Multi-dimensional parameter estimation method based on non-concurrent uniform linear array mutual coupling scene

Abstract

The invention discloses a multi-dimensional parameter estimation method based on a non-concurrent uniform linear array mutual coupling scene, and relates to the technical field of signal processing, and the method can achieve the joint estimation of DOA and polarization parameters in the presence of a mutual coupling effect, and comprises the steps: firstly, effectively eliminating a mutual coupling matrix through sub-array selection, and carrying out the sub-array selection; dependence on prior knowledge of array mutual coupling characteristics is not needed; an improved high-resolution algorithm is adopted to complete DOA estimation, polarization parameters are accurately estimated through parameter matching, and simulation results show that the method can significantly improve estimation precision in a complex mutual coupling environment, and shows good application prospects and robust performance.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a multidimensional parameter estimation method based on a non-common uniform linear array mutual coupling scenario. Background Technology

[0002] The increasing complexity of modern signal processing environments makes precise target localization and parameter estimation crucial in applications such as radar systems, wireless communications, and electronic warfare. However, these environments often involve multiple targets and strong interference signals, posing significant challenges to traditional array signal processing techniques. Current array signal processing methods primarily rely on spatial information acquired by array antennas. While classic high-resolution parameter estimation algorithms, such as Multiple Signal Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance (ROI), typically perform well under ideal conditions for traditional Direction of Arrival (DOA) and polarization parameter estimation algorithms, their performance significantly degrades in real-world applications due to mutual coupling effects between array elements. Summary of the Invention

[0003] In view of the above-mentioned prior art, the present invention provides a multi-dimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario, which mainly solves the technical problems existing in the above-mentioned background art.

[0004] To achieve the above objectives, the technical solution of this invention is implemented as follows: This application provides a multidimensional parameter estimation method based on a non-common uniform linear array with mutual coupling. The method includes the following steps: Step S1: Construct a uniform linear array, and obtain a received signal model considering mutual coupling interference based on the uniform linear array. Estimate the covariance matrix of the received signal model under the mutual coupling scenario. Perform eigenvalue decomposition on the signal covariance matrix to obtain the signal subspace. Step S2: Divide the uniform array into a first subarray and a second subarray. Calculate the first signal subspace based on the signal subspace, and construct a matrix based on the first signal subspace. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated value; Step S3: Re-divide the uniform array into a third sub-array and a fourth sub-array, calculate the second signal sub-space based on the signal sub-space, and construct the matrix based on the second signal sub-space. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated value; Step S4: Adjust parameters With parameters Perform parameter pairing to obtain parameters With parameters The estimated value.

[0005] As a preferred embodiment of the present invention, step S1, which involves obtaining a received signal model based on a uniform linear array considering mutual coupling interference, and estimating its covariance matrix under the mutual coupling scenario based on the received signal model, specifically includes: [The text abruptly ends here, so the translation stops as well.] Several far-field, uncorrelated narrowband electromagnetic wave signals are incident on a uniform array, which then performs joint sampling of the signals within the space-polarization domain; among them... and These represent the elevation and azimuth angles of the incident signal, respectively. and These represent the auxiliary polarization angle and polarization phase difference of the incident signal, respectively; No. The information of an incident signal in the spatial-polarized domain can be represented as follows: , which includes spatial vectors and polarization vector and will Its definition is as follows:

[0006]

[0007] in, , indicating the first The spatial phase factor between two dipoles in a set of electric dipoles for an incident signal. Indicates the wavelength of the signal. This represents the distance between two adjacent dipoles. Indicates the first The elevation angle of the incident signal. Indicates the first The azimuth angle of the incident signal. Indicates the first The auxiliary polarization angle of the incident signal. Indicates the first The polarization phase difference of the incident signal is then the... The joint steering vector of a uniform array of incident signals is represented as:

[0008] in, If the Krone Technology operator is used, then the signal received at the output of this array is represented as:

[0009] in, Indicates the received number An incident signal, Then it means If the array outputs a Gaussian white noise vector of dimension 1, then the received signal is... It can be represented as: in, for 1D orientation matrix, for The polarization matrix of dimension, for The spatial-polar domain joint matrix of dimension; the influence on the uniform matrix considering the mutual coupling scenario will be defined as a strip-shaped symmetric mutual coupling matrix. :

[0010] in, This indicates that the first electric short dipole is parallel to its second... The mutual coupling coefficient between the short electric dipoles This represents the mutual coupling coefficient of a dipole with respect to itself. Let represent the degrees of freedom of the mutual coupling matrix, then consider the final received signal model considering mutual coupling interference. for:

[0011] The covariance matrix of the uniform array output Represented as:

[0012] in, Indicates the incident signal The autocorrelation matrix, Indicates noise power. express The identity matrix, Represents the signal space. This represents the conjugate transpose of the final received signal model. This represents the conjugate transpose of the spatial-polarization domain joint matrix. Denotes the conjugate transpose of symmetric mutually coupled matrices. This represents the conjugate transpose of the original matrix.

