A method and system for designing a strongly constrained wide-angle scanning array antenna

Abstract

The application discloses a kind of strong constraint wide-angle scanning array antenna design method and system, belong to array antenna design technical field, comprising the following steps: S1: sector region division;S2: region random arrangement;S3: neighborhood joint scanning;S4: output adaptive value;S5: evolution iteration calculation.The application adopts neighborhood joint tracking mode, which can effectively exclude overlapping units between two adjacent sector regions, and limit the optimization interval to the initial sector region, effectively obtaining array element positions that meet the spacing constraint condition;Using multiple constraints can ensure that the results obtained by optimization have engineering realizability;Using area tracking adjustment method, invalid array elements can be effectively adjusted to valid positions, increasing the number of valid solutions and improving optimization efficiency.

Description

Technical Field

[0001] This invention relates to the field of array antenna design technology, specifically to a design method and system for a strongly constrained wide-angle scanning array antenna. Background Technology

[0002] As a device for transmitting and receiving electromagnetic waves, the antenna primarily transmits and acquires information. Its performance fundamentally determines the reliability and accuracy of long-distance information transmission in a system. Therefore, it has attracted considerable attention from scholars since its inception. In radar systems, antenna elements need to be arrayed to form an array antenna due to gain and other requirements. The most common form of array antenna is the uniform array, due to its simple array structure and convenient mathematical calculation model. However, uniform arrays also have some drawbacks: First, when the element spacing is less than λ / 2 (λ is the wavelength), only one main lobe exists within the visible area, and there are no grating lobes, allowing the array antenna to function normally. However, when the incident wavelength is small, the element spacing is very small, leading to mutual coupling effects between elements, which in turn affects the radiation characteristics of the array antenna. Second, the main lobe width of the array antenna pattern is inversely proportional to its aperture. To achieve a narrower main lobe, more antenna elements are needed, increasing the system cost.

[0003] To avoid the above-mentioned drawbacks, a sparse array layout can be adopted. This is because it has the following advantages: First, a sparse array has the same main lobe width as a regular array of the same aperture size, thus achieving the same resolution. Second, a sparse array uses fewer elements to achieve lower sidelobe levels and a narrower main lobe width, significantly reducing engineering and maintenance costs, and also lowering power supply complexity and failure rate to some extent. Third, with the same number of elements, a sparse array achieves a larger aperture, resulting in a smaller main lobe width. Due to the increased element spacing, the mutual coupling between elements is weakened.

[0004] With the development of electronic countermeasures technology, higher requirements are placed on phased array technology. Considering the need for wide-spatial-domain target jamming in practical applications, phased array antennas must have wide-angle scanning characteristics. Therefore, to reduce costs and achieve wide-spatial-domain jamming, a sparse array with wide-angle scanning performance can be used. However, the sidelobes of sparse arrays deteriorate when scanning at large angles, making the acquisition of sparse array antennas with lower sidelobes a key research focus. These problems urgently need to be solved; therefore, a strongly constrained wide-angle scanning array antenna design method and system are proposed. Summary of the Invention

[0005] The technical problem to be solved by this invention is: how to achieve wide-angle scanning performance of array antenna under the premise of sparse array arrangement, and provides a design method for strongly constrained wide-angle scanning array antenna.

[0006] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0007] S1: Sector-shaped region division

[0008] The entire array is divided into multiple identical sector regions, and the corresponding optimization parameters and variables are determined.

[0009] S2: Random arrangement of regions

[0010] Achieve random arrangement of array elements within a single sector region under sector constraints;

[0011] S3: Neighborhood Joint Scan

[0012] Based on the random arrangement of array elements in a single sector area, the array element arrangement in the parent sector area is determined by combining the array element arrangements in adjacent sector areas; based on the determined array element arrangement in the parent sector area, the array element arrangement of the entire array surface is obtained by rotation and replication.

[0013] S4: Output fitness value

[0014] After obtaining the position arrangement of all array elements, the fitness value is calculated according to its objective function; the array element positions are substituted into the radiation pattern calculation formula to obtain the radiation pattern characteristics, and the sidelobe level of the radiation pattern is extracted as the fitness value;

[0015] S5: Evolutionary Iterative Calculation

[0016] Based on the generated random numbers of positions within the population, repeat steps S1 to S4, iterating and calculating according to the evolutionary algorithm, where the random numbers of positions within the population are the random numbers of the array element position coordinates.

