Anti-angle-of-arrival mismatch robust adaptive beam forming method

Abstract

The invention discloses an anti-arrival angle mismatch robust adaptive beam forming method, which considers a communication anti-interference scene when an arrival angle observation value and a true value of a desired signal or an interference signal are mismatched, and controls a directional diagram main lobe center to be aligned with an arrival angle of the desired signal through orthogonal projection and main feature vector extraction. The control pattern forms a wide and deep recess over the neighborhood of the interference signal angle of arrival. On the premise of assuming that the signal arrival angle is accurate, a pre-weighted vector capable of controlling a directional diagram to form accurate null at the interference signal arrival angle is obtained through orthogonal projection, and aiming at the arrival angle mismatching condition, the steering vector of an expected signal and the steering vector of the interference signal are estimated through covariance matrix reconstruction and main feature vector extraction. And a beamforming weight vector capable of resisting angle of arrival mismatch is obtained in combination with the pre-weighted vector. The model is complete, the design method is reasonable and effective, and the airspace anti-interference effect of the receiver array can be effectively improved under the condition that the observation value of the signal angle of arrival is mismatched.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a robust adaptive beamforming method based on orthogonal projection against angle-of-arrival mismatch. Background Art

[0002] With the development of array signal processing technology, modern interference technologies such as directional interference are constantly advancing, and the security and reliability of wireless communication are facing increasingly serious threats. Therefore, it is urgent to improve the spatial anti-interference ability of communication receivers. In order to suppress interference signals from different directions, the receiving-end array usually adopts an adaptive beamforming method to improve the signal-to-interference-plus-noise ratio (SINR) at the receiving end and thus improve the communication quality. Adaptive beamforming technology generally refers to using an adaptive beamformer to perform adaptive weighting on the signal vector sampled by the receiving array, amplifying the desired signal as much as possible while suppressing the interference signal, which is an effective means of spatial anti-interference. Current adaptive beamformers usually adopt means such as diagonal loading, eigen-subspace, uncertainty set technology, covariance matrix reconstruction, etc.

[0003] Traditional adaptive beamforming methods can generally meet the spatial anti-interference requirements of communication receivers. However, when there is an angle-of-arrival mismatch of the desired signal or interference signal, the interference suppression ability of traditional adaptive beamforming methods will decline because at this time, the position of the null in the pattern may deviate from the direction of the interference arrival angle, resulting in a poor interference suppression effect. Especially when there is an angle-of-arrival mismatch of the desired signal, the center of the main lobe of the pattern may deviate from the direction of arrival of the desired signal, resulting in a certain degree of suppression of the desired signal and a decrease in the output SINR. Summary of the Invention

[0004] The object of the present invention is to solve the problems raised in the background art, and propose a robust adaptive beamforming method against angle-of-arrival mismatch, which can control the center of the main lobe of the pattern to align with the angle of arrival of the desired signal when there is an angle-of-arrival mismatch of the signal, and at the same time control the pattern to form a wide and deep depression in the neighborhood range of the interference signal arrival angle to achieve robust spatial anti-interference, and specific implementation steps are given.

[0005] To achieve the object of the present invention, the present invention discloses a robust adaptive beamforming method against angle-of-arrival mismatch, including the following steps:

[0006] Step 1: Assume the angle of arrival is accurate, and use orthogonal projection to obtain a pre-weighting vector that can precisely control the null of the pattern;

[0007] Step 2: Estimate the steering vector of the desired signal based on covariance matrix reconstruction and extraction of the main eigenvector;

[0008] Step 3: Estimate the steering vector of the interference signal based on angle-domain integration and eigenvalue decomposition;

[0009] Step 4: Obtain a robust adaptive beamformer that can resist angle-of-arrival mismatch.

