×M unit matrix. Then, the CMT algorithm is combined to perform null-steering beamforming. The CMT algorithm uses a sharpening matrix to sample the covariance matrix for sharpening, and replaces the original single interference source with a cluster of virtual interference sources, thereby achieving null-steering beamforming. i+n To sharpen:

[0034]

[0035] In the formula, represents the Hadamard product algorithm, T CMT Represents the sharpening matrix, whose mth row and nth column element is

[0036]

[0037] Wherein, sinc(x)=sin(πx) / πx, Δ>0 represents the width of the broadened null.

[0038] Further, in step S6, a space containing all interference signal steering vectors is established.

[0039]

[0040] in, is the sidelobe interval constraint matrix, is the sidelobe interval. In order to control the output power in the sidelobe area, a constraint condition is added

[0041] Further, in step S7, since the actual steering vector a and the assumed steering vector There is a mismatch error vector e between

[0042]

[0043] The error vector e can be decomposed into two parts parallel to the assumed steering vector The weight of || and is orthogonal to the assumed steering vector The weight of ⊥ , parallel to the assumed steering vector The weight of || It will not affect beamforming, as it only Any scaling of the steering vector will not affect the output SINR. It is only necessary to obtain a vector orthogonal to the assumed steering vector The weight of ⊥ .

[0044] right Eigenvalue decomposition gives

[0045]

[0046] In order to maximize the array output power and reduce the impact of interference and noise on the target guidance vector, the constraint relationship is established as follows:

[0047]

[0048]

[0049] In the formula, ε is a very small parameter to avoid e ⊥ =0 is the only solution.

[0050] Further, the desired signal steering vector is estimated

[0051] Further, in step S8, the steering vector a(θ0) optimized in step S7 and the inverse matrix of the interference plus noise covariance matrix reconstructed in step S5 are used. Calculate the beamforming weight vector w:

[0052]

[0053] The effective effect of the present invention is that when the interference direction is unstable or the antenna platform vibrates, the beam nulling and the interference direction are inconsistent. The present invention widens the nulling by inserting a virtual interference source at the interference source position, and enhances the interference component by projecting it into the interference subspace, thereby increasing the nulling depth. At the same time, the main lobe offset problem caused by the mismatch of the target steering vector and the reduction of the output signal interference-to-noise ratio in the adaptive beamforming technology are solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to make the purpose, technical solution and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0055] Figure 1 A schematic diagram of an array receiving data according to an embodiment of the present invention;

[0056] Figure 2 A flow chart of an interference suppression method based on covariance matrix reconstruction and steering vector optimization of an embodiment of the present invention; DETAILED DESCRIPTION

[0057] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0058] In order to solve the problem of inconsistency between beam nulling and interference direction caused by vibration of the antenna platform, and the problem of desired signal deviating from the optimal receiving position of the beam pattern, an interference suppression method based on covariance matrix reconstruction and steering vector optimization of projection transformation was proposed. The output performance of the array system was improved by optimizing the steering vector of the desired signal and widening the nulling.

[0059] Further, in step S1, the received signal covariance matrix R is constructed using the received data x ;

[0060]

[0061] Where K is the number of snapshots, (·) H represents conjugate transpose, and x(k) is the array receiving the data vector.

[0062] Further, in step S2, the observation space is divided into a desired signal region θ and an undesired signal region In the area of ​​undesired signals Integrate and reconstruct the covariance matrix of the acquired array received signal:

[0063]

[0064] Where a(θ) is the steering vector of the uniform linear array angle θ, d is the interval between each array element, and λ is the wavelength.

[0065] Further, in step S3, the reconstructed interference plus noise covariance matrix R i+n Perform eigenvalue decomposition,

[0066]

[0067] In the formula, M represents the number of array elements, λ i Represents the matrix R i+n M eigenvalues ​​after eigenvalue decomposition, u i Represents λ i The corresponding eigenvector; Λ j and Λ n They represent the eigenvalue matrix of the interference signal subspace and the eigenvalue matrix of the noise subspace respectively; U j and U n They represent the interference signal subspace and the noise subspace respectively, where the eigenvector corresponding to the noise subspace is U j =[v1,v2,…,v j ], (1,2,…,j) represents the number of interferences.

