Robust beamforming method based on maximum a posteriori and covariance matrix reconstruction

Abstract

The application discloses a kind of robust beam forming methods based on maximum posterior probability and covariance matrix reconstruction, for the mismatch problem of guiding vector caused by the uncertainty of the direction of expected signal, accurate expected signal direction is obtained using maximum posterior probability method estimation, so as to essentially correct the mismatch of expected signal guiding vector, and the expected signal component is removed from the sampling covariance matrix by combining covariance matrix reconstruction method, so as to avoid the purpose of expected signal cancellation phenomenon and improve system output SINR performance;Gauss-Chebyshev quadrature formula is derived to calculate the method of reconstructed interference plus noise covariance matrix, so as to greatly reduce the calculation complexity and improve the method efficiency;It is applied to radar anti-jamming, when the snapshot data contains expected signal, and the direction of expected signal cannot be accurately predicted, i.e. with uncertainty, the application can obtain better anti-jamming performance.

Description

Technical Field

[0001] This invention belongs to the field of information systems such as navigation, sonar and communication, and particularly relates to anti-jamming applications of radar, specifically a robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction. Background Technology

[0002] Adaptive beamforming (ABF), a key technology in phased array radar, represents a significant breakthrough in technological innovation within the field and has been widely applied in radar, communication, and sonar. However, conventional adaptive beamforming techniques lack robustness and only function correctly under ideal conditions. In practical engineering applications, the DOA of the desired signal is not accurately predictable but may be a random variable occurring within a certain range. This can lead to a mismatch in the steering vector of the target signal. Furthermore, when the snapshot data contains the desired signal, the sampling covariance matrix estimated using the snapshot data will suffer a severe mismatch with the steering vector. Under high signal-to-noise ratio (SNR) conditions, this can result in the cancellation of the desired signal, severely degrading the performance of these conventional methods and even rendering them inoperable.

[0003] To address these challenges, various adaptive beamforming methods have been proposed. Diagonal loading is a widely used method for improving robustness and can improve output performance to some extent. However, a method for calculating the optimal diagonal loading amount is currently lacking. Therefore, a worst-case performance optimization method has been proposed. It can be proven that this method actually calculates the optimal diagonal loading amount by introducing an uncertainty set, but in practical applications, the upper bound of the uncertainty set required by this method is difficult to determine. Adaptive Bayesian beamforming fully utilizes the prior information of the observation data and the source signal's DOA; however, this method only performs well when the SNR is low, and it still fails when the SNR is high due to the cancellation of the desired signal. To remove the desired signal component from the sample covariance matrix, a robust adaptive beamforming technique based on interference plus noise covariance matrix (INCM) reconstruction has been proposed. This method first uses the Capon power spectrum to linearly integrate the angular sector of the desired signal removal direction range, which can effectively remove the desired signal component. However, this method is highly dependent on the accuracy of the estimated Capon power spectrum and the interference steering vector, and the large amount of computation due to integration reduces computational efficiency. Recently, a method based on Sparse Bayesian Learning (SBL) and covariance matrix reconstruction has been proposed. This method uses the sampling positions of the coarse grid in the SBL model as adjustable parameters, and refines them iteratively to estimate the steering vector and power of the source signal, reconstructing a more accurate INCM and obtaining a high output SINR. However, the estimation accuracy of this method depends on the precision of the grid division, and it also suffers from excessively high computational complexity. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction, which can improve the system's output SINR performance.

[0005] Robust beamforming methods based on maximum a posteriori probability and covariance matrix reconstruction include:

[0006] Step 1: Establish a radar received signal model;

[0007] Suppose that Q+1 narrowband far-field plane wave signals are incident on a uniform linear array, including one desired signal and Q interference signals incident from the sidelobes, with incident angles of θ0, θ1, ... θ1. Q Assuming the desired signal, interference, and noise are uncorrelated, then at t k The snapshot data received at any given time is represented as follows:

[0008]

[0009] In the formula, s0(t) k ) and s1(tk ),…,s q (t k Let n(t) represent the complex envelopes of the desired signal and the interference signal, respectively. k ) is additive zero-mean Gaussian white noise, a0 and a q Let K represent the steering vectors of the desired signal and the q-th interference signal, respectively, and K represent the number of snapshots.