[0010] Further, in Step 1, assume that the receiver array is a non-uniform linear array with M elements; the array receives L + 1 far-field narrowband signals, where the desired signal is s0(t), and the L interference signals are s1(t), …, s L (t); then the sampled data vector of the array at the k-th (k = 1, 2, +, K) snapshot is

[0011]

[0012] where represent the desired signal component, interference signal component, and noise respectively. Assume that the three satisfy statistical independence; x m (k)(m…1, 2, …, M) represents the sampled data at the m-th element of the receiver; θ0 and θ l represent the direction-of-arrival (DOA) of the desired signal and the arrival angle of the l-th interference signal respectively; a(θ) is the steering vector corresponding to the arrival angle θ:

[0013]

[0014] where x m (m = 1, 2, …, M) represents the distance from the m-th element to the reference point, and λ is the wavelength;

[0015] If the receiver filtering weight vector is then the signal x(k) becomes

[0016]

[0017] The normalized power response (i.e., the pattern) T(θ, θ0) of the filtering weight vector w in the θ direction relative to the θ0 direction is

[0018]

[0019] Assume that θ0 and θ l (l = 1, 2, …, L) can be accurately obtained. Then the weight vector w makes the pattern form an accurate null at θ l (l = 1, 2, …, L), that is, |w H a(θ l )| 2 / |w H a(θ0)| 2 = 0, which is equivalent to

[0020] w H a(θl ) = 0 (5)

[0021] Express the L interference signal steering vectors as a matrix A = [a(θ1), a(θ2), …, a(θ L )]. Through the orthogonal projection theory, obtain the orthogonal projection matrix that projects onto the orthogonal complement space of the column space of A

[0022]

[0023] From equation (6), we get That is

[0024]

[0025] To make T(θ l , θ0) (l = 1, 2, …, L) equal to 0, construct w in the following form

[0026]

[0027] Where is a random vector that satisfies . From equations (4), (7), and (8), we get

[0028]

[0029] Equation (9) shows that as long as the weighted vector w satisfies it can make the pattern form an exact null at the arrival angles of the interference signals;

[0030] From equation (3), for a given weighted vector w, the output signal-to-interference-plus-noise ratio (SINR) of the receiver array is

[0031]

[0032] Where is the desired signal power, R i+n is the covariance matrix shown as follows

[0033]

[0034] Where is the power of the l-th interference signal, is the noise power, and I is the M×M identity matrix;

[0035] To optimize w to improve the output signal-to-interference-plus-noise ratio on the premise that the weighted vector w satisfies equation (8), the following problem is to be solved

[0036]

[0037] Equation (12) is transformed into the following form

[0038]

[0039] To solve problem (13), substitute the in equation (13) into w H R i+n to obtain w

[0040]

[0041] Note that is a constant, then problem (13) is transformed into

[0042]

[0043] The solution to problem (15) is obtained as

[0044]

[0045] where is an arbitrary vector; from equation (8), the pre-weighting vector w pre

[0046]

[0047] The pre-weighting vector w pre can accurately control the pattern to form a null at the arrival angle of the interference signal.

[0048] Furthermore, in step 2, when the pre-weighting vector w obtained in step 1 pre at θ0 and θ l (l = 1, 2,..., L) can be accurately obtained, it can effectively suppress interference; however, in practice, there are often cases where the measured arrival angle deviates from the true value. This arrival angle mismatch makes the and a(θ0) in equation (17) inaccurate, resulting in a significant decline in the spatial anti-interference performance; to improve the spatial anti-interference performance of the beamformer at arrival angle shipei, the steering vectors of the desired signal and the interference signal are estimated respectively;

[0049] First, estimate the actual steering vector of the desired signal; first, reconstruct the covariance matrix of the desired signal through integration in the angular domain

[0050]

[0051] where Θ s represents the angular sector where the true arrival angle of the desired signal is located; R xDenote the sampling covariance matrix

[0052]

[0053] Let the matrix The eigenvector corresponding to the largest eigenvalue of is d1, then d1 is used as the estimation result of the actual desired signal steering vector.

[0054] Furthermore, in step 3, in order to estimate the actual interference signal steering vector, first reconstruct the matrix by integrating over the angular range Θ jam where the actual arrival angle of the interference signal is located.

