A monopulse radar antenna and a subarray partitioning method for difference beamforming

Abstract

The present invention proposes a subarray division method for sum and difference beamforming of a monopulse radar antenna. The method comprises: dividing a given 2N-element symmetrical linear array of the monopulse radar antenna into 2M symmetrical subarrays, exciting the array elements in each subarray with equal amplitude and phase, and weighting #imgabs0# and #imgabs1# only at the subarray level to form desired sum and difference beams; deriving an array element excitation vector #imgabs4# corresponding to the sum beam and an array element excitation vector #imgabs5# corresponding to the difference beam from the subarray-level sum and difference beam weighted excitation vectors #imgabs2# and #imgabs3#, and forming a matrix W from these two sets of vectors. ele , according to W ele The compressible characteristics of each column vector construct a sparse matrix S' ele , and perform sparse representation on it; according to the radiation requirements of the sum beam and difference beam, based on the joint sparse recovery theory, a convex optimization model of sum and difference beamforming that minimizes the number of sub-arrays is established; solve the convex optimization model and calculate the sparse matrix S' ele , from which we extract the number of subarrays M, the subarray-level weighted excitations corresponding to the sum beam #imgabs6#, and the subarray-level weighted excitations corresponding to the difference beam #imgabs7#

Description

Technical Field

[0001] The present invention relates to the field of wireless communications, and in particular to a monopulse radar antenna and a subarray division method for difference beamforming. Background Art

[0002] Monopulse radar antennas typically need to generate a mainlobe sum pattern and two mainlobe difference patterns to track and locate high-speed targets. To achieve both sum and difference beams with low sidelobes, the most direct approach is to optimize the excitation amplitude of each array element to form the desired sum and difference patterns. While this direct beamforming method is the simplest—for example, Taylor weighting can be used to achieve the sum beam and Bayes weighting to achieve the difference beam—it requires two completely different feed networks to form the sum and difference beams. For large array elements, the hardware cost and complexity of beamforming become prohibitive. Therefore, a subarray-level weighted difference pattern method has been proposed. This method uses element-level weighting to directly derive the desired sum pattern. The array is then partitioned into subarrays, and the desired low-sidelobe difference pattern is achieved by optimizing the subarray-level weights. In this case, a large portion of the feed network corresponding to the sum and difference beams is shared, reducing system complexity. To further simplify the design of monopulse array antennas, the entire array is divided into several subarrays, and the desired sum and difference beams are achieved through different subarray-level weightings. Comparison shows that under this design framework, the number of subarrays is far smaller than the number of array elements, significantly reducing the number of channels and the overall system complexity. However, the corresponding optimization problem becomes more complex, involving the joint optimization of subarray partitioning, including the number of subarrays, subarray structure, and subarray-level sum and difference beam weighting. Xiong Ziyuan et al. proposed a hierarchical clustering non-uniform subarray partitioning method based on the weight vector approximation criterion. While this method can effectively reduce the approximation error of the weight vector, it requires extensive training to select control parameters, is computationally intensive, and requires pre-determined array element excitations as prior information. Furthermore, it must be noted that many current subarray partitioning methods are based on a known number of subarrays. The difference in the number of subarrays directly affects the optimization results of the subarray partitioning and sum and difference beam weighting. Research on optimizing the number of subarrays, particularly minimizing the number of subarrays, has yet to be conducted. However, in practical engineering, achieving the desired sum and difference beams under a subarray partitioning method that minimizes the number of subarrays is more practical and relevant. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem of subarray partitioning to minimize the number of subarrays in single-pulse and difference beamforming. Only when the number of subarrays is minimized can the feeding network be simplified to the maximum extent, thereby realizing various desired functions with the lowest software and hardware costs.