[0010] The sampling covariance matrix (SCM) is estimated using snapshot data, and the SCM is preprocessed using a diagonal loading method. Its expression is:

[0011]

[0012] In the formula, This represents the diagonal loading amount, and I is the identity matrix.

[0013] Step 2: Obtain the DOA of the desired signal through maximum a posteriori estimation;

[0014] Assuming the desired signal's DOA is a random variable with a prior probability density function p(θ) defined on a prior angle set Φ, the following derivation yields a set of K snapshots: X = [x(t1), x(t2), ..., x(t...]. K Under the premise of )], the desired signal is directed towards θ i The posterior probability is of the following form:

[0015]

[0016] In the formula, c and γ are both constants, and a(θ) i ) is the guide vector. The sampling covariance matrix is ​​used; the accurate estimate of the desired signal DOA is obtained through maximum a posteriori estimation.

[0017]

[0018] Step 3: Reconstruct the interference plus noise covariance matrix;

[0019] The reconstructed interference plus noise covariance matrix is ​​obtained by integrating the Capon power spectrum over the angular interval containing the desired signal, as shown below:

[0020]

[0021] The integral angle range is corrected as follows:

[0022]

[0023] In the formula, θ mb The width of the interval containing the desired signal to be removed;

[0024] Step 4: Use the estimated DOA value of the expected signal. The reconstructed interference plus noise covariance matrix Calculate the beamforming weight vector:

[0025]

[0026] Step 5: By weighting the received data with the obtained weight vector, the output signal of each array element can be obtained, thus completing robust beamforming.

[0027] Preferably, in step 3, the Gauss-Chebyshev quadrature formula is used to quickly obtain the reconstructed interference plus noise matrix, specifically:

[0028] First, using the method of substitution through integration, i.e., letting x = sinθ, we can express a(θ) as a(x) = [1, e^(-θ)]. jπx ,…,e j(N -1)πx ] T In the form of Represent as Form, that is:

[0029]

[0030] Let f(x) denote the integrand after substitution. The Gauss-Chebyshev quadrature formula can be used to quickly find the product in the above equation.

[0031]

[0032] In the formula x k =(ba)y k / 2+(b+a) / 2,y k =cos((2k-1)π / (2n)), w k =π / n, where n is the Chebyshev order.

[0033] Preferably, the Chebyshev order n is set to an integer greater than 20.

[0034] Better It is taken as 10 to 20 times the noise power.

[0035] The better one is θ mb Take the main lobe width as 3dB, i.e., θ mb =50.7λ / Nd(°), where λ, N, and d are the wavelength, number of array elements, and element spacing, respectively.

[0036] The beneficial effects of this invention are as follows:

[0037] This invention addresses the steering vector mismatch problem caused by the uncertainty of the direction of the desired signal. It uses the maximum a posteriori probability method to estimate the accurate direction of the desired signal, thereby fundamentally correcting the mismatched steering vector of the desired signal. Furthermore, it combines the covariance matrix reconstruction method to remove the desired signal component from the sampling covariance matrix, thereby avoiding the cancellation phenomenon of the desired signal and improving the SINR performance of the system output.

[0038] In addition, this invention derives a method for calculating the reconstructed interference plus noise covariance matrix using the Gauss-Chebyshev quadrature formula, thereby greatly reducing computational complexity and improving method efficiency.

[0039] This invention is applied to radar anti-jamming. When the snapshot data contains a desired signal and the direction of the desired signal cannot be accurately predicted, i.e., it has uncertainty, this invention can achieve better anti-jamming performance and belongs to a robust adaptive anti-jamming method. Attached Figure Description

[0040] Figure 1 This is a flowchart of a robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction according to the present invention.

