A robust beamforming method

Abstract

This invention discloses a robust beamforming method, comprising: S1: acquiring the output signal X of the receiving array, gridding the observation space, and obtaining a sparsely represented received signal model; S2: establishing a sparse Bayesian probability model; S3: using the expectation-maximization algorithm and a modified inverse iterative algorithm to estimate the direction of arrival of the interference signal, the signal power, and the noise covariance matrix; S4: performing INCM reconstruction based on the estimated direction of arrival of the interference signal, the signal power, and the noise covariance matrix; S5: calculating the beamforming weighting vector w using the reconstructed INCM and the estimated expected signal angle information to form a robust beam. This method solves the problem of limited application of the traditional RAB algorithm under non-uniform noise conditions and effectively improves the performance of the beamformer.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a robust beamforming method. Background Technology

[0002] MVDR beamformers are ideal beamformers, but their optimal output performance depends on the precise knowledge of the desired signal (SOI), steering vector, and interference-plus-noise covariance matrix (INCM). However, in reality, ideal conditions are difficult to meet.

[0003] Currently, many robust adaptive beamforming (RAB) algorithms are relatively mature. The diagonal loading method introduces a diagonal loading term into the sampling covariance matrix to reduce the dispersion of noise eigenvalues, further weakening their impact on the weight vector. The worst-case performance optimization method constrains the mismatched steering vector to an uncertainty set and imposes distortion-free response constraints on all possible SOI steering vectors. The INCM-based RAB algorithm constructs a more accurate INCM to eliminate the desired signal component of the covariance matrix, thus achieving robust beamforming. While these algorithms achieve better performance than other RAB algorithms, the INCM-based RAB algorithm requires accurate parameter estimation to reconstruct the INCM and obtain the desired signal steering vector for calculating adaptive weights. Under non-uniform noise conditions, the eigenvalues ​​of the covariance matrix are perturbed, making it impossible to separate the signal and noise subspaces of the covariance matrix. General subspace-based algorithms cannot perform accurate parameter estimation and are only applicable to relatively ideal array models, limiting their application to specific non-ideal situations. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides a robust beamforming method. It utilizes a Sparse Bayesian Learning (SBL) framework to first estimate the signal power, then reconstructs the noise covariance matrix using a modified inverse iterative algorithm, and finally reconstructs the INCM based on the estimated parameters to perform robust beamforming.

[0005] This invention provides a robust beamforming method, the specific technical solution of which is as follows:

[0006] S1. Obtain the output signal X of the receiving array, grid the observation space, and obtain the sparse representation of the received signal model.

[0007] S2. Establish a sparse Bayesian probability model;

[0008] S3. Using the expectation-maximization algorithm and the modified inverse iterative algorithm, the direction of interference signal, signal power, and noise covariance matrix are estimated.

[0009] S4. Based on the estimated interference signal, signal power, and noise covariance matrix, perform INCM reconstruction.

[0010] S5. Calculate the beamforming weighting vector w using the reconstructed INCM and the estimated desired signal angle information to form a robust beam.

[0011] Furthermore, the receiving array is a uniform linear array with M array elements and an element spacing of half a wavelength.

[0012] Furthermore, when J narrowband far-field signals are incident on the receiving array, the first signal is denoted as the desired signal, and the remaining J-1 signals are interference signals. The J signals are uncorrelated with each other, and the signals and noise are uncorrelated with each other. The output signal X = AS + N.

[0013] A = [a(θ1), ..., a(θ)] J S = [s(1), s(2), ..., s(L)] is the array manifold matrix of the signal, S = [s(1), s(2), ..., s(L)] is the signal matrix, and N = [n(1), n(2), ..., n(L)] represents the non-uniform noise received by the array;

[0014] Where, θ j Indicates the direction of arrival of the signal, -90° < θ j <90°, L is the number of snapshots, a(θ) j θ represents the direction of the incoming wave. j The steering vector, j = 1, 2, ..., J; s(l) represents the vector formed by the l-th frame of all signals; n(l) represents the vector formed by the l-th frame of noise in each channel, l = 1, 2, ..., L;

[0015] Furthermore, in step S1, the observation angle space is uniformly divided into G equal parts, and the sparsed received signal model is as follows:

[0016] To complete the array manifold, The signal matrix after sparsening;

[0017] Where, θ g a(θ) represents the angle corresponding to the g-th grid point in the observation space. g ) represents θ g The guiding vector, g = 1, 2, ..., G, Let l represent the vector formed by the l-th snapshot of the sparse signal to be recovered, where l = 1, 2, ..., L.

