Precise directional diagram null control robust airspace anti-interference method

Abstract

The invention discloses an accurate directional diagram null control robust airspace anti-interference method, which considers a multi-antenna receiver communication scene with interference signals in different incoming wave directions, and improves the output signal to interference plus noise ratio of a receiving end by controlling a receiving array directional diagram to form accurate null in the direction of an interference angle of arrival. Therefore, robust airspace anti-interference is realized. In order to control the nulling direction of a directional diagram, the nulling control problem of the directional diagram is converted, and then a filtering weight vector form capable of accurately controlling nulling of the directional diagram is obtained by using an orthogonal projection theory. And then establishing an optimization problem to maximize the output signal to interference plus noise ratio on the premise of controlling the null of the directional diagram. And finally, solving the optimization problem to obtain an optimal filtering weight vector capable of controlling the directional diagram to form accurate null at the angle of arrival of the interference signal. The model is complete, the design method is reasonable and effective, and directional diagram nulling can be effectively controlled in a communication scene in which a receiver faces interference in multiple directions so as to effectively suppress interference.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a robust spatial domain anti-interference method for precise directional pattern nulling control. Background Art

[0002] In the field of wireless communications, the natural openness and broadcast nature of electromagnetic wave propagation makes the communication receiver extremely vulnerable to third-party interference. In particular, with the development of modern jamming technologies such as low-power jamming and directional jamming, the security and reliability of wireless communications are more vulnerable to threats. Therefore, there is an urgent need to improve the spatial interference resistance of the communication receiver. Spatial interference resistance based on adaptive beamforming is an important array antenna technology, widely used in military and civilian wireless communications for spatial interference suppression. It can effectively improve the signal-to-interference-noise ratio (SIR) at the receiving end and improve communication quality. Adaptive beamforming technology generally refers to the use of an adaptive beamformer to adaptively weight the signal vectors sampled by the receiving array, thereby suppressing interference signals from different directions. It is a means of spatial interference resistance. Currently, adaptive beamformers can be divided into various technologies based on their design principles, such as diagonal loading, subspace projection, uncertainty set technology, and covariance matrix reconstruction.

[0003] Traditional adaptive beamforming methods can generally meet the spatial anti-interference requirements of communication receivers. However, traditional adaptive beamforming methods often ignore the suppression effect on interference signals whose arrival directions are close to the desired signal. When the arrival directions of the interference signal and the desired signal are close, the spatial anti-interference performance of the traditional adaptive beamforming method will be severely degraded because the directional pattern of the traditional adaptive beamforming method may be distorted, and the null direction deviates from the arrival direction of the interference signal, resulting in a decrease in the interference suppression effect. In particular, when the number of array elements is limited, the problem of directional pattern distortion will be more serious because the receiver array will find it difficult to provide sufficient angular resolution to suppress interference signals whose arrival directions are close to the desired signal. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems raised in the background technology and propose a method for robust spatial interference resistance with precise directional pattern nulling control, which can accurately control the nulling direction of the directional pattern and maximize the output signal-to-interference-noise ratio in a multi-antenna receiver communication scenario facing multiple incoming interference signals, so as to achieve robust spatial interference resistance.

[0005] To achieve the purpose of the present invention, the present invention discloses a robust spatial domain anti-interference method for precise pattern nulling control, comprising the following steps:

[0006] Step 1: Transform the directional pattern nulling control problem;

[0007] Step 2: Using orthogonal projection, a filter weight vector form capable of accurately controlling the nulling of the directional pattern is obtained;

[0008] Step 3: Establish an optimization problem to maximize the output signal-to-interference-and-noise ratio while controlling the nulling of the directional pattern;

[0009] Step 4: Obtain the optimal filter weight vector that can accurately control the directional pattern to form a null at the arrival angle of the interference signal.