[0013] As a preferred embodiment of the present invention, in step S1, the covariance matrix is... The eigenvalue decomposition yields the signal subspace, which specifically includes:

[0014] Among them, matrix sum matrix and represent the contents of the covariance matrix, respectively. A diagonal matrix with different eigenvalues; a matrix sum matrix Corresponding to the signal subspace and noise subspace respectively, and These represent the conjugate transposes of the signal subspace and the noise subspace, respectively.

[0015] In a preferred embodiment of the present invention, step S2 involves dividing the uniform array into a first subarray and a second subarray, calculating the first signal subspace based on the signal subspace, and specifically including: from the first signal subspace... Group to No. The first subarray is formed by the group, starting from the first... Group to No. The second subarray is formed by combining the selected subarrays; the mutual coupling coefficient matrix is ​​then obtained from the new subarray. and Through mutual coupling matrices Obtained from a specific submatrix: where the mutual coupling coefficient matrix Depend on The former In the column, the first Arrive at the The first subarray corresponding to each row is formed; and the mutual coupling coefficient matrix Then by After In the column, the first Arrive at the The second subarray corresponding to each row forms the resulting cross-coupling coefficient matrix. With the mutual coupling coefficient matrix They are represented as follows:

[0016] At this time, the mutual coupling coefficient matrix Then the joint space-polarization steering matrices of the corresponding first and second subarrays are respectively and They respectively correspond to the joint steering vector The former and after The first signal subspace spanned by the first subarray and the second subarray is: and They respectively correspond to the signal subspace The former Actions and After The rows are represented as follows:

[0017]

[0018] in, yes The transformation matrix of dimension, because The signals are independent of each other, so the matrix It is a full-rank matrix. Let be the rotation factor matrix. A 3D diagonal matrix, representing elements on the diagonal as... The phase difference between the two subarrays of the incident signal.

[0019] As a preferred embodiment of the present invention, in step S2, a matrix is ​​constructed based on the first signal subspace. and the matrix The estimated values ​​obtained from eigenvalue decomposition specifically include: Due to the structural rotation invariance of the two subarrays, the received signals from both subarrays are rotation invariant. Therefore, the received signal from the second subarray is equivalent to the received signal from the first subarray multiplied by a rotation factor matrix. ,Right now , where the rotation factor matrix Represented as:

[0020] Then the rotation factor matrix is ​​estimated. You can get Estimation of the elevation angle of each incident signal, while simultaneously eliminating the mutual coupling coefficient matrix. and ,get:

[0021] According to the least squares criterion, we get:

[0022]

[0023] in, The pseudo-inverse matrix represents the first signal subspace matrix formed by the first subarray. make Constructing a matrix :

[0024] Due to the matrix With rotation factor matrix If they are similar matrices, then they have the same eigenvalues. Therefore, for matrices... Eigenvalue decomposition can be used to estimate the rotation factor matrix. The diagonal elements can be obtained. , If pi, then the parameter The estimated value can be obtained by the following formula:

[0025] in, Representation matrix The 1 eigenvalue, This represents the phase angle when taking a complex number.

[0026] In a preferred embodiment of the present invention, step S3 involves re-dividing the uniform array into a third sub-array and a fourth sub-array, and calculating the second signal sub-space based on the signal sub-space. Specifically, this includes selecting the array parallel to the X-axis of the uniform array as the third sub-array and the array parallel to the Y-axis as the fourth sub-array, and determining their mutual coupling matrix. and As shown in the following formula: The third and fourth subarrays received the first The joint steering vectors of the signals are respectively and , and The relationship is:

[0027] in, Then we have:

[0028] in, , , , Representation matrix The 1 eigenvalue, These represent the joint steering matrices of the third and fourth subarrays, respectively. express The minimum solution in; The second signal subspace corresponding to the third and fourth subarrays and They respectively correspond to the signal subspace The He Xing Di Okay, the details are as follows:

[0029]

[0030] in, yes A full-rank transformation matrix of dimension .

[0031] As a preferred embodiment of the present invention, a matrix is ​​constructed based on the second signal subspace. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated values ​​include: According to the least squares criterion, we get:

[0032] in, The pseudo-inverse matrix represents the second signal subspace matrix formed by the third subarray; make Constructing a matrix :

[0033] Due to the matrix With matrix If they are similar matrices, they have the same eigenvalues. Eigenvalue decomposition can yield a matrix Parameters on the diagonal Estimated value.

[0034] As a preferred embodiment of the present invention, step S4 specifically includes: since the feature vector of each signal is unique and has a magnitude of 1, this property can be used for parameter matching. Specifically, the feature vector obtained by DOA estimation is first calculated, and then the feature vector obtained by polarization estimation is multiplied by it to complete the matching process; then the parameters... and The estimated value can be obtained by the following formula:

[0035]

[0036] in, This represents the modulus of a complex number.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) By using a uniform linear array configuration, the mutual polarization coupling between dipoles and the mutual element coupling between adjacent array elements in the electromagnetic vector sensor are effectively alleviated. In addition, the proposed array model significantly expands the effective aperture of the array while reducing hardware costs and achieving more stable parameter estimation performance in complex mutual coupling environments.

