Array signal processing method based on unitary transform real-valued block sparse bayesian learning

Abstract

The application relates to the technical field of radar signal processing, in particular to an array signal processing method based on unitary transformation real-value block sparse Bayesian learning, which can significantly improve parameter estimation performance, wherein, first, for a double-orthogonal dipole array, a horizontal polarization subarray and a vertical polarization subarray are respectively constructed; second, unitary transformation is respectively performed on the received data of the two subarrays, the received data is converted into real-value data, the DOA and polarization parameters are decoupled, and then a block sparse algorithm is used for estimation; then, the reconstructed block signals are converted by using the characteristics of the unitary transformation, and the polarization parameters are estimated by using the correlation between the block signals.

Description

Technical fields:

[0001] This invention relates to the field of radar signal processing technology, specifically to an array signal processing method based on unitary transform real-valued block sparse Bayesian learning that can significantly improve parameter estimation performance. Background technology:

[0002] Array signal processing is an important branch of modern signal processing, and it has developed rapidly in recent decades. Compared with traditional arrays, polarization-sensitive arrays can acquire both spatial and polarization information of electromagnetic signals, giving them a significant theoretical advantage and promising military and civilian applications. Coherent source scenarios are quite common in practice, such as multipath effects and electronic interference. However, many classic parameter estimation algorithms fail under coherent source conditions, making parameter estimation under coherent source conditions another major challenge.

[0003] In existing technologies, the spatial smoothing technique proposed by Ong LT is an effective decoherence algorithm, but it sacrifices the number of effective array elements, resulting in some loss of array aperture, and its performance is poor at low signal-to-noise ratios. Furthermore, to ensure identical subarray structures, the array configuration must be a uniform linear array. JIAN L extended the spatial smoothing technique to the polarization domain, obtaining polarization smoothing, which effectively achieves DOA estimation of coherent sources and overcomes the array configuration limitation of spatial smoothing. However, this type of algorithm has a limited number of decoherent signals, which is equal to the number of array element polarization modes, and the smoothing process obscures the polarization parameters of the signal, making it impossible to estimate the polarization parameters of the coherent signal. Combining spatial smoothing and polarization smoothing techniques can double the number of decoherent signals, but this type of algorithm is still limited by the array configuration and cannot estimate polarization parameters. The concept of subspace fitting was proposed after the 1990s. Its basic idea is to construct the fact that there is a fitting relationship between the array manifold matrix and the subspace of the array received data. This type of algorithm does not cause array aperture loss and is suitable for any array configuration without manifold ambiguity. Meanwhile, for polarization DOA estimation, researchers have proposed generalized maximum likelihood algorithms and generalized subspace fitting algorithms. These algorithms decouple DOA and polarization parameters, reducing the search dimensionality, but they still require multi-dimensional search, thus incurring high computational costs. Furthermore, their performance degrades in small snapshots. Sparse reconstruction theory research originated from the concept of sparse signals proposed by Santosa et al. in 1986, which can be described as follows: given a complete matrix, the original signal can be represented relatively completely by a few non-zero coefficients. DOA estimation methods based on sparse representation exhibit superior performance in small snapshots and possess natural decoherence capabilities, leading to their widespread application in array parameter estimation. Xu Bin et al. applied the Block Orthogonal Matching Pursuit (BOMP) algorithm to L-shaped polarization-sensitive arrays, achieving DOA and polarization parameter estimation. However, due to the lack of correction capability of atomic blocks in the BOMP algorithm, the parameter estimation performance was poor. Zhang Zhilin proposed the classic Block Sparse Bayesian Learning (BSBL) algorithm, which outperformed the BOMP algorithm. LI BB et al. used the Expectation Maximization (BSBL-EM) algorithm to achieve joint estimation of polarization and DOA parameters of polarization-sensitive arrays in the one-dimensional case. However, the classic Block Sparse Bayesian Learning algorithm is only applicable to real numbers, and the existing technology does not provide a specific real-valued method. Summary of the Invention:

[0004] This invention addresses the shortcomings and deficiencies of existing technologies by proposing an array signal processing method based on unitary transform real-valued block sparse Bayesian learning, which can significantly improve parameter estimation performance.

