A method for forming null points of array antenna beam pattern in a specified direction

Abstract

This invention discloses a method for forming nulls in the beam pattern of an array antenna in a specified direction, belonging to the field of electronic defense technology. The method includes the following steps: S1, calculating the weighting coefficients of the signal for each antenna element using an iterative solution method to obtain multiple weighting coefficients; S2, using the multiple weighting coefficients obtained in step S1 to weight the signal passing through multiple antenna elements, thereby forming the main beam of the antenna pattern in the specified direction and simultaneously forming nulls in the antenna beam pattern in other specified directions. Based on this invention, the method can effectively control the null depth in the null direction and achieve the beneficial effect of rapid and effective null beam modulation.

Description

Technical Field

[0001] This invention relates to the field of array antennas, and more specifically, to a method for forming null points in the beam pattern of an array antenna in a specified direction. Background Technology

[0002] Weighting the signals from each element of an array antenna to synthesize a null in the antenna beam pattern in a specified direction is a common application of array antennas. For array receiving antennas, setting a null in the direction of incoming interference signals can significantly reduce the antenna gain in that direction, decrease the strength of the received interference signal, improve the signal-to-interference ratio (SIR) of the entire system receiving normal signals, and enhance the system's anti-interference capability. For array transmitting antennas, setting a null in the direction of a third-party reconnaissance receiver can significantly reduce the antenna gain of the user signal in that direction, decrease the effective radiated power of the user signal in that direction, and enhance the user signal's counter-reconnaissance capability. Therefore, this has significant practical engineering implications for both transmitting and receiving array antennas.

[0003] Currently, setting the beam pattern nulls of an array antenna is mainly achieved by adjusting the weighting coefficients of each antenna element. The weighting coefficients can be solved using the following methods:

[0004] 1) Solve constrained optimization problems using the Lagrange multiplier method.

[0005] This method first generates an ideal beam pattern function only for the main beam direction, thereby obtaining the ideal weighting coefficient vector corresponding to each element antenna under this condition. Where N A Let W be the number of antenna elements in the array antenna. Then, express the nulls of the antenna beam pattern as the null constraint equations of the weighting coefficients of each antenna element, and solve for the ideal weighting coefficient vector W under the above null constraint equations. f The weighted coefficient vector with the minimum mean square error This serves as the actual weighting coefficient vector. The method is explained in detail in Section 3.7, "Null Steering," of the paper (Harry L. VanTrees. Optimum Array Processing, Part IV of Detection, Estimation, and Modulation Theory [M]. USA, New York: John Wiley & Sons, Inc. 2002.), and will not be repeated here.

[0006] 2) Use intelligent optimization algorithms to solve the optimization problem under zero-point constraints and other additional constraints.

[0007] In addition to the null constraint conditions of the array antenna beam pattern in a specified direction, other constraints can be added, including: array antenna beam gain conditions in the main beam direction, maximum sidelobe gain conditions of the entire array antenna beam pattern, etc. Then, various intelligent optimization algorithms, including: genetic algorithm, particle swarm optimization algorithm, immune algorithm, etc., are used to solve for the maximum value of the objective function under the above constraints. The objective function can be set as an evaluation function about the weighting coefficients or the array pattern function. The method designed in the literature (Ye Jianfeng, He Guorong, Guo Lili, Array antenna pattern null generation technology based on niche immune algorithm [J]. Journal of Shenzhen Institute of Information Technology, 2011, 9(3): 23-28.) is a typical example of this.

[0008] 3) Solve the optimization problem using the Schmidt orthogonal projection method.

[0009] Similar to the methods described above, an ideal beam pattern function is first generated only for the main beam direction. Then, null constraints on the array antenna beam pattern are constructed in the specified direction, and the optimal weighting coefficients are obtained under these constraints. This minimizes the deviation from the ideal beam pattern. This is still an optimization problem, which can be solved using the Schmidt orthogonal projection method. The literature (Jie Li, Luo Jingqing, Performance Comparative Analysis of Transmit Beam Zeroing Synthesis Method [J]. Modern Defense Technology, 2010, 38(5): 110-115, 120.) compares the method under different conditions such as amplitude and phase weighting, phase-only weighting, and amplitude-only weighting, and summarizes their respective characteristics and applicable scenarios.

[0010] 4) After transforming the underdetermined system of equations into a full-rank system of equations, the matrix inversion method is used for solving the problem.