[0038] (2) By decoupling the mutual coupling matrix through a novel subarray selection strategy and then performing parameter matching, the influence of mutual coupling on parameter estimation is effectively eliminated. Furthermore, this method does not rely on prior knowledge of the MCM, thus making it more robust and feasible in practical applications. Compared with traditional algorithms, this improved method significantly enhances the accuracy and stability of parameter estimation under strong mutual coupling conditions.

[0039] (3) The overall computational complexity is significantly reduced by using non-common array design and simplified subarray selection strategy. Unlike the traditional EMVS design method that relies on multi-dipole common structure and high-dimensional optimization, the method in this paper effectively suppresses mutual coupling interference under a low-complexity framework and achieves high-precision joint parameter estimation. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the steps of this method; Figure 2 This is a schematic diagram illustrating the effects of mutual coupling between elements parallel to the X-axis. Figure 3 This is a schematic diagram illustrating the effects of mutual coupling between elements parallel to the Y-axis. Figure 4 A schematic diagram illustrating the selection of a new subarray for estimating DOA; Figure 5 A schematic diagram illustrating the selection of a new subarray for estimating polarization parameters; Figure 6 Parameter estimation for three algorithms Comparison diagram; Figure 7 Parameters when the amplitude of the mutual coupling coefficient changes A diagram showing the comparison of RMSE values; Figure 8 Parameters when the amplitude of the mutual coupling coefficient changes A diagram showing the comparison of RMSE values; Figure 9 Parameters when the amplitude of the mutual coupling coefficient changes A diagram showing the comparison of RMSE values; Figure 10 Parameters when signal-to-noise ratio changes A diagram showing the comparison of RMSE values; Figure 11 Parameters when signal-to-noise ratio changes A diagram showing the comparison of RMSE values; Figure 12 Parameters when signal-to-noise ratio changes A diagram showing the comparison of RMSE values. Detailed Implementation

[0041] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. In the following description, the expression "some embodiments" refers to a subset of all possible embodiments; however, it should be understood that "some embodiments" can be the same subset or different subsets of all possible embodiments and can be combined with each other without conflict.

[0042] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0043] It should be understood that the present invention can be embodied in various forms and should not be construed as being limited to the embodiments set forth herein. Rather, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Furthermore, the terminology used herein is intended only to describe particular embodiments and is not intended to limit the invention. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “compose” and / or “comprising,” when used in this specification, identify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups. When used herein, the term “and / or” includes any and all combinations of the associated listed items.

[0044] It should also be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "inner," "outer," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0045] To fully understand this invention, a detailed structure will be presented in the following description to illustrate the technical solution proposed by this invention. Optional embodiments of the invention are described in detail below; however, in addition to these detailed descriptions, the invention may have other embodiments.

[0046] Please refer to the attached document. Figure 1 This application provides a multidimensional parameter estimation method based on a non-common uniform linear array with mutual coupling. The method includes the following steps: Step S1: Construct a uniform linear array, and obtain a received signal model considering mutual coupling interference based on the uniform linear array. Estimate the covariance matrix of the received signal model under the mutual coupling scenario. Perform eigenvalue decomposition on the signal covariance matrix to obtain the signal subspace. Step S2: Divide the uniform array into a first subarray and a second subarray. Calculate the first signal subspace based on the signal subspace, and construct a matrix based on the first signal subspace. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated value; Step S3: Re-divide the uniform array into a third sub-array and a fourth sub-array, calculate the second signal sub-space based on the signal sub-space, and construct the matrix based on the second signal sub-space. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated value; Step S4: Adjust parameters With parameters Perform parameter pairing to obtain parameters With parameters The estimated value.

[0047] Specifically, a uniform linear array (ULA) is composed of... It consists of groups of split dipoles. For ease of description, dipoles are uniformly referred to as "array elements" in this paper. All array elements are uniformly arranged along the Y-axis. Each group of array elements contains two orthogonal components, arranged along the X-axis and Y-axis respectively. The spacing between adjacent groups of array elements... Set as The distance between the two orthogonal dipoles in each group is , which indicates The wavelength of the signal.