[0005] This invention achieves its purpose through the following measures:

[0006] An array signal processing method based on unitary transform real-valued block sparse Bayesian learning, characterized by the following steps:

[0007] Step 1: For the biorthogonal dipole array, construct the horizontal polarization subarray and the vertical polarization subarray respectively;

[0008] Step 2: Perform unitary transformation on the received data of the two subarrays respectively to convert the received data into real-valued data. At the same time, decouple the DOA and polarization parameters, and then use the block sparse algorithm for estimation.

[0009] Step 3: Utilize the properties of the unitary transform to transform the reconstructed block signal, and then use the correlation between the block signals to estimate the polarization parameters.

[0010] This invention is based on a uniform linear array model, where the resolvable spatial domain angles of the linear array are [-90°, 90°]. It considers a uniform linear array composed of M orthogonal dipole array elements with a spatial spacing of half a wavelength d = λ / 2, and P far-field narrowband fully polarized signals. The azimuth angle of the p-th signal is θ. p The polarization auxiliary angle and polarization phase angle are γ p and η p Assuming the incident signals are uncorrelated and independent of the noise, the received signal of the polarization-sensitive array can be expressed as:

[0011] y(t)=As(t)+n(t)(1),

[0012] in, It is the joint array manifold matrix of the spatial polarization domain of the array signal, s(t)=[s1(t),s2(t),…,s P (t)] T ∈C P×1 Let there be P independent incident sources, n(t) = [n1(t), n2(t), ..., n 2M (t)] T ∈C 2M×1 The mean is zero and the variance is σ. 2 The additive white Gaussian noise, and the ideal steering vector corresponding to the p-th signal is specifically expressed as:

[0013]

[0014] in, Let be the spatial steering vector of the p-th signal; Let be the polarization vector of the p-th signal; It represents the Kronecker product.

[0015] In step 1 of this invention, for a biorthogonal dipole array, horizontally polarized array elements and vertically polarized array elements are selected to construct subarray 1 and subarray 2, respectively; wherein, for subarray 1, the following applies:

[0016]

[0017] Among them, a(θ)=[1,exp(-j2πdsin(θ) / λ),…,exp(-j2π(M-1)dsin(θ) / λ)] T ,

[0018]

[0019] The data received by subarray 1 can be represented as

[0020]

[0021] Where E = diag(e1, e2, ..., e P ), A1(θ)=A(θ)·V1,

[0022] A(θ)=[a(θ1),a(θ2),…,a(θ P V1 = diag(v) 1,x ,v 2,x ,…,v P,x ),

[0023] Similarly, for subarray 2, we have

[0024] Y2=A2(θ)E·X+N2(8),

[0025] in, A2(θ)=A(θ)·V2,

[0026] V2 = diag(v 1,y ,v 2,y ,…,v P,y );

[0027] Construct the augmented matrix:

[0028] Y aug1 =[Y1,J M Y1 * J L (9),

[0029] Y aug2 =[Y2,J M Y2* J L (10),

[0030] Among them, J M ∈R M J L ∈R L It is a permutation matrix in which all elements on the secondary diagonal are 1 and all other elements are 0.

[0031] Step 2 of this invention describes performing unitary transforms on the received data from the two subarrays to convert the received data into real-valued data, while simultaneously decoupling the DOA and polarization parameters. Specifically, this includes:

[0032] For subarray 1, we have:

[0033] Y aug1 =[Y1,J M Y1 * J L ]

[0034] =[A1EX+N1 J M (A1EX+N1) * J L ]

[0035] =[A1EX+N1 J M A1 * E * X * J L +J M N1 * J L ]

[0036] =[A1EX J M A1 * E * X * J L ]+[N1 J M N1 * J L (11),

[0037] For a uniform linear array, the spatial steering vector has the following relationship:

[0038] A1Λ=J M A1 * (12),

[0039] in,

[0040] Λ=diag{exp(j2π(M-1)sin(θ1) / λ),…,exp(j2π(sin(θ P ) / λ),1}

[0041] Performing a unitary transformation on the augmented matrix, we have

[0042] Y r1 =U M H Y aug1 U 2L (13),

[0043] Substitution method

[0044] Y r1 =U M H [A1EX J M A1 * E * X * J L ]U 2L +U M H [N1 J M N1 * J L ]U 2L (14),

[0045] For the signal section

[0046] U M H [A1EX J M A1 * E * X * J L ]U 2L =U M H [A1EX A1ΛE * X * J L ]U 2L

[0047] =U M H A1[EXΛE * X * J L ]U 2L (15),

[0048] Let AA1 = U M H A1, S = [EXΛE] * X * J L ]U 2L

[0049] Then we have: Y r1 =AA1·S+N r1 (16),

[0050] Similarly, for subarray 2, we have

[0051] Y r2 =AA2·S+N r2 (17),

[0052] Constructing a matrix

[0053]