[0055]

[0056] Then perform eigenvalue decomposition on the matrix which is expressed as follows:

[0057]

[0058] where V = [v1,…, v M and Ω = diag([ω1,…, ω M ) represent the eigenvector matrix and the eigenvalue diagonal matrix respectively; assume that ω1≥ω2≥…≥ω M , then take the eigenvectors corresponding to Q (1 < Q < M) larger eigenvalues as the estimation results of the steering vectors of all interference signals, and construct the matrix

[0059]

[0060] Obtain the projection matrix that projects onto the orthogonal complement space of the column space of in a manner similar to equation (6).

[0061]

[0062] The projection matrix is used to construct an adaptive beamformer that can resist arrival angle mismatch in the subsequent stage.

[0063] Furthermore, in step 4, based on the pre - weighting vector in step 1, the estimation result of the desired signal steering vector in step 2, and the projection matrix in step 3, a robust adaptive beamformer that can resist arrival angle mismatch is obtained; that is, combining equation (17), equation (23) and the vector d1, the robust adaptive beamformer that can resist arrival angle mismatch is

[0064]

[0065] w prop It can still maintain good spatial anti-interference performance in the case of arrival angle mismatch.

[0066] Compared with the prior art, the significant progress of the present invention lies in: 1) A robust adaptive beamforming method against arrival angle mismatch is given, and the obtained weighted vector can effectively suppress interference signals when the signal arrival angle is mismatched, improving the output signal-to-interference-plus-noise ratio of the receiver; 2) The proposed robust adaptive beamforming method based on orthogonal projection against arrival angle mismatch can control the center of the main lobe of the pattern to align with the arrival angle of the desired signal, and at the same time control the pattern to form a wide and deep depression in the neighborhood range of the arrival angle of the interference signal, thereby effectively improving the robustness against arrival angle mismatch.

[0067] To more clearly illustrate the functional characteristics and structural parameters of the present invention, the following further explains in conjunction with the drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The drawings described herein are used to provide a further understanding of the present invention, form a part of this application, and the schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0069] Figure 1 is the pattern of a robust adaptive beamforming method against arrival angle mismatch and a comparison method.

[0070] Figure 2 is a schematic curve diagram of the output signal-to-interference-plus-noise ratio of the receiver of a robust adaptive beamforming method against arrival angle mismatch and a comparison method changing with the input signal-to-noise ratio.

[0071] Figure 3 is a schematic curve diagram of the output signal-to-interference-plus-noise ratio of the receiver of a robust adaptive beamforming method against arrival angle mismatch and a comparison method changing with the number of snapshots. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] The present invention proposes a robust adaptive beamforming method against arrival angle mismatch, which can control the center of the main lobe of the pattern to align with the arrival angle of the desired signal when the signal arrival angle is mismatched, and at the same time control the pattern to form a wide and deep depression in the neighborhood range of the arrival angle of the interference signal to achieve robust spatial anti-interference, and specific implementation steps are given.

[0073] Step 1: Assume that the arrival angle is accurate, and use orthogonal projection to obtain a pre-weighted vector that can precisely control the null of the pattern.

[0074] Step 2: Estimate the steering vector of the desired signal based on covariance matrix reconstruction and principal eigenvector extraction.

[0075] Step 3: Estimate the interference signal steering vector based on angular domain integration and eigenvalue decomposition.

[0076] Step 4: Obtain a robust adaptive beamformer that can resist angle-of-arrival mismatch.

[0077] Specifically, in Step 1, on the premise of assuming accurate angle-of-arrival, an initial weighting vector that can precisely control the null of the pattern is obtained by using orthogonal projection.

[0078] Without loss of generality, assume that the receiver array is a non-uniform linear array with M elements. The array receives L + 1 far-field narrowband signals, where the desired signal is s0(t), and the L interference signals are s1(t), …, s L (t). Then the sampled data vector of the array at the k-th (k = 1, 2, …, K) snapshot is

[0079]

[0080] where represent the desired signal component, interference signal component, and noise respectively, and assume that the three satisfy statistical independence. x m (k) (m = 1, 2, …, M) represents the sampled data at the m-th element of the receiver. θ0 and θ l represent the direction-of-arrival (DOA) of the desired signal and the arrival angle of the l-th interference signal respectively. a(θ) is the steering vector corresponding to the arrival angle θ:

[0081]

[0082] where x m (m = 1, 2, …, M) represents the distance from the m-th element to the reference point, and λ is the wavelength.

