Robust Beamforming Method Based on Covariance Matrix Quadratic Reconstruction

Abstract

This application relates to a robust beamforming method based on secondary reconstruction of the covariance matrix. The method includes: calculating the power spectrum of the radar echo signal using the sampled covariance matrix and estimating the DOA of the interference signal based on the power spectrum; reconstructing the interference covariance matrix over an integral interval of a certain size to obtain an initial reconstructed interference plus noise covariance matrix; performing eigenvalue decomposition on the initial reconstructed interference plus noise covariance matrix to calculate the interference signal power and the optimized interference signal steering vector; secondary reconstruction of the interference covariance matrix based on the interference signal power and the optimized interference signal steering vector; solving for the optimized desired signal steering vector using the RCB algorithm; calculating the optimal adaptive weight vector based on the optimized desired signal steering vector and the secondary reconstructed interference plus noise covariance matrix; and performing robust beam output based on the optimal adaptive vector. This method can improve beamforming accuracy under various error factors.

Description

Technical Field

[0001] This application relates to the field of array signal processing technology, and in particular to a robust beamforming method based on covariance matrix quadratic reconstruction. Background Technology

[0002] Adaptive beamforming is an important research direction in the field of array signal processing, widely used in radar, sonar, wireless communication, speech processing, medical imaging, and other fields. Its essence is that, based on changes in the signal environment, the antenna array uses an adaptive algorithm to weight each element, performing spatial filtering on the received signal. This allows the array beam's main lobe to point towards the desired signal and creates nulls in the interference direction, improving the output signal-to-interference-and-noise ratio (SINR). In practical operation of array antennas, various errors are often unavoidable, mainly including: direction of arrival (DOA) estimation errors, amplitude and phase perturbation errors, array geometric errors, and incoherent local scattering, leading to deviations between the actual and ideal signal steering vectors. Due to these errors, at low SNR, beam main lobe shift may occur, resulting in a decrease in output SINR; at high SNR, if the desired signal is present in the sampling covariance matrix, target "self-cancellation" may occur, causing a sharp deterioration in output SINR.

[0003] To address the performance degradation of traditional Capon beamformers caused by the aforementioned errors, several robust beamforming algorithms have emerged: 1) Diagonal loading algorithms: By adding a diagonal matrix consisting of a constant to the sampling covariance matrix, the influence of noise eigenvectors on the weight vector during beamforming is reduced, but the optimal loading amount is difficult to determine; 2) Feature subspace algorithms: Constructing a projection matrix of the signal subspace, projecting and correcting the assumed steering vector, and removing components not belonging to the signal subspace, thereby estimating a more accurate desired signal steering vector. This method exhibits good robustness at high SNR and with a known number of signal interferences, but at low SNR or with an unknown number of signal sources, subspace entanglement is prone to occur, leading to a degradation in beamformer performance; 3) Worst-case performance optimization algorithms: Predicting the desired signal steering vector based on prior information, modeling the true steering vector as the sum of the predicted steering vector and an arbitrary estimation error vector, while limiting the norm of the estimation error vector to be less than or equal to a certain known constant. This algorithm constrains the mismatched steering vector within a spherical uncertainty set, but does not provide any closed-form solution. The choice of the constraint range affects the beamformer performance. 4) Robust Capon Beamforming (RCB) algorithm: Under the condition of maximizing the desired signal output power, the desired signal steering vector is constrained within an uncertainty set, thereby solving for the desired signal steering vector. In practical applications, when the target steering vector is severely mismatched, a large uncertainty set is needed to constrain the desired signal steering vector, but an excessively large uncertainty set will reduce the beamformer's noise and interference suppression performance.

[0004] The main problems with existing technologies are: 1) When various error factors exist, such as signal arrival estimation error, amplitude and phase perturbation error, array geometric error, and incoherent local scattering, directly using the sampling covariance matrix is ​​inaccurate; 2) In practical applications, the desired signal often exists in the received signal sample. Using the sampling covariance matrix containing the desired signal to replace the actual interference plus noise covariance matrix will still result in target "self-cancellation" when the input SNR is high; 3) Most existing methods only correct the error of the steering vector of the desired signal. When interference exists, the steering vector of the interference signal also has various error factors. Because this part of the error is not corrected, the covariance matrix error is large. In summary, the performance of existing beamforming algorithms is insufficient and needs further improvement. Summary of the Invention

[0005] Therefore, it is necessary to provide a robust beamforming method based on covariance matrix quadratic reconstruction that can improve beamforming accuracy under various error factors, addressing the aforementioned technical problems.