[0048] As a preferred embodiment of the present invention, step S1, which involves obtaining a received signal model based on a uniform linear array considering mutual coupling interference, and estimating its covariance matrix under the mutual coupling scenario based on the received signal model, specifically includes: [The text abruptly ends here, so the translation stops as well.] Several far-field, uncorrelated narrowband electromagnetic wave signals are incident on a uniform array, which then performs joint sampling of the signals within the space-polarization domain; among them... and These represent the elevation and azimuth angles of the incident signal, respectively. and These represent the auxiliary polarization angle and polarization phase difference of the incident signal, respectively; No. The information of an incident signal in the spatial-polarized domain can be represented as follows: , which includes spatial vectors and polarization vector and will Its definition is as follows:

[0049]

[0050] in, , indicating the first The spatial phase factor between two dipoles in a set of electric dipoles for an incident signal. Indicates the wavelength of the signal. This represents the distance between two adjacent dipoles. Indicates the first The elevation angle of the incident signal. Indicates the first The azimuth angle of the incident signal. Indicates the first The auxiliary polarization angle of the incident signal. Indicates the first The polarization phase difference of the incident signal, then the... The joint steering vector of a uniform array of incident signals is represented as:

[0051] in, If the Krone Technology operator is used, then the signal received at the output of this array is represented as:

[0052] in, Indicates the received number An incident signal, Then it means If the array outputs a Gaussian white noise vector of dimension 1, then the received signal is... It can be represented as: in, for 1D orientation matrix, for The polarization matrix of dimension, for The spatial-polarization domain joint matrix of dimension 1; Specifically, in practical applications, the mutual coupling problem between antennas is a key issue in antenna array design and array signal processing, especially prominent in polarization-sensitive arrays. Antenna mutual coupling refers to the influence of one antenna array element on its neighboring antenna array elements when transmitting or receiving signals. The mutual coupling effect is mainly caused by the interaction of electromagnetic fields, and is particularly evident in array antennas, and cannot be completely avoided in practical applications.

[0053] Assuming the array elements arranged along the X and Y axes are orthogonal to each other, the mutual coupling effect between orthogonal elements can be ignored, and only the mutual coupling effect between parallel elements needs to be considered. Further assuming that the spacing between two array elements is equal, their mutual coupling coefficient will be the same regardless of whether they are arranged along the X or Y axis. Moreover, the magnitude of the mutual coupling coefficient is closely related to the distance between array elements. When the spacing between array elements exceeds a certain threshold, the mutual coupling effect becomes extremely small or even negligible. The specific effects of mutual coupling between array elements are as follows: Figure 2 and Figure 3 As shown. Therefore, the influence of the uniform matrix under the consideration of mutual coupling scenarios will be defined as a strip-shaped symmetric mutual coupling matrix. :

[0054] in, This indicates that the first electric short dipole is parallel to its second... The mutual coupling coefficient between the short electric dipoles This represents the mutual coupling coefficient of a dipole with respect to itself. The degrees of freedom of the mutual coupling matrix are used to represent the final received signal model considering mutual coupling interference. for:

[0055] The covariance matrix of the uniform array output Represented as:

[0056] in, Indicates the incident signal The autocorrelation matrix, Indicates noise power. express The identity matrix, Represents the signal space. This represents the conjugate transpose of the final received signal model. This represents the conjugate transpose of the spatial-polarization domain joint matrix. Denotes the conjugate transpose of symmetric mutually coupled matrices. This represents the conjugate transpose of the original matrix.

[0057] Specifically, the proposed method achieves DOA estimation through an improved ESPRIT algorithm, and combines it with careful subarray selection to decouple mutual coupling effects. A conventional direct subarray selection method is: ... The array element is treated as a subarray, and the subsequent elements are... The array element acts as another subarray. But This makes it impossible to eliminate the mutual coupling matrix, thus rendering most existing algorithms ineffective. To solve this problem, two new subarrays should be selected to ensure... ; As a preferred embodiment of the present invention, in step S1, the covariance matrix is... The eigenvalue decomposition yields the signal subspace, which specifically includes:

[0058] Among them, matrix sum matrix and represent the contents of the covariance matrix, respectively. A diagonal matrix with different eigenvalues; a matrix sum matrix Corresponding to the signal subspace and noise subspace respectively, and These represent the conjugate transposes of the signal subspace and the noise subspace, respectively.

[0059] In a preferred embodiment of the present invention, step S2 involves dividing the uniform array into a first subarray and a second subarray, calculating the first signal subspace based on the signal subspace, and specifically including the following division method between the first subarray and the second subarray: Figure 4 As shown, from the first Group to No. The first subarray is formed by the group, starting from the first... Group to No. The second subarray is formed by combining the selected subarrays; the mutual coupling coefficient matrix is ​​then obtained from the new subarray. and Through mutual coupling matrices Obtained from a specific submatrix: where the mutual coupling coefficient matrix Depend on The former In the column, the first Arrive at the The first subarray corresponding to each row is formed; and the mutual coupling coefficient matrix Then by After In the column, the first Arrive at the The second subarray corresponding to each row forms the resulting cross-coupling coefficient matrix. With the mutual coupling coefficient matrix They are represented as follows:

[0060] At this time, the mutual coupling coefficient matrix Then the joint space-polarization steering matrices of the corresponding first and second subarrays are respectively and They respectively correspond to the joint steering vector The former and after The first signal subspace spanned by the first subarray and the second subarray is: and They respectively correspond to the signal subspace The former Actions and After The rows are represented as follows:

[0061]

[0062] in, yes The transformation matrix of dimension, because The signals are independent of each other, so the matrix It is a full-rank matrix. Let be the rotation factor matrix. A 3D diagonal matrix, representing elements on the diagonal as... The phase difference between the two subarrays of the incident signal.

