Subarray-level outer-sparse and inner-dense array antenna based on cylindrical antenna and design method thereof

Abstract

The invention belongs to the technical field of array antennas, and particularly relates to a sub-array-level sparse-outside and dense-inside array antenna based on a cylindrical antenna and a design method of the sub-array-level sparse-outside and dense-inside array antenna. Aiming at the problem that the design thought that feed sources are arranged on cylindrical reflecting surfaces is lacked in the current array antenna design field, array elements are distributed on a plurality of cylindrical surfaces according to a preset proportion, each cylindrical surface is divided into a center sub-array and an edge sub-array, and an array in which the center sub-arrays and the edge sub-arrays are distributed in a mirror symmetry manner is adopted; and optimizing the distance between adjacent array elements in the sub-array through a bat algorithm to obtain an optimal solution of the sparse-outside dense-inside array.

Description

Technical Field

[0001] This invention belongs to the field of array antenna technology, specifically relating to a subarray-level sparse-inner-dense array antenna based on cylindrical antennas and its design method. Background Technology

[0002] Cylindrical antennas, due to the focusing effect of their reflectors, produce a narrow beam along the curved surface and a wide beam along the axis. This property makes them crucial in radar, communication, and astronomical observation. However, traditional array methods have limitations. For example, in uniform arrays, if cylindrical arrays are arranged uniformly at half-wavelength intervals, although the Nyquist sampling theorem is satisfied, the number of array elements increases with the aperture, raising antenna costs. Furthermore, when the spacing exceeds half-wavelength, grating lobes appear, interfering with the antenna signal. Non-uniform arrays can effectively suppress grating lobes, and by breaking the periodicity of the element arrangement, the element spacing can be appropriately increased, thereby reducing antenna costs. However, completely random array arrangements lead to high computational complexity and engineering difficulties. Therefore, subarray technology has gradually become a research hotspot in the field of array antennas.

[0003] Subarray-level arrays divide the array into subarrays, each with identical element arrangements, allowing each subarray to use the same feed network, reducing design complexity and system cost. Traditional subarrays are often regularly partitioned. For example, Chai Xuefeng et al., in their paper "Research on Adaptive Beamforming of Phased Array Antennas Based on Subarray Partitioning," used swarm intelligence optimization algorithms to partition uniformly adjacent subarrays, regularly overlapping subarrays, and non-uniformly adjacent subarrays under the premise of uniform element arrangement. Junming D et al., in their paper "Sidelobe Level and Aperture Efficiency Optimization for TiledAperiodicArrayAntennas," studied aperiodic subarrays (rotated) and aperiodic arrays composed of non-uniform elements. Non-uniformly adjacent subarrays can effectively suppress grating lobes, but lack boundary constraints and optimization strategies for cylindrical scenarios. Summary of the Invention

[0004] To address the current lack of design ideas for arranging feed sources on cylindrical reflectors in the field of array antenna design, this invention provides a subarray-level sparse-outer-dense-inner array antenna based on a cylindrical antenna and its design method. By employing a mirror-symmetrical distribution of center and edge subarrays, the optimal solution for the sparse-outer-dense-inner-inner array is obtained through optimization of the element arrangement within the subarrays using the bat algorithm.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] In a first aspect, the present invention provides a subarray-level sparse-inner-dense array antenna based on a cylindrical antenna, comprising:

[0007] The array elements are distributed on multiple cylindrical reflective surfaces according to a preset ratio. Edge subarrays are set at both ends of the cylindrical reflective surfaces, and a central subarray is set between two edge subarrays. The central subarray and the edge subarrays are mirror-symmetrical about the center of the array.

[0008] Both the central subarray and the edge subarrays comprise subarray grids and subarray boundaries. A spacing of 0.25 wavelengths exists between the subarray boundaries and the subarray grids to prevent the spacing between boundary elements of two adjacent subarrays from failing to meet the minimum element spacing requirement (half a wavelength). The subarray boundary refers to the location of the boundary elements.

[0009] The bat algorithm is used to optimize the spacing between adjacent array elements to obtain the overall array arrangement. The spacing between adjacent array elements within a subarray is the optimization variable of the algorithm. The optimization variable has a maximum and a minimum value. The smaller the maximum and minimum values, the denser the array elements, and vice versa.

[0010] Furthermore, the number of array elements contained in the central subarray and the edge subarray can be the same or different.

[0011] Furthermore, the size of the subarray boundary and the subarray grid is not fixed, but changes according to the position of the boundary elements obtained by the bat algorithm.

