Space-time undistorted anti-interference processing method based on linear phase constraint

Abstract

The invention relates to the technical field of wireless anti-interference, and provides a space-time undistorted anti-interference processing method based on linear phase constraint. The method mainly comprises the following steps: step 1, acquiring antenna array receiving signals; step 2, calculating a covariance matrix by using the receiving signals in the step 1; step 3, adding linear phase constraint to a beam pointing algorithm to obtain the beam pointing algorithm meeting linear phase characteristics; and 4, solving the optimal weight of the BS space-time adaptive algorithm meeting the linear phase constraint. The influence of space-time processing on the GNSS signal phase can be avoided, and the carrier tracking error is reduced. Simulation results show that the method can compensate code phase errors caused by space-time adaptive processing, and the positioning precision of a GNSS receiver is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless anti - interference, and proposes a space - time distortion - free anti - interference processing method based on linear phase constraint. Background Art

[0002] The MVDR algorithm (adaptive beamforming algorithm) has the best interference suppression performance and the least impact on GNSS signals. However, the MVDR algorithm requires the known steering vector and frequency of GNSS signals. The direction of arrival of GNSS signals can be obtained through the direction - of - arrival estimation algorithm, and the steering vector can be obtained according to the array manifold. However, the frequency of GNSS signals is affected by Doppler and cannot be accurately obtained. GNSS receivers can estimate the Doppler frequency of signals and compensate for it, but these processes cannot be implemented when interference is not suppressed. When there are errors in the prior information of GNSS signals, the performance of the MVDR algorithm will seriously decline.

[0003] In summary, the beam - pointing algorithm can ensure a small code tracking error for GNSS signals when suppressing interference, but its phase error is large because the algorithm does not set time - domain constraints. Summary of the Invention

[0004] The object of the present invention: To propose a space - time distortion - free anti - interference processing method based on linear phase constraint, by constraining the linear phase characteristics of the space - time processing equivalent complex FIR filter, avoiding phase distortion of GNSS signals after space - time processing, so as to ensure that no phase tracking error occurs in the carrier tracking loop.

[0005] The technical solution of the present invention: To achieve the above - mentioned invention object, according to the first aspect of the present invention, a space - time distortion - free anti - interference processing method based on linear phase constraint is proposed, which mainly includes the following steps:

[0006] Step 1: Obtain the antenna array received signal:

[0007] Step 2: Calculate the covariance matrix using the received signal in Step 1:

[0008] Step 3: Add a linear phase constraint to the beam - pointing algorithm to obtain a beam - pointing algorithm that satisfies the linear phase characteristics;

[0009] Step 4: Solve the optimal weight of the BS space - time adaptive algorithm that satisfies the linear phase constraint.

[0010] In a possible embodiment, in Step 1, the long - vector form of the signal received by the space - time adaptive processor is as shown in Equation (1)

[0011]

[0012] where xk = [x k1 , x k2 , … x kN T , where \(k = 1, 2, \ldots, K\) is the received signal composed of all \(N\) complex weights corresponding to the \(k\)th delay section, and \(N\) is the number of array elements.

[0013] In a possible embodiment, in the said step 2, the covariance matrix of the space-time adaptive processor is

[0014]

[0015] where \(L\) is the number of sampling snapshots, and \((\cdot)^H\) H denotes the conjugate transpose.

[0016] In a possible embodiment, in the said step 3, a \(K\times K\) matrix is defined

[0017] The adaptive weights of the BS (beam steering) algorithm satisfy the linear phase constraint condition

[0018] A H \(\mathbf{w} = \mathbf{T}(\mathbf{A}\) H \(\mathbf{w})\) * , is an \(NK\times K\) matrix, \(\mathbf{0}\) N×1 is an \(N\times1\) zero vector, and \(\mathbf{w}\) is the array weight to be solved;

[0019]

[0020] \(\mathbf{a}\) is the GNSS signal steering vector; where \(\theta\) is the signal arrival direction, \(\lambda\) is the signal wavelength, and \(d\) is the element spacing;

[0021] Combining the constraint condition with the BS algorithm optimization model, the BS algorithm satisfying the linear phase characteristic can be obtained as where denotes the Kronecker product.