[0010] Furthermore, step 1 is as follows:

[0011] The receiving end uniform linear array carries M array elements. The array receives L+1 far-field narrowband signals, including the desired signal s0(t) and L interference signals s1(t),…,s L (t); then the sampling data of the receiver array at the kth (k=1,2,…,K) snapshot is expressed as

[0012]

[0013] in[·] T represents transpose; represents an M×1-dimensional complex vector) represents the desired signal, interference signal and noise respectively, assuming that the three satisfy statistical independence; x m (k) (m = 1, 2, ..., M) represents the sampling data of the kth snapshot of the mth array element of the receiver array; θ0 and θ l denote the arrival angle of the desired signal and the arrival angle of the lth interference signal respectively; a(θ) is the steering vector corresponding to the arrival angle θ, expressed as

[0014]

[0015] Where d is the interval between adjacent array elements, and ε is the wavelength;

[0016] If the receiver filter weight vector is Then the signal x(k) becomes

[0017]

[0018] In the field of array signal processing, the directivity pattern usually refers to the normalized power response. The normalized power response T(θ,θ0) of the filter weight vector w in the θ direction relative to the θ0 direction is expressed as

[0019]

[0020] If the filtering weight vector w can make the normalized power response of the interference direction equal to 0, that is, the control pattern is in θ l (l=1,2,…,L) forms an accurate zero sink, then

[0021]

[0022] Considering that the denominator in the above formula is not equal to 0, formula (5) is equivalent to |w H a(θ l )| 2 =0, that is

[0023] w H a(θ l )=0 (6)

[0024] That is, the problem of directivity pattern null control is transformed.

[0025] Furthermore, step 2 is as follows:

[0026] First, the L interference signal steering vectors are expressed as matrix A

[0027] A=[a(θ1),a(θ2),…,a(θ L )] (7)

[0028] Through the orthogonal projection theory, we get the orthogonal projection matrix projected onto the orthogonal complement space of the column space of A.

[0029]

[0030] From the properties of the projection matrix, we know that the matrix Satisfies idempotence and Hermitian symmetry; from formula (8) we get Right now

[0031]

[0032] In order to optimize the weight vector w while controlling T(θ l ,θ0)(l=1,2,…,L) is 0, and w is constructed as follows

[0033]

[0034] in To satisfy Random vector; from formula (4), (9), (10) we get

[0035]

[0036] Formula (11) shows that as long as the weight vector w satisfies This enables the directional pattern to form a precise null in the direction of the interference signal arrival angle.

[0037] Furthermore, step 3 is as follows:

[0038] From formula (3), for a given weight vector w, the receiver array output signal to interference and noise ratio SINR is

[0039]

[0040] in (E{·} means expectation) represents the expected signal power, R i+n Represents the interference plus noise covariance matrix as follows

[0041]

[0042] in represents the power of the lth interference signal, represents the noise power, I represents the M×M dimensional identity matrix;

[0043] In order to further optimize w under the premise that the weight vector w satisfies equation (10) to improve the output signal-to-interference-noise ratio shown in equation (12), the following optimization problem is modeled:

[0044]

[0045] Remove the constant in the optimized target molecule of formula (14) Further transform the above formula into

[0046]

[0047] That is, an optimization problem of maximizing the output signal-to-interference-and-noise ratio under the premise of controlling the nulling of the directional pattern is established.

[0048] Furthermore, step 4 is as follows:

[0049] In order to solve the optimization problem (15), Substitute w H R i+n w

[0050]

[0051] Considering the formula (16) is a constant, and the optimization problem (15) is transformed into

[0052]

[0053] By matrix The idempotent property of That means is a matrix The eigenvector of , and the corresponding eigenvalue is 1.

[0054] Pair Matrix Perform eigenvalue decomposition as follows

[0055]

[0056] where Λ=Diag([λ1,λ2,…,λ M ]) is the matrix whose main diagonal elements are The eigenvalues of U=[u1,u2,…,u M ] column vector u in m For the corresponding λ m The unit eigenvector of (m=1,…,M); From formula (9) and the properties of the orthogonal projection matrix, we know that the matrix The eigenvalues of are ML 1s and L 0s; without loss of generality, let

[0057]

[0058] Then the matrix Re-expressed as

[0059]

[0060] Substituting formula (20) into the optimization objective of formula (17) yields

[0061]

[0062] The derivation of formula (21) uses Note that when a(θ0) and A are given, the matrix is also determined, then in formula (21) is a fixed value, so we have

