Efficient Direction Finding Method for Coherent Sources in Real Domain Space under Arbitrary Linear Array Structure

Abstract

The present invention relates to the technical field of radar signal processing, and specifically to an efficient real-domain spatial direction finding method for coherent sources under an arbitrary linear array structure that can significantly improve the estimation accuracy of radar signals. According to the properties of the rank of the array manifold under different array structures, sum-difference transformation is performed on the covariance matrix after forward-backward smoothing of the I / Q channel outputs. By utilizing the inherent mapping relationship between the real-valued noise subspace and the original noise subspace, the spatial spectrum of the coherent sources is reconstructed. The present invention not only realizes the effective estimation of coherent signal sources under arbitrary linear array conditions, but also greatly reduces the computational complexity by using real-valued calculations, providing theoretical support for the adaptation of array direction finding algorithms to the requirements of engineering applications.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and specifically to a coherent source real-domain space efficient direction finding method under an arbitrary linear array structure that can significantly improve the estimation accuracy of radar signals. Background Art

[0002] Array direction finding has always been an important part of radar signal processing and has been widely used in various civil-military integration fields, such as radar, earthquake warning, indoor positioning, UAV detection, etc. The early beamforming method was trapped by the "Rayleigh limit" and could not distinguish many targets within the same beam width. Since the proposal of the Multiple Signal Classification (MUSIC) algorithm in 1986, array direction finding has been officially pushed onto the fast track of super-resolution, breaking through the dilemma of the traditional Rayleigh limit. After that, considering the huge computational amount of spectral peak search in the MUSIC algorithm, many efficient super-resolution algorithms have been proposed, such as the root-MUSIC algorithm, the ESPRIT algorithm, and the unitary transformation method. The above methods all improve the efficiency of array direction finding from different angles. The root-MUSIC algorithm uses the equidistant structure of a uniform linear array to construct a polynomial that is only related to the target angle, and replaces spectral peak search with root finding. The ESPRIT algorithm also uses the rotation-invariant structure of a uniform linear array to divide subarrays, and through the linear relationship of the subarray subspaces, replaces the overall eigenvalue decomposition with local eigenvalue decomposition, thus having the theoretical calculation advantage of low complexity. It should be noted that both the root-MUSIC and ESPRIT algorithms utilize the special structure of a uniform linear array and achieve fast array direction finding through specific mathematical relationships. Therefore, the algorithms are limited by the array structure. In addition, the ESPRIT algorithm improves efficiency by dividing subarrays and reducing the array aperture, but loses the estimation accuracy of the angle.

[0003] In order to achieve a win-win situation between parameter estimation accuracy and system computational complexity, the unitary transformation method provides a novel idea. As is well known, the computational amount of real number operations is only one-fourth of that of complex number operations. The unitary transformation utilizes the Hermitian property of the covariance matrix under a uniform linear array to map the traditional complex eigenvalue decomposition to real-domain space processing. At the same time, existing research shows that although the real-value method only uses part of the information of the array, the estimation accuracy is still within an acceptable range. It should be emphasized that the unitary transformation method is still only applicable to a uniform linear array. In addition, these efficient array direction finding algorithms cannot effectively estimate coherent signals. Considering the limitations of a uniform linear array in practical applications, the above direction finding algorithms can no longer meet the growing actual application requirements.

[0004] In order to effectively estimate coherent signals, many researchers have proposed relevant solutions. The most common one is the spatial smoothing (FBSS) decoherence algorithm. This method still strictly limits the array structure and is only applicable to uniform linear arrays and two-dimensional arrays with rotational invariance structures, and can only have good angle estimation performance at relatively high signal-to-noise ratios. In addition, due to the loss of array aperture and multiple smoothings, the spatial smoothing algorithm also makes the same strict restrictions on the number of detected targets. To avoid array aperture loss, reconstructing the covariance data matrix has become another research direction for decoherence. However, to improve the resolution, a large number of sampling snapshots are essential. Therefore, the computational complexity of the matrix reconstruction algorithm is high, which is not conducive to real-time processing. Summary of the Invention

[0005] Aiming at the problem that the direction finding of coherent source arrays is limited by the array structure, the present invention proposes an efficient real-domain spatial direction finding method for coherent sources under an arbitrary linear array structure. According to the properties of the rank of the array manifold under different array structures, a sum-difference transformation is performed on the covariance matrix after forward and backward smoothing of the I / Q channel outputs, and the spatial spectrum of the coherent sources is reconstructed by using the inherent mapping relationship between the real-valued noise subspace and the original noise subspace. The present invention not only realizes the effective estimation of coherent sources under the condition of an arbitrary linear array, but also greatly reduces the computational complexity by using real-valued calculations, providing theoretical support for the adaptation of array direction finding algorithms to the requirements of engineering applications.