[0011] Typically, the number N of the array antenna elements is... A The number of nulls is usually greater than the number required to construct the array antenna beam pattern nulls in the specified direction. Without other constraints, this problem is an underdetermined equations problem. To solve it, additional engineering boundary conditions can be added, such as main beam pointing constraints and antenna beam pattern null constraints in other non-specified directions, until the number of equations listed equals the number of weighting coefficients to be solved. This transforms the underdetermined equations into a full-rank system of equations, which is linear. Therefore, N can be solved directly by matrix inversion. A Each weighted coefficient. Summary of the Invention

[0012] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for forming null points in the beam pattern of an array antenna in a specified direction. Based on this method, the null depth in the null direction can be effectively controlled, achieving technical effects such as rapid and effective null beam modulation.

[0013] The objective of this invention is achieved through the following solution:

[0014] A method for forming null points in the beam pattern of an array antenna in a specified direction, assuming N A In a uniform linear array composed of 100 antenna elements, the distance between two adjacent antenna elements is denoted as d. For transmitting and receiving signals with wavelength λ, the angle between the direction of the main beam and the normal to the array baseline is denoted as θ. M And require that in other N Z one direction To form the null point of the antenna beam pattern, the following steps are involved:

[0015] S1, the weighting coefficients of each antenna element for the signal are calculated using an iterative solution method to obtain N. A Each weighting coefficient;

[0016] S2, N is obtained using the iterative solution method in step S1. A Each weighted coefficient is used to calculate the weighted coefficients after N steps. A The signals from each antenna element are weighted, which allows for the calculation of θ. M The main beam that forms the antenna pattern in the direction, and simultaneously in other N... Z one direction The null point forms the antenna beam pattern.

[0017] Further, step S1 includes the following sub-steps:

[0018] Step S11: For N Z +1 area of ​​focus Construction (N) Z +1)×N A The signal direction matrix A1 is as follows:

[0019]

[0020] Further, following step S11, the following sub-steps are included:

[0021] Step S12: For the aforementioned N Z +1 area of ​​focus Construct N A ×(N ZThe +1) dimension array antenna preset beam pattern sampling matrix A2 is as follows:

[0022]

[0023] In equation (2), N A ×1 dimensional column vector Main beam pointing to θ Z,i The preset beam pattern sampling vector in the direction, wherein each component n = 1, 2, ..., N A As expressed in the following formula:

[0024]

[0025] In equation (3), w Z,n For the preset weighting coefficients, low sidelobe weighting coefficients are used. These low sidelobe weighting coefficients include weighting coefficients similar to those in the Hamming window form. Then w Z,n As expressed in the following formula:

[0026]

[0027] In equation (2), N A ×1 dimensional column vector Main beam pointing to θ M The preset beam pattern sampling vector in the direction, wherein each component As expressed in the following formula:

[0028]

[0029] Further, following step S12, the following sub-steps are included:

[0030] Step S13: Transfer (N) Z +1)×N A The signal direction matrix A1 and N of the dimension A ×(N Z Multiply by the (+1)-dimensional array antenna preset beam pattern sampling matrix A2 to generate (N) Z +1)×(N Z +1) dimensional intermediate matrix G Mid As expressed in the following formula:

[0031] G Mid =A1·A2 (6)

[0032] And denote the intermediate matrix G Mid Each element in is

[0033] Further, following step S13, the following sub-steps are included:

[0034] Step S14: Set (N) Z +1)×1 dimensional intermediate weighted vector W Mid The initial value is expressed by the following formula:

[0035]

[0036] Simultaneously, the iteration number variable N RE Initialize to zero, i.e., N RE =0; and set an error control threshold γ. sh and the maximum number of iterations control threshold M RE Then, proceed with the next steps.

[0037] Further, following step S14, the following sub-steps are included:

[0038] Step S15: Using the intermediate matrix G Mid With the intermediate weighted vector W Mid Multiply to obtain (N) Z +1)×1 dimensional error vector E rror As expressed in the following formula:

[0039] E rror =G Mid ·W Mid (8)

[0040] And denote the error vector as

[0041] Further, following step S15, the following sub-steps are included:

[0042] Step S16: The error vector E calculated in step S15 rror The first N in Z Each component is used to weight the intermediate vector W. Mid The correction is made to obtain a new intermediate weighted vector W. Mid,new As expressed in the following formula:

[0043]

[0044] At the same time, the number of iterations increases by 1, that is, N RE ←N RE +1.