[0017] Furthermore, in step S1, the number of sectors is determined by the number of blocks Ns. Given the total number of array elements Ne, the number of array elements per block is Ne / Ns, and the corresponding central angle θ is 360 / Ns degrees. The remaining sector regions are obtained by rotating and copying the initial sector region. The initial sector region is defined as the mother sector region, and the sector regions obtained by rotating and copying are the child sector regions, wherein the number of blocks Ns is greater than or equal to 4.

[0018] Furthermore, in step S1, the corresponding optimization parameters and variables include the total number of array elements on the array surface and the radius of the sector.

[0019] Furthermore, in step S2, the sector constraint includes distance constraint and angle constraint, that is, the distance between the line connecting the array element at the generated random position and the origin is less than the radius of the sector, and the angle between the line connecting the array element to the origin and the x-axis is less than the central angle of the sector region; array elements that do not simultaneously meet the distance constraint and angle constraint are discarded, and only array elements that meet the constraints are retained.

[0020] Furthermore, in step S3, the specific process of the neighborhood joint scan is as follows:

[0021] S31: Based on the array element positions within the fan-shaped region obtained in step S2, the array element positions of the mother fan-shaped region are rotated and copied according to the central angle to obtain a new sub-fan-shaped region and its internal array element positions. The rotation center is the origin, and the rotation angle is set to θ or -θ when rotating and copying.

[0022] S32: Determine the spacing constraints based on the physical model of the antenna element and the desired number of elements;

[0023] S33: Merge the mother sector region and the child sector region into a single double sector region with a central angle of 2θ, and merge the array element position parameters of the two regions into a single array.

[0024] S34: Calculate the element spacing between each pair of elements within the double-fan region, find the smallest spacing value, and determine whether the smallest value satisfies the spacing constraint condition. If it does, exit the neighborhood joint scan; otherwise, perform tracking adjustment within the region.

[0025] S35: Based on the array element arrangement within the mother sector area determined in step S34, rotate and copy to obtain the array element arrangement of the entire array surface. The rotation center is the origin, and the central angle of rotation of the nth sub-sector area is n*θ.

[0026] Furthermore, in step S32, when determining the spacing constraints, the antenna element model covering the required frequency band is simulated and optimized to obtain the final element model that meets the standing wave performance and radiation performance. The maximum size of the antenna is determined by measuring the physical model scale. The number of array elements in each block is calculated based on the total number of array elements, and the average array surface area occupied by each array element is calculated. This area is converted into the area of ​​a circular region to obtain the radius of the equivalent circle. The final spacing constraints are determined by comprehensively considering the maximum size of the antenna and the radius of the equivalent circle, and the maximum value of the two is taken as the constraint spacing.

[0027] Furthermore, in step S34, the tracking adjustment within the region only adjusts the positions of the array elements within the mother sector region. The specific process is as follows:

[0028] S341: Based on the spacing between pairs of array elements within the double-fan region, filter out array elements that do not meet the spacing constraint conditions.

[0029] S342: Based on the selected array elements, filter out the array element numbers in the mother sector region that do not meet the double sector region spacing constraint condition.

[0030] S343: Track and adjust the array elements in the mother sector region that do not meet the spacing condition one by one. The tracking and adjustment method is two-dimensional adjustment, including the angle and radius directions. The direction of change is from zero to the boundary value of the region. The adjusted position must be within the mother sector region. When one of the array elements that does not meet the spacing constraint meets the spacing constraint, or when the tracking and adjustment process is completed but there is no point that meets the constraint, the tracking and adjustment of the next array element begins, and this process is repeated.

[0031] Furthermore, in step S4, it is determined whether the position of the array elements meets the spacing constraint condition. If it does, the pattern performance is obtained by substituting it into the pattern calculation formula, and its sidelobe level value is extracted as the fitness value; if it does not meet the constraint condition, the fitness value is set to 100.

[0032] Furthermore, in step S5, the position coordinates of the array elements within the regenerated sector are substituted into the evolutionary algorithm for optimization. Specifically, the optimization process involves substituting the newly generated population into the algorithm, calculating the fitness value of the population, selecting individuals with excellent performance based on the fitness value, generating a new generation of population, and continuing iterative optimization until the optimal solution is obtained. The evolutionary algorithm is either a genetic algorithm or a particle swarm optimization algorithm.