[0063]

[0064] Obviously Assumptions Can get the minimum value 0, get the following problem about solving b

[0065]

[0066] If formula b H u m =0(m=2,…,ML) holds, then b∈R ⊥ ([u2,…,u M-L ]), since the matrix U is a unitary matrix, we know from the properties of the unitary matrix that

[0067]

[0068] From formula (24), we know that b∈R ⊥ ([u2,…,u M-L]) is equivalent to b∈R([u1,u M-L+1 ,u M-L+2 ,…,u M ]); From formula (19) we know Combined with the constraints of formula (23), the solution of formula (23) Expressed as

[0069]

[0070] Where the matrix U0=[u M-L+1 ,u M-L+2 ,…,u M ], is an arbitrary complex vector; from formula (19) we know that λ M-L+1 =…=λ=0, that is Right now Then, the optimal weight vector w is obtained from equations (10) and (25): prop for

[0071]

[0072] From formula (26), we know that as long as we know the interference signal steering vector a(θ l )(l=1,2,…,L) and the desired signal steering vector a(θ0), we can get the weight vector w that can form an accurate null in the interference direction prop ; Since w in formula (26) prop The calculation of is independent of the interference plus noise covariance matrix and does not require a complex iterative process, so the computational complexity is low.

[0073] Compared with the existing technology, the significant advancements of the present invention are: 1) a robust spatial anti-interference method with precise directional pattern nulling control is proposed. The resulting optimal filter weight vector can control the directional pattern to form a precise null in the direction of the interference signal and maximize the output signal-to-interference-noise ratio, and the computational complexity of the optimal filter weight is low; 2) the proposed robust spatial anti-interference method with precise directional pattern nulling control can effectively suppress interference signals from multiple directions, especially when the directions of the desired signal and the interference signal are close. The proposed spatial anti-interference method has a complete model and clear physical meaning, providing a specific implementation plan for spatial anti-interference in multi-antenna receiver communication scenarios.

[0074] In order to more clearly illustrate the functional characteristics and structural parameters of the present invention, further description is given below with reference to the accompanying drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0076] Figure 1 It is a schematic diagram showing the directional diagrams of the method proposed in the present invention and the comparative method;

[0077] Figure 2 1 is a schematic diagram of a curve showing how the receiver output signal-to-interference-and-noise ratio varies with the input signal-to-noise ratio for the method proposed in the present invention and the comparative method;

[0078] Figure 3 1 is a schematic diagram of a curve showing how the receiver output signal to interference and noise ratio changes with the input signal to interference and noise ratio for the method proposed in the present invention and the comparative method;

[0079] Figure 4 3 is a graph showing how the receiver output signal to interference and noise ratio (SINR) changes with the number of snapshots for the method proposed in the present invention and the comparative method. DETAILED DESCRIPTION

[0080] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only 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 ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0081] A robust spatial anti-interference method with precise pattern nulling control can precisely control the nulling direction of the pattern and maximize the output signal-to-interference-noise ratio in a multi-antenna receiver communication scenario facing multiple incoming interference signals, thereby achieving robust spatial anti-interference. The specific implementation method is as follows:

[0082] Step 1: Transform the pattern nulling control problem.

[0083] Step 2: Use orthogonal projection to obtain the filter weight vector form that can accurately control the direction pattern null.

[0084] Step 3: Establish an optimization problem to maximize the output signal-to-interference-and-noise ratio while controlling the nulling of the directional pattern.

[0085] Step 4: Obtain the optimal filter weight vector that can accurately control the directivity pattern to form a null at the arrival angle of the interference signal.

[0086] Specifically, in step 1, the pattern nulling control problem is transformed into:

[0087] Without loss of generality, assume that the receiving end uniform linear array carries M array elements, and the array receives L+1 far-field narrowband signals, including the desired signal s0(t) and L interference signals s1(t),…,s L (t). Then the sampling data of the receiver array at the kth (k=1,2,…,K) snapshot is expressed as

[0088]

[0089] in They represent the desired signal, interference signal and noise respectively, assuming that the three satisfy statistical independence. m (k)(m=1,2,…,M) represents the sampled data of the mth element of the receiver array. θ0 and θ l denote the direction-of-arrival (DOA) of the desired signal and the arrival angle of the lth interference signal, respectively. a(θ) is the steering vector corresponding to the arrival angle θ, expressed as

[0090]

[0091] Where d is the interval between adjacent array elements and ε is the wavelength.