[0083] If the receiver filtering weighting vector is then the signal x(k) becomes

[0084]

[0085] The normalized power response (i.e., the pattern) T(θ, θ0) of the filtering weighting vector w in the θ direction relative to the θ0 direction is

[0086]

[0087] Assume that θ0 and θ l (l = 1, 2, …, L) can be accurately obtained, then the weighting vector w makes the pattern form an accurate null at θ l (l = 1, 2, …, L), that is, |w H a(θl )| 2 / |w H a(θ0)| 2 = 0, which is equivalent to

[0088] w H a(θ l ) = 0 (5)

[0089] Express the steering vectors of L interference signals as matrix A = [a(θ1), a(θ2), …, a(θ L )]. Through the orthogonal projection theory, the orthogonal projection matrix projected onto the orthogonal complement space of the column space of A can be obtained

[0090]

[0091] From equation (6), we can get That is

[0092]

[0093] To make T(θ l , θ0) (l = 1, 2, …, L) equal to 0, construct w in the following form

[0094]

[0095] where is a random vector that satisfies From equations (4), (7), and (8), we can get

[0096]

[0097] Equation (9) shows that as long as the weighted vector w satisfies it can make the pattern form an exact null at the arrival angles of the interference signals

[0098] From equation (3), for a given weighted vector w, the signal-to-interference-plus-noise ratio (SINR) of the receiver array output is

[0099]

[0100] where is the desired signal power, and R i+n is the covariance matrix shown as follows

[0101]

[0102] where is the power of the l-th interference signal is the noise power, and I is an M×M identity matrix.

[0103] To optimize w to improve the output signal-to-interference-plus-noise ratio on the premise that the weighting vector w satisfies equation (8), the following problem is to be solved

[0104]

[0105] Equation (12) can be transformed into the following form

[0106]

[0107] To solve problem (13), substitute the in equation (13) into w H R i+n to get w

[0108]

[0109] Note that is a constant, then problem (13) can be transformed into

[0110]

[0111] It is not difficult to obtain the solution of problem (15) as

[0112]

[0113] where is an arbitrary vector. Furthermore, the beamforming vector that can accurately control the pattern to form a null at the arrival angle of the interference signal can be obtained, that is, the pre-weighting vector w pre is

[0114]

[0115] Specifically, step 2 estimates the steering vector of the desired signal based on covariance matrix reconstruction and principal eigenvector extraction.

[0116] The pre-weighting vector w obtained in step 1 pre at θ0 and θ l (l = 1, 2, …, L) can effectively suppress interference when accurately obtained. However, in practice, there are often situations where the measured arrival angle deviates from the true value. This situation of arrival angle mismatch makes the and a(θ0) in equation (17) inaccurate, resulting in a significant decline in the spatial anti-jamming performance. To improve the spatial anti-jamming performance of the beamformer when the arrival angle is mismatched, we estimate the steering vectors of the desired signal and the interference signal respectively.

[0117] First, estimate the actual steering vector of the desired signal. First, reconstruct the covariance matrix of the desired signal through integration in the angular domain

[0118]

[0119] where Θ s represents the angular sector where the true arrival angle of the desired signal is located. R x represents the sample covariance matrix

[0120]

[0121] Without loss of generality, assume that the eigenvector corresponding to the largest eigenvalue of the matrix is d1, then d1 is taken as the estimation result of the actual steering vector of the desired signal.

[0122] Specifically, step 3 estimates the steering vector of the interference signal based on angular domain integration and eigenvalue decomposition.