[0033] This invention also provides a strongly constrained wide-angle scanning array antenna design system, which optimizes the element positions of the phased array antenna using the above-described design method, including:

[0034] The sector region division module is used to divide the entire array into multiple identical sector regions and determine the corresponding optimization parameters and variables;

[0035] The regional random arrangement module is used to realize the random arrangement of array elements within a single sector region under sector constraints;

[0036] The neighborhood joint scanning module is used to determine the array element arrangement in the parent sector area by combining the array element arrangements of adjacent sector areas based on the random arrangement of array elements in a single sector area; and to obtain the array element arrangement of the entire array surface by rotating and copying based on the determined array element arrangement in the parent sector area.

[0037] The output fitness module is used to calculate the fitness value based on the objective function after obtaining the position arrangement of all array elements; the array element positions are substituted into the radiation pattern calculation formula to calculate the radiation pattern characteristics, and the sidelobe level of the radiation pattern is extracted as the fitness value;

[0038] The evolutionary iteration calculation module is used to repeat steps S1 to S4 based on the generated random numbers of positions within the population, and to perform iteration and calculation according to the evolutionary algorithm.

[0039] The present invention has the following advantages over the prior art:

[0040] 1. Using a sector-shaped block approach can increase the degree of freedom in optimization. In the later design stage, only optimization needs to be performed on a single sector area, which can greatly reduce the workload and design costs in the engineering implementation stage.

[0041] 2. By adopting a random arrangement of units within a sector-shaped region, compared to a dense arrangement, the degree of freedom for optimization can be greatly increased, making it easier to find the optimal solution and improving the efficiency of the algorithm optimization.

[0042] 3. The neighborhood joint tracing method can effectively eliminate overlapping elements between two adjacent sector regions, and limiting the optimization interval to the initial sector region can effectively obtain the array element positions that meet the spacing constraints. The use of multiple constraints can ensure that the optimization results are feasible in engineering. The use of the region tracing adjustment method can effectively adjust invalid array elements to valid positions, increase the number of valid solutions, and improve optimization efficiency. The phased array antenna obtained by this method can have low cost and wide-angle scanning characteristics. When this method is applied to information warfare systems, it can effectively improve the system's effective range while reducing the system's cost. Attached Figure Description

[0043] Figure 1 This is a flowchart of the strongly constrained wide-angle scanning array antenna design method in Embodiment 1 of the present invention;

[0044] Figure 2 This is the optimized array element position arrangement diagram obtained in Embodiment 2 of the present invention;

[0045] Figure 3 This is the normal sectional plane pattern of the array antenna at 15GHz after optimization in Embodiment 2 of the present invention;

[0046] Figure 4 This is the 45° cross-sectional radiation pattern of the array antenna at 15GHz after optimization in Embodiment 2 of the present invention;

[0047] Figure 5 This is the optimized array element position arrangement diagram obtained in Embodiment 3 of the present invention;

[0048] Figure 6 This is the normal tangential pattern of the array antenna at 12GHz after optimization in Embodiment 3 of the present invention;

[0049] Figure 7 This is the 60° cross-sectional radiation pattern of the array antenna at 12GHz after optimization in Embodiment 3 of the present invention. Detailed Implementation

[0050] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0051] Example 1

[0052] This embodiment provides a strongly constrained wide-angle scanning array antenna design method, ultimately obtaining the element distribution and array pattern of a wide-angle scanning sparsely arranged phased array antenna. For example... Figure 1 As shown, Figure 1 This is a flowchart illustrating the design method for a strongly constrained wide-angle scanning array antenna in this embodiment. The design is based on evolutionary algorithms, such as genetic algorithms and particle swarm optimization. The specific optimization approach is as follows: random numbers are generated and assigned to variables in the optimization system. A population of a certain size is calculated and analyzed to obtain initial results. Evolutionary upgrade operations, such as crossover and mutation, are performed on these populations. The resulting population is used as the new initial population. This process is repeated multiple times to obtain the optimal solution.