[0004] The present invention aims to overcome the defects of the prior art and proposes a subarray partitioning method for a monopulse radar antenna and difference beamforming, the method comprising:

[0005] Step S01) The 2N-element symmetrical linear array given by the monopulse radar antenna is divided into 2M symmetrical sub-arrays. The array elements in each sub-array are excited with equal amplitude and phase, and weighted only at the sub-array level. and Forming desired sum beam and difference beam;

[0006] Step S02) The weighted excitation vector is obtained by summing the subarray level and difference beams. and Derive the array element excitation vector corresponding to the beam And the array element excitation vector corresponding to the difference beam The two sets of vectors form the matrix W ele , according to W ele The compressible characteristics of each column vector construct a sparse matrix S' ele , and perform sparse representation on it;

[0007] Step S03) According to the radiation requirements of the sum beam and the difference beam, based on the joint sparse recovery theory, a sum and difference beamforming convex optimization model that minimizes the number of sub-arrays is established;

[0008] Step S04) Solve the convex optimization model and calculate the sparse matrix S' ele , from which the number of subarrays M and the subarray-level weighted excitation corresponding to the beam are extracted And the sub-array level weighted excitation corresponding to the difference beam

[0009] As an improvement to the above method, step S01) specifically includes:

[0010] The 2N-element symmetrical linear array given by the monopulse radar antenna is divided into 2M symmetrical sub-arrays. The array elements in each sub-array are excited with equal amplitude, and excitation is added to the sub-array ports. To achieve the desired sum beam, where represents the excitation value of the mth subarray port when forming the sum beam, the superscript (s) represents the sum beam related parameters, and the superscript T represents the transpose;

[0011] Keep the subarray structure unchanged and add another set of excitations at the subarray ports To achieve the desired difference beam, represents the excitation value of the mth subarray port when forming the difference beam, and the superscript (d) represents the difference beam related parameters;

[0012] For the same subarray partitioning structure, sum beam and difference beam are generated only by weighting at the subarray level.

[0013] As an improvement to the above method, in step S01), the number of positive semi-axis array elements N is much larger than the number of positive semi-axis sub-arrays M, and the number of array elements N of the mth sub-array is m Satisfy the following formula:

[0014]

[0015] As an improvement to the above method, step S02) specifically includes:

[0016] Sub-array-level weight vector and The element-level weighted vector is derived, that is, the element excitation vector corresponding to the beam for:

[0017]

[0018] Array element excitation vector corresponding to the difference beam for:

[0019]

[0020] By column vector and The matrix W ele for:

[0021]

[0022] According to the matrix W ele The characteristics of each column element are calculated by performing a difference operation:

[0023]

[0024] In order to keep the two matrices of the same size, we can transform the matrix W ele The first row vector Add to matrix W' ele In the matrix W' ele Then update to:

[0025]

[0026] Matrix S' ele is the matrix W ele The sparse representation of

[0027] W ele =TS' ele (7)

[0028] The T matrix is ​​called the sparse transformation matrix and satisfies the following formula:

[0029]

[0030] As an improvement to the above method, the sparse matrix S' ele is a row sparse matrix with M non-zero rows, Represents the number of non-zero rows of this row sparse matrix, satisfying the following formula:

[0031]

[0032] in Represents the nth row of the matrix. The number of non-zero rows of a row-sparse matrix is ​​approximated by its mixed l2 / l1 norm, that is:

[0033]

[0034] represents the 2-norm of the n-th row of the matrix, and the 2-norm of any vector x is defined as Where Q is the length of vector x.

[0035] As an improvement to the above method, the sparse matrix S' ele The two column vectors are and The sparse representation of satisfies the following formula:

[0036]

[0037] Where ξ represents the sparse matrix S' ele The first column, ψ represents the sparse matrix S' ele The second column of

[0038] and They have the same sparse characteristics, that is, the number of non-zero elements is the same and the positions of non-zero elements in the vector are the same.