[0018] Furthermore, the specific process of step S2 is as follows:

[0019] S21: Obtain the complex Gaussian distribution of the output signal X;

[0020] S22: For the sparsed signal matrix Construct sparse hierarchical priors, including two layers of priors;

[0021] The first layer of priors involves the sparsed signal matrix. Assume a complex Gaussian distribution with zero mean;

[0022] The second layer of priors involves making a gamma prior distribution assumption about the signal power α.

[0023] Furthermore, the output signal X follows the mean. Let be a complex Gaussian distribution with variance Q, and be expressed as follows:

[0024]

[0025] in, This represents the sparsified signal, and Q represents the noise covariance matrix. Let x(t) represent the complete array manifold, x(t) represent the output signal, and L represent the number of snapshots.

[0026] Furthermore, for the sparsed signal matrix Assuming a complex Gaussian distribution with zero mean, it is represented as follows:

[0027]

[0028] Among them, Λ=diag(α), α=[α1,α2,…,α G ] T α g (g = 1, 2, ..., G) represents the sequence from grid point θ g The power of the incident signal in the direction.

[0029] Furthermore, the prior gamma distribution assumption for the signal power α is expressed as follows:

[0030]

[0031] Where ρ = 10 -4 .

[0032] Furthermore, the specific process of step S3 is as follows:

[0033] S31: Construct the expectation of the log-likelihood function and maximize the expectation to obtain an estimate of the signal power α;

[0034] S32: Iterative estimation based on the non-uniformity of the noise covariance matrix Q; estimation of the noise covariance matrix Q.

[0035] S33: To address the signal direction mismatch problem, the grid points are dynamically updated using the expectation-maximization algorithm combined with the polynomial root-finding method to obtain an estimate of the interference signal direction.

[0036] Furthermore, in step S4, the INCM is reconstructed as follows:

[0037]

[0038] Where, α i Let Q represent the power of the interference signal, and let Q represent the noise covariance matrix. The steering vector representing the interference signal. This represents the conjugate transpose of the interference signal steering vector, and J represents the number of narrowband far-field signals.

[0039] Furthermore, based on the expected signal angle estimate obtained in step S3... Obtain the steering vector of the desired signal Then, the beam weighting vector w is calculated based on the interference plus noise covariance matrix reconstructed in step S5, as follows:

[0040]

[0041] in, The expression represents the inverse of the interference plus noise covariance matrix. θ0 represents the conjugate transpose of the steering vector of the desired signal, and θ0 represents the angle of the desired signal.

[0042] The beneficial effects of this invention are as follows:

[0043] This invention constructs an INCM based on sparse Bayesian learning combined with a modified inverse iterative algorithm, enabling robust beamforming under non-uniform noise conditions. This solves the problem of limited application of the traditional RAB algorithm under non-uniform noise conditions and effectively improves beamformer performance. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0045] Figure 2 This is a schematic diagram showing the variation of SINR output by each beamforming algorithm with the input signal-to-noise ratio under non-uniform noise conditions.

[0046] Figure 3 This is a schematic diagram showing the variation of SINR output by each beamforming algorithm with the number of snapshots under non-uniform noise conditions.

[0047] Figure 4 This is a schematic diagram showing the change curves of the output SINR of each beamforming algorithm as a function of the input signal-to-noise ratio under the condition of simultaneous non-uniform noise and random pointing error.

[0048] Figure 5 This is a schematic diagram showing the change of SINR output by each beamforming algorithm with the number of snapshots under the condition of simultaneous non-uniform noise and random pointing error. Detailed Implementation

[0049] The technical solutions in the embodiments of the present invention are clearly and completely described in the following description. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0050] In the description of the embodiments of the present invention, it should be noted that the indicated orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of the invention is conventionally placed during use, or the orientation or positional relationship in which those skilled in the art conventionally understand it during use. This is only for the convenience of describing the present invention and simplifying the description, and is not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of the present invention. Furthermore, the terms "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0051] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances.

[0052] Example 1

[0053] Embodiment 1 of the present invention discloses a robust beamforming method, such as Figure 1 As shown, the specific steps are as follows:

[0054] S1. Obtain the output signal X of the receiving array, grid the observation space, and obtain the sparse representation of the received signal model.