[0063] As a preferred embodiment of the present invention, in step S2, a matrix is ​​constructed based on the first signal subspace. and the matrix The estimated values ​​obtained from eigenvalue decomposition specifically include: Due to the structural rotation invariance of the two subarrays, the received signals from both subarrays are rotation invariant. Therefore, the received signal from the second subarray is equivalent to the received signal from the first subarray multiplied by a rotation factor matrix. ,Right now , where the rotation factor matrix Represented as:

[0064] Then the rotation factor matrix is ​​estimated. You can get Estimation of the elevation angle of each incident signal, while simultaneously eliminating the mutual coupling coefficient matrix. and ,get:

[0065] According to the least squares criterion, we get:

[0066]

[0067] in, The pseudo-inverse matrix represents the first signal subspace matrix formed by the first subarray. make Constructing a matrix :

[0068] Due to the matrix With rotation factor matrix If they are similar matrices, then they have the same eigenvalues. Therefore, for matrices... Eigenvalue decomposition can be used to estimate the rotation factor matrix. The diagonal elements can be obtained. , If pi, then the parameter The estimated value can be obtained by the following formula:

[0069] in, Representation matrix The 1 eigenvalue, This represents the phase angle when taking a complex number.

[0070] In a preferred embodiment of the present invention, step S3 involves re-dividing the uniform array into a third sub-array and a fourth sub-array, and calculating a second signal sub-space based on the signal sub-space. Specifically, this includes the following division method for the third and fourth sub-arrays: Figure 5 As shown, the uniform array parallel to the X-axis is selected as the third subarray, and the array parallel to the Y-axis is selected as the fourth subarray. Their mutual coupling matrix is... and As shown in the following formula: The third and fourth subarrays received the first The joint steering vectors of the signals are respectively and , and The relationship is: .

[0071] in, and They are represented as follows:

[0072]

[0073] again Then we have:

[0074] in, , , , Representation matrix The 1 eigenvalue, These represent the joint steering matrices of the third and fourth subarrays, respectively. express The minimum solution in; The second signal subspace corresponding to the third and fourth subarrays and They respectively correspond to the signal subspace The He Xing Di Okay, the details are as follows:

[0075]

[0076] in, yes A full-rank transformation matrix of dimension .

[0077] As a preferred embodiment of the present invention, a matrix is ​​constructed based on the second signal subspace. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated values ​​include: According to the least squares criterion, we get:

[0078] in, The pseudo-inverse matrix represents the second signal subspace matrix formed by the third subarray; make Constructing a matrix :

[0079] Due to the matrix With matrix If they are similar matrices, they have the same eigenvalues. Eigenvalue decomposition can yield a matrix Parameters on the diagonal Estimated value.

[0080] As a preferred embodiment of the present invention, step S4 specifically includes: since the feature vector of each signal is unique and has a magnitude of 1, this property can be used for parameter matching. Specifically, the feature vector obtained by DOA estimation is first calculated, and then the feature vector obtained by polarization estimation is multiplied by it to complete the matching process; then the parameters... and The estimated value can be obtained by the following formula:

[0081]

[0082] in, This represents the modulus of a complex number.

[0083] For example, this invention evaluates the effectiveness and performance of the proposed method through three experiments. The root mean square error (RMSE) is used to measure the accuracy of the algorithm in parameter estimation, specifically defined as follows:

[0084] in, express In the 1st Monte Carlo simulation experiment, the 1st The estimated DOA or polarization parameter of a signal; Indicates the first The true value of the DOA or polarization parameter of the incident signal.

[0085] In the simulation experiment study, it is assumed that the uniform array is composed of The array is composed of groups of elements, each group containing two mutually orthogonal and non-competitive electric dipoles, arranged in a uniform linear array. The distance between adjacent elements is... In all simulation experiments, the mutual coupling coefficient vector between each component was set to... .

[0086] In the first experiment, we verified the effectiveness of the proposed algorithm and compared it with the undecoupled ESPRIT and RD-MUSIC algorithms in terms of angle. The performance in terms of estimation was compared. Assume a far-field narrowband signal is incident on the array, and its signal parameters are set as follows: , , The number of snapshots is... The signal-to-noise ratio is The three algorithms differ in parameters. The estimated performance comparisons are shown in Figure 6. The solid black lines in the figure represent... The true value is represented by three colors, which indicate the estimated values ​​obtained in multiple Monte Carlo simulations. The proposed method exhibits high stability, with the estimated values ​​fluctuating only slightly around the true value, showing minimal bias, and remains robust to noise and mutual coupling interference.