[0006] A robust beamforming method based on second-order reconstruction of the covariance matrix, the method comprising:

[0007] An omnidirectional uniform planar array is used to receive and acquire radar echo signals and calculate the sampling covariance matrix. The power spectrum of the radar echo signal is calculated using the sampling covariance matrix, and the DOA of the interference signal is estimated based on the power spectrum outside the angular range of the desired signal DOA. The interference covariance matrix is ​​reconstructed with a pre-set integration interval of a certain size. The noise covariance matrix is ​​added to the interference covariance matrix to obtain the initial reconstructed interference plus noise covariance matrix.

[0008] The eigenvalues ​​and noise subspace are obtained by performing eigenvalue decomposition on the initially reconstructed interference plus noise covariance matrix; the interference signal power is calculated based on the maximum eigenvalues; and the optimized interference signal steering vector is solved by convex optimization method using the projection matrix of the noise subspace and the estimated interference signal steering vector.

[0009] The interference covariance matrix is ​​reconstructed twice based on the interference signal power and the optimized interference signal steering vector. The noise covariance matrix is ​​then added to the reconstructed interference covariance matrix to obtain the second-reconstructed interference plus noise covariance matrix.

[0010] The sampling covariance matrix and the estimated desired signal steering vector are used as inputs to the RCB algorithm to solve for the optimized desired signal steering vector. The optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the covariance matrix of secondary reconstruction interference plus noise. Robust beam output is then performed based on the optimal adaptive vector.

[0011] In one embodiment, the sampling covariance matrix is ​​calculated as follows:

[0012]

[0013] in, Indicates the number of snapshots. This indicates the conjugate transpose. Indicates the first A quick snapshot of the radar echo signal.

[0014] In one embodiment, the power spectrum of the radar echo signal is calculated using the sampling covariance matrix, including:

[0015] The power spectrum of the radar echo signal is calculated using the sampling covariance matrix.

[0016]

[0017] in, Represents the sampling covariance matrix. This represents the guide vector. This represents the azimuth region of the entire observation interval. This indicates the azimuth region corresponding to the desired signal. This indicates the azimuth region corresponding to the interference signal. This indicates the azimuth region corresponding to the noise. This represents the pitch angle range across the entire observation interval. This indicates the pitch angle region corresponding to the desired signal. This indicates the pitch angle region corresponding to the interference signal. This indicates the pitch angle region corresponding to the noise.

[0018] In one embodiment, the DOA of the interference signal is estimated based on the power spectrum being outside the angular range of the desired signal DOA. The interference covariance matrix is ​​reconstructed using a pre-set integration interval of a certain size. A noise covariance matrix is ​​added to the interference covariance matrix to obtain the initial reconstructed interference plus noise covariance matrix, including:

[0019] The DOA of the interference signal is estimated based on the power spectrum outside the angular range of the desired signal DOA. The interference covariance matrix is ​​reconstructed using a pre-set integration interval of a certain size. The noise covariance matrix is ​​then added to the interference covariance matrix to obtain the initial reconstructed interference-plus-noise covariance matrix.

[0020]

[0021] in, For noise power, Power spectrum containing interference signals The integration interval of a certain size is set in advance. The power spectrum representing noise. This indicates the conjugate transpose. For the sampling covariance matrix, Indicates the guide vector. Represents the identity matrix. This represents the noise covariance matrix.

[0022] In one embodiment, eigenvalue decomposition is performed on the initial reconstructed interference plus noise covariance matrix to obtain the maximum eigenvalue and the noise subspace, including:

[0023] Eigenvalues ​​are obtained by performing eigenvalue decomposition on the initial reconstructed interference plus noise covariance matrix. ,in, It is a unitary matrix composed of eigenvectors. ; It is a diagonal matrix composed of eigenvalues. , The eigenvalues ​​in satisfy , eigenvectors and The eigenvalues ​​in the model correspond one-to-one;

[0024] After taking The eigenvectors constitute the noise subspace. Construct the projection matrix of the noise subspace .

[0025] In one embodiment, the interference signal power is calculated based on the maximum eigenvalue, including:

[0026] The interference signal power is calculated based on the maximum eigenvalue.

[0027]

[0028] in, Represents the largest eigenvalue. For noise power, Indicates the number of array elements.

[0029] In one embodiment, the optimized interference signal steering vector is solved using a convex optimization method based on the projection matrix of the noise subspace and the estimated interference signal steering vector, including:

[0030] Using the projection matrix of the noise subspace and the estimated interference signal steering vector, the optimized interference signal steering vector is obtained through a convex optimization method.

[0031]

[0032] in, Describing the 2-norm, It is a local minimum. This represents the optimized interference signal steering vector. The projection matrix of the noise subspace is represented. This represents the estimated steering vector of the interference signal. This indicates the conjugate transpose.

[0033] In one embodiment, the interference covariance matrix is ​​reconstructed twice based on the interference signal power and the optimized interference signal steering vector. A noise covariance matrix is ​​then added to the reconstructed interference covariance matrix to obtain a second-reconstructed interference plus noise covariance matrix, including:

[0034] Based on the interference signal power and the optimized interference signal steering vector, the interference covariance matrix is ​​reconstructed twice. Then, a noise covariance matrix is ​​added to the reconstructed interference covariance matrix to obtain the second-order reconstructed interference plus noise covariance matrix.