[0054] This invention is based on a uniform linear array model, where the resolvable spatial domain angles of the linear array are [-90°, 90°]. Dividing it into N grids yields a supercomplete set of angles. In this system, hollow circles represent the grid divisions, and solid circles represent the direction of signal arrival, resulting in a supercomplete set of angles. The matrix formed by the array guide vectors corresponding to each element is the extended array manifold matrix. Therefore, equation (18) is extended to the supercomplete angle set. The output model of the overcomplete array is obtained:

[0055] in,

[0056] Φ=[U M H a 1,1 ,…,U M H a 1,N ;U M H a 2,1 ,…,U M H a 2,N ], s n n∈[1,N]

[0057] This is a block signal.

[0058] In step 2 of this invention, in order to apply the BSBL framework to the multi-measurement vector model, the MMV should be...

[0059] The model is converted into a single measurement vector model:

[0060] YY = DD·XX + NN (20),

[0061] Where YY = vec(Y r T )∈C 4ML×1 ,

[0062] NN = vec(Nr T )∈C 4ML×1 vec(·) denotes vectorization. Therefore, the block structure of XX is represented as:

[0063] XX = [x(1:4L)] T x(4L+1:8L) T ,…,x(4L(i-1)+1:4Li) T ,…,x(4L(N-1)+1:4LN) T ] T , i = 1, 2, ..., N, x(4L(i-1)+1: 4Li) represents a 4L×1 vector consisting of elements from 4L(i-1)+1 to 4Li of XX. It should be noted that XX is block sparse, with each non-zero block containing 4L elements. Therefore, the block sparse Bayes algorithm can be used to estimate the parameters.

[0064] In step 2 of this invention, the BSBL algorithm architecture assumes the i-th signal block Follows Gaussian distribution

[0065]

[0066] γ i Control signal sparsity, B i It describes intra-block correlation information. γ i A value of 0 represents the corresponding signal block. γ is 0 i The larger the value, the greater the probability of it taking that value. Assuming that signal blocks are uncorrelated, then the signal... It can be modeled as

[0067] Where Γ=diag -1 (γ1B1,…,γ g B g ),

[0068] Assuming the observed noise is independent and identically distributed, i.e., follows a Gaussian distribution with mean 0 and variance βI, then The posterior distribution follows a Gaussian distribution as follows:

[0069]

[0070] in,

[0071] Σ -1 =Γ -1 +Φ T βΦ (24),

[0072] μ=ΣΦ T βy(25), in order to estimate the parameter {γi B i The cost function can be obtained using the type II maximum likelihood method, given β and β.

[0073] L({γ i B i},β)=logC|+y T C -1 y(26),

[0074] Where C = β -1 I+Φ T Taking the partial derivative of ΓΦ with respect to the expectation of the cost function and setting it equal to 0 yields the learning rule for the hyperparameters under the maximum likelihood algorithm.

[0075]

[0076] To uncover the correlation of signals within a block, the BSBL algorithm is used for signal x. i covariance matrix B i Add constraints

[0077]

[0078] Using B i The updated formula yields an empirical formula for calculating the correlation coefficient r:

[0079] in, For B i The mean of the second diagonal, The mean of the main diagonal, and the hyperparameter γ in equation (27) i The computational complexity is relatively high, so a boundary optimization algorithm is used to optimize equation (26) and further refine γ. i Find the partial derivative and set it to 0 to obtain γ. i Learning rules:

[0080] The estimated DOA and the reconstructed value of the block signal can be obtained from equations (24) to (32).

[0081] In step 3 of this invention, the estimation of polarization parameters specifically includes the following: restoring the vectorized block signal to the signal before vectorization, and converting the 4L×1 block signal into a 2×2L block signal according to the corresponding rules;

[0082] According to the properties of unitary matrices UU H =I, then:

[0083]

[0084] Take the first L rows of this matrix, that is:

[0085]

[0086] Therefore, it can be concluded that

[0087] The polarization parameters can be estimated using equations (33) to (36).

[0088] Compared with existing technologies, this invention can significantly improve parameter estimation performance. Attached image description:

[0089] Figure 1 This is the uniform linear array model in this invention.