[0068] Further, in step S4, the steering vector of the interference signal can be estimated as:

[0069]

[0070] In the formula, ||·||2 represents the two-norm.

[0071] Constructing the projection transformation matrix using the estimated steering vector

[0072]

[0073] Then the interference plus noise covariance matrix R i+n Projecting to the projection transformation matrix, we get

[0074] R i+n =VR i+n V

[0075] Thereby, the interference component of the interference plus noise covariance matrix can be enhanced, thereby increasing the interference power.

[0076] Furthermore, in step S5, in order to improve the stability of the algorithm, Ri+n To perform diagonal loading:

[0077] R i+n =R i+n +μI

[0078] Among them, μ represents the diagonal loading factor, and I represents the M×M unit matrix. Then, the CMT algorithm is combined to perform null-steering beamforming. The CMT algorithm uses a sharpening matrix to sample the covariance matrix for sharpening, and replaces the original single interference source with a cluster of virtual interference sources, thereby achieving null-steering beamforming. i+n To sharpen:

[0079]

[0080] In the formula, represents the Hadamard product algorithm, T CMT Represents the sharpening matrix, whose mth row and nth column element is

[0081]

[0082] Wherein, sinc(x)=sin(πx) / πx, Δ>0 represents the width of the broadened null.

[0083] Further, in step S6, a space containing all interference signal steering vectors is established.

[0084]

[0085] in, is the sidelobe interval constraint matrix, is the sidelobe interval. In order to control the output power in the sidelobe area, a constraint condition is added

[0086] Further, in step S7, since the actual steering vector a and the assumed steering vector There is a mismatch error vector e between

[0087]

[0088] The error vector e can be decomposed into two parts parallel to the assumed steering vector The weight of || and is orthogonal to the assumed steering vector The weight of ⊥ , parallel to the assumed steering vector The weight of || It will not affect beamforming, as it only Any scaling of the steering vector will not affect the output SINR. It is only necessary to obtain a vector orthogonal to the assumed steering vector The weight of ⊥ .

[0089] right Eigenvalue decomposition gives

[0090]

[0091] In order to maximize the array output power and reduce the impact of interference and noise on the target guidance vector, the constraint relationship is established as follows:

[0092]

[0093]

[0094] In the formula, ε is a very small parameter to avoid e ⊥ =0 is the only solution.

[0095] Further, the desired signal steering vector is estimated

[0096] Further, in step S8, the steering vector a(θ0) optimized in step S7 and the inverse matrix of the interference plus noise covariance matrix reconstructed in step S5 are used. Calculate the beamforming weight vector w:

[0097]

[0098] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. An interference suppression method based on covariance matrix reconstruction and steering vector optimization based on projection transformation, characterized in that: The method comprises the following steps: S1: Construct the received signal covariance matrix R using the received data x ; S2: Calculate the reconstructed interference plus noise covariance matrix by integral reconstruction; S3: perform eigenvalue decomposition on the reconstructed interference plus noise covariance matrix; S4: construct a projection transformation matrix using the noise subspace obtained by decomposition, and perform projection transformation on the interference plus noise covariance matrix; S5: Use the interference plus noise covariance matrix with the optimal diagonal loading factor and perform sharpening processing; S6: Establish a space containing all interference signal steering vectors; S7: Optimize the steering vector based on the criterion of maximizing array output power; S8: Calculate beamformer weights using the optimized steering vector and the reconstructed interference plus noise covariance matrix.