[0035]

[0036] in, This represents the second-order reconstruction interference covariance matrix. Represents the noise covariance matrix. Indicates the power of the interference signal. This represents the optimized interference signal steering vector. This indicates the conjugate transpose. For noise power, Represents the identity matrix. Represents the noise covariance matrix. This represents the total number of interfering signals.

[0037] In one embodiment, the sampling covariance matrix and the estimated desired signal steering vector are used as inputs to the RCB algorithm to solve for the optimized desired signal steering vector, including:

[0038] Using the sampling covariance matrix and the estimated desired signal steering vector as inputs to the RCB algorithm, the optimized desired signal steering vector is obtained as follows:

[0039]

[0040] in, As a preset value, For the sampling covariance matrix, The steering vector for the predicted desired signal. The optimized desired signal steering vector, This indicates the conjugate transpose.

[0041] In one embodiment, the optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the covariance matrix of the secondary reconstruction interference plus noise, including:

[0042] The optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the covariance matrix of the secondary reconstruction interference plus noise.

[0043]

[0044] in, The second-order reconstruction interference plus noise covariance matrix, The optimized desired signal steering vector, This indicates the conjugate transpose.

[0045] The robust beamforming method based on secondary reconstruction of the covariance matrix described above, in this application, integrates the small-angle sector containing the interference signal based on the Capon power spectrum of the radar echo signal to initially reconstruct the interference plus noise covariance matrix. This can fundamentally eliminate the desired signal component in the covariance matrix, thereby effectively avoiding the target "self-cancellation" phenomenon. The initial reconstructed interference plus noise covariance matrix is ​​subjected to eigenvalue decomposition to obtain the maximum eigenvalue and the noise subspace. The interference signal power is calculated based on the maximum eigenvalue. The optimized interference signal steering vector is solved using a convex optimization method with the projection matrix of the noise subspace and the estimated interference signal steering vector. The interference covariance matrix is ​​then reconstructed a second time based on the interference signal power and the optimized interference signal steering vector. Finally, a noise covariance matrix is ​​added to the second-reconstructed interference covariance matrix to obtain the secondary-reconstructed interference plus noise covariance matrix. The initial reconstructed interference-noise covariance matrix is ​​eigenvalued to construct a projection matrix of the noise subspace. The interference signal steering vector is then corrected by projection, improving the orthogonality between the interference and noise subspaces. This leads to a more accurate estimation of the interference signal steering vector and a more precise reconstruction of the interference-noise covariance matrix, thus improving the accuracy of generating the optimal adaptive weight vector. Finally, the sampled covariance matrix and the estimated desired signal steering vector are used as inputs to the RCB algorithm to solve for the optimized desired signal steering vector. The optimal adaptive weight vector is then calculated based on the optimized desired signal steering vector and the secondary reconstructed interference-noise covariance matrix. Because both the desired and interference signal steering vectors are corrected separately, robust adaptive beamforming is still possible even when both the desired and interference signals have simultaneous errors such as direction-of-arrival estimation errors, amplitude and phase perturbation errors, and array geometry errors, resulting in a high output SINR. This application demonstrates excellent robustness to various error factors, including direction-of-arrival estimation errors, amplitude and phase perturbation errors, array geometry errors, and incoherent local scattering, making it a valuable engineering reference. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating a robust beamforming method based on second-order reconstruction of the covariance matrix in one embodiment.

[0047] Figure 2 This is a schematic diagram illustrating the relationship between the output SINR and input SNR of six algorithms under the DOA error condition in one embodiment.

[0048] Figure 3 This is a schematic diagram illustrating the relationship between the output SINR and the number of snapshots for six algorithms under the DOA error condition in one embodiment.

[0049] Figure 4 This is a schematic diagram illustrating the relationship between the output SINR and DOA error of six algorithms in one embodiment;

[0050] Figure 5 This is a schematic diagram illustrating the relationship between the output SINR and input SNR of six algorithms under amplitude and phase error conditions in one embodiment.

[0051] Figure 6 This is a schematic diagram illustrating the relationship between the output SINR and the number of snapshots for six algorithms under the condition of amplitude and phase error in one embodiment.

[0052] Figure 7 This is a schematic diagram illustrating the relationship between the output SINR and input SNR of six algorithms under array geometric error conditions in one embodiment.

[0053] Figure 8 This is a schematic diagram illustrating the relationship between the output SINR and the number of snapshots for six algorithms under the condition of array geometric error in one embodiment.

[0054] Figure 9 This is a schematic diagram illustrating the relationship between the output SINR and input SNR of six algorithms in the case of incoherent local scattering in one embodiment.