[0006] The present invention is achieved by the following measures:

[0007] An efficient real-domain spatial direction finding method for coherent sources under an arbitrary linear array structure, characterized by comprising the following steps:

[0008] The first step: Arrange an antenna array with an arbitrary linear structure for receiving far-field signals: Assume that there is a linear array with M array elements in space and each array element is isotropic, and the positions of the array elements are {D 1 , D 2 , …, D M};

[0009] The second step: Calculate the forward and backward smoothing covariance matrix of the array according to the statistical second moment of the signals received by the array:

[0010] If there are P narrowband signals in the far-field space incident on the array in the directions of θ i , i = 1, …, P with respect to the normal of the linear array axis, then the vector form of the array received data is expressed as:

[0011] x(t) = A(θ)s(t) + n(t),

[0012] where x(t) = [x 0(t),…,x M-1 (t)] T is the output of the array element, s(t) = [s 0 (t),…,s P-1 (t)] T is the complex envelope of the signal, (·) T is the transpose operation, n(t) is Gaussian white noise with zero mean and variance ; the array manifold matrix A(θ) is expressed as:

[0013] A(θ) = [α(θ 1 ),…,α(θ P )],

[0014] where is the direction vector of the p-th signal, λ is the carrier wavelength, d is the element spacing, and to avoid array direction finding ambiguity, it is required that d ≤ λ / 2;

[0015] The covariance matrix of the snapshot data received by the array elements is expressed as:

[0016]

[0017] where E(·) is the mathematical expectation, (·) H is the conjugate transpose operation, I is the identity matrix, R ss = E[s(t)s H (t)] is the L×L signal covariance matrix. In practical applications, since the data length is not infinite; therefore, the sampling covariance matrix is constructed using N snapshot data of the received signal x(t), that is

[0018]

[0019] is regarded as the forward average of the array received data, so its forward-backward average is expressed as:

[0020]

[0021] where J is the anti-diagonal identity matrix, is the backward average, x FB (t) is defined as

[0022]

[0023] After jointly considering the array manifold A(θ) and x FB (t), x FB (t) is expressed as:

[0024] x FB (t) = A FB (θ)sFB (t) + n(t),

[0025] where A FB (θ) = [A(θ)JA * (θ)],

[0026] is the covariance matrix of the virtual received signal x FB (t). Under different array structures, the virtual array manifold A FB (θ) has different properties. For a uniform linear array, the column vectors of the array manifold A(θ) have a Vandermonde structure, that is,

[0027] rank(A FB (θ)) = rank(A(θ)) = P,

[0028] while for a non-uniform linear array (NULA), A(θ) is a non-singular matrix, so

[0029] rank(A FB (θ)) = 2P;

[0030] Performing eigenvalue decomposition on to obtain the signal and noise subspaces after decoherence

[0031]

[0032] where and are diagonal matrices containing 2P large eigenvalues and M - 2P small eigenvalues respectively, and are the signal and noise subspaces containing 2P signal components and M - 2P noise components respectively;

[0033] Step 3: Perform sum-difference transformation on the forward-backward smoothed covariance matrix to obtain the real-valued covariance matrix:

[0034] Considering that has the properties of wide symmetry and central Hermitian, define the parameter matrix:

[0035]

[0036] Left-multiplying and right-multiplying by the parameter matrix T gives

[0037]

[0038] where is the real part of for is the imaginary part of . Obviously,

[0039] is a real-valued matrix composed of the sum of the real and imaginary parts of , which is simply called the real-domain space. Next, perform eigenanalysis on the real-domain space to verify that there is no subspace leakage in the real-domain subspace after the forward-backward averaging operation in the case of coherent sources;

[0040] Suppose η and are the eigenvalue and eigenvector of respectively. According to the matrix decomposition principle, we have:

[0041]

[0042] Using T H T = I, after the above matrix decomposition, we have:

[0043]

[0044]

[0045]