[0045] Further, following step S16, the following sub-steps are included:

[0046] Step S17: If the error vector E rror The first N in Z The magnitude of each component is less than a pre-set threshold γ. shThen proceed to step S18; if the number of iterations N RE Exceeding the preset threshold value M RE Then proceed to step S18; if neither of the above two conditions is met, then the newly obtained intermediate weighted vector W is... Mid,new Reassign to the intermediate weighted vector W Mid Proceed to step S15 for further iterative calculations.

[0047] Further, following step S17, the following sub-steps are included:

[0048] Step S18: Use the latest intermediate weighted vector W obtained after the iteration. Mid,new N is obtained by solving the following formula. A Weighting coefficients

[0049] W h =A2·W Mid , new (10).

[0050] Furthermore, the uniform linear array comprises 21 element antennas.

[0051] The beneficial effects of this invention include:

[0052] This invention avoids matrix inversion operations throughout the process of forming nulls in the beam pattern of an array antenna in a specified direction, resulting in simplified calculations and rapid convergence of iterative calculations. This improvement allows for the rapid acquisition of weighting coefficients for each antenna element, whether for beamforming of the transmitting or receiving array. Physically, the entire iterative solution process is essentially a gradual reduction of the gain of the sidelobe beams in the null directions. Furthermore, considering practical engineering applications, this method can effectively control the null depth in the null directions, achieving rapid and effective null beam manipulation. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 The beam pattern of the array antenna is obtained by synthesizing the weighted coefficients using the method of the embodiments of the present invention. Detailed Implementation

[0055] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.

[0056] As can be seen from the various weighting coefficient solutions for beam pattern null formation in the background, most of these methods involve solving optimization problems, resulting in relatively large computational loads. Furthermore, some methods require matrix inversion operations, especially when a large number of beam pattern nulls are required, making them inconvenient for engineering applications. After creative consideration, the inventors of this invention address the aforementioned technical problems of inconvenience, slow speed, and low beam control efficiency in beam pattern null formation due to large computational loads. They propose a method for forming beam pattern nulls in a specified direction based on iterative weighting coefficient solution. The main inventive concept is that, based on the formation of the main antenna beam, an iterative cancellation method is used to solve for the weighting coefficients corresponding to each element antenna of the array antenna, considering the constraints in the direction of each beam null. This method is computationally simple, has clear physical meaning, and is suitable for practical engineering applications.

[0057] In the specific implementation process, the following inventive concepts are also included:

[0058] By N A In a uniform linear array composed of 100 antenna elements, the distance between two adjacent antenna elements is denoted as d. For transmitting and receiving signals with wavelength λ, the angle between the direction of the main beam and the normal to the array baseline is denoted as θ. M And require that in other N Z one direction This forms the null point of the antenna beam pattern. Therefore, for the beam pattern passing through N... A N signals from each unit antenna A Weighting coefficients The solution can be found through the following steps:

[0059] Step 1: For the aforementioned N Z +1 area of ​​focus Construction (N) Z +1)×N A The signal direction matrix A1 is as follows:

[0060]

[0061] Step 2: Regarding the aforementioned N Z +1 area of ​​focus Construct N A ×(N Z The +1) dimension array antenna preset beam pattern sampling matrix A2 is as follows:

[0062]

[0063] In equation (2), N A ×1 dimensional column vector Main beam pointing to θ Z,i The preset beam pattern sampling vector in the direction, wherein each component n = 1, 2, ..., N A As expressed in the following formula:

[0064]

[0065] In equation (3), w Z,n For the preset weighting coefficients, low sidelobe weighting coefficients are generally used, such as weighting coefficients similar to the Hamming window form, then w Z,n As expressed in the following formula:

[0066]

[0067] In equation (2), N A ×1 dimensional column vector Main beam pointing to θ M The preset beam pattern sampling vector in the direction, wherein each component As expressed in the following formula:

[0068]

[0069] Step 3: Place (N) Z +1)×N A The signal direction matrix A1 and N of the dimension A ×(N Z Multiply by the (+1)-dimensional array antenna preset beam pattern sampling matrix A2 to generate (N) Z +1)×(N Z +1) dimensional intermediate matrix G Mid As expressed in the following formula:

[0070] G Mid =A1·A2 (6)

[0071] And denote the intermediate matrix G Mid Each element in is

[0072] Step 4: Set (N) Z +1)×1 dimensional intermediate weighted vector W Mid The initial value is expressed by the following formula:

[0073]

[0074] Simultaneously, the iteration number variable N RE Initialize to zero, i.e., N RE =0. And set a very small error control threshold γ. sh and the maximum number of iterations control threshold M RE Then, proceed with the next steps.