[0041] Figure 2 This is a comparison diagram of the beamforming patterns of the present invention and other spatial anti-interference methods;

[0042] Figure 3 This is a comparison chart of the output signal-to-interference-plus-noise ratio (SINR) of the present invention and other spatial anti-interference methods when there is uncertainty in the direction of the desired signal;

[0043] Figure 4 This is a comparison chart showing the output signal-to-interference-plus-noise ratio (SINR) versus the input signal-to-noise ratio (SNR) of the present invention and other spatial anti-interference methods when there is uncertainty in the direction of the desired signal. Detailed Implementation

[0044] The purpose of this invention is to overcome the shortcomings of existing radar systems, such as receiving uncertain expected signals and slow computation speeds, and to provide a robust, adaptive anti-jamming method with low complexity. This invention is applicable to electronic defense applications such as multi-channel radar anti-jamming in the field of electronic warfare, and can also be applied to anti-jamming applications in information systems such as navigation, sonar, and communication.

[0045] Figure 1 This is a signal processing flowchart of a specific embodiment of the present invention. Figure 1 As shown, the present invention is achieved through the following steps:

[0046] Step 1: Establish a radar received signal model;

[0047] Suppose that Q+1 narrowband far-field plane wave signals are incident on a uniform linear array consisting of N elements, including one desired signal and Q interference signals incident from the sidelobes, with incident angles of θ0, θ1, ... θ1. Q Assuming the desired signal, interference, and noise are uncorrelated, then at t k The snapshot data received at any time can be represented as

[0048]

[0049] In the formula, s0(t) k ) and s1(t k ),…,s q (t k Let n(t) represent the complex envelopes of the desired signal and the interference signal, respectively. k ) is additive zero-mean Gaussian white noise, a0 and a q Let represent the steering vectors of the desired signal and the q-th interference signal, respectively, and K represent the number of snapshots.

[0050] The sampling covariance matrix (SCM) is estimated using snapshot data, and the SCM is preprocessed using a diagonal loading method. Its expression is as follows:

[0051]

[0052] In the formula This represents the diagonal loading amount, which is usually taken as 10 to 20 times the noise power, and I is the identity matrix.

[0053] Step 2: Obtain the DOA of the desired signal through maximum a posteriori estimation;

[0054] In practical applications, the direction of the desired signal is not predictable, but rather a random variable that may appear randomly within a certain angular interval. We can assume that the DOA is a random variable with a prior probability density function p(θ) defined on a prior angle set Φ. We can then derive the set X = [x(t1), x(t2), ..., x(t...]] of K snapshots. K Under the premise of )], the desired signal is directed towards θ i The posterior probability is in the following form

[0055]

[0056] In the formula, c and γ are both constants, and a(θ) i ) is the guide vector. Let be the sampling covariance matrix. Clearly, the above equation is a covariance matrix in terms of θ. i The function can be used to obtain an accurate estimate of the expected signal DOA through maximum a posteriori estimation.

[0057]

[0058] This estimation method makes full use of the prior information of the observation data and the source signal DOA, and can estimate high-precision angle information with very low computational cost. This will provide a more accurate expected signal direction for the subsequent covariance matrix reconstruction.

[0059] Step 3: Reconstruct the interference plus noise covariance matrix;

[0060] The reconstructed interference plus noise covariance matrix is ​​obtained by integrating the Capon power spectrum over the angular interval containing the desired signal, as shown below.

[0061]

[0062] The integral angle interval is corrected as follows:

[0063]

[0064] In the formula θ mb This refers to the width of the interval containing the desired signal to be removed, which can typically be taken as the main lobe width of 3dB, i.e., θ. mb =50.7λ / Nd(°), where λ, N, and d are the wavelength, number of array elements, and element spacing, respectively.