[0092] If the receiver filter weight vector is Then the signal x(k) becomes

[0093]

[0094] In the field of array signal processing, the directivity pattern usually refers to the normalized power response. The normalized power response T(θ,θ0) of the filter weight vector w in the θ direction relative to the θ0 direction is expressed as

[0095]

[0096] If the filtering weight vector w can make the normalized power response of the interference direction equal to 0, that is, the control pattern is in θ l (l=1,2,…,L) forms an accurate zero sink, then

[0097]

[0098] Considering that the denominator in the above formula is not equal to 0, formula (5) is equivalent to |w H a(θ l )| 2 =0, that is

[0099] w H a(θ l )=0 (6) That is, the problem of directivity pattern null control is transformed.

[0100] Specifically, in step 2, orthogonal projection is used to obtain the filtering weight vector form that can accurately control the nulling of the directional pattern:

[0101] First, the L interference signal steering vectors are expressed as matrix A

[0102] A=[a(θ1),a(θ2),…,a(θ L )] (7)

[0103] Through the orthogonal projection theory, we can get the orthogonal projection matrix of the orthogonal complement space of the column space of A:

[0104]

[0105] From the properties of the projection matrix, we can know that the matrix It satisfies idempotence and Hermitian symmetry. From formula (8), we can get

[0106] Right now

[0107]

[0108] In order to optimize the weight vector w while controlling T(θ l ,θ0)(l=1,2,…,L) is 0, we construct w as follows

[0109]

[0110] in To satisfy Random vector of . From equations (4), (9), and (10), we can get

[0111]

[0112] Formula (11) shows that as long as the weight vector w satisfies This enables the directional pattern to form a precise null in the direction of the interference signal arrival angle.

[0113] Specifically, in step 3, an optimization problem is established to maximize the output signal-to-interference-and-noise ratio while controlling the nulling of the directional pattern:

[0114] From formula (3), for a given weight vector w, the receiver array output signal-to-interference-plus-noise ratio (SINR) is

[0115]

[0116] in represents the expected signal power, R i+n Represents the interference plus noise covariance matrix as follows

[0117]

[0118] in represents the power of the lth interference signal, Represents the noise power, and I represents the M×M dimensional unit matrix.

[0119] In order to further optimize w under the premise that the weight vector w satisfies equation (10) to improve the output signal-to-noise ratio shown in equation (12), the following optimization problem is modeled:

[0120]

[0121] Remove the constant in the optimized target molecule of formula (14) Further transform the above formula into

[0122]

[0123] Specifically, in step 4, the optimal filtering weight vector capable of accurately controlling the directivity pattern to form a null at the arrival angle of the interference signal is obtained:

[0124] In order to solve the optimization problem (15), Substitute w H R i+n w

[0125]

[0126] Considering the formula (16) is a constant, the optimization problem (15) can be transformed into

[0127]

[0128] By matrix The idempotent property of That means is a matrix The eigenvector of , and the corresponding eigenvalue is 1.

[0129] Pair Matrix Perform eigenvalue decomposition as follows

[0130]

[0131] where Λ=Diag([λ1,λ2,…,λ M ]) is the matrix whose main diagonal elements are The eigenvalues of ,U=[u1,u2,…,uM ] column vector u in m For the corresponding λ m The unit eigenvector of (m=1,…,M). From formula (9) and the properties of the orthogonal projection matrix, we know that the matrix The eigenvalues of are ML 1s and L 0s. Without loss of generality, let

[0132]

[0133] Then the matrix Re-expressed as

[0134]

[0135] Substituting formula (20) into the optimization objective of formula (17) yields

[0136]

[0137] The derivation of formula (21) uses Note that when a(θ0) and A are given, the matrix is also determined, then in formula (21) is a fixed value, so we have

[0138]

[0139] Obviously Assumptions If we can get the minimum value 0, we can get the following problem about solving b