[0046] where is a real vector. It can be found that η is also the eigenvalue of , and is the corresponding eigenvector of . Considering , we have:

[0047]

[0048] This means that the original complex eigenvector is calculated by linear operations from the real eigenvector ;

[0049] Step 4: In the real-domain space, perform real-valued eigen decomposition on the real-valued covariance matrix to obtain the real-valued noise subspace:

[0050] Performing real-valued eigen decomposition on in the real-domain space gives:

[0051]

[0052] Since the real and imaginary parts of correspond to the I / Q channels of the orthogonal receiver respectively, therefore, performing real-valued eigen decomposition on can directly obtain the real-valued covariance matrix and the real-valued noise subspace by performing sum-difference transformation on the outputs of the I / Q two channels received by different array elements;​

[0053] Step 5: Utilize the mapping relationship between the original noise subspace and the real-valued noise subspace to recover the original subspace and reconstruct the spatial spectrum of the coherent sources:

[0054] Since and have the same eigenvalues, thus, the eigenvalue decomposition of

[0055]

[0056] where,

[0057] It should be noted that the real-domain signal subspace the original complex signal subspace Π s and the column dimension of the array manifold A FB (θ) are all 2P. Therefore, there is no subspace leakage. Thus, based on the forward-backward smoothing decoherence, further utilize the real-valued eigenvalue decomposition to construct the real-domain subspace. According to the properties of the array manifold, the proposed real and imaginary part hybrid decomposition method (RV-MUSIC) can be applied to any linear array and reconstruct the original spatial spectrum, that is

[0058]

[0059] Step 6: Use spectrum peak search to obtain the angles of the far-field signals to be estimated. The sixth step includes the following steps:

[0060] Perform angle traversal on the spatial spectrum f RV-MUSIC (θ). The angle corresponding to the peak is the angle of the signal to be estimated, which can be expressed as:

[0061]

[0062] Finally, the computational complexity of the present invention and the forward-backward smoothing algorithm is compared, as shown in Table 1, where represents the computational complexity of the complex value, and J is the number of search points. The proposed RV-MUSIC algorithm mainly includes three computational units: obtaining the covariance matrix, eigenvalue decomposition, and spectrum peak calculation. Compared with the traditional forward-backward smoothing algorithm with complex value calculation, the RV-MUSIC algorithm can reduce the overall complexity of the three computational units by 75% through real-valued calculation.

[0063] The beneficial effects of the present invention compared with the prior art are as follows: By clarifying the properties of the rank of the array manifold under different linear array structures, separating the I / Q channels corresponding to the forward and backward smoothed covariance matrices, constructing a real-valued covariance matrix using sum-difference transformation, and reconstructing the spatial spectrum of coherent sources based on the inherent mapping relationship between the real-valued noise subspace and the original noise subspace, the accurate estimation of coherent sources is completed under any linear array structure. Compared with the prior art, the present invention breaks the strict constraint of the decorrelation algorithm on the array structure and greatly improves the computational efficiency of array direction finding through real-valued calculations. Brief Description of the Drawings

[0064] Figure 1 is the flowchart of the present invention.

[0065] Figure 2 is a schematic diagram of the comparison of spectral peak searches between the present invention and the MUSIC algorithm under a uniform linear array, where M = 12, D ULA = {0, 1, … 11}, SNR = 5 dB, N = 100, P = 2, signal carrier frequency f = 1 GHz, signal complex gain [1, 0.85 + 0.93j], θ 1 = -15°, θ 2 = 10°.

[0066] Figure 3 is a schematic diagram of the comparison of spectral peak searches between the present invention and the MUSIC algorithm under a non-uniform linear array, where M = 12, D NULA = {0, 2, 5, 7, 8, 9, 13, 15, 17, 19, 20, 23}, SNR = 5 dB, N = 100, P = 2, signal carrier frequency f = 1 GHz, signal complex gain [1, 0.85 + 0.93j], θ 1 = -15°, θ 2 = 10°.

[0067] Figure 4 is the variation of RMSE with the input signal-to-noise ratio for different algorithms under a uniform linear array in the present invention, where M = 12, D ULA = {0, 1, … 11}, N = 100, P = 2, signal carrier frequency f = 1 GHz, signal complex gain [1, 0.85 + 0.93j], θ 1 = 10°, θ 2 = 45°.