[0055] In this embodiment, the receiving array is a uniform linear array with M array elements and an element spacing of half a wavelength.

[0056] Specifically as follows:

[0057] Suppose that J narrowband far-field signals are incident on the receiving array, the first signal is denoted as the desired signal, and the remaining J-1 signals are interference signals. The J signals are uncorrelated with each other, and the signals and noise are uncorrelated with each other. Then the output signal X = AS + N.

[0058] A = [a(θ1), ..., a(θ)] J S = [s(1), s(2), ..., s(L)] is the array manifold matrix of the signal, S = [s(1), s(2), ..., s(L)] is the signal matrix, and N = [n(1), n(2), ..., n(L)] represents the non-uniform noise received by the array;

[0059] Where, θ j Indicates the direction of arrival of the signal, -90° < θ j <90°, L is the number of snapshots, a(θ) j θ represents the direction of the incoming wave. j The steering vector, j = 1, 2, ..., J; s(l) represents the vector formed by the l-th frame of all signals; n(l) represents the vector formed by the l-th frame of noise in each channel, l = 1, 2, ..., L;

[0060] The observation angle space is uniformly divided into G equal parts, i.e., Θ={θ1,…,θ G The sparsed received signal model is as follows:

[0061] To complete the array manifold, The signal matrix after sparsening;

[0062] Where, θ g a(θ) represents the angle corresponding to the g-th grid point in the observation space. g ) represents θ g The guiding vector, g = 1, 2, ..., G, Let l represent the vector formed by the l-th snapshot of the sparse signal to be recovered, where l = 1, 2, ..., L.

[0063] S2. Establish a sparse Bayesian probability model, the specific process of which is as follows:

[0064] S21: Obtain the complex Gaussian distribution of the output signal X;

[0065] Since the signal and noise are uncorrelated, X follows a mean of 1 / 2. A complex Gaussian distribution with variance Q, i.e.

[0066]

[0067] in, This represents the sparsified signal, and Q represents the noise covariance matrix. Let x(t) represent the complete array manifold, x(t) represent the output signal, and L represent the number of snapshots.

[0068] In this embodiment, for non-uniform noise n(t), its covariance matrix Q is:

[0069]

[0070] in, This represents the noise power of the m-th channel.

[0071] S22: For the sparsed signal matrix Construct sparse hierarchical priors, including two layers of priors;

[0072] The first layer of priors involves the sparsed signal matrix. Assuming a complex Gaussian distribution with zero mean, it is represented as follows:

[0073]

[0074] Among them, Λ=diag(α), α=[α1,α2,…,α G ] T α g (g = 1, 2, ..., G) represents the sequence from grid point θ g The power of the incident signal in the direction.

[0075] The second layer of priors assumes a gamma prior distribution for the signal power α, as follows:

[0076]

[0077] Where ρ = 10 -4 .

[0078] S3. Using the expectation-maximization algorithm and the modified inverse iterative algorithm, the direction of interference signal, signal power, and noise covariance matrix are estimated.

[0079] The specific process is as follows:

[0080] S31: Construct the expectation L(α,Q) of the log-likelihood function as follows:

[0081]

[0082] in, The mean is The sum and variance are

[0083] Maximizing L(α,Q) yields an estimate of the signal power α, as follows:

[0084]

[0085] in, Represents the g-th row of the mean μ, Σ gg This represents the element in the g-th row and g-th column of Σ.

[0086] S32: Iterative estimation based on the non-uniformity of the noise covariance matrix Q; estimation of the noise covariance matrix Q.

[0087] Specifically as follows:

[0088] Rewrite the likelihood function as follows:

[0089]

[0090] Among them, the sampling covariance matrix Q represents the noise covariance matrix.

[0091] The derivative of the rewritten likelihood function is zero, and we get:

[0092]

[0093] Where, q m express The m-th element; E ij Let (i,j) represent an M×M dimensional matrix where the (i,j)th element is 1 and all other elements are 0.

[0094] Suppose that the diagonal matrix ΔQ represents an improvement direction, and If the above equation is satisfied, then the above equation can be written in matrix form:

[0095]

[0096] in, and

[0097] judge Check if Q+tΔQ<0 satisfies the condition. If it does, then t=βt. If it does not satisfy the condition, stop iterating. The estimated noise covariance matrix is ​​Q=Q+tΔQ. Here, α and β are two constants that satisfy 0<α<0.5 and 0<β<1, respectively.

