阅读说明：本技术 基于干扰加噪声协方差矩阵重构的稳健波束形成方法 (Robust beam forming method based on interference plus noise covariance matrix reconstruction ) 是由 潘涛 于 2020-07-06 设计创作，主要内容包括：本发明涉及一种基于干扰加噪声协方差矩阵重构的稳健波束形成方法,所述方法包括以下步骤：利用Capon空间谱重构干扰协方差矩阵,得到重构的干扰加噪声协方差矩阵；重构出期望信号加噪声协方差矩阵,建立并求解二次约束二次规划问题,获得误差矢量的正交分量,估计期望信号的导向矢量；计算波束形成器的权值矢量。本发明中改进的稳健自适应波束形成方法有效可行,性能可靠。(The invention relates to a robust beam forming method based on interference plus noise covariance matrix reconstruction, which comprises the following steps: reconstructing an interference covariance matrix by using a Capon space spectrum to obtain a reconstructed interference-plus-noise covariance matrix; reconstructing an expected signal plus noise covariance matrix, establishing and solving a quadratic constraint quadratic programming problem, obtaining an orthogonal component of an error vector, and estimating a guide vector of an expected signal; weight vectors of the beamformer are calculated. The improved robust adaptive beam forming method is effective and feasible and has reliable performance.)

1. A robust beam forming method based on interference plus noise covariance matrix reconstruction is characterized by comprising the following steps:

step 1: receiving an echo of a target to be detected by using a radar;

step 2: reconstructing an interference covariance matrix by using a Capon space spectrum to obtain a reconstructed interference-plus-noise covariance matrix;

step 2-1: setting a total of P targets, wherein P is 0 and is an expected target, other targets are interference targets, and the number of array elements of a radar receiving array is M; the following ellipsoid uncertainty set is defined:

wherein, theta_intThe angular region containing only the arrival direction of the interference signal is constant,is a nominal guide vector with the incoming wave direction of theta

wherein, a_pA steering vector for the p-th interfering signal;

step 2-2: because the real interference signal guide vector is always in the uncertain concentration S_a(θ∈Θ_int) In so doing, S is not determined at all_a(θ∈Θ_int) Performing integral operation on the Capon power spectrum to reconstruct an interference covariance matrix, wherein the integral operation is approximately equal to:

wherein, a_ilIs S_a(θ∈Θ_int) The steering vector corresponding to each sampling point of the surface region, I represents the angular region theta_intNumber of sampling points, L being the nominal steering vector of each sampling pointThe number of sample points in the uncertainty set of (c),is a sample covariance matrix;

step 2-3: reconstructing an interference plus noise covariance matrix by using the interference signal covariance matrix; the reconstructed interference plus noise covariance matrix is:

wherein I_mIs an identity matrix of order M,the noise energy estimated value is approximated by the minimum eigenvalue of the covariance matrix of the sampled data;

and step 3: reconstructing an expected signal plus noise covariance matrix, establishing and solving a quadratic constraint quadratic programming problem, and obtaining an orthogonal component of an error vector;

the following optimization problem was constructed:

in the formula, e_⊥Is composed ofThe vector of the vertical direction is,a nominal steering vector for the desired target;

the optimization problem is a quadratic constraint quadratic regularization problem and a convex problem, can be quickly solved based on an interior point method, and obtains the optimal solution of the optimization problem

and 4, step 4: calculating weight vectors of the beam former:

and (3) according to the covariance matrix obtained in the step (2) and the steering vector obtained in the step (3), obtaining a weight w by using a Capon beam former:

2. a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the steps of the method of claim 1 are implemented when the computer program is executed by the processor.

3. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method as claimed in claim 1.

Technical Field

The invention belongs to the technical field of radar, and particularly relates to a robust beam forming method based on interference plus noise covariance matrix reconstruction.