[0075] Step 5: Utilize the intermediate matrix G Mid With the intermediate weighted vector W Mid Multiply to obtain (N) Z +1)×1 dimensional error vector E rror As expressed in the following formula:

[0076] E rror =G Mid ·W Mid (8)

[0077] And denote the error vector as

[0078] Step 6: The error vector E calculated in Step 5 rror The first N in Z Each component is used to weight the intermediate vector W. Mid The correction is made to obtain a new intermediate weighted vector W. Mid,new As expressed in the following formula:

[0079]

[0080] At the same time, the number of iterations increases by 1, that is, N RE ←N RE +1.

[0081] Step 7: If the error vector E rror The first N in Z The magnitude of each component is less than a pre-set threshold γ. sh Then proceed to step 8; if the number of iterations N RE Exceeding the preset threshold value M RE Then proceed to step 8; if neither of the above two conditions is met, then the newly obtained intermediate weighted vector W is... Mid,new Reassign to the intermediate weighted vector W Mid Proceed to step 5 for further iterative calculations.

[0082] Step 8: Use the latest intermediate weighted vector W obtained after the iteration. Mid,new N is obtained by solving the following formula. A Weighting coefficients

[0083] W h =A2·WMid,new (10)

[0084] The N obtained by the above iterative solution method A Weighting coefficients For N A The signals from each antenna element are weighted, which allows for the calculation of θ. M The main beam that forms the antenna pattern in the direction, and simultaneously in other N... Z one direction The null point forms the antenna beam pattern.

[0085] The following is a practical application example using a uniform linear array containing 21 antenna elements.

[0086] This linear array operates at a frequency of 3 GHz, corresponding to a signal wavelength λ = 0.1 m. The spacing between adjacent array elements is d = 0.05 m, and the main beam direction is required to be oriented at an angle θ. M = -10°, and at the same time, it is required that the antenna beam pattern null be formed in the other three directions, namely -36°, 22°, and 45°.

[0087] Firstly, regarding the four areas of focus θ Z,1 = -36°, θ Z,2 =22°, θ Z,3 =45°, θ M = -10°, construct a 4×21-dimensional signal arrival direction matrix A1 according to equation (1), and construct a 21×4-dimensional array antenna preset beam pattern sampling matrix A2 according to equations (2) to (5).

[0088] Then, a 4×4 dimensional intermediate matrix G is generated according to equation (6). Mid Table 1 shows the 4×4 dimensional intermediate matrix G. Mid The elements in:

[0089] Table 1: The 4×4 dimensional intermediate matrix G in this example Mid List of elements in

[0090]

[0091] The 4×1 dimensional intermediate weighting vector W can be calculated according to equation (7). Mid The initial value and the number of iterations are set to N. RE =0, and set the error control threshold γ sh =0.0001, maximum iteration count control threshold M RE =10, and begin the iterative calculation and judgment operations from step 5 to step 7.

[0092] After the first iteration, the 4×1 dimensional error vector E rrorThe moduli of the first three components are 0.003301038552687, 0.009241766930689, and 0.004146429956931, respectively.

[0093] After the second iteration, the 4×1 dimensional error vector E rror The moduli of the first three components are 0.000054700019851, 0.000040848797167, and 0.000098590760926, respectively.

[0094] As can be seen from the above, after the second iteration, the error vector E rror The magnitudes of the first three components are all less than the preset threshold γ. sh The condition = 0.0001 is met, so the iteration exits, subsequent steps are executed, and the intermediate weighted vector W at the end of the iteration is obtained simultaneously. Mid,new as follows:

[0095]

[0096] Finally, the weighting coefficients for the 21 antenna elements are calculated according to equation (10) in step 8, as shown in the table below:

[0097] Table 2: List of 21 weighting coefficients calculated in this example

[0098]

[0099]

[0100] The signals of each element antenna in the array antenna are weighted using the 21 weighting coefficients obtained above, resulting in the synthesized array antenna beam pattern as shown below. Figure 1 As shown.