[0053] The optimization process begins with the array parameters and the number of blocks. The array parameters include the array shape and the array radius R; the array shape is chosen to be circular. The array is divided into multiple sector regions through block division. The number of blocks determines the array composition and the number of elements in each sector. The optimization process utilizes programming software such as MATLAB.

[0054] Specifically, the following steps are included:

[0055] S1: Sector-shaped region division

[0056] The entire array is divided into multiple identical sector regions, and corresponding optimization parameters and variables are determined. The number of sectors is determined by the number of blocks Ns. Given the total number of array elements Ne, the number of elements per block is Ne / Ns, and the corresponding central angle θ is 360 / Ns degrees. Since the remaining sector regions can be obtained by rotating and copying the initial sector region, the initial sector region is defined as the mother sector region, and the sector regions obtained by rotating and copying are called child sector regions.

[0057] S2: Random arrangement of regions

[0058] This study aims to achieve random arrangement of array elements within a single sector under sector constraints. Since each sector is relatively independent, the antenna and the back-end network are also independent. An initial value generation algorithm is needed for optimization iterations. The initial values ​​are derived from random numbers (the initial values ​​refer to the randomly generated coordinates of the array elements within the sector). Based on these random numbers, the array element parameters under the sector constraints are characterized; where the array element parameters refer to the position coordinates of the array elements in the coordinate system.

[0059] S3: Neighborhood Joint Scan

[0060] Based on the random arrangement of array elements in a single sector region, the array element arrangement in the parent sector region is determined by combining the array element arrangements of adjacent sector regions. A sector region adjacent to the parent sector region is obtained through rotation and replication. The two regions are merged into a double sector region. It is then considered whether the array elements within this region meet the element spacing requirements. If not, the positions that finally meet the requirements are found through tracking and adjustment within the region. Since the remaining sub-sector regions and their adjacent sector regions all constitute the same region as this double sector region, and the array element arrangements within them are also the same, only the above situation needs to be considered. This ensures that there is no element overlap on the array surface after rotation and replication to obtain the entire array.

[0061] S4: Output fitness value

[0062] After obtaining the positional arrangement of all array elements, the fitness value is calculated based on its objective function; the array element positions are substituted into the radiation pattern calculation formula to obtain the radiation pattern characteristics, and the sidelobe level of the radiation pattern is extracted as the fitness value.

[0063] S5: Evolutionary Iterative Calculation

[0064] Based on the random numbers of positions within the generated population, repeat steps S1 to S4, iterating and calculating according to the evolutionary algorithm.

[0065] In this embodiment, in step S1, it is recommended that the number of sector blocks be greater than or equal to 4. This is because if the number of blocks is too small, the array symmetry or periodicity will be too strong, making it impossible to reduce the sidelobes. When the number of blocks is large, the number of array elements in each region can be reduced, which simplifies the later design workload of sector blocks to a certain extent. It is recommended that the number of sector regions be an integer divisible by 360 to facilitate the subsequent selection of array elements in the sector regions.

[0066] In this embodiment, in step S2, the sector constraint includes distance constraint and angle constraint. That is, the array element at the generated random position must satisfy the following conditions: the distance between its line connecting to the origin is less than the radius of the sector, and the angle between its line connecting to the origin and the x-axis is less than the central angle of the sector region. Array elements that do not simultaneously meet the distance constraint and angle constraint are discarded, and only array elements that meet the constraints are retained.

[0067] In this embodiment, the specific process of the neighborhood joint scan in step S3 is as follows:

[0068] S31: Based on the array element positions within the fan-shaped region obtained in step S2, rotate and copy the array element positions of the parent fan-shaped region according to the central angle to obtain a new sub-fan-shaped region and its internal array element positions.

[0069] S32: Analyze and determine the spacing constraints based on the physical model of the antenna element and the desired number of elements;

[0070] S33: Merge the mother sector region and the child sector region into a single double sector region with a central angle of 2θ, and merge the array element position parameters of the two regions into a single array.

[0071] S34: Calculate the element spacing between each pair of elements in the double sector region, find the smallest spacing value, and determine whether the smallest value satisfies the spacing constraint condition. If it does, exit the neighborhood joint scan; if it does not, perform tracking adjustment within the region.

[0072] S35: Based on the array element arrangement within the mother sector area determined in step S34, rotate and copy to obtain the array element arrangement of the entire array surface. The rotation center is the origin, and the central angle of rotation of the nth sub-sector area is n*θ.