[0090] Figure 2 This is a schematic diagram of the array spatial domain division in this invention.

[0091] Figure 3 This is the sparsity spectrum of the real-valued block sparse Bayesian algorithm based on unitary transform in an embodiment of the present invention.

[0092] Figure 4 This is a graph showing the variation of the parameter estimation RMSE with the signal-to-noise ratio in an embodiment of the present invention. Detailed implementation method:

[0093] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0094] This invention is based on a uniform linear array model, where the resolvable spatial domain angles of the linear array are [-90°, 90°]. Consider a uniform linear array consisting of M orthogonal dipole array elements with a spatial spacing of half a wavelength d = λ / 2, and P far-field narrowband fully polarized signals. The azimuth angle of the p-th signal is θ. p The polarization auxiliary angle and polarization phase angle are γ p and η p ,like Figure 1 As shown.

[0095] Assuming the incident signals are uncorrelated and independent of the noise, the received signal of the polarization-sensitive array can be expressed as follows:

[0096] y(t)=As(t)+n(t) (1),

[0097] in, It is the joint array manifold matrix of the spatial polarization domain of the array signal, s(t)=[s1(t),s2(t),…,s P (t)] T ∈C P×1 Let there be P independent incident sources, n(t) = [n1(t), n2(t), ..., n 2M (t)] T ∈C2M×1 The mean is zero and the variance is σ. 2 The additive white Gaussian noise, and the ideal steering vector corresponding to the p-th signal is specifically expressed as:

[0098]

[0099] in, Let be the spatial steering vector of the p-th signal; Let be the polarization vector of the p-th signal; It represents the Kronecker product.

[0100] 1) Unitary transformation

[0101] For an N×N square matrix S, if S satisfies S -1 =S H Then S is called a unitary matrix. Where, [·] H Indicates conjugate transpose, [·] -1 This indicates that the matrix is ​​inverted.

[0102] For an M×N matrix G, if it satisfies G=J M G * J N If , then it is called the central Hermitian matrix. Where J M It is called a commutative matrix; it is a square matrix with all elements on the secondary diagonal being 1 and all other elements being 0. [·] * This represents the complex conjugate operation. (J) M The special characteristics are easy to know J M T =J M J M ·J M =I M

[0103] The main principle of unitary transformation is to utilize the properties of the central Hermitian matrix, specifically expressed as follows:

[0104] G r =U M H GU N (3),

[0105] Among them, G r U represents the result of transforming matrix G into a real number after unitary transformation. M It is a unitary matrix, represented as:

[0106]

[0107] 2) Real-valued sparse reconstruction model

[0108] For a single-polarization (horizontally or vertically polarized) array element, as long as the element is centrally symmetric, its spatial steering vector is also centrally symmetric. Therefore, a unitary transformation can be performed on the received data, and a definite relationship can be found. Based on this, for a biorthogonal dipole array, subarray 1 and subarray 2 are constructed by selecting horizontally polarized and vertically polarized elements, respectively. The received data of the two subarrays are then subjected to a unitary transformation, and the DOA and polarization parameters are separated. Subsequently, a block sparse algorithm can be used for estimation.

[0109] For subarray 1, we have

[0110]

[0111] Among them, a(θ)=[1,exp(-j2πdsin(θ) / λ),…,exp(-j2π(M-1)dsin(θ) / λ)] T ,

[0112]

[0113] The data received by subarray 1 can be represented as

[0114]

[0115] Where E = diag(e1, e2, ..., e P ), A1(θ)=A(θ)·V1, A(θ)=[a(θ1),a(θ2),…,a(θ P V1 = diag(v) 1,x ,v 2,x ,…,v P,x )

[0116] Similarly, for subarray 2, we have

[0117] Y2=A2(θ)E·X+N2 (8),

[0118] in, A2(θ)=A(θ)·V2,

[0119] V2 = diag(v 1,y ,v 2,y ,…,v P,y ).

[0120] Constructing augmented matrices

[0121] Y aug1 =[Y1,J M Y1 * J L (9),

[0122] Y aug2=[Y2,J M Y2 * J L (10),

[0123] Among them, J M ∈R M J L ∈R L It is a permutation matrix in which all elements on the secondary diagonal are 1 and all other elements are 0.