[0101] Depend on Figure 1 It can be seen that the main beam direction of the array antenna pattern synthesized by the solved weighted coefficients points to -10°, while forming zero points of the antenna beam pattern in the three directions of -36°, 22°, and 45°, which meets the design requirements.

[0102] Example 1

[0103] A method for forming null points in the beam pattern of an array antenna in a specified direction, assuming N A In a uniform linear array composed of 100 antenna elements, the distance between two adjacent antenna elements is denoted as d. For transmitting and receiving signals with wavelength λ, the angle between the direction of the main beam and the normal to the array baseline is denoted as θ. M And require that in other N Z one direction To form the null point of the antenna beam pattern, the following steps are involved:

[0104] S1, the weighting coefficients of each antenna element for the signal are calculated using an iterative solution method to obtain N. A Each weighting coefficient;

[0105] S2, N is obtained using the iterative solution method in step S1. A Each weighted coefficient is used to calculate the weighted coefficients after N steps. A The signals from each antenna element are weighted, which allows for the calculation of θ. M The main beam that forms the antenna pattern in the direction, and simultaneously in other N... Z one direction The null point forms the antenna beam pattern.

[0106] Example 2

[0107] Based on Example 1, step S1 includes the following sub-steps:

[0108] Step S11: For N Z +1 area of ​​focus Construction (N) Z +1)×N A The signal direction matrix A1 is as follows:

[0109]

[0110] Example 3

[0111] Based on Example 2, after step S11, the following sub-steps are included:

[0112] Step S12: For the aforementioned N Z +1 area of ​​focus Construct N A ×(N Z The +1) dimension array antenna preset beam pattern sampling matrix A2 is as follows:

[0113]

[0114] In equation (2), N A ×1 dimensional column vector Main beam pointing to θ Z,i The preset beam pattern sampling vector in the direction, wherein each component n = 1, 2, ..., N A As expressed in the following formula:

[0115]

[0116] In equation (3), w Z,nFor the preset weighting coefficients, low sidelobe weighting coefficients are used. These low sidelobe weighting coefficients include weighting coefficients similar to those in the Hamming window form. Then w Z,n As expressed in the following formula:

[0117]

[0118] In equation (2), N A ×1 dimensional column vector Main beam pointing to θ M The preset beam pattern sampling vector in the direction, wherein each component As expressed in the following formula:

[0119]

[0120] Example 4

[0121] Based on Example 3, after step S12, the following sub-steps are included:

[0122] Step S13: Transfer (N) Z +1)×N A The signal direction matrix A1 and N of the dimension A ×(N Z Multiply by the (+1)-dimensional array antenna preset beam pattern sampling matrix A2 to generate (N) Z +1)×(N Z +1) dimensional intermediate matrix G Mid As expressed in the following formula:

[0123] G Mid =A1·A2 (6)

[0124] And denote the intermediate matrix G Mid Each element in is

[0125] Example 5

[0126] Based on Example 4, after step S13, the following sub-steps are included:

[0127] Step S14: Set (N) Z +1)×1 dimensional intermediate weighted vector W Mid The initial value is expressed by the following formula:

[0128]

[0129] Simultaneously, the iteration number variable N RE Initialize to zero, i.e., N RE =0; and set an error control threshold γ. sh and the maximum number of iterations control threshold MRE Then, proceed with the next steps.

[0130] Example 6

[0131] Based on Example 5, after step S14, the following sub-steps are included:

[0132] Step S15: Using the intermediate matrix G Mid With the intermediate weighted vector W Mid Multiply to obtain (N) Z +1)×1 dimensional error vector E rror As expressed in the following formula:

[0133] E rror =G Mid ·W Mid (8)

[0134] And denote the error vector as

[0135] Example 7

[0136] Based on Example 6, after step S15, the following sub-steps are included:

[0137] Step S16: The error vector E calculated in step S15 rror The first N in Z Each component is used to weight the intermediate vector W. Mid The correction is made to obtain a new intermediate weighted vector W. Mid,new As expressed in the following formula:

[0138]

[0139] At the same time, the number of iterations increases by 1, that is, N RE ←N RE +1.

[0140] Example 8

[0141] Based on Example 7, after step S16, the following sub-steps are included:

[0142] Step S17: If the error vector E rror The first N in Z The magnitude of each component is less than a pre-set threshold γ. sh Then proceed to step S18; if the number of iterations N RE Exceeding the preset threshold value M RE Then proceed to step S18; if neither of the above two conditions is met, then the newly obtained intermediate weighted vector W is... Mid,new Reassign to the intermediate weighted vector W MidProceed to step S15 for further iterative calculations.