[0123] To estimate the actual steering vector of the interference signal, first reconstruct the matrix by integrating over the angular range Θ jam where the true arrival angle of the interference signal is located

[0124]

[0125] Then perform eigenvalue decomposition on the matrix which is expressed as follows:

[0126]

[0127] where V = [v1,..., v M and Ω = diag([ω1,..., ω M ) represent the eigenvector matrix and the eigenvalue diagonal matrix respectively. Assume that ω1 ≥ ω2 ≥... ≥ ω M , then we take the eigenvectors corresponding to Q (1 < Q < M) larger eigenvalues as the estimation results of the steering vectors of all interference signals, and construct the matrix

[0128]

[0129] Then the projection matrix onto the orthogonal complement space of the column space of can be obtained in a manner similar to equation (6)

[0130]

[0131] Specifically, step 4 is based on the pre-weighted vector of step 1, the estimated result of the desired signal steering vector in step 2, and the projection matrix in step 3 A robust adaptive beamformer capable of resisting angle-of-arrival mismatch can be obtained. That is, by combining Equation (17), Equation (23), and vector d1, the robust adaptive beamformer capable of resisting angle-of-arrival mismatch is

[0132]

[0133] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0134] Embodiment

[0135] The embodiments of the present invention are specifically described as follows. System simulation uses MATLAB software, and the setting of parameters does not affect generality. The receiver uses a non-uniform linear array with an array size of M = 16. Taking element 1 as the reference point, the positions of the 16 elements are

[0136] λ·[0, 0.45, 1.18, 1.73, 2.35, 2.67, 3.35, 3.71, 4.04, 4.48, 4.76, 5.48, 5.75, 6.24, 6.57, 7.25]. The noise is additive white Gaussian noise. The parameter Q in Equation (22) is taken as 6. It is assumed that the observed value of the direction-of-arrival (DOA) of the desired signal is -13° while the true arrival angle is -10°. The observed arrival angles of the two interfering signals are -60° and 25°, and the random mismatch range of the arrival angles of the two interfering signals is [-2°, 2°], that is, the true arrival angles of the two interfering signals are respectively in the intervals [-62°, -58°] and [23°, 27°]. Unless otherwise specified, the interference-to-noise ratio (INR) is set to 30 dB, the signal-to-noise ratio (SNR) is set to 20 dB, the number of snapshots is set to 30, and the experimental results are the average of 1000 Monte Carlo simulation results.

[0137] The three comparison methods are the robust adaptive beamforming method based on the reconstruction of the covariance matrix with linear integration (Y. Gu and A. Leshem, "Robust adaptive beamforming based on interference covariance matrix reconstruction and steering vector estimation" [J], IEEE Transactions on Signal Processing, vol. 60, no. 7, pp. 3881-3885, Jul. 2012.), the robust adaptive beamforming method based on the reconstruction of the covariance matrix with maximum entropy power spectrum estimation (S.

[0138] Mohammadzadeh, V. H. Nascimento, R. C. de Lamare, and O. Kukrer, "Maximum entropy-based interference-plus-noise covariance matrix reconstruction for robust adaptive beamforming" [J], IEEE Signal Processing Letters, vol. 27, pp. 845-849, 2020.), the robust adaptive beamforming method based on power spectrum estimation and the reconstruction of the covariance matrix with an uncertainty interval (S. Mohammadzadeh, V. H. Nascimento, R. C. d. Lamare and O. Kukrer,

[0139] "Covariance matrix reconstruction based on power spectral estimation and uncertainty region for robust adaptive beamforming" [J], IEEE Transactions on Aerospace Electronic Systems, vol. 59, no. 4, pp. 3848-3858, Aug. 2023.). The above three methods are abbreviated as LINEAR, MEPS, and PSEUR respectively in the subsequent content and simulation results.