[0124] For subarray 1, we have:

[0125] Y aug1 =[Y1,J M Y1 * J L ]

[0126] =[A1EX+N1 J M (A1EX+N1) * J L ]

[0127] =[A1EX+N1 J M A1 * E * X * J L +J M N1 * J L ]

[0128] =[A1EX J M A1 * E * X * J L ]+[N1 J M N1 * J L (11),

[0129] For a uniform linear array, the spatial steering vector has the following relationship:

[0130] A1Λ=J M A1 * (12),

[0131] in,

[0132] Λ=diag{exp(j2π(M-1)sin(θ1) / λ),…,exp(j2π(sin(θ P ) / λ),1}

[0133] Performing a unitary transformation on the augmented matrix, we have

[0134] Y r1 =UM H Y aug1 U 2L (13),

[0135] Substitution method

[0136] Y r1 =U M H [A1EX J M A1 * E * X * J L ]U 2L +U M H [N1 J M N1 * J L ]U 2L (14),

[0137] For the signal section

[0138] U M H [A1EX J M A1 * E * X * J L ]U 2L =U M H [A1EX A1ΛE * X * J L ]U 2L

[0139] =U M H A1[EXΛE * X * J L ]U 2L (15) Let AA1 = U M H A1, S = [EXΛE] * X * J L ]U 2L

[0140] Then there is

[0141] Y r1 =AA1·S+N r1 (16),

[0142] Similarly, for subarray 2, we have

[0143] Yr2 =AA2·S+N r2 (17),

[0144] Constructing a matrix

[0145]

[0146] According to compressed sensing theory, the recovered signal must be sparse in the spatial domain. However, in reality, the number of incident signals is finite relative to the entire spatial domain and cannot fill it completely; that is, the number of signals is much smaller than the number of grid divisions. Therefore, sparse reconstruction algorithms can be widely applied to DOA estimation problems. This paper uses a uniform linear array model, where the resolvable spatial domain angles are [-90°, 90°]. Dividing the array into N grids yields a supercomplete set of angles. like Figure 2 As shown in the diagram. Hollow circles represent the grid divisions, while solid circles represent the direction of signal arrival.

[0147] We can obtain a supercomplete set of angles. The matrix formed by the array steering vectors corresponding to each element is the extended array manifold matrix, which can be called the overcomplete dictionary. Therefore, equation (18) can be extended to the overcomplete angle set. Obtain the overcomplete array output model

[0148]

[0149] Where, Φ=[U M H a 1,1 ,…,U M H a 1,N ;U M H a 2,1 ,…,U M H a 2,N ], s n ,n∈[1,N] is a block signal.

[0150] The augmented matrix is ​​similar to doubling the number of snapshots. Given a multi-measurement vector model, to apply the BSBL framework to this model, the MMV model should be converted to a single-measurement vector model.

[0151] YY = DD·XX + NN (20),

[0152] Where YY = vec(Y r T )∈C 4ML×1 , NN = vec(N r T )∈C 4ML×1 `vec(·)` denotes vectorization. Therefore, the block structure of XX is represented as XX = [x(1:4L)]. T x(4L+1:8L) T ,…,x(4L(i-1)+1:4Li) T ,…,x(4L(N-1)+1:4LN) T ] T Let i = 1, 2, ..., N, and x(4L(i-1)+1:4Li) represent a 4L×1 vector consisting of elements from 4L(i-1)+1 to 4Li of XX. Note that XX is block-sparse, with each non-zero block containing 4L elements. Therefore, a block-sparse Bayesian algorithm can be used to estimate the parameters.

[0153] Block Sparse Bayes Algorithm Based on Unitary Transformation

[0154] Block Sparse Bayes Algorithm:

[0155] The BSBL algorithm architecture assumes the i-th signal block Follows Gaussian distribution

[0156]

[0157] γ i Control signal sparsity, B i It describes intra-block correlation information. γ i A value of 0 represents the corresponding signal block. γ is 0 i The larger the value, the greater the probability of it taking that value. Assuming that signal blocks are uncorrelated, then the signal... It can be modeled as

[0158]

[0159] Where Γ=diag -1 (γ1B1,...,γ g B g ).

[0160] Assuming the observed noise is independent and identically distributed, i.e., follows a Gaussian distribution with mean 0 and variance βI, then The posterior distribution follows the following Gaussian distribution.

[0161]

[0162] in,

[0163] Σ -1 =Γ-1 +Φ T βΦ (24),

[0164] μ=ΣΦ T βy (25),

[0165] In order to estimate the parameter {γ i B i The cost function can be obtained using the type II maximum likelihood method, given β and β.