[0055] Figure 10 This is a schematic diagram illustrating the relationship between the output SINR and the number of snapshots for six algorithms in the case of incoherent local scattering in one embodiment. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0057] In one embodiment, such as Figure 1 As shown, a robust beamforming method based on second-order reconstruction of the covariance matrix is ​​provided, including the following steps:

[0058] Step 102: The radar echo signal is received and the sampling covariance matrix is ​​calculated using an omnidirectional uniform planar array. The power spectrum of the radar echo signal is calculated using the sampling covariance matrix. The DOA of the interference signal is estimated based on the power spectrum outside the angular range of the desired signal DOA. The interference covariance matrix is ​​reconstructed using a pre-set integration interval of a certain size. The noise covariance matrix is ​​added to the interference covariance matrix to obtain the initial reconstructed interference plus noise covariance matrix.

[0059] The number of array elements is A vertically placed omnidirectional uniform planar array with an element spacing of half a wavelength, receiving signals from... Signals from different directions (including one desired signal, (Several interference signals), assuming that the signal, interference, and noise are independent of each other, and that the noise in each channel is zero-mean Gaussian white noise. The array in The radar echo signal received at any time is :

[0060]

[0061] In the formula, These are the azimuth and elevation angles of the desired signal, respectively. The desired signal steering vector; The complex envelope of the desired signal; These are the azimuth and elevation angles of the interference signal, respectively. Steering vector for interference signals; For the complex envelope of the interference signal; It is Gaussian white noise.

[0062] The sampling covariance matrix of the array received signal is expressed as:

[0063]

[0064] In the formula, Indicates the number of snapshots. This indicates the conjugate transpose.

[0065] Then, the DOA of the interfering signal is estimated outside the angular range of the desired signal DOA using the Capon power spectrum, and the predicted steering vector of the interfering signal is calculated based on the DOA of the interfering signal. The Capon power spectrum is expressed as:

[0066]

[0067] The power spectrum estimate of the noise is expressed as:

[0068]

[0069] In the formula, For noise power, This indicates the area where the noise is located.

[0070] Since the power of the received interference signal is stronger than the power of the noise (weak interference can be considered as noise), the interference integration sector must meet the following conditions:

[0071]

[0072] In the formula, It is a constant greater than 1.

[0073] The initial reconstructed interference plus noise covariance matrix is:

[0074]

[0075] In the formula, A pre-defined small integrating sector containing interference signals.

[0076] By integrating the small-angle sector containing the interference signal based on the Capon power spectrum, the interference plus noise covariance matrix can be initially reconstructed. This can fundamentally eliminate the desired signal component in the covariance matrix, thereby effectively avoiding the "self-cancellation" phenomenon of the target.

[0077] Step 104: Perform eigenvalue decomposition on the initially reconstructed interference plus noise covariance matrix to obtain the maximum eigenvalue and noise subspace; calculate the interference signal power based on the maximum eigenvalue; and solve for the optimized interference signal steering vector using the projection matrix of the noise subspace and the estimated interference signal steering vector through a convex optimization method.

[0078] Step 106: Based on the interference signal power and the optimized interference signal steering vector, reconstruct the interference covariance matrix twice, and add the noise covariance matrix to the reconstructed interference covariance matrix to obtain the reconstructed interference plus noise covariance matrix.

[0079] The interference plus noise covariance matrix is ​​decomposed into eigenvalues ​​to construct the projection matrix of the noise subspace. The interference signal steering vector is then corrected by projection to improve the orthogonality between the interference subspace and the noise subspace. This allows for a more accurate estimation of the interference signal steering vector and the reconstruction of a more precise interference plus noise covariance matrix, which helps to improve the accuracy of generating the optimal adaptive weight vector.

[0080] Step 108: The sampling covariance matrix and the estimated desired signal steering vector are used as inputs to the RCB algorithm to solve for the optimized desired signal steering vector; the optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the covariance matrix of secondary reconstruction interference plus noise; and robust beam output is performed based on the optimal adaptive vector.

[0081] Based on the interference plus noise covariance matrix of the second reconstruction and the optimized desired signal steering vector Solve for the optimal adaptive weight vector:

[0082]

[0083] The antenna array output signal is:

[0084] .

[0085] Because this application corrects the desired signal steering vector and the interference signal steering vector separately, it can still perform robust adaptive beamforming when both the desired signal and the interference signal have factors such as direction of arrival estimation error, amplitude and phase perturbation error, and array geometric error, and has a high output SINR.