[0039] As an improvement to the above method, step S03) specifically includes:

[0040] According to the radiation requirements of the sum beam and difference beam, the main beam and side lobe levels of the expected sub-array-level weighted sum pattern are consistent with the array element-level Taylor weighted pattern F s Main beam and side lobe levels SLL (θ) s The main beam and side lobe levels of the expected sub-array-level weighted difference pattern are the same as the element-level Baylis-weighted pattern F d Main beam and side lobe levels SLL (θ) d Similarly, with minimizing the number of sub-arrays as the optimization goal, the convex optimization model for the joint optimization of sum and difference beams is established as follows:

[0041]

[0042] where K(s) represents the number of sampling points of the main beam of the sum pattern, ε is the reconstruction error of the main beam, is the first zero point of the main beam of the sum pattern, is the first zero point of the main beam of the difference pattern, A(θ i ) represents the i-th observation direction θ i The corresponding sum direction map steering vector;

[0043] According to the characteristic that the sum beam excitation weight value is symmetrical about the center of the array, A(θ i ) is expressed as:

[0044] A(θ i )=[2cos(βd1sin(θ i )) 2cos(βd2sin(θ i )) … 2cos(βd N sin(θ i ))] (13)

[0045] Where wave number β = 2π / λ, λ is the wavelength, d i represents the position of the i-th array element;

[0046] K (d) Indicates the number of sampling points of the main beam of the difference pattern, B(θ i ) represents the i-th observation direction θ i The corresponding difference pattern steering vector, according to the characteristic that the difference beam excitation weight value is antisymmetric about the array center, B(θ i ) is expressed as:

[0047] B(θ i )=[2sin(kd1sin(θ i )) 2sin(kd2sin(θ i )) … 2sin(kd N sin(θ i ))] (14).

[0048] As an improvement to the above method, step S04) specifically includes:

[0049] Step S04-1) solves the convex optimization model established in step S03) in the CVX solver, and converts the module value of the calculation result to be less than 10 -4 The value of is set to 0, and the sparse matrix S' is obtained ele ;

[0050] Step S04-2) Detection matrix S' eleThe numerical characteristics of the elements in the middle column are traversed. If two consecutive elements are non-zero, the sum of the two is assigned to the element with the larger modulus value, and the other element is set to zero. The next column of elements is processed accordingly to ensure the same sparse characteristics as the previous column, and the sparse matrix S' is updated. ele ;

[0051] Step S04-3) Update the sparse matrix S' ele Substitute into formula (11) and calculate and Then extract the number of subarrays M and the subarray-level weighted excitation corresponding to the beam And the sub-array level weighted excitation corresponding to the difference beam

[0052] Compared with the prior art, the advantages of the present invention are:

[0053] 1. In the sub-array division of the monopulse radar antenna and differential beamforming of the present invention, minimizing the number of sub-arrays is taken as the optimization goal to achieve the desired function with the lowest software and hardware cost;

[0054] 2. Based on the joint sparse recovery theory, the present invention transforms the multi-constraint, multi-target, and multi-parameter subarray partitioning problem of monopulse radar antennas and difference beamforming into a convex optimization problem of minimizing the hybrid l2 / l1 norm. This allows for an efficient solution to this complex subarray partitioning problem using a convex optimization algorithm.

[0055] 3. The present invention realizes simultaneous optimization of the number of subarrays, subarray structure, and subarray-level weighting values ​​corresponding to the sum and difference beams. Under the subarray division that minimizes the number of subarrays, the desired sum and difference beams can be obtained only by changing the subarray-level weighting values. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the monopulse radar antenna and the difference beamforming subarray division framework of the present invention.

[0057] Figure 2 It is a flow chart of the monopulse radar antenna and the difference beamforming subarray partitioning method of the present invention;

[0058] Figure 3 It is the result of the 200-element uniformly spaced linear array antenna subarray division of the present invention and the corresponding sum and difference beamforming subarray-level excitation weighted value;

[0059] Figure 4 It is the sum and difference beam obtained by sub-array level weighting of the present invention. DETAILED DESCRIPTION

[0060] A monopulse radar antenna and a subarray division method for difference beamforming, the method comprising:

[0061] Step S01) The 2N-element symmetrical linear array given by the monopulse radar antenna is divided into 2M symmetrical sub-arrays. The array elements in each sub-array are excited with equal amplitude and phase, and weighted only at the sub-array level. and Forming desired sum beam and difference beam;