[0068] Figure 5 is the variation of RMSE with the number of array elements for different algorithms under a uniform linear array in the present invention, where M = 12, D ULA = {0, 1, … 11}, SNR = 10 dB, N = 100, P = 2, signal carrier frequency f = 1 GHz, signal complex gain [1, 0.85 + 0.93j], θ1 = 10°, θ 2 = 45°.

[0069] Figure 6 is the variation of the spectral peak resolution probability of the present invention with respect to the signal-to-noise ratio under a uniform linear array, where M = 12, D ULA = {0, 1, … 11}, N = 100, P = 2, the signal carrier frequency f = 1 GHz, the signal complex gain [1, 0.85 + 0.93j], θ 1 = 10°, θ 2 = 10° + △θ.

[0070] Figure 7 is the variation of the theoretical computational complexity of the present invention with respect to the number of array elements under a uniform linear array and different algorithms. Detailed implementation manner

[0071] An efficient real-domain spatial direction-finding method for coherent sources under any linear array structure, the specific steps are as Figure 1 shown.

[0072] The first step is to arrange an antenna array with an arbitrary linear structure for receiving far-field signals. The first step includes the following steps:

[0073] Assume that there is a linear array with M array elements in space and each array element is isotropic. The positions of the array elements are {D 1 , D 2 , …, D M}.

[0074] The second step: Calculate the forward and backward smoothing covariance matrix of the array according to the statistical second moment of the signals received by the array. The second step includes the following steps:

[0075] If there are P narrowband signals in the far-field space incident on the array in the directions of θ i , i = 1, …, P with respect to the normal of the linear array axis, then the vector form of the data received by the array can be expressed as:

[0076] x(t) = A(θ)s(t) + n(t),

[0077] where x(t) = [x 0 (t), …, x M-1 (t)] T is the output of the array elements, s(t) = [s 0 (t), …, s P-1 (t)] T is the complex envelope of the signal, (·) T is the transpose operation, and n(t) is Gaussian white noise with zero mean and variance of . The array manifold matrix A(θ) can be expressed as:

[0078] A(θ) = [α(θ 1 ), …, α(θ P )],

[0079] where is the direction vector of the p-th signal, λ is the carrier wavelength, d is the element spacing. To avoid array direction finding ambiguity, it is generally required that d ≤ λ / 2.

[0080] The covariance matrix of the snapshot data received by the array elements can be expressed as:

[0081]

[0082] where E(·) is the mathematical expectation, (·) H is the conjugate transpose operation, I is the identity matrix, and R ss = E[s(t)s H (t)] is the L×L signal covariance matrix. In practical applications, since the data length is not infinite; therefore, the sampling covariance matrix is usually constructed using N snapshot data of the received signal x(t), that is

[0083]

[0084] When the array receives signals, if the signal sources are coherent, it will cause the dimension of the signal subspace to be less than the number of signal sources, that is, the information of the signal subspace "diffuses" into the noise subspace, making the direction vector of the coherent signal sources not completely orthogonal to the noise subspace. Therefore, the commonly used subspace algorithms will not be able to correctly estimate the target azimuth.

[0085] can be regarded as the forward average of the array received data, so its forward-backward average can be expressed as:

[0086]

[0087] where J is the anti-diagonal identity matrix, is the backward average, and x FB (t) is defined as

[0088]

[0089] Furthermore, after jointly considering the array manifold A(θ) and x FB (t), x FB (t) can be expressed as:

[0090] x FB (t) = A FB (θ)s FB (t) + n(t),

[0091] where A FB (θ) = [A(θ)JA * (θ)],

[0092] can be regarded as the covariance matrix of the virtual received signal x FB (t). Considering that for coherent signals, the forward-backward averaging of is a conventional rank restoration operation. Therefore, under different array structures, the virtual array manifold A FB (θ) has different properties. Specifically, for a uniform linear array (ULA), the column vectors of the array manifold A(θ) have a Vandermonde structure, that is,

[0093] rank(A FB (θ)) = rank(A(θ)) = P,

[0094] while for a non-uniform linear array (NULA), A(θ) is a non-singular matrix, so

[0095] rank(A FB (θ)) = 2P.

[0096] It should be emphasized that according to the element spacing, any linear array can be divided into a uniform linear array and a non-uniform linear array. Among them, a sparse linear array with a specific element spacing can also be regarded as a non-uniform linear array. For the sake of convenience, the non-uniform linear array will be used as the discussion basis in the following. Performing the eigen-decomposition method on can obtain the signal and noise subspaces after decoherence

[0097]

[0098] where and are diagonal matrices containing 2P large eigenvalues and M - 2P small eigenvalues respectively. and are the signal and noise subspaces containing 2P signal components and M - 2P noise components respectively.