[0086] In the robust beamforming method based on secondary reconstruction of the covariance matrix described above, this application integrates the small-angle sector where the interference signal is located based on the Capon power spectrum of the radar echo signal to initially reconstruct the interference plus noise covariance matrix. This can fundamentally eliminate the desired signal component in the covariance matrix, thereby effectively avoiding the "self-cancellation" phenomenon of the target. The initially reconstructed interference plus noise covariance matrix is ​​eigenvalued by eigenvalue decomposition to obtain the maximum eigenvalue and the noise subspace. The interference signal power is calculated based on the maximum eigenvalue. The optimized interference signal steering vector is solved using a convex optimization method with the projection matrix of the noise subspace and the estimated interference signal steering vector. The interference covariance matrix is ​​then reconstructed a second time based on the interference signal power and the optimized interference signal steering vector. Finally, a noise covariance matrix is ​​added to the second-reconstructed interference covariance matrix to obtain the second-reconstructed interference plus noise covariance matrix. The initial reconstructed interference-noise covariance matrix is ​​eigenvalued to construct a projection matrix of the noise subspace. The interference signal steering vector is then corrected by projection, improving the orthogonality between the interference and noise subspaces. This leads to a more accurate estimation of the interference signal steering vector and a more precise reconstruction of the interference-noise covariance matrix, thus improving the accuracy of generating the optimal adaptive weight vector. Finally, the sampled covariance matrix and the estimated desired signal steering vector are used as inputs to the RCB algorithm to solve for the optimized desired signal steering vector. The optimal adaptive weight vector is then calculated based on the optimized desired signal steering vector and the secondary reconstructed interference-noise covariance matrix. Because both the desired and interference signal steering vectors are corrected separately, robust adaptive beamforming is still possible even when both the desired and interference signals have simultaneous errors such as direction-of-arrival estimation errors, amplitude and phase perturbation errors, and array geometry errors, resulting in a high output SINR. This application demonstrates excellent robustness to various error factors, including direction-of-arrival estimation errors, amplitude and phase perturbation errors, array geometry errors, and incoherent local scattering, making it a valuable engineering reference.

[0087] In one embodiment, the sampling covariance matrix is ​​calculated as follows:

[0088]

[0089] in, Indicates the number of snapshots. This indicates the conjugate transpose. Indicates the first A quick snapshot of the radar echo signal.

[0090] In one embodiment, the power spectrum of the radar echo signal is calculated using the sampling covariance matrix, including:

[0091] The power spectrum of the radar echo signal is calculated using the sampling covariance matrix.

[0092]

[0093] in, Represents the sampling covariance matrix. This represents the guide vector. This represents the azimuth region of the entire observation interval. This indicates the azimuth region corresponding to the desired signal. This indicates the azimuth region corresponding to the interference signal. This indicates the azimuth region corresponding to the noise. This represents the pitch angle range across the entire observation interval. This indicates the pitch angle region corresponding to the desired signal. This indicates the pitch angle region corresponding to the interference signal. This indicates the pitch angle region corresponding to the noise.

[0094] In one embodiment, the DOA of the interference signal is estimated based on the power spectrum being outside the angular range of the desired signal DOA. The interference covariance matrix is ​​reconstructed using a pre-set integration interval of a certain size. A noise covariance matrix is ​​added to the interference covariance matrix to obtain the initial reconstructed interference plus noise covariance matrix, including:

[0095] The DOA of the interference signal is estimated based on the power spectrum outside the angular range of the desired signal DOA. The interference covariance matrix is ​​reconstructed using a pre-set integration interval of a certain size. The noise covariance matrix is ​​then added to the interference covariance matrix to obtain the initial reconstructed interference-plus-noise covariance matrix.

[0096]

[0097] in, For noise power, Power spectrum containing interference signals The integration interval of a certain size is set in advance. The power spectrum representing noise. This indicates the conjugate transpose. For the sampling covariance matrix, Indicates the guide vector. Represents the identity matrix. This represents the noise covariance matrix.

[0098] In one embodiment, eigenvalue decomposition is performed on the initial reconstructed interference plus noise covariance matrix to obtain the maximum eigenvalue and the noise subspace, including:

[0099] Eigenvalues ​​are obtained by performing eigenvalue decomposition on the initial reconstructed interference plus noise covariance matrix. ,in, It is a unitary matrix composed of eigenvectors. ; It is a diagonal matrix composed of eigenvalues. , The eigenvalues ​​in satisfy , eigenvectors and The eigenvalues ​​in the model correspond one-to-one;

[0100] After taking The eigenvectors constitute the noise subspace. Construct the projection matrix of the noise subspace .

[0101] In one embodiment, the interference signal power is calculated based on the maximum eigenvalue, including:

[0102] The interference signal power is calculated based on the maximum eigenvalue.

[0103]

[0104] in, Represents the largest eigenvalue. For noise power, This represents the number of array elements, which is the same as the number of eigenvectors.

[0105] In one embodiment, the optimized interference signal steering vector is solved using a convex optimization method based on the projection matrix of the noise subspace and the estimated interference signal steering vector, including:

[0106] Using the projection matrix of the noise subspace and the estimated interference signal steering vector, the optimized interference signal steering vector is obtained through a convex optimization method.