[0140]

[0141] If formula b H u m =0(m=2,…,ML) holds, then b∈R ⊥ ([u2,…,u M-L ]), since the matrix U is a unitary matrix, we know from the properties of the unitary matrix that

[0142]

[0143] From formula (24), we know that b∈R ⊥ ([u2,…,u M-L ]) is equivalent to b∈R([u1,u M-L+1 ,u M-L+2 ,…,u M ]). From formula (19), we know Combined with the constraints of formula (23), the solution of formula (23) can be Expressed as

[0144]

[0145] Where the matrix U0=[u M-L+1 ,u M-L+2 ,…,u M ], is an arbitrary complex vector. From formula (19), we know that M-L+1 =…=λ=0, that is Right now Then, the optimal weight vector w can be obtained from equations (10) and (25): prop for

[0146]

[0147] From formula (26), we can see that as long as we know the interference signal steering vector a(θ l )(l=1,2,…,L) and the desired signal steering vector a(θ0), we can get the weight vector w that can form an accurate null in the interference direction prop Since w in formula (26) prop The calculation of is independent of the interference plus noise covariance matrix and does not require a complex iterative process, so the computational complexity is low.

[0148] Example

[0149] The embodiments of the present invention are described in detail as follows. MATLAB software is used for system simulation, and the parameter settings do not affect generality. The receiver uses a uniform linear array with an array size of and an element spacing of half a wavelength. During the simulation, in order to test the robustness of the proposed method, it is assumed that there is always a random error in the steering vector. The element of the actual steering vector is , where represents random amplitude jitter and satisfies a Gaussian distribution, and represents random phase jitter and satisfies a Gaussian distribution. The noise is additive white Gaussian noise. In order to fully test the spatial domain anti-interference performance of the proposed method, the arrival angle of the interference signal is set to be close to the arrival angle of the desired signal. The direction-of-arrival (DOA) of the desired signal is . The arrival angles of the two interference signals are and respectively. Unless otherwise specified, the interference-to-noise ratio (INR) is set to 30 dB, the signal-to-noise ratio (SNR) is set to 30 dB, the number of snapshots is set to 30, and the experimental results are the average of 1000 Monte Carlo simulation results.

[0150] The three compared methods are the robust adaptive beamforming method based on Gauss-Legendre integral (T.Luo, P.Chen, Z.Cao, L.Zheng and Z.Wang.URGLQ:An efficient covariance matrix reconstruction method for robust adaptive beamforming[J],IEEE Transactions on Aerospace Electronic Systems,vol.59,no.5,pp.5634-5645,Oct.2023.), the robust adaptive beamforming method based on covariance matrix reconstruction based on maximum entropy power spectrum estimation (S.Mohammadzadeh,VHNascimento,RCde 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.), Robust adaptive beamforming method based on covariance matrix reconstruction of three-dimensional volume integral (L. Huang, J. Zhang, X. Xu, and Z. Ye, “Robust adaptive beamforming with a novel interference-plus-noise covariance matrix reconstruction method [J], IEEE Transactions on Signal Processing, vol. 63, no. 7, pp. 1643-1650, Apr. 2015.). The above three methods are respectively referred to as URGLQ, MEPS, and VOLUME in the subsequent content and simulation results.

[0151] Figure 1 It is a directional diagram display of the proposed method and the comparative method. Figure 1 It shows that the proposed spatial domain anti-interference method can control the directional pattern to form an accurate deep null at the arrival angle and direction of the interference signal, while the directional pattern null direction formed by the comparison method deviates from the arrival angle and direction of the interference signal. Figure 1It also shows that the directional patterns formed by the comparison methods VOLUME and MEPS produce different degrees of distortion. The center of the main lobe of the directional pattern corresponding to the VOLUME method is slightly offset from the direction of the expected signal arrival angle, while the main lobe of the directional pattern corresponding to the MEPS method deviates seriously from the direction of the expected signal arrival angle. Figure 1 It shows that the method proposed in the present invention has significant advantages in pattern control and can control the pattern to form a precise null in the direction of the interference arrival angle to effectively suppress interference.