[0065] Furthermore, to reduce the computational burden of integration, the Gauss-Chebyshev quadrature formula is used to quickly obtain the reconstructed interference and noise matrix. First, the integral substitution method is used, i.e., letting x = sinθ, thus expressing a(θ) as a(x) = [1, e^(-θ)]. jπx ,…,e j(N-1)πx ] T In this form, therefore it can be Represent as Form, that is:

[0066]

[0067] Observing the above equation, we find that the integrand has The form is given by f(x), where f(x) represents the integrand after substitution. Therefore, the Gauss-Chebyshev quadrature formula can be used to quickly obtain the quadrature of the above equation.

[0068]

[0069] In the formula x k =(ba)y k / 2+(b+a) / 2,y k =cos((2k-1)π / (2n)), wk =π / n, where n is the Chebyshev order, which can be freely set to an integer greater than 20 according to the accuracy requirements of the calculation.

[0070] Step 4: Utilize the estimated desired signal The reconstructed interference plus noise covariance matrix Calculate the beamforming weight vector;

[0071]

[0072] Then, by weighting the received data using the obtained weight vectors, the output signal of each array element can be obtained. This completes a robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction.

[0073] Example

[0074] To verify the robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction proposed in this invention, three sets of simulation experiments were conducted for analysis: array beamforming pattern analysis, output SINR performance analysis under different snapshot numbers, and output SINR performance analysis under different input SNR conditions. The simulations used a uniform linear array, and the simulation parameters are shown in Table 1.

[0075] In the simulation, we assume that the direction of the desired signal is a random variable uniformly distributed within the prior angle interval Φ = [-8°, 8°]. This will lead to a mismatch in the desired signal steering vector, resulting in a severe loss of output performance when the desired signal component is present in the snapshot data. The performance of the method of this invention is analyzed below using simulation results. The method of this invention is compared with the diagonal loading method, the worst-case performance optimization (WCPO) method, and the method based on the covariance matrix reconstruction of the Capon power spectrum linear integral (hereinafter referred to as the reconstruction method).

[0076] Table 1 Simulation Parameter Settings

[0077]

[0078]

[0079] Depend on Figure 2As can be seen from the beamforming pattern, all methods can form deep nulls in the direction of interference to suppress it. However, the diagonal loading method and the WCPO method also form nulls in the actual direction of the desired signal, treating the desired signal as interference and suppressing it accordingly, resulting in a severe loss of output SINR performance. This is because the snapshot data contains a desired signal component, and the uncertainty in the direction of the desired signal causes a mismatch in the steering vector of the desired signal, leading to the cancellation of the desired signal. The reconstruction method and the method of this invention remove the influence of the desired signal component by reconstructing the interference plus noise covariance matrix, thus both can align the main lobe direction with the desired signal. Furthermore, the method of this invention is more accurate, has a lower sidelobe level, and requires less computation. Therefore, by analyzing the beamforming pattern, the method of this invention can effectively suppress interference. Figure 2 Analysis of the radiation pattern shows that the advantage of the method of the present invention is that it can more accurately align the main lobe with the desired signal and has a lower sidelobe level. This feature can well cope with the situation where there is uncertainty in the direction of the desired signal.

[0080] Figure 3 The variation of output SINR with the number of snapshots was compared for different methods when the input SNR = 20dB. Figure 3 It is evident that the WCPO algorithm exhibits the worst performance, and its performance does not improve with increasing snapshot count. This is because the uncertainty in the direction of the desired signal leads to excessive mismatch, making it impossible for the WCPO method to correct the steering vector through convex optimization. In contrast, the diagonal loading method shows some performance improvement, and the output SINR increases with the number of snapshots and gradually converges, but it is still far from the theoretical optimum. The reconstruction method converges with a small number of snapshots, but still suffers significant performance loss compared to the theoretical optimum curve. In contrast, the method of this invention converges with a small number of snapshots and is very close to the theoretical optimum curve. Therefore, the method of this invention has no requirement for the number of snapshots and can achieve output SINR performance close to the theoretical optimum under very small snapshot count conditions.