[0099] Step 3: Perform a sum-difference transformation on the forward-backward smoothed covariance matrix to obtain a real-valued covariance matrix. The third step includes the following steps:

[0100] Considering that has the properties of wide symmetry and central Hermitian, define the parameter matrix:

[0101]

[0102] Left - multiplying and right - multiplying the parameter matrix \(T\) gives

[0103]

[0103]

[0104] where, is the real part of, is the imaginary part of.

[0105] Obviously, is a real - valued matrix composed of the sum of the real part and the imaginary part of , which is simply called the real - domain space. Next, perform eigenvalue analysis on the real - domain space to verify that there is no subspace leakage in the real - domain subspace after the forward - backward averaging operation in the case of coherent sources.

[0106] Suppose \(\eta\) and are the eigenvalue and eigenvector of respectively. According to the matrix decomposition principle, we have:

[0107]

[0108] Using \(T\) H \(T = I\), after the above matrix decomposition, we have:

[0109]

[0110]

[0111]

[0112] where, is a real vector. It can be found that \(\eta\) is also the eigenvalue of, and is the corresponding eigenvector of. Considering we can have:

[0113]

[0114] This means that the original complex eigenvector can be calculated by linear operations from the real eigenvector .

[0115] Step 4: In the real - domain space, perform real - valued eigenvalue decomposition on the real - valued covariance matrix to obtain the real - valued noise subspace. The fourth step includes the following steps:

[0116] Performing real - valued eigenvalue decomposition on in the real - domain space gives:

[0117]

[0118] Since the real and imaginary parts respectively correspond to the I / Q channels of the orthogonal receiver, thus, for performing real-valued eigenvalue decomposition can directly obtain the real-valued covariance matrix and the real-valued noise subspace by performing sum-difference transformation on the outputs of the I / Q two channels received by different array elements.

[0119] Step 5: Utilize the mapping relationship between the original noise subspace and the real-valued noise subspace to restore the original subspace and reconstruct the spatial spectrum of the coherent source. The fifth step includes the following steps:

[0120] Since and have the same eigenvalues, thus, the eigenvalue decomposition of

[0121]

[0122] wherein,

[0123] It should be noted that the real-domain signal subspace the original complex signal subspace Π s and the column dimension of the array manifold A FB (θ) are all 2P. Therefore, there is no subspace leakage. Thus, on the basis of forward-backward smoothing decoherence, further construct the real-domain subspace by using real-valued eigenvalue decomposition. According to the properties of the array manifold, the proposed real-imaginary hybrid decomposition method (RV-MUSIC) can be applied to any linear array and reconstruct the original spatial spectrum, that is

[0124]

[0125] Step 6: Utilize spectral peak search to obtain the angles of the far-field signals to be estimated. The sixth step includes the following steps:

[0126] Perform angle traversal on the spatial spectrum f RV-MUSIC (θ), and the angle corresponding to the peak is the angle of the signal to be estimated, which can be expressed as:

[0127]

[0128] The performance of the present invention can be illustrated by the following simulations:

[0129] 1. Simulation conditions

[0130] The proposed RV-MUSIC algorithm is discussed respectively from uniform linear arrays and non-uniform linear arrays. P = 2 coherent signals are incident on the above arrays, and they have the same carrier frequency f = 1 GHz, and the signal amplitude gains are [1, 0.85 + 0.93j]. To further evaluate the performance of the present invention, the number of Monte Carlo experiments is set to 500, and the root mean square error (RMSE) and the spectral peak resolution probability are used as evaluation indexes.

[0131] 2. Simulation content and results

[0132] Simulation 1: Set the number of array elements M = 12, and the array element positions D ULA = {0, 1, … 11} and D NULA = {0, 2, 5, 7, 8, 9, 13, 15, 17, 19, 20, 23}, and the signal incident directions are θ 1 = -15° and θ 2 = 10°. Compare the decoherence effectiveness of the present invention and the MUSIC algorithm. The results are as Figure 2 and Figure 3 shown.