[0107]

[0108] in, Describing the 2-norm, It is a local minimum. This represents the optimized interference signal steering vector. The projection matrix of the noise subspace is represented. This represents the estimated steering vector of the interference signal. This indicates the conjugate transpose.

[0109] In one embodiment, the interference covariance matrix is ​​reconstructed twice based on the interference signal power and the optimized interference signal steering vector. A noise covariance matrix is ​​then added to the reconstructed interference covariance matrix to obtain a second-reconstructed interference plus noise covariance matrix, including:

[0110] Based on the interference signal power and the optimized interference signal steering vector, the interference covariance matrix is ​​reconstructed twice. Then, a noise covariance matrix is ​​added to the reconstructed interference covariance matrix to obtain the second-order reconstructed interference plus noise covariance matrix.

[0111]

[0112] in, This represents the second-order reconstruction interference covariance matrix. Represents the noise covariance matrix. Indicates the power of the interference signal. This represents the optimized interference signal steering vector. This indicates the conjugate transpose. For noise power, Represents the identity matrix. Represents the noise covariance matrix. This represents the total number of interfering signals.

[0113] In one embodiment, the sampling covariance matrix and the estimated desired signal steering vector are used as inputs to the RCB algorithm to solve for the optimized desired signal steering vector, including:

[0114] Using the sampling covariance matrix and the estimated desired signal steering vector as inputs to the RCB algorithm, the optimized desired signal steering vector is obtained as follows:

[0115]

[0116] in, As a preset value, For the sampling covariance matrix, The steering vector for the predicted desired signal. The optimized desired signal steering vector, This indicates the conjugate transpose.

[0117] In one embodiment, the optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the covariance matrix of the secondary reconstruction interference plus noise, including:

[0118] The optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the covariance matrix of the secondary reconstruction interference plus noise.

[0119]

[0120] in, The second-order reconstruction interference plus noise covariance matrix, The optimized desired signal steering vector, This indicates the conjugate transpose.

[0121] In a specific embodiment, the method of this application is verified by comparing this application (Proposed) with five existing algorithms, including: Optimal, Loaded Sample Matrix Inverse (LSMI), Worst-Case Performance Optimization (WCPO), Robust Capon Beamforming (RCB), and General Linear Combined Bi Interation Quadratically Constrained Quadratic Programming (GLC-BIQCQP).

[0122] In the verification process of the method in this application, the number of array elements is... A vertically placed omnidirectional uniform planar array, The element spacing is half a wavelength. Assume there are three incident far-field narrowband signals, including one desired signal and two interfering signals. The true direction of arrival of the target signal is... ( Indicates azimuth. (This indicates the pitch angle). Meanwhile, the true directions of arrival for the two interfering signals are respectively... and The JNR values ​​are 15 dB and 25 dB, respectively. The noise is Gaussian white noise with zero mean and unit variance. It is assumed that the signal, interference, and noise are independent of each other. When analyzing the effect of SNR, the number of snapshots is fixed at 500; when analyzing the effect of the number of snapshots, the SNR is fixed at 10 dB.

[0123] In this application, The integral interval of the interfering sector is , , In the LSMI algorithm, the diagonal loading factor In the WCPO algorithm, In the RCB algorithm, In the GLC-BI-QCQP algorithm, the angular domain range is selected as follows: .

[0124] Experiment 1: Comparison of signal direction-of-arrival error performance;

[0125] In Experiment 1, the influence of the random DOA error output SINR of the desired signal and the interference signal is considered. It is assumed that the random DOA error of the desired signal and the interference signal follows a uniform distribution U(-4°, 4°). Figure 2 The graph shows the relationship between output SINR and input SNR when the desired signal and interference signal have random DOA errors. As can be seen from the graph, the proposed method has a high output SINR at both low and high SNR, consistently approaching the optimal level. Especially at high SNR, the proposed method is far superior to other testing methods. Figure 3 This is a graph showing the relationship between output SINR and snapshot number when both the desired and interfering signals have random DOA errors. Figure 3 As can be seen, this application exhibits relatively stable performance with varying snapshot counts and demonstrates a high SINR, outperforming other testing methods. Figure 4 The graph shows the relationship between the angle error of the desired signal and the interference signal and the output SINR. It can be seen that as the angle error increases, the output SINR of the LSMI algorithm, WCPO algorithm, RCB algorithm, and GLC-BIQCQP algorithm all decrease to varying degrees. However, the SINR of this application remains close to the optimal value under different angle error conditions, demonstrating strong resistance to DOA mismatch.