[0140] Figure 1 It is the display of the radiation patterns of the proposed method and the comparison methods. Figure 1It shows that the pattern of the proposed beamforming method can form wide and deep notches in the angular sectors [-62°, -58°] and [23°, 27°] of the arrival angles of the interfering signals, while the patterns of the comparison methods LINEAR, MEPS, and PSEUR can only form nulls at single angles. Figure 1 It also shows that the center of the main lobe of the pattern of the proposed method is basically aligned with the true arrival angle of the desired signal, while the centers of the main lobes of the patterns of the comparison methods LINEAR, MEPS, and PSEUR are near the observed value of the arrival angle of the desired signal and have a deviation of about 3° from the true arrival angle. Figure 1 It shows that the beamforming method proposed in the present invention can improve the robustness of anti-interference when there is an arrival angle mismatch.

[0141] Figure 2 It is the curve of the received signal-to-interference-plus-noise ratio (SINR) of the proposed method and the comparison methods varying with the input signal-to-noise ratio (SNR). During the simulation, the range of SNR is set from -10 dB to 30 dB, and other parameters remain unchanged. Figure 2 It shows that for different input SNRs, the output SINR of the proposed method is higher than that of the comparison methods LINEAR, MEPS, and PSEUR, and the output SINR of the proposed method is closest to the theoretical optimal SINR. Figure 2 It shows that the beamforming method proposed in the present invention can effectively improve the spatial domain interference performance of the receiver array and increase the output SINR.

[0142] Figure 3 It is the curve of the received signal-to-interference-plus-noise ratio of the proposed method and the comparison methods varying with the number of snapshots. During the simulation, the range of the number of snapshots is set from -20 to 80, and other parameters remain unchanged. From Figure 3 It can be seen that for different numbers of snapshots, the output SINR performance of the proposed method is always better than that of the comparison methods and is closer to the theoretical optimal SINR, indicating that the proposed beamforming method has stronger interference suppression ability. Figure 3 It shows that the beamforming method proposed in the present invention can enable the receiver to maintain robust spatial domain interference performance under different numbers of snapshots.

[0143] In summary, the present invention proposes a robust adaptive beamforming method against arrival angle mismatch. By using the orthogonal projection theory, it controls the pattern to form wide and deep notches in the range of the arrival angles of the interfering signals, and at the same time aligns the center of the main lobe of the pattern with the true arrival angle of the desired signal to improve the robustness of spatial domain anti-interference when there is a DOA mismatch, and gives the expression of the robust adaptive beamformer. The model of the present invention is complete, the design method is reasonable and effective, it can effectively improve the robustness against DOA mismatch and the spatial domain anti-interference performance of the beamformer when there is an arrival angle mismatch, and gives the specific implementation steps.

[0144] It should be noted that in this document, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variation thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or elements inherent to such process, method, article or device.

[0145] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A robust adaptive beamforming method against angle-of-arrival mismatch, characterized in that Including the following steps: Step 1: Assuming the angle of arrival is accurate, use orthogonal projection to obtain a pre-weighting vector that can precisely control the null of the pattern; Step 2: Estimate the desired signal steering vector based on covariance matrix reconstruction and principal eigenvector extraction; Step 3: Estimate the interference signal steering vector based on angle domain integration and eigenvalue decomposition; Step 4: Obtain a robust adaptive beamformer that can resist angle of arrival mismatch.