[0022] In a possible embodiment, in the said step 3, in order to obtain a closed-form solution, the BS algorithm satisfying the linear phase characteristic is optimized, and an auxiliary variable \(\mathbf{w}_1\) is introduced a , where \(\mathbf{w}_1\) a is a \((K - 1) / 2\times1\) vector; the relationship between \(\mathbf{w}_2\) and \(\mathbf{w}\) is a , where is a \((K - 1) / 2\times(K - 1) / 2\) matrix;

[0023] The optimization model can be written in an equivalent form as follows ​

[0024] In a possible embodiment, in the said step 4, it specifically includes the following steps:

[0025] Solve the solution w of the optimization process;

[0026] Let Define the cost function by the Lagrange multiplier method as J = w H R x w+(w H A - f H )λ+λ H (A H w - f), where λ is a (K - 1) / 2×1 dimensional vector. Take the gradient of the cost function J with respect to w to get ΔJ = R x w + Aλ, and let the gradient be equal to zero to get

[0027] Solve the optimal process solution of the weight vector w:

[0028] Substitute the formula into the constraint condition A H w = f to obtain Substitute into to get the optimal solution of the weight vector w as

[0029]

[0030] Solve the variable w a :

[0031] Substitute the optimal solution of the weight vector w into to obtain the output power as

[0032]

[0033] Since the vector f has obvious symmetry, write the matrix in block form as

[0034]

[0035] where G 11 、G 13 、G 31 and G 33 are (K - 1) / 2×(K - 1) / 2 dimensional matrices; g 12 and g 32 are (K - 1) / 2×1 dimensional vectors, g 21 and g 23 are 1×(K - 1) / 2 dimensional vectors;

[0036] For w H Rx w with respect to w a Obtain by calculating the gradient Set the gradient to zero, and after rearrangement, the weight vector w can be obtained a The optimal solution of is

[0037]

[0038] where Re(·) and Im(·) respectively represent taking the real part and the imaginary part of a complex number;

[0039] Solve the optimal solution of the weight vector w;

[0040] Substitute w a into The optimal weights of the BS space-time adaptive algorithm that satisfies the linear phase constraint can be obtained.

[0041] According to the second aspect of the present invention, an electronic device is proposed, including a memory and a processor, and the memory and the processor are coupled; the memory stores program instructions, and when the program instructions are executed by the processor, the electronic device executes a space-time distortionless anti-interference processing method based on linear phase constraint as described above.

[0042] According to the third aspect of the present invention, a computer-readable storage medium is proposed, including a computer program, and when the computer program runs on an electronic device, the electronic device executes the above-mentioned space-time distortionless anti-interference processing method based on linear phase constraint.

[0043] According to the fourth aspect of the present invention, a computer program product including instructions is proposed, and when the computer program product runs on a computer, the computer executes the above-mentioned space-time distortionless anti-interference processing method based on linear phase constraint.

[0044] The advantages of the present invention are as follows: The space-time adaptive algorithm with linear phase characteristics proposed by the present invention obtains a vector weight that satisfies the linear phase constraint by constraining the time-domain response of the equivalent complex FIR filter of the space-time adaptive weight, which can avoid the influence of space-time processing on the phase of GNSS signals and reduce carrier tracking errors. The simulation results show that the proposed method can compensate for the code phase error caused by space-time adaptive processing and improve the positioning accuracy of GNSS receivers. Brief Description of the Drawings

[0045] Figure 1 Schematic diagram of the code phase deviation effect of the space-time power inversion algorithm of the preferred embodiment of the present invention under the condition of no interference;

[0046] Figure 2 Schematic diagram of the code phase deviation effect of the linear phase constraint space-time algorithm of the preferred embodiment of the present invention under the condition of no interference. Detailed implementation manners

[0047] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the protection scope of the present invention.