[0073] In this embodiment, in step S31, the rotation angle is set to θ or -θ when rotating and copying.

[0074] In this embodiment, in step S32, when determining the spacing constraints, it is necessary to perform simulation optimization on the antenna element model covering the required frequency band to obtain the final element model that meets the standing wave performance and radiation performance. The maximum size of the antenna is determined by measuring the physical model scale. The number of elements in each block is calculated based on the total number of array elements, and the average array area occupied by each element is calculated. This area is converted into the area of ​​a circular region to obtain the radius of the equivalent circle. The final spacing constraints are determined by comprehensively considering the maximum size of the antenna and the radius of the equivalent circle. It is recommended to take the maximum value of the two as the constraint spacing.

[0075] In this embodiment, during step S34, the position of the array elements within the mother sector area is adjusted only during the tracking adjustment within the region. The specific process is as follows:

[0076] S341: Based on the spacing between pairs of array elements within the double-fan region, filter out array elements that do not meet the spacing constraint conditions.

[0077] S342: Based on the selected array elements, filter out the array element numbers in the mother sector region that do not meet the double sector region spacing constraint condition.

[0078] S343: Track and adjust the array elements in the mother sector region that do not meet the spacing condition one by one. The tracking and adjustment method is two-dimensional adjustment, including the angle and radius directions. It is recommended that the change direction be from zero to the region boundary value. The adjusted position must be ensured to be within the mother sector region. When one of the array elements that does not meet the spacing constraint meets the spacing constraint, or when the tracking and adjustment process is completed but there is no point that meets the constraint, start tracking and adjusting the next array element and repeat this process.

[0079] In this embodiment, in step S4, it is determined whether the position of the array elements meets the spacing constraint condition. If it does, the pattern performance is obtained by substituting it into the pattern calculation formula, and its sidelobe level value is extracted as the fitness value. If it does not meet the constraint condition, the fitness value is set to 100.

[0080] In this embodiment, in step S5, the position coordinates of the array elements within the regenerated sector are substituted into the evolutionary algorithm for optimization. Specifically, the optimization process involves substituting the newly generated population into the algorithm, calculating the fitness value of the population, selecting individuals with excellent performance based on the fitness value, and generating a new generation of population to continue iterative optimization until the optimal solution is obtained. The evolutionary algorithm can be a genetic algorithm, a particle swarm optimization algorithm, etc.

[0081] Example 2

[0082] This embodiment optimizes the normal and scanning pattern of the circular aperture antenna, setting the x-axis and y-axis as follows: Figure 2 As shown. The antenna array to be optimized operates at a frequency of 15 GHz, with an element size of 8.6 mm and an element spacing of 10 mm. All elements are arranged as independent units within a region, with 10 blocks and 12 elements per block. The radiation pattern to be optimized is the normal and 45° cross-sectional radiation pattern of the antenna array, with a target sidelobe below -15 dB. The parameters to be optimized consist of the x-axis and y-axis coordinates of the 12 elements. A set of randomly generated element positions is used as initial values ​​in the optimization process. Sector division, random module arrangement, and neighborhood joint scanning are performed sequentially to obtain the element coordinates. During optimization, a fitness function is constructed based on the antenna's target sidelobes. The initial element coordinates and the fitness function are then substituted into the genetic algorithm for calculation. The population size is set to 400, and the number of optimization iterations is set to 100. A better solution is obtained through optimization.

[0083] like Figures 2 to 4 As shown, Figure 2 This is the optimized array element position layout obtained in this embodiment. Figure 3 This is the normal cross-sectional radiation pattern of the array antenna at 15GHz after optimization in this embodiment. Figure 4 The image shows the optimized 45° cross-sectional radiation pattern of the array antenna at 15 GHz.

[0084] As can be seen from the above, the normal and scanning state sidelobe levels of the optimized array obtained in this embodiment are below -15dB, and no grid lobes appear within the ±90° range.

