A robust beamforming method under coherent sources

Abstract

This invention discloses a robust beamforming method for coherent sources, comprising: obtaining a sparse received signal model based on the equal division of array received data and observation angle space; constructing a sparse hierarchical prior model for the signal matrix based on the sparse received signal model; obtaining the true angle estimate and its corresponding power estimate based on the sparse hierarchical prior model; obtaining a selection transformation matrix based on the true angle estimate; processing the array received data using the selection transformation matrix to reconstruct an interference plus noise covariance matrix; and calculating a beamforming weighting vector using the reconstructed interference plus noise covariance matrix and the desired signal angle estimate to form a robust beam. This invention, based on sparse Bayesian learning combined with auxiliary transformation processing, constructs a covariance matrix that does not contain the desired signal component, thereby achieving robust beamforming; and achieves better performance than traditional methods in the case of coherent sources.

Description

Technical Field

[0001] This invention relates to the field of beamforming technology, and in particular to a robust beamforming method for coherent sources. Background Technology

[0002] Ideal beamformers rely on precise knowledge of the desired signal of interest (SOI) steering vector and the interference-plus-noise covariance matrix (INCM). However, achieving this ideal condition is difficult in practical applications, leading to the development of robust adaptive beamforming (RAB) algorithms. Existing diagonal loading methods reduce the impact of noise eigenvalue perturbations on beamformer performance by adding a weighted identity matrix to the sampling covariance matrix. Uncertainty set methods constrain the desired signal steering vector within the uncertainty set, effectively mitigating the impact of SOI steering vector mismatch. The INCM reconstruction RAB algorithm based on the accumulation method estimates INCM parameters and performs INCM reconstruction, thus achieving robust beamforming. This algorithm, adhering to the theoretical definition of INCM, achieves superior performance compared to other RAB algorithms. However, the theoretical research for this algorithm is still based on a relatively ideal array model, and there remains a gap between its theoretical foundation and practical applications.

[0003] Since the RAB algorithm based on INCM reconstruction requires accurate parameter estimation to reconstruct INCM and obtain the desired signal steering vector for calculating adaptive weights, in the case of coherent sources, the correlation between signals makes it impossible for general subspace algorithms to accurately estimate the direction of arrival (DOA) of the signal, and INCM also becomes a more complex form. Therefore, it is not possible to effectively use the INCM reconstruction method for robust beamforming. Summary of the Invention

[0004] In view of this, the present invention provides a robust beamforming method for coherent sources. Based on the robustness of coherent signals by sparse Bayesian learning and combined with auxiliary transform processing, a covariance matrix that does not contain the desired signal component is constructed, thereby performing robust beamforming.

[0005] This invention discloses a robust beamforming method for coherent sources, comprising the following steps:

[0006] Step 1: Based on the equal division of array received data and observation angle space, obtain the sparsed received signal model;

[0007] Step 2: Based on the sparsed received signal model, construct a sparse hierarchical prior model for the signal matrix;

[0008] Step 3: Based on the sparse hierarchical prior model, obtain the true angle estimate and its corresponding power estimate;

[0009] Step 4: Obtain the selection transformation matrix based on the estimated true angle values;

[0010] Step 5: Process the array received data using the selected transformation matrix to reconstruct the interference plus noise covariance matrix;

[0011] Step 6: Calculate the beamforming weighting vector using the reconstructed interference plus noise covariance matrix and the expected signal angle estimate to form a robust beam.

[0012] Further, step 1 includes:

[0013] Step 11: Assume that K narrowband far-field signals are incident on a uniform linear array with M elements and an element spacing of half a wavelength. The direction of arrival of the k-th narrowband far-field signal is θ. k Assuming the first signal is the desired signal and the remaining K-1 signals are interference signals, and that the signals and noise are uncorrelated, then the array receives the following data:

[0014] Y = AX + N

[0015] Where Y represents the observed data, and A = [a(θ1), ..., a(θ)] K [x(1), x(2), ..., x(L)] is the array manifold matrix of the signal, X = [x(1), x(2), ..., x(L)] is the signal matrix, N = [n(1), n(2), ..., n(L)] represents the zero-mean Gaussian white noise received by the array, and L is the number of snapshots; where K, M, and L are all integers, k = 1, 2, ..., K, -90°≤θ k ≤90°;

[0016] Step 12: Divide the observation angle space into G equal parts, i.e., Θ = {θ1, ..., θ2} G}, then the sparsed received data signal model is:

[0017]

[0018] Among them, Φ=[a(θ1), a(θ2),…, a(θ G X = [x(1), x(2), ..., x(L)] is the complete array manifold, and X = [x(1), x(2), ..., x(L)] is the sparsed signal matrix.