[0166] L({γ i B i},β)=logC+y T C -1 y (26),

[0167] Where C = β -1 I+Φ T ΓΦ.

[0168] Taking the partial derivative of the expectation of the cost function and setting it to zero yields the learning rule for the hyperparameters under the maximum likelihood algorithm.

[0169]

[0170] To uncover the correlation of signals within a block, the BSBL algorithm is used for signal x. i covariance matrix B i Add constraints

[0171]

[0172] Using B i The updated formula yields an empirical formula for calculating the correlation coefficient r:

[0173]

[0174] in, For B i The mean of the second diagonal, The mean of the main diagonals.

[0175] Note that in equation (27), the hyperparameter γ i The computational complexity is relatively high, so a boundary optimization algorithm is used to optimize equation (26) and further refine γ. i Find the partial derivative and set it to 0 to obtain γ. i Learning rules

[0176]

[0177] The estimated DOA and the reconstructed value of the block signal can be obtained from equations (24) to (32).

[0178] Estimation of polarization parameters:

[0179] Obviously, the XX estimated by the block sparse algorithm is not the actual received X, but there is a certain relationship between the two. According to the properties of the unitary transform, X can be reconstructed from the estimated XX, and then the polarization parameters can be estimated.

[0180] The vectorized block signal is restored to the original signal, and the 4L×1 block signal is converted into a 2×2L block signal according to the corresponding rules.

[0181] According to the properties of unitary matrices UU H =I, has

[0182]

[0183] Take the first L rows of the matrix, that is

[0184]

[0185] Therefore, it can be concluded that

[0186]

[0187] The polarization parameters can be estimated using equations (33) to (36).

[0188] Example:

[0189] The effectiveness of the algorithm of the present invention will be verified through simulation experiment 1 below.

[0190] Consider a uniform linear array consisting of 12 orthogonal dipole elements, with an element spacing of d = λ / 2. There are two incident signal sources with source parameters (θ, γ, η) of (-10°, 40°, 50°) and (10°, 20°, 30°), respectively. The number of sampling snapshots is 5, and the signal-to-noise ratio is 20 dB. The effectiveness of the proposed algorithm is verified through simulation results as follows: Figure 3 As shown.

[0191] Depend on Figure 3 It can be seen that the real-valued block sparse Bayesian algorithm based on unitary transform has zero sparsity at locations where no signal is present, and non-zero sparsity at locations where a signal is present, thus achieving effective angle measurement. Simulation Experiment 2 is used to analyze the estimation accuracy performance of the algorithm of this invention.

[0192] Consider a uniform linear array consisting of 12 elements, with an element spacing of d = λ / 2. There are two incident signal sources with source parameters (θ, γ, η) of (-5.01°, 40°, 50°) and (5.02°, 20°, 30°), respectively. The number of sampling snapshots is 5. The SNR is set from 10dB, varying in 2dB increments to 30dB. 200 Monte Carlo simulations are performed for each SNR. The parameter estimation accuracy of the real-valued block sparse Bayes algorithm and the BOMP algorithm based on unitary transform is statistically analyzed and compared with the theoretical CRB. The simulation results are as follows: Figure 4 As shown, where Figure 4 (a) is a graph showing the change of spatial angle RMSE with signal-to-noise ratio. Figure 4 (b) is a graph showing the variation of polarization parameter γRMSE with signal-to-noise ratio. Figure 4 (c) shows the variation of polarization parameter ηRMSE with signal-to-noise ratio.

[0193] Simulation results show that, compared with the BOMP algorithm, the real-valued sparse Bayes algorithm based on unitary transformation has better parameter estimation performance.

[0194] This invention constructs subarray 1 and subarray 2 using horizontally polarized array elements and vertically polarized array elements, respectively. The received data matrices of each subarray are transformed from the complex domain to the real domain using unitary transform. Then, a block sparse Bayesian learning algorithm is used to estimate the DOA and block signal. Based on this, the properties of the unitary transform are used to reconstruct the block signal, further enabling the estimation of polarization parameters. Simulation results verify the effectiveness of this invention; compared with the BOMP algorithm, this invention has better parameter estimation performance.