[0152] Figure 2 The curves below show how the receiver output signal-to-interference-plus-noise ratio (SINR) varies with the input signal-to-noise ratio (SNR) for the proposed and comparative methods. The simulations vary the input SNR from -20dB to 30dB, while keeping other parameters constant. Figure 2 It shows that the output SINR of the proposed method is higher than that of the three comparison methods in a larger input SNR range, and the output SINR of the proposed method is closest to the theoretical optimal output SINR. Figure 2 It shows that the method proposed in the present invention can effectively improve the spatial interference performance of the receiver array and increase the output SINR.

[0153] Figure 3 The following curves plot the receiver output signal-to-interference-and-noise ratio (SINR) versus the input interference-to-noise ratio (INR) for the proposed and comparative methods. The simulations vary the input INR from 0dB to 50dB, while keeping other parameters constant. Figure 3 It shows that the output SINR of the proposed method is higher than that of the three comparison methods in a larger input INR range, and the output SINR of the proposed method is closest to the theoretical optimal output SINR. Figure 3 It is also shown that as the input INR increases, the output SINR of different methods decreases, but the proposed method decreases the slowest. Figure 3 It shows that the method proposed in the present invention can effectively improve the interference signal suppression capability of the receiver under interference of different intensities.

[0154] Figure 4 Figure 2 shows the curves of the receiver output signal-to-interference-and-noise ratio (SINR) versus snapshot number for the proposed and comparative methods. The simulations vary the snapshot number from 20 to 80, while keeping other parameters constant. Figure 4 It shows that when the number of snapshots changes, the output SINR performance of the proposed method is always better than the comparison method and is closer to the theoretical optimal output SINR. In addition, the output SINR of the proposed method is less affected by the change of the number of snapshots. Figure 4 It shows that the method proposed in the present invention can enable the receiver to maintain robust spatial interference performance.

[0155] In summary, this paper proposes a robust spatial interference mitigation method with precise pattern nulling control. This method uses orthogonal projection theory to control the nulling direction of the pattern and provides the optimal weight vector that achieves precise pattern nulling while maximizing the output signal-to-interference-noise ratio (SINR). This method has a comprehensive model and a rational and effective design approach. It can precisely control pattern nulling to effectively suppress interference in communication scenarios where the receiver faces interference from multiple directions, and also provides specific implementation steps.

[0156] It should be noted that, in this document, relational terms such as first and second, etc., are used only 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 terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0157] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A robust spatial domain anti-interference method for precise pattern nulling control, characterized in that: The following steps are involved: Step 1: Transform the directional pattern nulling control problem; Step 2: Using orthogonal projection, a filter weight vector form capable of accurately controlling the nulling of the directional pattern is obtained; Step 3: Establish an optimization problem to maximize the output signal-to-interference-and-noise ratio while controlling the nulling of the directional pattern; Step 4: Obtain the optimal filter weight vector that can accurately control the directional pattern to form a null at the arrival angle of the interference signal.

2. The method for robust spatial domain anti-interference with precise pattern nulling control according to claim 1, characterized in that: Step 1 is as follows: The receiving end uniform linear array carries M array elements. The array receives L+1 far-field narrowband signals, including the desired signal s0(t) and L interference signals s1(t),…,s L (t); then the sampling data of the receiver array at the kth (k=1,2,…,K) snapshot is expressed as in[·] T represents transpose; ( represents an M×1-dimensional complex vector) represents the desired signal, interference signal and noise respectively, assuming that the three satisfy statistical independence; x m (k) (m = 1, 2, ..., M) represents the sampling data of the kth snapshot of the mth array element of the receiver array; θ0 and θ l denote the arrival angle of the desired signal and the arrival angle of the lth interference signal respectively; a(θ) is the steering vector corresponding to the arrival angle θ, expressed as Where d is the interval between adjacent array elements, and ε is the wavelength; If the receiver filter weight vector is Then the signal x(k) becomes In the field of array signal processing, the directivity pattern usually refers to the normalized power response. The normalized power response T(θ,θ0) of the filter weight vector w in the θ direction relative to the θ0 direction is expressed as If the filtering weight vector w can make the normalized power response of the interference direction equal to 0, that is, the control pattern is in θ l (l=1,2,…,L) forms an accurate zero sink, then Considering that the denominator in the above formula is not equal to 0, formula (5) is equivalent to |w H a(θ l )| 2 =0, that is w H a(θ l )=0 (6) That is, the problem of directivity pattern null control is transformed.