[0126] Experiment 2: Comparison of amplitude and phase disturbance error performance;

[0127] In Experiment 2, the effects of amplitude and phase perturbation errors of the array channel on the output SINR are considered. It is assumed that the amplitude error of each sensor follows a Gaussian distribution. The phase error follows a Gaussian distribution. . Figure 5 The graph shows the relationship between output SINR and input SNR under the condition of array channel amplitude and phase perturbation error. It can be found that when the SNR is greater than 5dB, the output SINR of the LSMI algorithm, WCPO algorithm, RCB algorithm, and GLC-BIQCQP algorithm begins to decrease, while the output SINR of this application is not affected by the SNR, demonstrating strong robustness. Figure 6 This is a graph showing the relationship between output SINR and snapshot number under the condition of array channel amplitude and phase perturbation error. Figure 6 As can be seen, among the various testing methods, this application has the highest output SINR, and it consistently maintains the best performance regardless of the number of snapshots.

[0128] Experiment 3: Comparison of array geometric error performance;

[0129] In Experiment 3, the effect of array geometric errors on the output SINR is considered. It is assumed that the element position errors follow a Gaussian distribution. . Figure 7 The graph shows the relationship between output SINR and input SNR under the condition of array geometric error. As can be seen from the graph, when SNR<0, the output SINR of various algorithms are similar; when SNR>0, the output SINR of WCPO algorithm, RCB algorithm, and GLC-BIQCQP algorithm begins to decrease; when SNR>20dB, the output SINR of LSMI algorithm begins to decrease, while the output SINR of this application remains unaffected. Figure 8 The graph shows the relationship between output SINR and the number of snapshots under the condition of array geometric error. As can be seen from the graph, when the input SNR is 10dB, as the number of snapshots gradually increases, the output SINR of the LSMI algorithm gradually approaches the output SINR of this application, which is much higher than the other three algorithms. However, the output SINR of this application is not affected by the number of snapshots, and its performance is close to the optimal situation.

[0130] Experiment 4: Comparison of incoherent local scattering performance;

[0131] In Experiment 4, the effect of incoherent local scattering on the output SINR is considered. Due to the influence of incoherent local scattering, the echo signal has time-varying spatial characteristics, meaning that each snapshot is different. The snapshot data of the desired signal are expressed as:

[0132]

[0133] In the formula, For the desired signal complex envelope, The true steering vector of the desired signal. The complex envelope of the incoherently scattered signal follows a Gaussian distribution. , The steering vector of the incoherent scattered signal, and the angular difference between the incoherent scattered signal and the desired signal. Follows Gaussian distribution , The experiment varied in each experiment, but remained constant in different snapshots within the same experiment.

[0134] Since the signal covariance matrix at this time It is no longer a single-rank matrix; the weight vector is represented as:

[0135]

[0136] In the formula, This represents the principal eigenvector.

[0137] Accordingly, the output SINR is represented as:

[0138]

[0139] Figure 9The graph shows the relationship between output SINR and input SNR under the condition of incoherent local scattering error. Figure 9 As can be seen, the output SINR of this application is close to the optimal case, and it is significantly better than other testing methods, especially at high SNR. Figure 10 The graph shows the relationship between output SINR and snapshot number under the condition of incoherent local scattering error. Figure 10 As can be seen, as the number of snapshots gradually increases, the output SINR of the LSMI algorithm gradually approaches the output SINR of this application. The other three methods always have a large gap from the optimal case, while the performance of this application is closest to the optimal case.

[0140] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0141] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0142] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A robust beamforming method based on quadratic reconstruction of the covariance matrix, characterized in that, The method includes: An omnidirectional uniform planar array is used to receive and acquire radar echo signals and calculate the sampling covariance matrix. The power spectrum of the radar echo signal is calculated using the sampling covariance matrix, and the DOA of the interference signal is estimated based on the power spectrum outside the angular range of the desired signal DOA. The interference covariance matrix is ​​reconstructed with a pre-set integration interval of a certain size, and a noise covariance matrix is ​​added to the interference covariance matrix to obtain the initial reconstructed interference plus noise covariance matrix. The initial reconstructed interference plus noise covariance matrix is ​​subjected to eigenvalue decomposition to obtain the maximum eigenvalue and noise subspace; the interference signal power is calculated based on the maximum eigenvalue; the optimized interference signal steering vector is solved by convex optimization method using the projection matrix of the noise subspace and the estimated interference signal steering vector. Based on the interference signal power and the optimized interference signal steering vector, the interference covariance matrix is ​​reconstructed twice. Then, a noise covariance matrix is ​​added to the reconstructed interference covariance matrix to obtain the reconstructed interference plus noise covariance matrix. The sampling covariance matrix and the estimated desired signal steering vector are used as inputs to the RCB algorithm to solve for the optimized desired signal steering vector. Based on the optimized desired signal steering vector and the secondary reconstruction interference plus noise covariance matrix, the optimal adaptive weight vector is calculated. Robust beam output is performed based on the optimal adaptive vector. Eigenvalue decomposition is performed on the initial reconstruction interference plus noise covariance matrix to obtain the maximum eigenvalue and the noise subspace, including: The eigenvalues ​​of the initial reconstructed interference plus noise covariance matrix are obtained by performing eigenvalue decomposition. ,in, It is a unitary matrix composed of eigenvectors. ; It is a diagonal matrix composed of eigenvalues. , The eigenvalues ​​in satisfy , eigenvectors and The eigenvalues ​​in the model correspond one-to-one; After taking The eigenvectors constitute the noise subspace. Construct the projection matrix of the noise subspace. ; The optimized interference signal steering vector is solved using a convex optimization method based on the projection matrix of the noise subspace and the estimated interference signal steering vector, including: Using the projection matrix of the noise subspace and the estimated interference signal steering vector, the optimized interference signal steering vector is obtained through a convex optimization method. in, Describing the 2-norm, It is a local minimum. This represents the optimized interference signal steering vector. The projection matrix of the noise subspace is represented. This represents the estimated steering vector of the interference signal. Indicates conjugate transpose; Using the sampling covariance matrix and the estimated desired signal steering vector as inputs to the RCB algorithm, the optimized desired signal steering vector is solved, including: Using the sampling covariance matrix and the estimated desired signal steering vector as inputs to the RCB algorithm, the optimized desired signal steering vector is obtained as follows: in, As a preset value, For the sampling covariance matrix, The steering vector for the predicted desired signal. The optimized desired signal steering vector, This indicates the conjugate transpose.