[0062] Step S02) The weighted excitation vector is obtained by summing the subarray level and difference beams. and Derive the array element excitation vector corresponding to the beam And the array element excitation vector corresponding to the difference beam The two sets of vectors form the matrix W ele , according to W ele The compressible characteristics of each column vector construct a sparse matrix S' ele , and perform sparse representation on it;

[0063] Step S03) According to the radiation requirements of the sum beam and the difference beam, based on the joint sparse recovery theory, a sum and difference beamforming convex optimization model that minimizes the number of sub-arrays is established;

[0064] Step S04) Solve the convex optimization model and calculate the sparse matrix S' ele , from which the number of subarrays M and the subarray-level weighted excitation corresponding to the beam are extracted And the sub-array level weighted excitation corresponding to the difference beam

[0065] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0066] Example

[0067] The embodiments of the present invention provide a monopulse radar antenna and a subarray division method for difference beamforming.

[0068] like Figure 1 As shown, the monopulse radar antenna sum and difference beamforming subarray division framework of the present invention divides the entire array antenna into multiple non-uniform non-overlapping subarrays, and only adds different weights to each subarray port to obtain the desired sum and difference beams.

[0069] like Figure 2 As shown, the process of determining the subarray size, structure, and subarray-level weighted values ​​corresponding to the sum and difference beamforming specifically includes the following steps:

[0070] Step S01) Divide the given 2N-element symmetrical linear array into 2M symmetrical sub-arrays. The elements in each sub-array are excited with equal amplitude and phase, and weighted only at the sub-array level. and The desired sum beam and difference beam are formed.

[0071] Step S01 specifically includes the following process:

[0072] Divide the given 2N-element symmetrical linear array into 2M symmetrical sub-arrays, excite the elements in each sub-array with equal amplitude, and add excitation to the sub-array ports. To achieve the desired sum beam, where Indicates the excitation value of the mth subarray port when forming the sum beam. The superscript (s) represents the sum beam related parameters, and the superscript T represents the transpose. While keeping the subarray structure unchanged, add another set of excitations to the subarray port To achieve the desired difference beam, The number of positive semi-axis array elements N is much larger than the number of positive semi-axis sub-arrays M, and N is used to represent the excitation value of the mth sub-array port when forming the difference beam. m represents the number of elements of the mth sub-matrix, then we have

[0073]

[0074] Moreover, for the same sub-array division structure, different weights are added to the sub-array ports to generate sum beams and difference beams.

[0075] Step S02) The weighted excitation vector is obtained by summing the subarray level and difference beams. and Derived element-level weighted excitation vector and The two sets of vectors form the matrix W ele , according to W ele The compressible characteristics of each column vector construct a sparse matrix S' ele , and perform sparse representation on it.

[0076] Step S02 specifically includes the following process:

[0077] Sub-array-level weight vector and The element-level weight vector can be derived, that is, the element excitation vector corresponding to the beam It can be specifically expressed as

[0078]

[0079] Array element excitation vector corresponding to the difference beam It can be specifically expressed as

[0080]

[0081] Then the column vector and The matrix W ele Then

[0082]

[0083] According to the matrix W ele The characteristics of each column element can be obtained by performing a differential operation on it.

[0084]

[0085] Comparing equations (4) and (5), we can see that after the differential transformation, the matrix W' ele Ratio matrix W ele To keep the two matrices of the same size, we need to make the matrix W ele The first row vector Add to matrix W' ele Then the matrix W' ele Then update to

[0086]

[0087] From (6), we can see that the matrix S' ele It is a matrix of size N×2. Although it has N rows, there are only M rows with non-zero elements, and the values ​​of the elements in the remaining rows are all 0. From equations (4) and (6), we can see that the matrix W ele With the sparse matrix S' ele There is the following relationship between the two

[0088] W ele =TS' ele (7)

[0089] The T matrix is ​​called the sparse transformation matrix, which is specifically expressed as

[0090]

[0091] Therefore, the matrix S' ele is the matrix W ele sparse representation of , and is a row sparse matrix with only M non-zero rows, Represents the number of non-zero rows of this row sparse matrix, that is

[0092]

[0093] in Denotes the nth row of the matrix. The number of non-zero rows of a row-sparse matrix can be approximated by its mixed l2 / l1 norm, i.e.