[0087] In contrast, the traditional ESPRIT algorithm has a larger estimation error, with its estimated values ​​deviating significantly from the true values, resulting in poor accuracy and lack of robustness to disturbances. While the RD-MUSIC algorithm outperforms ESPRIT, it still exhibits a larger bias compared to our proposed method, indicating its greater sensitivity to mutual coupling effects, which leads to a decrease in estimation accuracy.

[0088] The above results demonstrate that our proposed method outperforms the other two methods in both accuracy and stability, with its estimation results consistently closely aligned with the true values. In contrast, the ESPRIT algorithm exhibits significant bias and is highly sensitive to noise and mutual coupling. Although RD-MUSIC represents an improvement over ESPIRIT, it still demonstrates a higher estimation error compared to our proposed method.

[0089] This section analyzes the impact of the magnitude of the mutual coupling coefficients on parameter estimation and compares it with the traditional undecoupled ESPRIT algorithm and RD-MUSIC algorithm. Assume that... A far-field narrowband signal with DOA parameter and polarization parameters , Incident on the array. The signal-to-noise ratio is fixed at... Quick shot number , the mutual coupling coefficients , The magnitude of the error was increased from 0 to 1 in increments of 0.1. 1000 Monte Carlo experiments were conducted to compare and observe the root mean square error (RMSE). Figure 7 Three algorithms were demonstrated. Comparison of the impact of the magnitude of the cross-coupling coefficients on the root mean square error (RMSE) in parameter estimation. Figure 8 and Figure 9 Showing Parameter estimation and Comparison of the magnitude of the mutual coupling coefficients with the root mean square error (RMSE) in parameter estimation.

[0090] Figure 7 This demonstrates how different algorithms affect the DOA parameter as the magnitude of the cross-coupling coefficient increases from 0 to 1. The proposed algorithm maintains a low root mean square error (RMSE) across the entire range of mutual coupling coefficients. In contrast, the RMSE of the traditional undecoupled ESPRIT algorithm increases rapidly with the magnitude of the mutual coupling coefficients, indicating its poor performance in high-mutual-coupling scenarios and resulting in inaccurate parameter estimation. Furthermore, the estimation accuracy of the RD-MUSIC algorithm is consistently lower than that of the proposed method. Notably, when the mutual coupling coefficients are small, the traditional undecoupled ESPRIT algorithm slightly outperforms the proposed algorithm. This is because the undecoupled algorithm utilizes more array elements, and in low-mutual-coupling scenarios, the number of array elements significantly impacts estimation accuracy. However, the proposed algorithm achieves effective decoupling by sacrificing some array elements. This allows the proposed algorithm to significantly outperform the undecoupled algorithm even when array mutual coupling effects are enhanced, while maintaining a low estimation error and demonstrating stronger stability and robustness.

[0091] exist Figure 8 and Figure 9 The paper demonstrates the effects of three algorithms on the polarization auxiliary angle under different mutual coupling coefficient magnitudes. and polarization phase difference The root mean square error (RMSE) of the estimation is calculated. As the magnitude of the mutual coupling coefficients increases, the estimation errors of the traditional undecoupled ESPRIT and RD-MUSIC algorithms gradually increase. In contrast, the algorithm presented in this paper maintains a lower error under a wide range of mutual coupling conditions. This result further verifies that the proposed algorithm can achieve more stable parameter estimation in environments with significant mutual coupling effects, and still exhibits significant anti-interference performance even with a reduced number of array elements.

[0092] In this embodiment, the impact of signal-to-noise ratio (SNR) on parameter estimation is investigated and compared with the traditional undecoupled ESPRIT and RD-MUSIC algorithms. The same incident signal parameters as in the previous experiment are used. The number of snapshots is fixed. Signal-to-noise ratio from Increase to 1000 Monte Carlo simulations were conducted to compare and observe the root mean square error (RMSE).

[0093] Figure 10 Three methods are shown for DOA parameters. Comparison of signal-to-noise ratio magnitude with root mean square error (RMSE) in estimation. Figure 11 and Figure 12 Three methods were demonstrated in terms of parameters. Estimate and A comparison of the impact of signal-to-noise ratio (SNR) on the root mean square error (RMSE) during estimation. Figure 10As can be seen, the estimation error of all algorithms decreases with increasing signal-to-noise ratio (SNR). However, at lower SNRs, the estimation error of the traditional undecoupled ESPRIT algorithm is significantly greater than that of the decoupled algorithm proposed in this paper. Although the RD-MUSIC algorithm exhibits some stability, its estimation accuracy is still inferior to that of the proposed algorithm. In contrast, the proposed algorithm can significantly reduce the estimation error even with mutual coupling and demonstrates higher robustness under low SNR conditions.