2. The robust adaptive beamforming method against angle-of-arrival mismatch according to claim 1, characterized in that In step 1, assume that the receiver array is a non-uniform linear array with M array elements; the array receives L + 1 far-field narrowband signals, where the desired signal is s0(t), and the L interference signals are s1(t), …, s L (t); then the sampling data vector of the array at the kth (k = 1, 2, …, K) snapshot is where represent the desired signal component, the interference signal component, and the noise respectively, assuming that the three satisfy statistical independence; x m (k) (m = 1, 2, …, M) represents the sampling data of the receiver on the m-th array element; θ0 and θ l represent the direction of arrival (DOA) of the desired signal and the direction of arrival of the l-th interference signal respectively; a(θ) is the steering vector corresponding to the arrival angle θ: where x m (m = 1, 2, …, M) represents the distance from the m-th array element to the reference point, and λ is the wavelength; If the receiver filtering weight vector is then the signal x(k) becomes after being processed by the filtering weight w The normalized power response \(T(\theta,\theta_0)\) of the filtering weight vector \(w\) in the \(\theta\) direction relative to the \(\theta_0\) direction is Assume that θ0 and θ l (l = 1, 2, …, L) can be accurately obtained, then the weighted vector w makes the radiation pattern form an accurate null at θ l (l = 1, 2, …, L), that is, |w H a(θ l )| 2 / |w H a(θ0)| 2 = 0, which is equivalent to w H a(θ l ) = 0 (5) Express the steering vectors of L interference signals as a matrix A = [a(θ1), a(θ2), …, a(θ L )]. Through the theory of orthogonal projection, obtain the orthogonal projection matrix that projects onto the orthogonal complement space of the column space of A Obtained from Equation (6) That is To control T(θ l , θ0) (l = 1, 2, …, L) to be 0, construct w in the following form Among them To satisfy The random vector; obtained from equations (4), (7), and (8) Equation (9) shows that as long as the weighted vector w satisfies it can make the pattern form an accurate null at the arrival angle of the interference signal; From Equation (3), for a given weight vector \(w\), the signal-to-interference-plus-noise ratio (SINR) of the receiver array output is where is the desired signal power, R i+n is the covariance matrix as shown below where is the power of the l-th interference signal, is the noise power, and I is an M×M identity matrix; In order to optimize \(w\) to improve the output SINR on the premise that the weight vector \(w\) satisfies Equation (8), the following problem is to be solved Equation (12) is transformed into the following form To solve problem (13), substitute into w H R i+n to obtain w Noted that is a constant, then the problem (13) is transformed into The solution to Problem (15) is obtained as where U0 = [u M-L+1 , u M-L+2 , …, u M , is an arbitrary vector; from Equation (8), the pre-weighted vector w pre Pre-weighted vector w pre It can accurately control the pattern to form a null at the arrival angle of the interference signal.

3. The robust adaptive beamforming method against angle-of-arrival mismatch according to claim 2, characterized in that, In Step 2, in order to improve the spatial anti-interference performance of the beamformer when the angle of arrival is matched, the steering vectors of the desired signal and the interference signal are estimated respectively; First, estimate the actual steering vector of the desired signal; first, reconstruct the covariance matrix of the desired signal through integration in the angular domain where Θ s represents the angular sector where the true arrival angle of the desired signal is located; R x represents the sampling covariance matrix Let the matrix The eigenvector corresponding to the maximum eigenvalue is d1, then d1 is used as the estimation result of the steering vector of the actual desired signal.

4. A robust adaptive beamforming method against angle-of-arrival mismatch according to claim 3, characterized in that In step 3, in order to estimate the actual interference signal steering vector, first, the matrix is reconstructed by integrating over the angular range Θ where the true arrival angle of the interference signal lies. jam ​ Then perform eigenvalue decomposition on the matrix which is expressed as follows: where \(V = [v_1,\ldots,v M \) and \(\Omega=\text{diag}([\Theta_1,\ldots,\Theta M )\) represent the eigenvector matrix and the eigenvalue diagonal matrix respectively; assume that \(\omega_1\geq\omega_2\geq\ldots\geq\omega M \), then take the eigenvectors corresponding to \(Q\) (\(1 < Q < M\)) larger eigenvalues as the estimation result of the steering vectors of all interference signals, and construct the matrix Obtain the projection matrix projected onto the orthogonal complement space of the column space of in a manner similar to Equation (6). ​ Projection matrix It is used to subsequently construct an adaptive beamformer that is resistant to angle-of-arrival mismatch.

5. A robust adaptive beamforming method against angle-of-arrival mismatch according to claim 4, characterized in that, In step 4, based on the pre-weighted vector in step 1, the estimated result of the desired signal steering vector in step 2, and the projection matrix in step 3 a robust adaptive beamformer capable of resisting angle-of-arrival mismatch is obtained; that is, combining equation (17), equation (23), and vector d1, the robust adaptive beamformer capable of resisting angle-of-arrival mismatch is w prop It can still maintain good anti-jamming performance in the airspace in the case of angle-of-arrival mismatch.

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