[0048] The features and exemplary embodiments of various aspects of the present invention will be described in detail below. In the following detailed description, many specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to those of ordinary skill in the art that the present invention may be practiced without some of these specific details. The description of the embodiments is merely provided to better understand the present invention by way of illustration of examples of the present invention. The present invention is in no way limited to any specific arrangements and methods set forth below, but covers any improvements, substitutions and modifications of structures, methods, and devices without departing from the spirit of the present invention. Well-known structures and technologies are not shown in the drawings and the following description to avoid unnecessarily obscuring the present invention.

[0049] It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other, and the various embodiments may be referenced and cited with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0050] Refer to the attached Figure 1-2 , a space-time distortionless anti-interference processing method based on linear phase constraint mainly includes the following steps:

[0051] Step 1: Array received signal: The space-time adaptive processor has a delay section K = 5 and an array element number N = 7. The long vector form of the received signal can be written as

[0052]

[0053] where x k = [x k1 , x k2 , … x k4 T , and k = 1, 2, …, K is the received signal composed of all 4 complex weights corresponding to the k-th delay section.

[0054] Step 2: Covariance matrix calculation: The covariance matrix of the space-time adaptive processor is

[0055] ​

[0056] where (·) H denotes the conjugate transpose.

[0057] Step 3: Add linear phase constraint: Define a 5×5 matrix The adaptive weights of the BS algorithm satisfy the linear phase constraint condition A H w = T(A H w) * , is a 20×5 matrix, 0 4×1 is a 4×1 zero vector, and w is the array weight to be solved.

[0058]

[0059] is the GNSS signal steering vector, θ is the signal arrival direction at 270°, λ is the signal wavelength of 190 mm, and d is the element spacing of 95 mm.

[0060] Combining the constraint condition with the BS algorithm optimization model, the BS algorithm that satisfies the linear phase characteristic can be obtained as where denotes the Kronecker product.

[0061] Step 4: Optimize the model: To obtain a closed-form solution, introduce an auxiliary variable w a , where w a is a 2D vector. The relationship between w a and w is where is a 4D matrix.

[0062] The optimization model can be written in an equivalent form as follows

[0063] Step 6: Solve the optimization variable w: Let Define the cost function by the Lagrange multiplier method as J = w H R x w + (w H A - f H )λ + λ H (A H w - f), where λ is a 2D vector. Take the gradient of the cost function J with respect to w to get Let the gradient be equal to zero to get

[0064] Step 7: Solve the optimal process solution of the weight vector w: Substitute Equation into the constraint condition A H w = f to obtain Substitute into The optimal solution of the weight vector w is

[0065]

[0066] Step 8: Solve for the variable w a : Substitute the optimal solution of the weight vector w into to obtain the output power in

[0067]

[0068] Since the vector f has obvious symmetry, the matrix is written in block form as

[0069]

[0070] , where G 11 , G 13 , G 31 and G 33 are (K - 1) / 2 × (K - 1) / 2 dimensional matrices. g 12 and g 32 are 2 - dimensional vectors, and g 21 and g 23 are 2 - dimensional vectors.

[0071] Take the gradient of w H R x w with respect to w a to obtain Set the gradient to zero and after rearrangement, the optimal solution of the weight vector w a is

[0072]

[0073] where Re(·) and Im(·) represent taking the real part and imaginary part of a complex number respectively.

[0074] Step 9: Solve for the optimal solution of the weight vector w: Substitute w a into to obtain the optimal weight of the BS space - time adaptive algorithm that satisfies the linear phase constraint.

[0075] Figure 1 and 2The code phase deviation of the traditional space-time power inversion algorithm and the linear phase constraint space-time algorithm proposed in the present invention under the condition of no interference is given. It can be seen from the comparison that for the traditional space-time power inversion algorithm, only a good code phase deviation is maintained in the directly overhead direction. Therefore, when the satellite enters the antenna aperture from other elevation angles, additional deviation will be introduced. However, the linear phase constraint space-time algorithm proposed in the present invention can maintain a small code phase deviation throughout the airspace coverage range, that is, it can maintain an ideal linear response characteristic.