[0085] Example 3

[0086] This embodiment optimizes the normal and scanning pattern of the circular aperture antenna, setting the x-axis and y-axis as follows: Figure 5As shown. The antenna array to be optimized operates at a frequency of 12 GHz, with an element size of 11.3 mm and an element spacing of 12.5 mm. All elements are arranged as independent units within a region, with 12 blocks and 19 elements per block. The radiation pattern to be optimized is the normal and 60° cross-sectional radiation pattern of the antenna array, with a target sidelobe below -10 dB. The parameters to be optimized consist of the x-axis and y-axis coordinates of the 19 elements. A set of randomly generated element positions is used as initial values ​​in the optimization process. Sector division, random module arrangement, and neighborhood joint scanning are performed sequentially to obtain the element coordinates. During optimization, a fitness function is constructed using the antenna's target sidelobes. The initial element coordinates and the fitness function are then substituted into the genetic algorithm for calculation. The population size is set to 400, and the number of optimization iterations is set to 100. A better solution is obtained through optimization.

[0087] like Figures 5 to 7 As shown, Figure 5 This is the optimized array element position layout obtained in this embodiment. Figure 6 This is the normal cross-sectional radiation pattern of the array antenna at 12GHz after optimization in this embodiment. Figure 7 The image shows the optimized 60° cross-sectional radiation pattern of the array antenna at 12 GHz.

[0088] As can be seen from the above, the normal and scanning state sidelobe levels of the optimized array obtained in this embodiment are below -10dB, and no grid lobes appear within the ±90° range.

[0089] In summary, the strongly constrained wide-angle scanning array antenna design method in the above embodiments effectively eliminates overlapping elements between two adjacent sector regions by employing a neighborhood joint tracing approach, and effectively obtains array element positions that meet the spacing constraints by limiting the optimization interval to the initial sector region. The use of multiple constraints ensures the engineering feasibility of the optimized results. The region tracing adjustment method effectively adjusts invalid array elements to valid positions, increasing the number of valid solutions and improving optimization efficiency. The phased array antenna obtained by this method has low cost and wide-angle scanning characteristics. When this method is applied to information warfare systems, it can effectively increase the system's effective range while reducing system costs.

[0090] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A design method for a strongly constrained wide-angle scanning array antenna, characterized in that, Includes the following steps: S1: Sector-shaped region division The entire array is divided into multiple identical sector regions, and the corresponding optimization parameters and variables are determined. S2: Random arrangement of regions Achieve random arrangement of array elements within a single sector region under sector constraints; S3: Neighborhood Joint Scan Based on the random arrangement of array elements in a single sector area, the array element arrangement in the parent sector area is determined by combining the array element arrangements in adjacent sector areas; based on the determined array element arrangement in the parent sector area, the array element arrangement of the entire array surface is obtained by rotation and replication. S4: Output fitness value After obtaining the positional arrangement of all array elements, calculate its fitness value based on its objective function; The array element positions are substituted into the radiation pattern calculation formula to obtain the radiation pattern characteristics, and the sidelobe level of the radiation pattern is extracted as the fitness value. S5: Evolutionary Iterative Calculation Based on the generated random numbers of positions within the population, repeat steps S1 to S4, iterating and calculating according to the evolutionary algorithm, where the random numbers of positions within the population are the random numbers of the array element position coordinates; In step S1, the number of sectors is determined by the number of blocks Ns. Given the total number of array elements Ne, the number of array elements per block is Ne / Ns, and the corresponding central angle θ is 360 / Ns degrees. The remaining sector regions are obtained by rotating and copying the initial sector region. The initial sector region is defined as the mother sector region, and the sector regions obtained by rotating and copying are the child sector regions, where the number of blocks Ns is greater than or equal to 4. In step S2, the sector constraint includes distance constraint and angle constraint, that is, the distance between the line connecting the array element at the generated random position and the origin is less than the radius of the sector, and the angle between the line connecting the array element to the origin and the x-axis is less than the central angle of the sector region; array elements that do not simultaneously meet the distance constraint and angle constraint are discarded, and only array elements that meet the constraints are retained; In step S3, the specific process of the neighborhood joint scan is as follows: S31: Based on the array element positions within the fan-shaped region obtained in step S2, the array element positions of the mother fan-shaped region are rotated and copied according to the central angle to obtain a new sub-fan-shaped region and its internal array element positions. The rotation center is the origin, and the rotation angle is set to θ or -θ when rotating and copying. S32: Determine the spacing constraints based on the physical model of the antenna element and the desired number of elements; S33: Merge the mother sector region and the child sector region into a single double sector region with a central angle of 2θ, and merge the array element position parameters of the two regions into a single array. S34: Calculate the element spacing between each pair of elements within the double-fan region, find the smallest spacing value, and determine whether the smallest value satisfies the spacing constraint condition. If it does, exit the neighborhood joint scan; otherwise, perform tracking adjustment within the region. S35: Based on the array element arrangement within the mother sector area determined in step S34, rotate and copy to obtain the array element arrangement of the entire array surface. The rotation center is the origin, and the central angle of rotation of the nth sub-sector area is n*θ.