[0019] Further, step 2 includes:

[0020] Step 21: The observed data Y follows a mean of The variance is β -1 IM The complex Gaussian distribution, i.e.

[0021]

[0022] in, Representation matrix The t-th column, Y ·t Let t represent the t-th column of matrix Y, β be the noise precision, i.e., the reciprocal of the noise power, and I M It is an M-order identity matrix;

[0023] Step 22: For the signal matrix Construct sparse hierarchical priors.

[0024] Further, step 22 includes:

[0025] In the first level of prior, it is assumed that... The zero-mean complex Gaussian distribution

[0026]

[0027] Among them, Γ=diag(γ), γ=[γ1, γ2,…,γ G ]represent The variance of different rows, that is, the signal power corresponding to each grid point;

[0028] In the second layer of priors, a gamma prior distribution hypothesis is made for the hyperparameter γ.

[0029]

[0030] Where, ξ n These are the parameters of the gamma distribution;

[0031] In the third layer of priors, the parameter ξ is given. n The gamma prior distribution hypothesis, i.e.

[0032]

[0033] Where h is a constant.

[0034] Further, step 3 includes:

[0035] Step 31: When using the expectation-maximization algorithm for parameter estimation, the expectation of the log-likelihood function is obtained based on the sparse hierarchical prior model:

[0036]

[0037] in, The mean and variance are respectively Where, ∑ Y =β-1 I M +ΦΓΦ H ;

[0038] By taking the derivative of Q(γ,ξ,β) with respect to the parameters to be estimated, γ,ξ,β respectively, we can obtain the update expressions for each parameter:

[0039]

[0040]

[0041]

[0042] Among them, R Y =YY H / L, Σ nn μ represents the element in the nth row and nth column of Σ. n· For the nth row of μ, A manifold matrix for an array of K signals;

[0043] Step 32: Initialize the signal variance vector Parameter ξ = 1 N×1 Noise accuracy Among them, 1 N×1 Represents an N-dimensional column vector of all 1s; it iteratively updates the mean μ, variance Σ, hyperparameters γ, ξ, and β until the convergence condition is met, at which point the iteration stops;

[0044] Step 33: The True Angle and its corresponding power parameters The likelihood function is:

[0045]

[0046] in, Γ k =diag(γ) k ), From a realistic perspective The guide vector at that location, From a realistic perspective The array manifold is composed of the guiding vectors at the left and right endpoints of the grid; for the likelihood function By performing maximum likelihood estimation, we can obtain the true angle estimate and the corresponding power estimate.

[0047]

[0048]

[0049] in, This indicates the operation of taking the real part.

[0050] Furthermore, the convergence condition is ||γ (i) -γ (i-1) ||2 / ||γ (i-1) ||2<10 -3 , of which (g) (i) This represents the variable in the i-th iteration.

[0051] Further, step 4 includes:

[0052] Using the DOA information estimated in step 3, the following selection transformation matrix is ​​obtained:

[0053]

[0054] Among them, A c =[a(θ1),a(θ2),…,a(θ K )], R Y Let B be the sampling covariance matrix, λ be the diagonal loading factor, and B be the sampling covariance matrix. c = [0, a(θ2), ..., a(θ)] K )).

[0055] Further, step 5 includes:

[0056] Step 51: Process the array-received data using the obtained transformation matrix, which is TY. The covariance matrix of TY is then...