Claims

1. A space-time distortion-free anti-interference processing method based on linear phase constraint, characterized in that: The following steps are involved: Step 1: Get the antenna array receiving signal: Step 2: Calculate the covariance matrix using the received signal in step 1: Step 3: Adding a linear phase constraint to the beam pointing algorithm to obtain a beam pointing algorithm that satisfies the linear phase characteristic; Step 4: Solve the optimal weights of the BS space-time adaptive algorithm that satisfies the linear phase constraint.

2. According to the linear phase constraint-based space-time distortion-free anti-interference processing method described in claim 1, it is characterized in that: In step 1, the long vector form of the signal received by the space-time adaptive processor is shown in formula (1): where x k =[x k1 ,x k2 ,…x kN ] T , k=1,2,…,K is the received signal composed of all N complex weighted values ​​corresponding to the k-th delay section, and N is the number of array elements.

3. According to the linear phase constraint-based space-time distortion-free anti-interference processing method of claim 1, characterized in that: In step 2, the covariance matrix of the space-time adaptive processor is L is the number of sampling snapshots, where (·) H represents the conjugate transpose.

4. According to the linear phase constraint-based space-time distortion-free anti-interference processing method of claim 1, characterized in that: In step 3, define a K×K dimensional matrix The adaptive weights of the BS algorithm satisfy the linear phase constraint A H w=T(A H w) * , is a NK×K dimensional matrix, 0 N×1 is a zero vector of N×1 dimension, and w is the array weight to be solved; a is the GNSS signal steering vector; where θ is the signal direction, λ is the signal wavelength, and d is the array element spacing; Combining the constraint conditions with the BS algorithm optimization model can obtain the BS algorithm that satisfies the linear phase characteristic: in represents the Kronecker product.

5. A space-time distortion-free anti-interference processing method based on linear phase constraint according to claim 4, characterized in that: In step 3, in order to obtain a closed-form solution, the BS algorithm that satisfies the linear phase characteristic is optimized and an auxiliary variable w is introduced. a , where w a is a (K-1) / 2×1-dimensional vector; w a The relationship with w is, in It is a (K-1) / 2×(K-1) / 2 dimensional matrix; The optimization model can be written in an equivalent form as follows 6. A space-time distortion-free anti-interference processing method based on linear phase constraint according to claim 5, characterized in that: In step 4, the following steps are specifically included: Solve the optimization process solution w; make The cost function is defined by the Lagrange multiplier method as J = w H R x w+(w H A H )λ+λ H (A H wf), where λ is a (K-1) / 2×1 dimensional vector. The gradient of the cost function J with respect to w is obtained Setting the gradient equal to zero gives Find the optimal process solution for the weight vector w: General Substitute the constraint A H w=f, we can get Will Substitution The optimal solution of the weight vector w is Solving for variable w a : The optimal solution of the weight vector w Substitution The output power in Since the vector f has obvious symmetry, the matrix Written in block form Among them G 11 , G 13 , G 31 and G 33 is a (K-1) / 2×(K-1) / 2 dimensional matrix; g 12 and g 32 is a (K-1) / 2×1 dimensional vector, g 21 and g 23 is a 1×(K-1) / 2 dimensional vector; to w H R x wAbout w a Find the gradient and get Let the gradient be zero, and after sorting, we can get the weight vector w a The optimal solution is Where Re(·) and Im(·) represent the real and imaginary parts of the complex number, respectively; Find the optimal solution for the weight vector w; w a Substitution The optimal weights of the BS space-time adaptive algorithm that satisfies the linear phase constraint can be obtained.

7. An electronic device, characterized in that: It includes a memory and a processor, the memory and the processor are coupled; the memory stores program instructions, and when the program instructions are executed by the processor, the electronic device executes a space-time distortion-free anti-interference processing method based on linear phase constraints as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: It includes a computer program, which, when running on an electronic device, enables the electronic device to execute a space-time distortion-free anti-interference processing method based on linear phase constraints as described in any one of claims 1 to 6.

9. A computer program product comprising instructions, characterized in that When the computer program product runs on a computer, the computer is enabled to execute the space-time distortion-free anti-interference processing method based on linear phase constraint as described in any one of claims 1 to 6.

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