[0098] S33: For the signal direction mismatch problem, the expectation-maximization algorithm combined with the polynomial root-finding method is used to solve the grid points Θ={θ1,…,θ G The system is dynamically updated to obtain an estimate of the direction of the interference signal.

[0099] Specifically as follows:

[0100] Ignoring terms irrelevant to the angle parameter, the objective function is constructed as follows:

[0101]

[0102] Where, x t Let μ represent the t-th column of X. t Let μ represent the t-th column. Find the objective function with respect to μ. Take the partial derivative and set it to 0, as follows:

[0103]

[0104] in, express The m-th element.

[0105] Choose the solution whose modulus is closest to 1 from the above equation (defined as...). To update the grid points, i.e.:

[0106]

[0107] Here, angle() is used to find the phase of a complex number.

[0108] S4. Based on the estimated interference signal, signal power, and noise covariance matrix, perform INCM reconstruction.

[0109] The expected signal direction range is generally known a priori, therefore the expected signal direction can be determined from the signal angle information estimated in step S3. and interference signals The steering vector of the interference signal is denoted as... The powers of the interference signals are α1,…,α J-1 If the noise covariance matrix is ​​Q, then INCM can be reconstructed as:

[0110]

[0111] Where, α i This indicates the power corresponding to the interference signal. The steering vector representing the interference signal. This represents the conjugate transpose of the interference signal steering vector, and J represents the number of narrowband far-field signals.

[0112] S5. Calculate the beamforming weighting vector w using the reconstructed INCM and the estimated desired signal angle information;

[0113] Specifically as follows:

[0114] Based on the expected signal angle estimate obtained in step S3 Obtain the steering vector of the desired signal Then, the beam weighting vector w is calculated based on the interference plus noise covariance matrix reconstructed in step S5, as follows:

[0115]

[0116] in, The expression represents the inverse of the interference plus noise covariance matrix. θ0 represents the conjugate transpose of the steering vector of the desired signal, and θ0 represents the angle of the desired signal.

[0117] Consider a 10-element ULA with an element spacing of half a wavelength. The prior information assumes that the expected signal is coming from 0°, and the two interference signals are coming from -20° and 40° respectively. The interference-to-noise ratio is 30dB.

[0118] Assume the non-uniform noise covariance matrix is ​​Q = diag{20,2,1.5,0.5,8,0.7,1.1,3,6,3}.

[0119] Comparative simulation experiments were conducted between the above method and the non-iterative subspace method, 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). Specifically, the diagonal loading factor λ of the DL algorithm was set to 10, and the upper bound of the uncertainty set error of the WCB method was set to ε = 0.3M = 3.

[0120] like Figure 2 and Figure 3 As shown, the curves of the output SINR of each beamforming algorithm as a function of the input signal-to-noise ratio and the curves of the output SINR as a function of the number of snapshots are respectively shown under non-uniform noise conditions.

[0121] See Figure 2 The SINR range is -5 to 30 dB, and the number of snapshots is fixed at 100.

[0122] The method of this invention increases the output SINR with the increase of SNR and is close to the theoretical optimal output SINR. Due to the excellent parameter estimation performance of SBL-type algorithms, the output SINR of the method of this invention is slightly higher than that of the subspace iteration method, and it has better beamformer performance.

[0123] See Figure 3 The number of snapshots varies from 10 to 100, and the SNR is fixed at 10dB.

[0124] The method of this invention has the highest output SINR, meaning its performance is superior to other algorithms. Unlike subspace algorithms, SBL algorithms are not sensitive to low signal-to-noise ratio and small snapshots. Therefore, the method of this invention can guarantee superior beamformer performance even with a small number of snapshots.

[0125] like Figure 4 and Figure 5 The figures show the output SINR curves of various beamforming algorithms under different signal-to-noise ratios and different number of snapshots, respectively, under the condition of simultaneous non-uniform noise and random pointing error following a uniform distribution of [-4°, 4°].

[0126] The method of this invention can still achieve the highest output SINR even in the presence of both non-uniform noise and random pointing error, outperforming other algorithms. In contrast, the SMI and DL algorithms, due to the presence of SOI components, suffer from pointing errors that cause the beamformer to mistakenly suppress the desired signal as interference, resulting in a "self-cancellation" effect of the desired signal under high SNR.