[0057]

[0058] Further refinements to the covariance matrix:

[0059]

[0060] Step 52: If the correlation exists only between the desired signal and the interference signal, and the interference signals are independent of each other, then based on the angle information, signal power, and noise accuracy estimated in Step 3, the interference plus noise covariance matrix can be reconstructed using the accumulation method.

[0061]

[0062] in, From a realistic perspective The guiding vector at that location is...

[0063] Further, step 6 includes:

[0064] Based on the expected signal in step 3 Obtain the steering vector of the desired signal Then, based on the interference plus noise covariance matrix reconstructed in step 5, calculate the beam weighting vector:

[0065] or

[0066] Where w is the beam weighting vector.

[0067] Because of the adoption of the above technical solution, the present invention has the following advantages:

[0068] Traditional RAB algorithms fail under coherent source conditions, failing to effectively improve beamformer performance. This invention, based on sparse Bayesian learning combined with auxiliary transform processing, constructs a covariance matrix that does not contain the desired signal component, thereby enabling robust beamforming. This invention achieves better performance than traditional methods under coherent source conditions. Attached Figure Description

[0069] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0070] Figure 1 This is a schematic diagram of the output SINR under different signal-to-noise ratios according to an embodiment of the present invention;

[0071] Figure 2 This is a schematic diagram illustrating the output SINR under different snapshot conditions according to an embodiment of the present invention;

[0072] Figure 3 This is a schematic diagram of the output SINR under different signal-to-noise ratios according to an embodiment of the present invention;

[0073] Figure 4 This is a schematic diagram illustrating the output SINR under different snapshot conditions according to an embodiment of the present invention;

[0074] Figure 5 This is a flowchart illustrating a robust beamforming method using a coherent source according to an embodiment of the present invention. Detailed Implementation

[0075] The present invention will be further described in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0076] See Figure 5This invention provides an embodiment of a robust beamforming method for coherent sources. First, it utilizes a sparse Bayesian learning (SBL) algorithm to estimate the coherent signal angle for robustness of the coherent source. Then, based on the estimated DOA information, a linear transformation matrix is ​​obtained, which is used to reconstruct the covariance matrix without the desired signal component. Finally, by combining the estimated desired signal steering vector and the covariance matrix, the optimal weights are obtained for robust beamforming.

[0077] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0078] S1. Obtain the output signal Y of the receiving array, grid the observation space, and obtain the sparse representation of the received signal model.

[0079] S2. Establish a sparse Bayesian probability model; design a three-level hierarchical prior model so that the marginal distribution of the complex signal follows a generalized double Pareto distribution, which significantly improves sparsity.

[0080] S3. Use the expectation-maximization algorithm combined with the off-grid DOA estimation method to update parameters such as signal power and noise power;

[0081] S4. Based on the parameters obtained in step S3, obtain the selection transformation matrix T;

[0082] S5. The received signal is processed using a selection transformation matrix to obtain a covariance matrix that does not contain the desired signal component.

[0083] S6. Calculate the beamforming weighting vector w using the reconstructed INCM and the desired signal angle information estimated in step S3.

[0084] Furthermore, step S1 includes the following steps:

[0085] S11. Assume that K narrowband far-field signals are incident on a uniform linear array with M elements and an element spacing of half a wavelength, and the incoming directions of the K signals are θ. k Let the first signal be the desired signal, and the remaining K-1 signals be interference signals, with no correlation between the signals and noise. Then the array receives the data as Y = AX + N, where A = [a(θ1), ..., a(θ2)]. K [x(1), x(2), ..., x(L)] is the array manifold matrix of the signal, X = [x(1), x(2), ..., x(L)] is the signal matrix, N = [n(1), n(2), ..., n(L)] represents the zero-mean Gaussian white noise received by the array, and L is the number of snapshots; where K, M, and L are all integers, k = 1, 2, ..., K, -90°≤θ k ≤90°.

[0086] S12. Divide the observation angle space into G equal parts, i.e., Θ = {θ1, ..., θ2}. G}, then the sparsed received signal model is

[0087]

[0088] Among them, Φ=[a(θ1), a(θ2),…, a(θ G X = [x(1), x(2), ..., x(L)] is the complete array manifold, and X = [x(1), x(2), ..., x(L)] is the sparsed signal matrix.