[0094]

[0095] Then it is the 2-norm of the nth row of the matrix, and the 2-norm of any vector x is defined as Where Q is the length of vector x. Sparse matrix S' ele The two column vectors are and The sparse representation of

[0096]

[0097] Where ξ represents the sparse matrix S' ele The first column, ψ represents the sparse matrix S' ele The second column of ; it can be seen that the two have the same sparse characteristics, that is, the number of non-zero elements is the same, and the positions of non-zero elements in the vector are the same.

[0098] Step S03) According to the radiation requirements of the sum beam and the difference beam, based on the joint sparse recovery theory, a sum and difference beamforming convex optimization model that minimizes the number of sub-arrays is established.

[0099] Step S03 specifically includes:

[0100] The 2N-element symmetrical linear array is divided into 2M symmetrical sub-arrays. It is expected that the radiation characteristics equivalent to the array element level excitation can be achieved by weighting at the sub-array level. That is, the main beam and side lobe levels of the desired sub-array level weighted sum pattern are the same as the array element level Taylor weighted pattern F. s Main beam and side lobe levels SLL (θ) s The main beam and side lobe levels of the expected sub-array-level weighted difference pattern are the same as the element-level Baylis-weighted pattern F d Main beam and side lobe levels SLL (θ) d If the optimization goal is to minimize the number of sub-arrays, the convex optimization model for the combined optimization of sum and difference beams is established as follows:

[0101]

[0102] where K (s) represents the number of sampling points of the main beam of the sum pattern, ε is the reconstruction error of the main beam, is the first zero point of the main beam of the sum pattern, is the first zero point of the main beam of the difference pattern, A(θ i ) represents the i-th observation direction θ i The corresponding sum direction pattern steering vector can be specifically expressed as follows according to the symmetry characteristics of the array:

[0103] A(θ i )=[2cos(βd1sin(θ i )) 2cos(βd2sin(θ i )) … 2cos(βd N sin(θ i ))] (13)

[0104] Where wave number β = 2π / λ, λ is the wavelength, d i Indicates the position of the i-th array element. Similarly, K (d) Indicates the number of sampling points of the main beam of the difference pattern, B(θ i ) represents the i-th observation direction θ i The corresponding difference pattern steering vector is specifically expressed as follows according to the symmetry characteristics of the array:

[0105] B(θ i )=[2sin(kd1sin(θ i )) 2sin(kd2sin(θ i )) … 2sin(kd N sin(θ i ))] (14)

[0106] Step S04) Solve the convex optimization model and calculate the sparse matrix S' ele , from which the number of subarrays M and the subarray-level weighted excitation corresponding to the beam are extracted And the sub-array level weighted excitation corresponding to the difference beam

[0107] Step S04 specifically includes:

[0108] Step S04-1) Solve the convex optimization model established in step S03 in the CVX solver, and convert the module value of the calculation result to be less than 10 -4 The value of is set to 0, and the sparse matrix S' is obtained ele .

[0109] Step S04-2) Detection matrix S' ele The numerical characteristics of the elements in the middle column, taking the first column as an example, if two consecutive element values ​​are non-zero, the sum of the two elements is assigned to the element with the larger modulus value, and the other element is set to zero. The elements in the second column are processed accordingly to ensure the same sparse characteristics as the first column, and the sparse matrix S' is updated. ele .

[0110] Step S04-3) Bring the sparse matrix into Calculate separately and Then extract the number of subarrays M and the subarray-level weighted excitation corresponding to the beam And the sub-array level weighted excitation corresponding to the difference beam

[0111] The sub-array division method of the monopulse radar antenna and difference beamforming proposed by the present invention according to the above method can be further verified and illustrated through the following specific simulation examples.