[0094] Figure 11 and Figure 12 The three algorithms were further demonstrated in estimating the polarization auxiliary angle. and polarization phase difference The root mean square error (RMSE) results are shown. As the signal-to-noise ratio increases, the algorithm... and The root mean square error (RMSE) in the estimation is significantly lower than that of the undecoupled ESPRIT and RD-MUSIC algorithms, and this advantage is even more pronounced under low signal-to-noise ratio (SNR) conditions. This result demonstrates that the proposed algorithm is superior in effectively suppressing the influence of mutual coupling effects on parameter estimation and can maintain high estimation accuracy and stability under various SNR conditions.

[0095] Experimental results show that the proposed algorithm outperforms the ESPRIT and RD-MUSIC algorithms in terms of estimation accuracy, anti-coupling capability, and noise interference resistance. Table 1 summarizes the key performance indicators, including the range of root mean square error (RMSE) under different coupling and signal-to-noise ratio (SNR) conditions. These results demonstrate that the proposed method can effectively suppress the coupling effect and maintain a low estimation error under different SNR conditions, making it a more reliable and practical scheme for joint estimation of DOA and polarization parameters.

[0096] Table 1 Comparison of different algorithms

[0097] This invention proposes a novel multidimensional parameter estimation method based on a non-common cross-dipole array model, applicable to scenarios with mutual coupling interference. This method effectively eliminates the influence of the mutual coupling matrix by combining the ESPRIT algorithm with a subarray selection strategy, significantly reducing the interference of mutual coupling effects while achieving high-precision parameter estimation. Simulation results show that this method exhibits good robustness under different signal-to-noise ratios and mutual coupling strengths. Compared with this method, when the mutual coupling strength increases from a low level to a high level, the estimation error of the traditional ESPRIT algorithm is approximately -7.9% to 454.28% higher, and under different signal-to-noise ratios, its estimation error increases by 148.55% to 2329.22%. Similarly, the RD-MUSIC algorithm's estimation error increases by 29.91% to 83.22% during changes in mutual coupling strength, and by 33.73% to 351.11% under changes in signal-to-noise ratio. Therefore, this method shows good application potential in real-world environments where mutual coupling is unavoidable.

[0098] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multidimensional parameter estimation method based on a non-common uniform linear array mutual coupling scenario, characterized in that, The method includes the following steps: Step S1: Construct a uniform linear array. Based on the uniform linear array, consider mutual coupling interference to obtain the received signal model. Estimate its covariance matrix according to the received signal model under the mutual coupling scenario. Perform eigenvalue decomposition on the signal covariance matrix to obtain the signal subspace. Step S2: Divide the uniform array into a first subarray and a second subarray. Calculate the first signal subspace based on the signal subspace, and construct a matrix based on the first signal subspace. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated value; Step S3: Re-divide the uniform array into a third sub-array and a fourth sub-array. Calculate the second signal sub-space based on the signal sub-space, and construct the matrix based on the second signal sub-space. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated value; Step S4: Adjust parameters With parameters Perform parameter pairing to obtain parameters With parameters The estimated value.

2. The multidimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario according to claim 1, characterized in that, In step S1, the received signal model is obtained by considering mutual coupling interference based on a uniform linear array. Estimating the covariance matrix of the received signal model under the mutual coupling scenario specifically includes: It has Several far-field, uncorrelated narrowband electromagnetic wave signals are incident on a uniform array, which then performs joint sampling of the signals within the space-polarization domain; among them... and These represent the elevation and azimuth angles of the incident signal, respectively. and These represent the auxiliary polarization angle and polarization phase difference of the incident signal, respectively; No. The information of an incident signal in the spatial-polarized domain can be represented as follows: , which includes spatial vectors and polarization vector and will Its definition is as follows: in, , indicating the first The spatial phase factor between two dipoles in a set of electric dipoles for an incident signal. Indicates the wavelength of the signal. This represents the distance between two adjacent dipoles. Indicates the first The elevation angle of the incident signal. Indicates the first The azimuth angle of the incident signal. Indicates the first The auxiliary polarization angle of the incident signal. Indicates the first The polarization phase difference of the incident signal is then the... The joint steering vector of a uniform array of incident signals is represented as: in, If the Krone Technology operator is used, then the signal received at the output of this array is represented as: in, Indicates the received number An incident signal, Then it means If the array outputs a Gaussian white noise vector of dimension 1, then the received signal is... It can be represented as: in, for 1D orientation matrix, for The polarization matrix of dimension, for The spatial-polarization domain joint matrix of dimension 1; The effect on the uniform matrix under the consideration of mutual coupling scenarios will be defined as a strip-shaped symmetric mutual coupling matrix. : in, This indicates that the first electric short dipole is parallel to its second... The mutual coupling coefficient between the short electric dipoles This represents the mutual coupling coefficient of a dipole with respect to itself. Let represent the degrees of freedom of the mutual coupling matrix, then consider the final received signal model considering mutual coupling interference. for: The covariance matrix of the uniform array output Represented as: in, Indicates the incident signal The autocorrelation matrix, Indicates noise power. express The identity matrix, Represents the signal space. This represents the conjugate transpose of the final received signal model. This represents the conjugate transpose of the spatial-polarization domain joint matrix. Denotes the conjugate transpose of symmetric mutually coupled matrices. This represents the conjugate transpose of the original matrix.