[0081] Figure 4The curves of output signal-to-interference-plus-noise ratio (SINR) versus input signal-to-noise ratio (SNR) of the proposed method and the comparative methods were compared. The figures show that the diagonal loading method maintains comparable output SINR performance to other methods when the input SNR is low, but suffers significant performance loss when the input SNR is high. This is due to the cancellation of the desired signal caused by the mismatch of the desired signal steering vector. While the WCPO and reconstruction methods do not show a significant performance degradation with increasing input SNR, their performance still suffers a substantial loss relative to the theoretically optimal curve. This is because the direction of the desired signal is uncertain; when it varies significantly, neither the reconstruction nor the WCPO method can effectively correct the mismatched desired signal steering vector. The output SINR of the proposed method increases with increasing input SNR and is very close to the theoretical value. This is because the proposed method obtains an accurate estimate of the desired signal's DOA through MAP estimation, thus fundamentally correcting the desired signal's steering vector and solving the desired signal cancellation problem.

[0082] pass Figure 2 , Figure 3 and Figure 4 Simulation results show that the method of the present invention can effectively solve the problem of uncertainty in the direction of the desired signal, and can achieve output performance close to the theoretical optimum even under a very small number of snapshots.

[0083] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction, characterized in that, include: Step 1: Establish a radar received signal model; Assumption Q +1 narrowband far-field plane wave signal is incident on a uniform linear array, including one desired signal and Q Interference signals incident from the sidelobe, with incident angles of respectively... Assuming the desired signal, interference, and noise are uncorrelated, then in The snapshot data received at any given time is represented as follows: ； In the formula, and Let these represent the complex envelopes of the desired signal and the interference signal, respectively. It is additive zero-mean Gaussian white noise. and Representing the desired signal and the first q The steering vector of the interference signal, K Indicates the number of snapshots; The sampling covariance matrix (SCM) is estimated using snapshot data, and the SCM is preprocessed using a diagonal loading method. Its expression is: In the formula, Indicates diagonal loading amount. It is the identity matrix; Step 2: Obtain the DOA of the desired signal through maximum a posteriori estimation; Assume the DOA of the desired signal has a prior probability density function. The definition is in a set of prior angles From the random variables on the given, we can derive the given... K A collection of snapshot data Under the premise of expecting the signal to come from The posterior probability is of the following form: In the formula and All are constants. As the guide vector, The sampling covariance matrix is ​​used; the accurate estimate of the desired signal DOA is obtained through maximum a posteriori estimation. Step 3: Reconstruct the interference plus noise covariance matrix; The reconstructed interference plus noise covariance matrix is ​​obtained by integrating the Capon power spectrum over the angular interval containing the desired signal, as shown below: The integral angle range is corrected as follows: In the formula, The width of the interval containing the desired signal to be removed; Step 4: Use the estimated DOA value of the expected signal. The reconstructed interference plus noise covariance matrix Calculate the beamforming weight vector: Step 5: By weighting the received data with the obtained weight vector, the output signal of each array element can be obtained, thus completing robust beamforming.

2. The robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction as described in claim 1, characterized in that, In step 3, the Gauss-Chebyshev quadrature formula is used to quickly obtain the reconstructed interference plus noise matrix, specifically: First, we use the method of substitution through integration, that is, let Thus Represent as In the form of Represent as Form, that is: make Describe the integrand after substitution ; The Gauss-Chebyshev quadrature formula can be used to quickly find the product in the above equation. : In the formula , , , n Let be the Chebyshev order.

3. The robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction as described in claim 2, characterized in that, The Chebyshev order n Set to an integer greater than 20.

4. The robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction as described in claim 1, characterized in that, Take it as 10 to 20 times the noise power.

5. The robust beamforming method based on maximum a posteriori probability and covariance matrix reconstruction as described in claim 1, characterized in that, Take the main lobe width as 3dB, i.e. , These are wavelength, number of array elements, and element spacing, respectively.

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