2. The method according to claim 1, characterized in that, Calculate the sampling covariance matrix, including: The sampling covariance matrix is ​​calculated as follows: in, Indicates the number of snapshots. This indicates the conjugate transpose. Indicates the first A quick snapshot of the radar echo signal.

3. The method according to claim 1, characterized in that, Calculating the power spectrum of the radar echo signal using the sampling covariance matrix includes: The power spectrum of the radar echo signal is calculated using the sampling covariance matrix. in, Represents the sampling covariance matrix. Indicates the guide vector. This represents the azimuth region of the entire observation interval. This indicates the azimuth region corresponding to the desired signal. This indicates the azimuth region corresponding to the interference signal. This indicates the azimuth region corresponding to the noise. This represents the pitch angle range across the entire observation interval. This indicates the pitch angle region corresponding to the desired signal. This indicates the pitch angle region corresponding to the interference signal. This indicates the pitch angle region corresponding to the noise.

4. The method according to claim 3, characterized in that, Based on the power spectrum outside the angular range of the desired signal DOA, the DOA of the interference signal is estimated. The interference covariance matrix is ​​reconstructed using a pre-set integration interval of a certain size. A noise covariance matrix is ​​added to the interference covariance matrix to obtain the initial reconstructed interference plus noise covariance matrix, including: Based on the power spectrum outside the angular range of the desired signal DOA, the DOA of the interference signal is estimated. The interference covariance matrix is ​​reconstructed using a pre-set integration interval of a certain size. A noise covariance matrix is ​​then added to the interference covariance matrix to obtain the initial reconstructed interference plus noise covariance matrix. in, For noise power, Power spectrum containing interference signals The integration interval of a certain size is set in advance. The power spectrum representing noise. This indicates the conjugate transpose. For the sampling covariance matrix, Indicates the guide vector. Represents the identity matrix. This represents the noise covariance matrix.

5. The method according to claim 1, characterized in that, The interference signal power is calculated based on the maximum eigenvalue, including: The interference signal power is calculated based on the maximum eigenvalue. in, Represents the largest eigenvalue. For noise power, Indicates the number of array elements.

6. The method according to claim 1, characterized in that, Based on the interference signal power and the optimized interference signal steering vector, a secondary reconstruction of the interference covariance matrix is ​​performed. A noise covariance matrix is ​​then added to the secondary reconstruction interference covariance matrix to obtain a secondary reconstruction interference plus noise covariance matrix, including: Based on the interference signal power and the optimized interference signal steering vector, a secondary reconstruction of the interference covariance matrix is ​​performed. Then, a noise covariance matrix is ​​added to the secondary reconstruction interference covariance matrix to obtain the secondary reconstruction interference plus noise covariance matrix. in, This represents the second-order reconstruction interference covariance matrix. Represents the noise covariance matrix. Indicates the power of the interference signal. This represents the optimized interference signal steering vector. This indicates the conjugate transpose. For noise power, Represents the identity matrix. Represents the noise covariance matrix. This represents the total number of interfering signals.

7. The method according to claim 6, characterized in that, The optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the secondary reconstruction interference plus noise covariance matrix, including: The optimal adaptive weight vector is calculated based on the optimized desired signal steering vector and the covariance matrix of the secondary reconstruction interference plus noise. in, The second-order reconstruction interference plus noise covariance matrix, The optimized desired signal steering vector, This indicates the conjugate transpose.

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