[0127] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A robust beamforming method, characterized in that, include: S1: Obtain the output signal X of the receiving array, grid the observation space, and obtain the sparse representation of the received signal model; When there is J Several narrowband far-field signals are incident on the receiving array. The first signal is denoted as the desired signal, and the remaining signals are... J -1 are all interference signals. J The signals are uncorrelated with each other, and the signals and noise are uncorrelated with each other. The output signal X = AS + N. The array manifold matrix of the signal. For the signal matrix, This indicates non-uniform noise received by the array; in, Indicates the direction of arrival of the signal. , L Let a be the number of snapshots. () indicates the direction of incoming wave The guide vector, ;s( l ) represents the first of all signals l The vector formed by the snapshot; n ( l () indicates the noise level of each channel. l Vectors formed by snapshots ; S2: Establish a sparse Bayesian probability model; S3: The expected-maximization algorithm and the modified inverse iterative algorithm are used to estimate the direction of interference signal, signal power and noise covariance matrix; S31: Construct the expectation of the log-likelihood function and maximize the expectation to obtain the signal power. The estimate; S32: Based on the noise covariance matrix The non-uniform characteristics are iteratively estimated, and the noise covariance matrix is ​​obtained. The estimates are as follows: Rewrite the likelihood function as follows: Among them, the sampling covariance matrix , Represents the noise covariance matrix; The derivative of the rewritten likelihood function is zero, and we get: in, express The One element; Indicates the first One element is 1, and all other elements are 0. 3D matrix; Assume a diagonal matrix This is one direction for improvement, and If the above equation is satisfied, then the equation can be written in matrix form: in, ,and , ; judge or Does the condition meet? If it does, then... If the condition is not met, the iteration stops, and the estimated noise covariance matrix is ​​obtained as follows: ;in, and There are two constants, which respectively satisfy... , ; S33: To address the signal direction mismatch problem, the grid points are dynamically updated using the expectation-maximization algorithm combined with the polynomial root-finding method to obtain an estimate of the interference signal direction. S4: Based on the estimated interference signal, signal power, and noise covariance matrix, perform INCM reconstruction; S5: Calculate the beamforming weighting vector w using the reconstructed INCM and the estimated desired signal angle information to form a robust beam.

2. The robust beamforming method according to claim 1, characterized in that, The receiving array is a uniform linear array with M array elements and an element spacing of half a wavelength.

3. The robust beamforming method according to claim 1, characterized in that, In step S1, the observation angle space is uniformly divided into G equal parts, and the sparsed received signal model is as follows: ; For a complete array manifold, The signal matrix after sparsening; in, Represents the observation space of the first g The angle corresponding to each grid point; a ( )express The guide vector, , Indicates the sparse signal to be recovered. l Vectors formed by snapshots .

4. The robust beamforming method according to claim 1, characterized in that, The specific process of step S2 is as follows: S21: Obtain the complex Gaussian distribution of the output signal X; S22: For the sparsed signal matrix Construct sparse hierarchical priors, including two layers of priors; The first layer of priors involves the sparsed signal matrix. Assume a complex Gaussian distribution with zero mean; The second layer of priors concerns signal power. Make the gamma prior distribution assumption.

5. The robust beamforming method according to claim 4, characterized in that, The output signal X follows the mean. For, variance is The complex Gaussian distribution of is represented as follows: in, This represents the sparsified signal. Represents the noise covariance matrix. Represents a complete array manifold. Indicates the output signal. L Indicates the number of snapshots.

6. The robust beamforming method according to claim 5, characterized in that, For the sparsed signal matrix Assuming a complex Gaussian distribution with zero mean, it is represented as follows: in, , , Indicates from grid point The power of the incident signal in the direction; For signal power The prior distribution hypothesis of the gamma is expressed as follows: in, .

7. The robust beamforming method according to claim 1, characterized in that, In step S4, the INCM is reconstructed as follows: in, Let Q represent the power of the interference signal, and let Q represent the noise covariance matrix. The steering vector representing the interference signal. This represents the conjugate transpose of the interference signal steering vector. J This indicates the number of narrowband far-field signals.

8. The robust beamforming method according to claim 1, characterized in that, Based on the expected signal angle estimate obtained in step S3 To obtain the steering vector of the desired signal Then, the beam weighting vector w is calculated based on the interference plus noise covariance matrix reconstructed in step S5, as follows: in, The expression represents the inverse of the interference plus noise covariance matrix. This represents the conjugate transpose of the steering vector of the desired signal. This indicates the desired signal angle.

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