[0089] Furthermore, step S2 includes the following steps:

[0090] S21. Since the signal is uncorrelated with additive noise, the observed data Y follows a mean of . The variance is β -1 I M The complex Gaussian distribution, i.e.

[0091]

[0092] in, Representation matrix The t-th column, Y ·t Let represent the t-th column of matrix Y, (·) .t Let I represent the t-th column of the matrix, β be the noise precision (i.e., the reciprocal of the noise power), and I M It is an M-order identity matrix.

[0093] S22, Regarding the signal matrix Construct sparse hierarchical priors; in the first layer prior, for Assuming a complex Gaussian distribution with zero mean

[0094]

[0095] Among them, Γ=diag(γ), γ=[γ1, γ2,…,γ G ]represent The variance of different rows, that is, the signal power corresponding to each grid point.

[0096] In the second layer of priors, a gamma prior distribution hypothesis is made for the hyperparameter γ.

[0097]

[0098] Where, ξ n represents the parameters of the gamma distribution.

[0099] In the third layer of priors, the parameter ξ is... n Furthermore, the prior distribution hypothesis of gamma is given, namely

[0100]

[0101] Where h is a constant, usually a small positive number.

[0102] This hierarchical prior design enables a more sparse signal distribution, thereby improving the accuracy of DOA estimation.

[0103] Furthermore, step S3 includes the following steps:

[0104] S31. When using the Expectation-Maximization (EM) algorithm for parameter estimation, first write down the expectation of the log-likelihood function. in The mean and variance are respectively Where, ∑ Y =β -1 I M +ΦΓΦ H Then, by taking the derivatives of Q(γ,ξ,β) with respect to the parameters to be estimated, γ,ξ,β, respectively, we can obtain the update expressions for each parameter.

[0105]

[0106]

[0107]

[0108] Among them, R Y =YY H / L, Σ nn μ represents the element in the nth row and nth column of Σ. n· For the nth row of μ, It is an array manifold matrix of K signals.

[0109] S32. Initialize the signal variance vector Parameter ξ = 1 N×1 Noise accuracy Among them 1 N×1 Let represent an N-dimensional column vector of all 1s; iteratively update the mean μ, variance Σ, hyperparameters γ, ξ, and β until the convergence condition is met, at which point the iteration stops. The convergence condition is ||γ||. (i) -γ (i-1) ||2 / ||γ (i-1) ||2<10 -3 , of which (g) (i) This represents the variable in the i-th iteration.

[0110] S33. A more refined DOA estimation method is adopted to address the signal direction grid mismatch problem. First, the true angle is written out. and its corresponding power parameters likelihood function

[0111]

[0112] in, Γ k =diag(γ) k ), From a realistic perspective The guide vector at that location, From a realistic perspective The array manifold is composed of the guiding vectors at the left and right endpoints of the grid; then the likelihood function is... The true angle estimate and the corresponding power estimate can be obtained by performing maximum likelihood estimation.

[0113]

[0114]

[0115] in, This indicates the operation of taking the real part.

[0116] Furthermore, step S4 includes the following steps:

[0117] S41. Using the DOA information estimated in step S3, the following transformation matrix is ​​obtained:

[0118]

[0119] Among them, A c =[a(θ1),a(θ2),…,a(θ K )], R Y Let B be the sampling covariance matrix, λ be the diagonal loading factor, and B be the sampling covariance matrix. c = [0, a(θ2), ..., a(θ)] K )).

[0120] Furthermore, step S5 includes the following steps:

[0121] S51. The received data is processed using the obtained transformation matrix, which is TY. The covariance matrix of TY is then given by...

[0122]

[0123] However, the noise components in the processed data covariance matrix have changed due to the linear transformation, therefore the covariance matrix of the data needs further correction:

[0124]

[0125] S52. If the correlation exists only between the desired signal and the interference signal, and the interference signals are independent of each other, then the interference plus noise covariance matrix can be reconstructed using the accumulation method based on the angle information, signal power, and noise accuracy estimated in step S3.

[0126]

[0127] in, From a realistic perspective The guide vector at that location.