[0112] Simulation example:

[0113] This example considers a monopulse radar linear array antenna, where the array elements are evenly spaced at half wavelengths, and the total number of elements is 200. If the desired sum and difference beams are achieved by weighting at the element level, such as using low sidelobe Taylor weighting, Get the sum beam, use low sidelobe Baylis weighting Although the traditional synthesis method can directly weight the array element level to obtain the desired sum and difference beams, it requires two independent feeding systems, and the number of channels is the same as the number of array elements. Obviously, the feeding structure is large and complex. Here, the subarray division method of the monopulse radar antenna sum and difference beam forming proposed by the present invention is used to design, achieving the same main beam as Taylor weighting and Baylis weighting, and constraining the sum and difference beam sidelobe level SLL ≤ -20dB. The simulation results show that the present invention can divide 200 array elements into 10 bilaterally symmetrical subarrays, such as Figure 3 As shown in Table 1, the number of array elements in each sub-array and the sub-array-level weighted results corresponding to the sum and difference beams are shown in Table 1. Since the sub-array division structure is symmetrical, Table 1 also lists only the sub-array division results of the right half. The sum and difference beams obtained are shown in Table 1. Figure 4 As shown in the figure, it can be seen that only sub-array-level weighting can achieve the desired sum and difference beam radiation characteristics, and the number of sub-arrays is much smaller than the number of array elements, which greatly saves the number of channels and effectively reduces the complexity of the entire system. This will have great application value in early warning, search, tracking, precision guidance and strike.

[0114] Table 1 Subarray structure and weights of sum and difference beamforming

[0115] Subarray number 1 2 3 4 5 Number of array elements 25 11 24 20 20 and beam weights 1 0.9304 0.7925 0.6004 0.686 Difference beam weight 0.4209 0.8786 1 0.8549 0.7392

[0116] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention and are intended to be encompassed by the claims of the present invention.

Claims

1. A method for subarray division of a monopulse radar antenna and difference beamforming, the method comprising: Step S01) The 2N-element symmetrical linear array given by the monopulse radar antenna is divided into 2M symmetrical sub-arrays. The array elements in each sub-array are excited with equal amplitude and phase, and weighted only at the sub-array level. and Forming desired sum beam and difference beam; Step S02) The weighted excitation vector is obtained by summing the subarray level and difference beams. and Derive the array element excitation vector corresponding to the beam And the array element excitation vector corresponding to the difference beam The two sets of vectors form the matrix W ele , according to W ele The compressible characteristics of each column vector construct a sparse matrix S' ele , and perform sparse representation on it; Sparse matrix S' ele The two column vectors are and The sparse representation of satisfies the following formula: Where ξ represents the sparse matrix S' ele The first column, ψ represents the sparse matrix S' ele In the second column of , ξ and ψ have the same sparse characteristics, that is, the number of non-zero elements is the same and the positions of non-zero elements in the vector are the same; Step S03) According to the radiation requirements of the sum beam and the difference beam, based on the joint sparse recovery theory, a sum and difference beamforming convex optimization model that minimizes the number of sub-arrays is established; The step S03) specifically includes: According to the radiation requirements of the sum beam and difference beam, the main beam and side lobe levels of the expected sub-array-level weighted sum pattern are consistent with the array element-level Taylor weighted pattern F s Main beam and side lobe levels SLL (θ) s The main beam and side lobe levels of the expected sub-array-level weighted difference pattern are the same as the element-level Baylis-weighted pattern F d Main beam and side lobe levels SLL (θ) d Similarly, with minimizing the number of sub-arrays as the optimization goal, the convex optimization model for the joint optimization of sum and difference beams is established as follows: where K (s) represents the number of sampling points of the main beam of the sum pattern, ε is the reconstruction error of the main beam, is the first zero point of the main beam of the sum pattern, is the first zero point of the main beam of the difference pattern, A(θ i ) represents the i-th observation direction θ i The corresponding sum direction map steering vector; According to the characteristic that the sum beam excitation weight value is symmetrical about the center of the array, A(θ i ) is expressed as: A(θ i )=[2cos(βd1 sin(θ i )) 2cos(βd2 sin(θ i )) … 2cos(βd N sin(θ i ))] (13) Where wave number β = 2π / λ, λ is the wavelength, d i represents the position of the i-th array element; K (d) Indicates the number of sampling points of the main beam of the difference pattern, B(θ i ) represents the i-th observation direction θ i The corresponding difference pattern steering vector, according to the characteristic that the difference beam excitation weight value is antisymmetric about the array center, B(θ i ) is expressed as: B(θ i )=[2sin(kd1 sin(θ i )) 2sin(kd2 sin(θ i )) … 2sin(kd N sin(θ i ))] (14); Step S04) Solve the convex optimization model and calculate the sparse matrix S' ele , from which the number of subarrays M and the subarray-level weighted excitation corresponding to the beam are extracted And the sub-array level weighted excitation corresponding to the difference beam 2. The sub-array division method for monopulse radar antenna and difference beamforming according to claim 1, characterized in that: The step S01) specifically includes: The 2N-element symmetrical linear array given by the monopulse radar antenna is divided into 2M symmetrical sub-arrays. The array elements in each sub-array are excited with equal amplitude, and excitation is added to the sub-array ports. To achieve the desired sum beam, where represents the excitation value of the mth subarray port when forming the sum beam, the superscript (s) represents the sum beam related parameters, and the superscript T represents the transpose; Keep the subarray structure unchanged and add another set of excitations at the subarray ports To achieve the desired difference beam, represents the excitation value of the mth subarray port when forming the difference beam, and the superscript (d) represents the difference beam related parameters; For the same subarray partitioning structure, sum beam and difference beam are generated only by weighting at the subarray level.