Background

In practical applications, the theoretical covariance matrix of the received data is unknown, and is generally replaced by the sample covariance matrix, but the sample covariance matrix is susceptible to the number of samples, thereby causing covariance matrix errors. For the steering vector of the expected signal, it is a vector function that characterizes the array structure and the incoming wave direction of the expected signal, so it is often affected by some adverse factors such as a priori knowledge, process accuracy and environmental transformation, and a certain degree of error occurs. The standard Capon beamformer is highly sensitive to covariance matrix errors and steering vector errors caused by these non-idealities, and tends to suffer drastic performance degradation, even worse than that of the static beamformer. This is because under these non-ideal conditions, there is a risk that the desired signal is suppressed as interference (this phenomenon is called signal "self-cancellation"), and especially when the weight vector is calculated using the sampling covariance matrix containing the desired signal component, the beamforming performance is even worse, and the subsequent signal detection and estimation are directly affected, resulting in an inestimable effect.

Disclosure of Invention

Technical problem to be solved

In order to avoid the defects of the prior art, the invention provides a robust beam forming method based on interference and noise covariance matrix reconstruction.

Technical scheme

A robust beam forming method based on interference plus noise covariance matrix reconstruction is characterized by comprising the following steps:

step 1: receiving an echo of a target to be detected by using a radar;

step 2: reconstructing an interference covariance matrix by using a Capon space spectrum to obtain a reconstructed interference-plus-noise covariance matrix;

step 2-1: setting a total of P targets, wherein P is 0 and is an expected target, other targets are interference targets, and the number of array elements of a radar receiving array is M; the following ellipsoid uncertainty set is defined:

wherein, theta_intTo contain only interfering signalsThe angular region of the direction of arrival, being constant,

is a nominal guide vector with the incoming wave direction of thetaThe conditions of (a); in order to constrain all the steering vectors of each interfering signal interval to an equally sized set of ellipsoid uncertainties, the following inequality should be satisfied:

wherein, a_pA steering vector for the p-th interfering signal;

step 2-2: because the real interference signal guide vector is always in the uncertain concentration S_a(θ∈Θ_int) In so doing, S is not determined at all_a(θ∈Θ_int) Performing integral operation on the Capon power spectrum to reconstruct an interference covariance matrix, wherein the integral operation is approximately equal to:

wherein, a_ilIs S_a(θ∈Θ_int) The steering vector corresponding to each sampling point of the surface region, I represents the angular region theta_intNumber of sampling points, L being the nominal steering vector of each sampling point

The number of sample points in the uncertainty set of (c),is a sample covariance matrix;

step 2-3: reconstructing an interference plus noise covariance matrix by using the interference signal covariance matrix; the reconstructed interference plus noise covariance matrix is:

wherein, I_mIs an identity matrix of order M,the noise energy estimated value is approximated by the minimum eigenvalue of the covariance matrix of the sampled data;

and step 3: reconstructing an expected signal plus noise covariance matrix, establishing and solving a quadratic constraint quadratic programming problem, and obtaining an orthogonal component of an error vector;

the following optimization problem was constructed:

in the formula, e_⊥Is composed ofThe vector of the vertical direction is,

a nominal steering vector for the desired target;

the optimization problem is a quadratic constraint quadratic regularization problem and a convex problem, can be quickly solved based on an interior point method, and obtains the optimal solution of the optimization problemObtaining an estimated value of the steering vector:

and 4, step 4: calculating weight vectors of the beam former:

and (3) according to the covariance matrix obtained in the step (2) and the steering vector obtained in the step (3), obtaining a weight w by using a Capon beam former:

a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the steps of the method of claim 1 are implemented when the computer program is executed by the processor.

A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method as claimed in claim 1.

Advantageous effects

Compared with the prior art, the robust beam forming method based on the interference plus noise covariance matrix reconstruction has the remarkable advantages that: (1) the improved method obtains a circular ring uncertainty set which is more suitable for the actual situation by modeling the possible space region of the interference signal guide vector again, restrains all potential errors based on the circular ring uncertainty set, and collects the information of all interference signal guide vectors by means of Capon power spectrum integration on the surface of a circular ring, so that the estimated interference signal covariance matrix is more accurate; (2) the covariance matrix can also be solved accurately when there are various factors that cause the array information to be inaccurate, such as direction of arrival errors, calibration errors, and local scattering sources.