3. The multidimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario according to claim 2, characterized in that, In step S1, the covariance matrix is... The eigenvalue decomposition yields the signal subspace, which specifically includes: Among them, matrix sum matrix and represent the contents of the covariance matrix, respectively. A diagonal matrix with different eigenvalues; a matrix sum matrix Corresponding to the signal subspace and noise subspace respectively, and These represent the conjugate transposes of the signal subspace and the noise subspace, respectively.

4. The multidimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario according to claim 3, characterized in that, In step S2, the uniform array is divided into a first subarray and a second subarray. The first signal subspace is calculated based on the signal subspace, and the specific steps based on the first signal subspace include: From the Group to No. The first subarray is formed by the group, starting from the first... Group to No. The second subarray is formed by combining the selected subarrays; the mutual coupling coefficient matrix is ​​then obtained from the new subarray. and Through mutual coupling matrices Obtained from a specific submatrix: where the mutual coupling coefficient matrix Depend on The former In the column, the first Arrive at the The first subarray corresponding to each row is formed; and the mutual coupling coefficient matrix Then by After In the column, the first Arrive at the The second subarray corresponding to each row forms the resulting cross-coupling coefficient matrix. With the mutual coupling coefficient matrix They are represented as follows: At this time, the mutual coupling coefficient matrix Then the joint space-polarization steering matrices of the corresponding first and second subarrays are respectively and They respectively correspond to the joint steering vector The former and after The first signal subspace spanned by the first subarray and the second subarray are respectively and They respectively correspond to the signal subspace The former Actions and After The rows are represented as follows: in, yes The transformation matrix of dimension, because The signals are independent of each other, so the matrix It is a full-rank matrix. Let be the rotation factor matrix. A 3D diagonal matrix, representing elements on the diagonal as... The phase difference between the two subarrays of the incident signal.

5. The multidimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario according to claim 4, characterized in that, In step S2, a matrix is ​​constructed based on the first signal subspace. and the matrix The estimated values ​​obtained from eigenvalue decomposition specifically include: Due to the structural rotation invariance of the two subarrays, the received signals from both subarrays are rotation invariant. Therefore, the received signal from the second subarray is equivalent to the received signal from the first subarray multiplied by a rotation factor matrix. ,Right now , where the rotation factor matrix Represented as: Then the rotation factor matrix is ​​estimated. You can get Estimation of the elevation angle of each incident signal, while simultaneously eliminating the mutual coupling coefficient matrix. and ,get: According to the least squares criterion, we get: in, The pseudo-inverse matrix represents the first signal subspace matrix formed by the first subarray. make Constructing a matrix : Due to the matrix With rotation factor matrix If they are similar matrices, then they have the same eigenvalues. Therefore, for matrices... Eigenvalue decomposition can be used to estimate the rotation factor matrix. The diagonal elements can be obtained. , If pi, then the parameter The estimated value can be obtained by the following formula: in, Representation matrix The 1 eigenvalue, This represents the phase angle when taking a complex number.

6. The multidimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario according to claim 5, characterized in that, In step S3, the uniform array is re-divided into a third sub-array and a fourth sub-array. The second signal sub-space is calculated based on the signal sub-space. Specifically, this includes selecting the array parallel to the X-axis as the third sub-array and the array parallel to the Y-axis as the fourth sub-array, and determining their mutual coupling matrix. and As shown in the following formula: The third and fourth subarrays received the first The joint steering vectors of the signals are respectively and , and The relationship is: in, Then we have: in, , , , Representation matrix The 1 eigenvalue, These represent the joint steering matrices of the third and fourth subarrays, respectively. express The minimum solution in; The second signal subspace corresponding to the third and fourth subarrays and They respectively correspond to the signal subspace The He Xing Di Okay, the details are as follows: in, yes A full-rank transformation matrix of dimension .

7. The multidimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario according to claim 6, characterized in that, And construct a matrix based on the second signal subspace. and the matrix The parameters are obtained by performing eigenvalue decomposition. The estimated values ​​include: According to the least squares criterion, we get: in, The pseudo-inverse matrix represents the second signal subspace matrix formed by the third subarray; make Constructing a matrix : Due to the matrix With matrix If they are similar matrices, they have the same eigenvalues. Eigenvalue decomposition can yield a matrix Parameters on the diagonal Estimated value.

8. The multidimensional parameter estimation method based on the non-common uniform linear array mutual coupling scenario according to claim 7, characterized in that, Step S4 specifically includes: Since the feature vector of each signal is unique and has a magnitude of 1, this property can be used for parameter matching. Specifically, the feature vector obtained through DOA estimation is first calculated, and then the feature vector obtained through polarization estimation is multiplied by it to complete the matching process; then the parameters... and The estimated value can be obtained by the following formula: in, This represents the modulus of a complex number.

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