3. The sub-array division method for monopulse radar antenna and difference beamforming according to claim 2, characterized in that: In the step S01), the number of positive semi-axis array elements N is much larger than the number of positive semi-axis sub-arrays M, and the number of array elements N of the mth sub-array is m Satisfy the following formula:

4. The sub-array division method for monopulse radar antenna and difference beamforming according to claim 3, characterized in that: The step S02) specifically includes: Sub-array weight vector and The element-level weighted vector is derived, that is, the element excitation vector corresponding to the beam for: Array element excitation vector corresponding to the difference beam for: By column vector and The matrix W ele for: According to the matrix W ele The characteristics of each column element are calculated by performing a difference operation: In order to keep the two matrices of the same size, we can transform the matrix W ele The first row vector Add to matrix W′ ele In the matrix W′ ele Then update to: Matrix S' ele is the matrix W ele The sparse representation of , there is the following relationship between the two: IN ele =T S' ele (7) The T matrix is ​​called the sparse transformation matrix and satisfies the following formula:

5. The sub-array division method for monopulse radar antenna and difference beamforming according to claim 4, characterized in that: Sparse matrix S' ele is a row sparse matrix with M non-zero rows, Represents the number of non-zero rows of this row sparse matrix, satisfying the following formula: in Represents the nth row of the matrix. The number of non-zero rows of a row-sparse matrix is ​​approximated by its mixed l2 / l1 norm, that is: represents the 2-norm of the n-th row of the matrix, and the 2-norm of any vector x is defined as Where Q is the length of vector x.

6. The method for sub-array division of a monopulse radar antenna and difference beamforming according to claim 1, characterized in that: The step S04) specifically includes: Step S04-1) solves the convex optimization model established in step S03) in the CVX solver, and converts the module value of the calculation result to be less than 10 -4 The value of is set to 0, and the sparse matrix S' is obtained ele ; Step S04-2) Detection matrix S' ele The numerical characteristics of the elements in the middle column are traversed. If two consecutive elements are non-zero, the sum of the two is assigned to the element with the larger modulus value, and the other element is set to zero. The next column of elements is processed accordingly to ensure the same sparse characteristics as the previous column, and the sparse matrix S' is updated. ele ; Step S04-3) Update the sparse matrix S' ele Substitute into formula (11) and calculate and Then extract the number of subarrays M and the subarray-level weighted excitation corresponding to the beam And the sub-array level weighted excitation corresponding to the difference beam

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