2. A method for suppressing interference based on covariance matrix reconstruction and steering vector optimization based on projection transformation according to claim 1, characterized in that: In step S1, the received signal covariance matrix R is constructed using the received data x . Where K is the number of snapshots, (·) H represents conjugate transpose, and x(k) is the array receiving the data vector.

3. A method for suppressing interference based on covariance matrix reconstruction and steering vector optimization based on projection transformation according to claim 1, characterized in that: In step S2, the observation space is divided into the desired signal region θ and the undesired signal region In the area of ​​undesired signals Integrate and reconstruct the covariance matrix of the collected array received signal: Where a(θ) is the steering vector of the uniform linear array angle θ, a(θ)=[1,e j2πdsinθ / λ ,…,e j2πd(M-1)sinθ / λ ], d is the interval between each array element, and λ is the wavelength.

4. A method for suppressing interference based on covariance matrix reconstruction and steering vector optimization based on projection transformation according to claim 1, characterized in that: In step S3, the reconstructed interference plus noise covariance matrix R i+n Perform eigenvalue decomposition, In the formula, M represents the number of array elements, λ i Represents the matrix R i+n M eigenvalues ​​after eigenvalue decomposition, u i Represents λ i The corresponding eigenvector; Λ j and Λ n They represent the eigenvalue matrix of the interference signal subspace and the eigenvalue matrix of the noise subspace respectively; U j and U n denote the interference signal subspace and the noise subspace respectively, where the noise subspace 5. A method for suppressing interference based on covariance matrix reconstruction and steering vector optimization based on projection transformation according to claim 1, characterized in that: In step S4, the steering vector of the interference signal can be estimated as In the formula, ||·||2 represents the two-norm, and the projection transformation matrix is ​​constructed using the estimated steering vector Then the interference plus noise covariance matrix R i+n Projecting to the projection transformation matrix, we get R i+n =VR i+n V Thereby, the interference component of the interference plus noise covariance matrix can be enhanced, thereby increasing the interference power.

6. The interference suppression method according to claim 1, characterized in that: In step S5, in order to improve the stability of the algorithm, R i+n Diagonal loading R i+n =R i+n +μI Among them, μ represents the diagonal loading factor, and I represents the M×M unit matrix. Then, the CMT algorithm is combined to perform null-steering beamforming. The CMT algorithm uses a sharpening matrix to sample the covariance matrix for sharpening, and replaces the original single interference source with a cluster of virtual interference sources, thereby achieving null-steering beamforming. Furthermore, for R i+n Sharpening In the formula, represents the Hadamard product algorithm, T CMT Represents the sharpening matrix, whose mth row and nth column element is Wherein, sinc(x)=sin(πx) / πx, Δ>0 represents the width of the broadened null.

7. The interference suppression method according to claim 1, characterized in that: In step S6, a space containing all interference signal steering vectors is established. in, is the sidelobe interval constraint matrix, is the sidelobe interval. In order to control the output power in the sidelobe area, a constraint condition is added 8. The interference suppression method according to claim 1, characterized in that: In step S7, since the actual steering vector a and the assumed steering vector There is a mismatch error vector e between The error vector e can be decomposed into two parts parallel to the assumed steering vector The weight of || and is orthogonal to the assumed steering vector The weight of ⊥ , parallel to the assumed steering vector The weight of || It will not affect beamforming, as it only Any scaling of the steering vector will not affect the output SINR. It is only necessary to obtain a vector orthogonal to the assumed steering vector The weight of ⊥ . right Eigenvalue decomposition gives In order to maximize the array output power and reduce the impact of interference and noise on the target guidance vector, the constraint relationship is established as follows: In the formula, ε is a very small parameter to avoid e ⊥ =0 is the only solution. Furthermore, by solving the above equation using the convex optimization method, the desired signal steering vector can be estimated 9. The interference suppression method according to claim 1, characterized in that: In step S8, the optimized steering vector a(θ0) and the inverse matrix of the reconstructed interference plus noise covariance matrix are used. Calculate the beamforming weight vector w:

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