[0128] Furthermore, step S6 includes the following steps:

[0129] S61. Based on the desired signal obtained in step S3 Write down the steering vector of the desired signal. Then, calculate the beam weighting vector based on the interference plus noise covariance matrix reconstructed in step S5.

[0130] or

[0131] Where w is the beam weighting vector.

[0132] For ease of understanding, the present invention provides a more specific embodiment:

[0133] The basic experimental setup was as follows: a 10-element ULA array with an element spacing of half a wavelength was considered. The prior information assumed the direction of the desired signal to be 0°, and the two interference signals were at -20° and 40°, respectively, with an interference-to-noise ratio of 30dB. 200 Monte Carlo simulations were performed for each simulation.

[0134] The simulation experiments compared algorithms including: the method of this invention, the sampling covariance matrix inversion method (SMI), the diagonal loading method (DL), the eigenspace projection method (ESB), and the worst-case performance optimization method (WCB). The diagonal loading factor of the DL algorithm was selected as λ = 10, and the upper bound of the uncertainty set error of the WCB method was set as ε = 0.3M = 3.

[0135] Experiment 1: Assume that the desired signal is coherent with one of the interferences, while the two interferences are independent. Figure 1The curves showing the output SINR as a function of the input signal-to-noise ratio for each beamforming algorithm are presented, with the SNR ranging from -5 to 30 dB and the number of snapshots fixed at 100. Simulation results show that the method of this invention has the highest output SINR, outperforming other comparative algorithms. Furthermore, the INCM algorithm based on the accumulation method reconstructs outperforms the auxiliary transform method because the accumulation method follows the definition of INCM for reconstruction. The ESB algorithm, however, suffers a significant performance degradation due to the influence of the coherent source on the subspace, even falling below the SMI algorithm. In addition, the DL algorithm loses its robustness and offers almost no improvement to the beamformer's performance. Figure 2 The graphs show the SINR output curves for each algorithm as a function of the number of snapshots, ranging from 10 to 100, with the SNR fixed at 10 dB. The graphs demonstrate that the method of this invention exhibits the best performance compared to other algorithms. The auxiliary transformation method, which uses the data covariance matrix after removing the desired signal to solve for optimal weights, performs worse than the accumulation method at low snapshot counts.

[0136] Experiment 2: Assume that the desired signal is coherent with the interference, and that the interferences are also completely coherent with each other. Figure 3 and Figure 4 The output SINR of each algorithm is shown under different SNR and different snapshots. Simulation results show that the method of this invention has the best performance, the highest output SINR, and exhibits a certain degree of robustness to coherent sources. The analysis of other algorithms is similar to that in Experiment 1.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A robust beamforming method for coherent sources, characterized in that, Includes the following steps: Step 1: Based on the equal division of array received data and observation angle space, obtain the sparsed received signal model; Step 2: Based on the sparsed received signal model, construct a sparse hierarchical prior model for the signal matrix; Step 3: Based on the sparse hierarchical prior model, the expectation-maximization algorithm is used to obtain the true angle estimate, signal power estimate, and noise power. Step 4: Obtain the selection transformation matrix based on the estimated true angle values; Step 5: Process the array received data using the selected transformation matrix to reconstruct the interference plus noise covariance matrix; Step 6: Using the reconstructed interference plus noise covariance matrix and the expected signal angle estimate, calculate the beamforming weighting vector to form a robust beam; Step 4 includes: Using the DOA information estimated in step 3, the following selection transformation matrix is ​​obtained: Among them, A c =[a(θ1),a(θ2),…,a(θ)] K )], R Y Let B be the sampling covariance matrix, λ be the diagonal loading factor, and B be the sampling covariance matrix. c =[0,a(θ2),…,a(θ)] K )]; Step 5 includes: Step 51: Process the array-received data using the obtained transformation matrix, which is TY. The covariance matrix of TY is then... Where L is the number of snapshots; Further refinements to the covariance matrix: Step 52: If the correlation exists only between the desired signal and the interference signal, and the interference signals are independent of each other, then based on the angle information, signal power, and noise accuracy estimated in Step 3, the interference plus noise covariance matrix can be reconstructed using the accumulation method. Where β is the noise accuracy, and the reciprocal of the noise accuracy is the noise power. for The guide vector at that location.