[0143] Example 9

[0144] Based on Example 8, after step S17, the following sub-steps are included:

[0145] Step S18: Use the latest intermediate weighted vector W obtained after the iteration. Mid,new N is obtained by solving the following formula. A Weighting coefficients

[0146] W h =A2·W Mid,new (10).

[0147] Example 10

[0148] Based on Embodiment 1, the uniform linear array comprises 21 element antennas.

[0149] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0150] According to one aspect of this application, a computer program product or computer program is provided, comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the methods provided in the various alternative implementations described above.

[0151] In another aspect, this application also provides a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods described in the above embodiments.

[0152] All parts not covered in this invention are the same as or can be implemented using existing technologies.

[0153] The above technical solution is only one embodiment of the present invention. For those skilled in the art, based on the application methods and principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the methods described in the above specific embodiments of the present invention. Therefore, the methods described above are only preferred and are not restrictive.

[0154] In addition to the examples above, other embodiments may be obtained by those skilled in the art based on the above disclosure or by making modifications using knowledge or technology in related fields. The features of each embodiment may be interchanged or replaced. Modifications and changes made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for forming null points in the beam pattern of an array antenna in a specified direction, characterized in that, Suppose that In a uniform linear array composed of 1000 antenna elements, the distance between two adjacent antenna elements is denoted as . For wavelengths of The signal is transmitted and received, and the angle between the direction of the formed main beam and the normal of the array baseline is denoted as . and requested in other one direction To form the null point of the antenna beam pattern, the following steps are involved: S1, the weighting coefficients of each antenna element for the signal are calculated using an iterative solution method, resulting in... Each weighting coefficient; S2, obtained using the iterative solution method in step S1. Each weighting coefficient, for the processed The signals from each antenna element are weighted and processed to achieve the desired effect. The main beam that forms the antenna pattern in the direction, and simultaneously in other directions. one direction Null points that form the antenna beam pattern; Step S1 includes the following sub-steps: Step S11: For One area of ​​focus structure 3D signal direction matrix as follows: （1）； Step S12: Regarding the aforementioned One area of ​​focus structure dimensional array antenna preset beam pattern sampling matrix as follows: （2） In formula (2) dimensional column vector , The main beam direction The preset beam pattern sampling vector in the direction, wherein each component , As expressed in the following formula: （3） In formula (3) The preset weighting coefficients are used, employing low sidelobe weighting coefficients. These low sidelobe weighting coefficients include weighting coefficients similar to those in the Hamming window format. As expressed in the following formula: （4） In formula (2) dimensional column vector The main beam direction The preset beam pattern sampling vector in the direction, wherein each component , As expressed in the following formula: （5）； Step S13: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] 3D signal direction matrix and dimensional array antenna preset beam pattern sampling matrix Multiplication, generation dimensional intermediate matrix As expressed in the following formula: （6） And denote the intermediate matrix Each element in is , , ; Step S14: Setting Dimensional intermediate weighted vector The initial value is expressed by the following formula: （7） Simultaneously, the iteration number variable Initialize to zero, that is And set an error control threshold. and maximum iteration count control threshold Then, proceed with the next steps; Step S15: Utilize the intermediate matrix With intermediate weighted vector Multiply and find dimensional error vector As expressed in the following formula: （8） And denote the error vector as ; Step S16: The error vector calculated in step S15 The front of the middle Each component is used to weight the intermediate vector. Make corrections to obtain a new intermediate weighted vector. As expressed in the following formula: （9） At the same time, the iteration count increases by 1, that is... ; Step S17: If the error vector The front of the middle The magnitude of each component is less than a pre-set threshold. Then proceed to step S18; if the number of iterations... Exceeding the preset threshold Then proceed to step S18; if neither of the above two conditions is met, then the newly obtained intermediate weighted vector will be... Reassign to the intermediate weighted vector Proceed to step S15 for further iterative calculation; Step S18: Use the latest intermediate weighted vector obtained after the iteration. The following formula can be used to solve for the problem. Weighting coefficients : （10）。 2. The method for forming null points of the beam pattern of an array antenna in a specified direction according to claim 1, characterized in that, The uniform linear array contains 21 antenna elements.

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