[0133] It can be seen from Figure 2 and Figure 3 that in the case of coherent sources, the traditional MUSIC algorithm will fail and false spectral peaks will appear, while the present invention can effectively estimate the coherent sources. At the same time, because the uniform linear array has a half-wavelength equidistant structure, and the non-uniform linear array has an ambiguity phenomenon, the decoherence effect under the uniform linear array is better than that under the non-uniform linear array.

[0134] Simulation 2: Set the number of snapshots N = 100, the number of array elements M = 12, and the array element positions D ULA = {0, 1, … 11}, and the signal incident directions are θ 1 = 10° and θ 2 = 45°. Compare the variation of the RMSE of the present invention, the spatial smoothing algorithm, the Toeplitz reconstruction algorithm, and the vector reconstruction algorithm with the input signal-to-noise ratio (SNR). The results are as Figure 4 shown.

[0135] It can be seen from Figure 4 that in the process of changing with the signal-to-noise ratio, the present invention has an angle estimation accuracy similar to that of the forward-backward smoothing and the Toeplitz algorithm, and is higher than that of the vector reconstruction algorithm.

[0136] Simulation 3: Set the number of snapshots N = 100, the array element positions D ULA = {0, 1, … M - 1}, and the signal incident directions are θ 1 = 10° and θ 2= 45°, the variation of the RMSE of the present invention with the number of array elements is compared, and the results are as Figure 5 shown.

[0137] It can be seen from Figure 5 that the angle estimation accuracy of the present invention improves with the increase in the number of array elements. This is because the increase in the number of array elements will simultaneously lead to an increase in the array aperture, thereby improving the estimation accuracy.

[0138] Simulation 4, set the number of snapshots N = 100, the number of array elements M = 12, and the array element positions D ULA = {0, 1, … 11}, the signal incident directions are θ 1 = 10° and θ 2 = 10° + △θ. The variation of the spectral peak resolution probability of the present invention and the spatial smoothing algorithm with the input SNR is compared, and the results are as Figure 6 shown.

[0139] It can be seen from Figure 6 that at the same angle interval, the present invention has a better spectral peak resolution probability than spatial smoothing; secondly, the spectral peak resolution probability of the present invention improves with the increase in the angle interval.

[0140] Simulation 5, from the two perspectives of theoretical computational complexity and actual CPU running time, the computational efficiency of the present invention and the spatial smoothing algorithm is compared. The actual CPU running time is examined when running MATLAB code in the same PC environment with an Intel(R) Core(TM) i5-9400 2.90GHz CPU processor and 16GB RAM memory, and the results are as Figure 7 and Table 2 shown.

[0141] It can be seen from Figure 7 that the present invention has a lower theoretical computational complexity than the forward-backward smoothing algorithm, which verifies the correctness of Table 1.

[0142] Table 1

[0143]

[0144] Table 2

[0145]

[0146] It can be seen from Table 2 that the present invention actually consumes the least CPU running time, which means that the present invention has the highest actual computational efficiency, corroborating the conclusion of the low-complexity computational advantage. Combining the above experimental results, it can be seen that the present invention not only realizes the effective estimation of the incident direction of coherent sources under any linear array, breaking through the limitation of the array structure of traditional methods, but also achieves a win-win situation for angle estimation accuracy and computational efficiency.