Drawings

Fig. 1 is a flow chart of a robust beamforming method based on interference plus noise covariance matrix reconstruction of the present invention.

Fig. 2 is a normalized directional diagram of the method of the present invention.

Fig. 3 is a graph of the output SINR versus SNR of the present invention.

Fig. 4 is a graph of output SINR versus DOA mismatch for the present invention.

Detailed Description

The invention will now be further described with reference to the following examples and drawings:

as shown in fig. 1, a robust beamforming method based on interference plus noise covariance matrix reconstruction according to the present invention includes the following steps:

step 1, obtaining radar receiving signals;

step 2, reconstructing an interference covariance matrix by using a Capon space spectrum to obtain a reconstructed interference-plus-noise covariance matrix;

and 2-1, setting a total number of P targets, wherein P is 0 and is an expected target, other targets are interference targets, and the array element number of the radar receiving array is M. The following ellipsoid uncertainty set is defined:

wherein Θ is_intThe angular region containing only the arrival direction of the interference signal is constant,is a nominal guide vector with the incoming wave direction of theta

The conditions of (1). In order to constrain all the steering vectors of each interfering signal interval to an equally sized set of ellipsoid uncertainties, the following inequality should be satisfied:

wherein a is_pIs the steering vector of the p-th interfering signal.

Step 2-2, because the real interference signal guide vector is always in the uncertain set S_a(θ∈Θ_int) In so doing, S is not determined at all_a(θ∈Θ_int) Integrating the Capon power spectrum to reconstruct an interference covariance matrix,approximately equal to:

wherein I represents the angular region Θ_intNumber of sampling points, L being the nominal steering vector of each sampling pointThe number of sample points in the uncertainty set of (c),is a sample covariance matrix.

The reconstructed interference plus noise covariance matrix is:

wherein I_MIs a matrix of the units,

and the noise energy estimation value is approximated by the minimum eigenvalue of the covariance matrix of the sampled data.

Step 3, reconstructing an interference and noise covariance matrix, establishing and solving a quadratic constraint quadratic programming problem, and obtaining an orthogonal component of an error vector;

the following optimization problem was constructed:

in the formula, e_⊥Is composed ofThe vertical vector.

The optimization problem is a quadratic constraint quadratic regularization problem and a convex problem, can be quickly solved based on an interior point method, and obtains the optimal solution of the optimization problem

Obtaining an estimated value of the steering vector:

step 4, calculating the weight vector of the beam former:

and (4) obtaining a weight w by using a Capon beam former according to the covariance matrix obtained in the step (2) and the steering vector obtained in the step (3).

The desired signal has an incoming wave direction of theta ₀0 °, interference is θ₁The angle areas of the incoming wave directions of the desired signal and the interference signal are set to be 10 degrees, and the snapshot number is 200 degrees. In step 2-2, 50 is taken as I, 2 is taken as L⁸. The DOAs are mismatched by 5 deg., and the beam patterns are as shown in fig. 2. As can be seen from the figure, the proposed method can align the main beam direction to the desired signal, where OPT is the optimal beamforming method based on the maximum output SINR criterion, DL is the diagonal loading method, and MVDR is the MVDR method.

To verify that the method output SINR varies with SNR, the SNR is set to vary from-10 dB to 20dB, and the dry-to-noise ratio INR is 30 dB. The output SINR versus SNR varies as shown in fig. 3. As can be seen from the figure, the output SINR of the proposed method increases as the SNR increases.

In order to verify the performance of the output SINR of the method in DOA mismatch, the DOA mismatch error is set to change from-5 degrees to 5 degrees. The output SINR as a function of DOA mismatch error is shown in fig. 4. As can be seen from the figure, the output SINR of the proposed method is not affected by DOA mismatch error, and thus has robustness.