3. The method for robust spatial domain anti-interference with precise pattern nulling control according to claim 2, characterized in that: Step 2 is as follows: First, the L interference signal steering vectors are expressed as matrix A A=[a(θ1),a(θ2),…,a(θ L )] (7) Through the orthogonal projection theory, we get the orthogonal projection matrix projected onto the orthogonal complement space of the column space of A. From the properties of the projection matrix, we know that the matrix Satisfies idempotence and Hermitian symmetry; from formula (8) we get Right now In order to optimize the weight vector w while controlling T(θ l ,θ0)(l=1,2,…,L) is 0, and w is constructed as follows in To satisfy A random vector of From formula (4), (9), and (10), we can get Formula (11) shows that as long as the weight vector w satisfies This enables the directional pattern to form a precise null in the direction of the interference signal arrival angle.

4. The method for robust spatial domain anti-interference of precise pattern nulling control according to claim 3, characterized in that: Step 3 is as follows: From formula (3), for a given weight vector w, the receiver array output signal to interference and noise ratio SINR is in (E{·} means expectation) represents the expected signal power, R i+n Represents the interference plus noise covariance matrix as follows in represents the power of the lth interference signal, represents the noise power, I represents the M×M dimensional identity matrix; In order to further optimize w under the premise that the weight vector w satisfies equation (10) to improve the output signal-to-noise ratio shown in equation (12), the following optimization problem is modeled: Remove the constant in the optimized target molecule of formula (14) Further transform the above formula into That is, an optimization problem of maximizing the output signal-to-interference-and-noise ratio under the premise of controlling the nulling of the directional pattern is established.

5. The method for robust spatial domain anti-interference of precise pattern nulling control according to claim 4, characterized in that: Step 4 is as follows: In order to solve the optimization problem (15), Substitute w H R i+n w Considering the formula (16) is a constant, and the optimization problem (15) is transformed into By matrix The idempotent property of That means is a matrix The eigenvector of , and the corresponding eigenvalue is 1; Pair Matrix Perform eigenvalue decomposition as follows where Λ=Diag([λ1,λ2,…,λ M ]) is the matrix whose main diagonal elements are The eigenvalues of U=[u1,u2,…,u M ] column vector u in m For the corresponding λ m The unit eigenvector of (m=1,…,M); From formula (9) and the properties of the orthogonal projection matrix, we know that the matrix The eigenvalues of are ML 1s and L 0s; without loss of generality, let Then the matrix Re-expressed as Substituting formula (20) into the optimization objective of formula (17) yields The derivation of formula (21) uses Note that when a(θ0) and A are given, the matrix is also determined, then in formula (21) is a fixed value, so we have Obviously Assumptions Can get the minimum value 0, get the following problem about solving b If formula b H u m =0(m=2,…,ML) holds, then b∈R ⊥ ([u2,…,u M-L ]), since the matrix U is a unitary matrix, we know from the properties of the unitary matrix that From formula (24), we know that b∈R ⊥ ([u2,…,u M-L ]) is equivalent to b∈R([u1,u M-L+1 ,u M-L+2 ,…,u M ]); From formula (19) we know Combined with the constraints of formula (23), the solution of formula (23) Expressed as Where the matrix U0=[u M-L+1 ,u M-L+2 ,…,u M ], is an arbitrary complex vector; From formula (19), we know that M-L+1 =…=λ=0, that is Right now Then, the optimal weight vector w is obtained from equations (10) and (25): prop for From formula (26), we know that as long as we know the interference signal steering vector a(θ l )(l=1,2,…,L) and the desired signal steering vector a(θ0), we can get the weight vector w that can form an accurate null in the interference direction prop ; Since w in formula (26) prop The calculation of is independent of the interference plus noise covariance matrix and does not require a complex iterative process, so the computational complexity is low.

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