Claims

1. An efficient direction finding method for coherent sources in the real domain under an arbitrary linear array structure, characterized in that, it includes the following steps: Step 1: Arrange an antenna array with an arbitrary linear structure for receiving far-field signals: Assume that there is a linear array with M array elements in space and each array element is isotropic, and the positions of the array elements are {D 1 , D 2 , …, D M}; Step 2: Calculate the forward-backward smoothed covariance matrix of the array according to the statistical second moment of the signals received by the array: If there are P narrowband signals in the far-field space, incident on the array in the direction with the normal of the linear array axis as the reference, θ i , i = 1, …, P, then the vector form of the received data of the array is expressed as: x(t) = A(θ)s(t) + n(t), where \(x(t)=[x 0 (t),\ldots,x M-1 (t)] T is the output of the array element, \(s(t)=[s 0 (t),\ldots,s P-1 (t)] T is the complex envelope of the signal, \((\cdot) T is the transpose operation, \(n(t)\) is Gaussian white noise with zero mean and variance ; the array manifold matrix \(A(\theta)\) is expressed as: A(θ) = [α(θ 1 ), …, α(θ P )], Among them, is the direction vector of the p-th signal, λ is the carrier wavelength, d is the element spacing. To avoid array direction finding ambiguity, it is required that d ≤ λ / 2; The covariance matrix of the snapshot data received by the array elements is expressed as: where E(·) is the mathematical expectation, (·) H is the conjugate transpose operation, I is the identity matrix, and R s = E[s(t)s H (t)] is an L×L signal covariance matrix. In practical applications, since the data length is not infinitely long, therefore, an N-snapshot data of the received signal x(t) is used to construct a sampling covariance matrix, that is It is regarded as the forward average of the data received by the array, so its forward and backward average is expressed as: where J is an anti-diagonal identity matrix, is the backward average, and x FB (t) is defined as Considering the array manifold A(θ) and x FB (t) jointly, x FB (t) is expressed as: x FB y(t) = A FB sin(θ)s FB y(t)+n(t), Among them, A FB (θ) = [A(θ)JA * (θ)], is the covariance matrix of the virtual received signal x FB (t). Under different array structures, the virtual array manifold A FB (θ) has different properties. For a uniform linear array, the column vectors of the array manifold A(θ) have a Vandermonde structure, that is, there is rank(A FB (θ)) = rank(A(θ)) = P, For a non-uniform linear array, A(θ) is a non-singular matrix, so rank(A FB (θ)) = 2P; Pairwise Perform eigen - decomposition to obtain the decorrelated signal and noise sub - spaces Among them, and are diagonal matrices containing 2P large eigenvalues and M - 2P small eigenvalues respectively, and are the signal and noise subspaces containing 2P signal components and M - 2P noise components respectively; Step 3: Perform a sum-difference transformation on the forward-backward smoothed covariance matrix to obtain a real-valued covariance matrix: Considering that has wide symmetry and central Hermitian properties, define the parameter matrix: Multiply on the left and right by the parameter matrix T to obtain Among them, is the real part of is the imaginary part of Obviously, is composed of the sum of the real and imaginary parts of, which is a real-valued matrix, simply referred to as the real domain space. Next, perform eigenvalue analysis on the real domain space to verify that there is no subspace leakage in the real domain subspace after the forward-backward averaging operation in the case of coherent sources; Suppose η and are the eigenvalue and eigenvector of respectively. According to the matrix decomposition principle, we have: Using T H T = I, after the above matrix decomposition, we have: Among them, is a real vector, and η is also 's eigenvalue, while is the corresponding 's eigenvector. Considering we have: This means that the original complex eigenvector is calculated from the real eigenvector by a linear operation; Step 4: In the real domain space, perform a real-valued eigen-decomposition on the real-valued covariance matrix to obtain a real-valued noise subspace; Step 5: Use the mapping relationship between the original noise subspace and the real-valued noise subspace to restore the original subspace and reconstruct the spatial spectrum of the coherent source; Step 6: Use spectral peak search to obtain the angles of the far-field signals to be estimated.

2. The efficient direction finding method for coherent sources in the real domain under an arbitrary linear array structure according to claim 1, characterized in that: Step 4 is implemented through the following steps: Pair Performing real-valued eigenvalue decomposition in the real domain space gives: Since the real and imaginary parts respectively correspond to the I / Q channels of the orthogonal receiver, therefore, for performing real-valued eigenvalue decomposition can directly obtain the real-valued covariance matrix and the real-valued noise subspace by performing sum-difference transformation on the outputs of the I / Q two channels received by different array elements.

3. The efficient direction finding method for coherent sources in the real domain under an arbitrary linear array structure according to claim 1, characterized in that: Step 5 is implemented through the following steps: Since and have the same eigenvalues, therefore, the eigenvalue decomposition of Among them, Real domain signal subspace Original complex signal subspace Π s And array manifold A FB (θ) has a column dimension of 2P. Therefore, there is no subspace leakage. Thus, based on forward-backward smoothing to decorrelate, A real domain subspace is further constructed using real eigenvalue decomposition. According to the properties of the array manifold, the proposed real and imaginary part hybrid decomposition method is applied to any linear array, and the original spatial spectrum is reconstructed, that is 4. The efficient direction finding method for coherent sources in the real domain under an arbitrary linear array structure according to claim 1, characterized in that: Step 6 is implemented through the following steps: Perform an angular traversal of the spatial spectrum f RV-MUSIC (θ). The angle corresponding to the peak is the angle of the signal to be estimated, which can be expressed as:

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