2. The design method for a strongly constrained wide-angle scanning array antenna according to claim 1, characterized in that: In step S1, the corresponding optimization parameters and variables include the total number of array elements and the radius of the sector.

3. The design method for a strongly constrained wide-angle scanning array antenna according to claim 1, characterized in that: In step S32, when determining the spacing constraints, the antenna element model covering the required frequency band is simulated and optimized to obtain the final element model that meets the standing wave performance and radiation performance. The maximum size of the antenna is determined by measuring the physical model scale. The number of array elements in each block is calculated based on the total number of array elements, and the average array surface area occupied by each array element is calculated. This area is converted into the area of ​​a circular region to obtain the radius of the equivalent circle. The final spacing constraints are determined by comprehensively considering the maximum size of the antenna and the radius of the equivalent circle, and the maximum value of the two is taken as the constraint spacing.

4. The design method for a strongly constrained wide-angle scanning array antenna according to claim 3, characterized in that: In step S34, the tracking adjustment within the region only adjusts the positions of the array elements within the mother sector region. The specific process is as follows: S341: Based on the spacing between pairs of array elements within the double-fan region, filter out array elements that do not meet the spacing constraint conditions. S342: Based on the selected array elements, filter out the array element numbers in the mother sector region that do not meet the double sector region spacing constraint condition. S343: Track and adjust the array elements in the mother sector region that do not meet the spacing condition one by one. The tracking and adjustment method is two-dimensional adjustment, including the angle and radius directions. The direction of change is from zero to the boundary value of the region. The adjusted position must be within the mother sector region. When one of the array elements that does not meet the spacing constraint meets the spacing constraint, or when the tracking and adjustment process is completed but there is no point that meets the constraint, the tracking and adjustment of the next array element begins, and this process is repeated.

5. The design method for a strongly constrained wide-angle scanning array antenna according to claim 1, characterized in that: In step S4, it is determined whether the position of the array elements meets the spacing constraint condition. If it does, the pattern performance is obtained by substituting it into the pattern calculation formula and the sidelobe level value is extracted as the fitness value. If the condition is not met, set the fitness value to 100.

6. The design method for a strongly constrained wide-angle scanning array antenna according to claim 1, characterized in that: In step S5, the position coordinates of the array elements within the regenerated sector are substituted into the evolutionary algorithm for optimization. Specifically, the optimization process involves substituting the newly generated population into the algorithm, calculating the fitness value of the population, selecting individuals with excellent performance based on the fitness value, generating a new generation of population, and continuing iterative optimization until the optimal solution is obtained. The evolutionary algorithm is either a genetic algorithm or a particle swarm optimization algorithm.

7. A strongly constrained wide-angle scanning array antenna design system, characterized in that: Optimizing the element positions of a phased array antenna using the design method described in any one of claims 1 to 6 includes: The sector region division module is used to divide the entire array into multiple identical sector regions and determine the corresponding optimization parameters and variables; The regional random arrangement module is used to realize the random arrangement of array elements within a single sector region under sector constraints; The neighborhood joint scanning module is used to determine the array element arrangement in the parent sector area by combining the array element arrangements of adjacent sector areas based on the random arrangement of array elements in a single sector area; and to obtain the array element arrangement of the entire array surface by rotating and copying based on the determined array element arrangement in the parent sector area. The output fitness module is used to calculate the fitness value based on the objective function after obtaining the position arrangement of all array elements; the array element positions are substituted into the radiation pattern calculation formula to calculate the radiation pattern characteristics, and the sidelobe level of the radiation pattern is extracted as the fitness value; The evolutionary iteration calculation module is used to repeat steps S1 to S4 based on the generated random numbers of positions within the population, and to perform iteration and calculation according to the evolutionary algorithm.

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