2. The method according to claim 1, characterized in that, Step 1 includes: Step 11: Assume that K narrowband far-field signals are incident on a uniform linear array with M elements and an element spacing of half a wavelength. The direction of arrival of the k-th narrowband far-field signal is θ. k Assuming the first signal is the desired signal and the remaining K-1 signals are interference signals, and that the signals and noise are uncorrelated, then the array receives the following data: Y = AX + N Where Y represents the observed data, and A = [a(θ1), ..., a(θ)] K [x(1), x(2), ..., x(L)] is the array manifold matrix of the signal, X = [x(1), x(2), ..., x(L)] is the signal matrix, N = [n(1), n(2), ..., n(L)] represents the zero-mean Gaussian white noise received by the array, and L is the number of snapshots; where K, M, and L are all integers, k = 1, 2, ..., K, -90°≤θ k ≤90°; Step 12: Divide the observation angle space into G equal parts, i.e., Θ = {θ1, ..., θ2} G }, then the sparsed received data signal model is: Among them, Φ=[a(θ1), a(θ2),…, a(θ G [] is a complete array manifold. This is the sparsed signal matrix.

3. The method according to claim 2, characterized in that, Step 2 includes: Step 21: The observed data Y follows a mean of The variance is β -1 I M The complex Gaussian distribution, i.e. in, Representation matrix The t-th column, Y ·t Let t represent the t-th column of matrix Y, β be the noise precision, i.e., the reciprocal of the noise power, and I M It is an M-order identity matrix; Step 22: For the signal matrix Construct sparse hierarchical priors.

4. The method according to claim 3, characterized in that, Step 22 includes: In the first level of prior, it is assumed that... The zero-mean complex Gaussian distribution Among them, Γ=diag(γ), γ=[γ1, γ2,…,γ G ]represent The variance of different rows, that is, the signal power corresponding to each grid point; In the second layer of priors, a gamma prior distribution hypothesis is made for the hyperparameter γ. Where, ξ n These are the parameters of the gamma distribution; In the third layer of priors, the parameter ξ is given. n The gamma prior distribution hypothesis, i.e. Where h is a constant.

5. The method according to claim 4, characterized in that, Step 3 includes: Step 31: When using the expectation-maximization algorithm for parameter estimation, based on the sparse hierarchical prior model, the expectation of the log-likelihood function is obtained: in, The mean and variance are respectively Where, ∑ Y =β -1 I M +ΦΓΦ H ; By taking the derivative of Q(γ,ξ,β) with respect to the parameters to be estimated, γ,ξ,β respectively, we can obtain the update expressions for each parameter: Among them, R Y =YY H / L, Σ nn μ represents the element in the nth row and nth column of Σ. n· For the nth row of μ, A manifold matrix for an array of K signals; Step 32: Initialize the signal variance vector Parameter ξ = 1 N×1 Noise accuracy Among them, 1 N×1 Represents an N-dimensional column vector of all 1s; it iteratively updates the mean μ, variance Σ, hyperparameters γ, ξ, and β until the convergence condition is met, at which point the iteration stops; Step 33: The True Angle and its corresponding power parameters The likelihood function is: in, Γ k =diag(γ) k ), From a realistic perspective The guide vector at that location, From a realistic perspective The array manifold is composed of the guiding vectors at the left and right endpoints of the grid; for the likelihood function By performing maximum likelihood estimation, we can obtain the true angle estimate and the corresponding power estimate. in, This indicates the operation of taking the real part.

6. The method according to claim 5, characterized in that, The convergence condition is ||γ (i) -γ (i-1) ||2 / ||γ (i-1) ||2<10 -3 ,in(·) (i) This represents the variable in the i-th iteration.

7. The method according to claim 1, characterized in that, Step 6 includes: Based on the expected signal in step 3 Obtain the steering vector of the desired signal Then, based on the interference plus noise covariance matrix reconstructed in step 5, calculate the beam weighting vector: or Where w is the beam weighting vector.

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