Claims

1. An array signal processing method based on unitary transform real-valued block sparse Bayesian learning, characterized in that, Includes the following steps: Step 1: For the biorthogonal dipole array, construct the horizontal polarization subarray and the vertical polarization subarray respectively; Step 2: Perform unitary transform on the received data of the two subarrays respectively, converting the received data into real-valued data. Simultaneously, decouple the DOA and polarization parameters, and then use a block sparse algorithm for estimation: Under the model of a uniform linear array, the angle of the resolvable spatial domain of the linear array is... Divided into By dividing the grid into grids, a supercomplete set of angles is obtained. This leads to a supercomplete set of angles. The matrix formed by the array steering vectors corresponding to each element is the extended array manifold matrix. The MMV model is converted into a single measurement vector model so that the BSBL framework can be applied to the multi-measurement vector model. The block sparse Bayes algorithm is used to estimate the parameters. Step 3: Utilize the properties of the unitary transform to transform the reconstructed block signal, and then use the correlation between the block signals to estimate the polarization parameters.

2. The array signal processing method based on unitary transform real-valued block sparse Bayesian learning according to claim 1, characterized in that, This is performed under the model of a uniform linear array, where the angle of the resolvable spatial domain of the linear array is... Consider a spatial distance of half a wavelength. of A uniform linear array composed of orthogonal dipole elements and The far-field narrowband fully polarized signal, the first The azimuth angle of each signal is The polarization auxiliary angle and polarization phase angle are respectively and Assuming the incident signals are uncorrelated and independent of the noise, the received signal of the polarization-sensitive array is expressed as: （1）， in, It is the joint array manifold matrix of the spatial polarization domain of the array signal. for Each independent incident source The mean is zero and the variance is . Additive white Gaussian noise, and corresponding to the first The ideal steering vector of a signal is specifically represented as: （2）， in, For the first The spatial steering vector of a signal; For the first The polarization vector of each signal; It represents the Kronecker product.

3. The array signal processing method based on unitary transform real-valued block sparse Bayesian learning according to claim 2, characterized in that, In step 1, for the biorthogonal dipole array, horizontally polarized array elements and vertically polarized array elements are selected to construct subarray 1 and subarray 2, respectively; wherein, for subarray 1, we have: (6), among which, , , Then the data received by subarray 1 is represented as （7）， in, , , , , Similarly, for subarray 2, we have （8）， in, , , ; Construct the augmented matrix: （9）， （10）， in, , It is a permutation matrix in which all elements on the secondary diagonal are 1 and all other elements are 0.

4. The array signal processing method based on unitary transform real-valued block sparse Bayesian learning according to claim 3, characterized in that, In step 2, the BSBL algorithm architecture assumes that the first Signal block Follows a Gaussian distribution: (twenty one), Controlling signal sparsity, Describes intra-block correlation information. A value of 0 represents the corresponding signal block. =0, The larger the value, the greater the probability of it taking that value. Assuming that the signal blocks are uncorrelated, then the signal... Modeled as (22), among which, , Assume that the observed noise is independent and identically distributed, i.e., follows a mean of 0 and a variance of . If it is a Gaussian distribution, then The posterior distribution follows a Gaussian distribution as follows: （23）， （24）， (25) In order to estimate parameters and The cost function is obtained using the type II maximum likelihood method: （26）， in, By taking the partial derivative of the expectation of the cost function and setting it to zero, we can obtain the learning rule for the hyperparameters under the maximum likelihood algorithm. （27）， （28）， （29）， To uncover the correlation of signals within a block, the BSBL algorithm analyzes the signals. covariance matrix Add constraints （30）， use The updated formula can be used to obtain the correlation coefficient. Empirical calculation formula: (31), among which, for The mean of the second diagonal, Using the mean of the main diagonal, equation (26) is optimized using a boundary optimization algorithm, and further refined... Find the partial derivative and set it to 0 to obtain the result. Learning rules: (32) The estimated value of DOA and the reconstructed value of the block signal can be obtained from equation (24)-equation (32).

5. The array signal processing method based on unitary transform real-valued block sparse Bayesian learning according to claim 3, characterized in that, Step 3, the estimation of polarization parameters specifically includes the following: restoring the vectorized block signal to the signal before vectorization, by... The block signal is converted according to the corresponding rules. block signals; Based on the properties of unitary matrices ,have: （33）， Take the first L rows of this matrix, that is: （34）， Therefore, it can be concluded that (35), (36) The polarization parameters can be estimated by equation (33)-(36).

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