[0012] Furthermore, the array elements in the central subarray and the edge subarray on the multiple cylindrical reflective surfaces are arranged differently.

[0013] Furthermore, the minimum spacing between adjacent array elements within the central subarray is 0.5 times the wavelength, and the maximum spacing is 0.875 times the wavelength.

[0014] Furthermore, the minimum spacing between adjacent array elements within the edge subarray is 0.75 times the wavelength, and the maximum spacing is 1 times the wavelength.

[0015] Secondly, the present invention provides a design method for a subarray-level sparse-inner-dense array antenna based on a cylindrical antenna, comprising the following steps:

[0016] S1. Determine the number of array elements allocated to each cylindrical reflector surface;

[0017] S2. Based on the number of array elements allocated to each cylindrical reflective surface, allocate the number of array elements in the central subarray and the edge subarray.

[0018] S3. Set the optimization variable of the optimization algorithm to the element spacing. The minimum value of the spacing between adjacent elements of the central subarray is half a wavelength, and the maximum value is 0.875 wavelengths. The minimum value of the spacing between adjacent elements of the edge subarray is 0.75 wavelengths, and the maximum value is 1 wavelength.

[0019] S4. Use the bat algorithm to iteratively optimize the spacing between adjacent array elements in each subarray, and then obtain the array element arrangement in the subarray.

[0020] S5. Arrange the central subarray and the edge subarray in sequence on the positive half of the y-axis. The distance between the boundaries of adjacent subarrays of the central subarray and the edge subarray is half a wavelength. Mirror the arrangement of the central subarray and the edge subarray to obtain the arrangement of the entire cylindrical reflective surface and the entire array.

[0021] S6. Calculate the radiation pattern of the array, determine the fitness function of the corresponding arrangement, and store the relevant data;

[0022] S7. When the bat algorithm reaches the maximum number of iterations, stop iterating and output the arrangement position and peak sidelobe level corresponding to the current best fitness function.

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] (1) The present invention adopts an irregular non-overlapping subarray form, and the array elements in the subarray adopt an aperiodic layout, which reduces the design complexity while ensuring the ability to suppress sidelobe levels.

[0025] (2) By specifying the optimizable spacing of array elements in different subarrays, the length range of the baselines contained in different subarrays can be defined, so that the array has more independent baselines, reducing array redundancy and effectively reducing sidelobe level.

[0026] (3) This array method can be extended to large-scale arrays while maintaining good grating lobe suppression characteristics. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the overall planar structure of the antenna array;

[0028] Figure 2 A schematic diagram of the structure of the central subarray or the edge subarray;

[0029] Figure 3 This invention presents a better actual array arrangement after optimizing the 96-element array antenna in simulation experiments.

[0030] Figure 4 This is the intensity distribution diagram of the beam pattern obtained in the simulation example of this invention on a two-dimensional plane;

[0031] Figure 5 This is a three-dimensional view of the beam pattern obtained in the simulation example of the present invention.

[0032] Figure 6 The beam pattern obtained in the simulation example of this invention is... Two-dimensional slices on a plane;

[0033] Figure 7 This is a comparison chart of the average convergence curves of the structure of this invention and other structures obtained by running the same optimization algorithm parameters five times.

[0034] Figure 8 To expand the array size to an array arrangement of 192 elements using the method in this invention;

[0035] Figure 9 This is the intensity distribution diagram of the beam pattern obtained in the simulation example of this invention on a two-dimensional plane;

[0036] Figure 10 This is a three-dimensional view of the beam pattern obtained in the simulation example of the present invention.

[0037] Figure 11 The beam pattern obtained in the simulation example of this invention is... Two-dimensional slices on a plane. Detailed Implementation

[0038] To further illustrate the technical solution of the present invention, the present invention will be further described below through embodiments.

[0039] Example 1

[0040] like Figure 1 and Figure 2 As shown, this embodiment of a subarray-level sparse-inner-dense array antenna based on a cylindrical antenna includes:

[0041] Array elements 1 are distributed on multiple cylindrical reflective surfaces 2 according to a preset ratio. Edge subarrays 4 are set at both ends of the cylindrical reflective surfaces 2, and a central subarray 3 is set between two edge subarrays 4. The central subarray 3 and the edge subarrays 4 are mirror-symmetrical about the array center. Both the central subarray 3 and the edge subarray 4 contain subarray grids and subarray boundaries. There is a spacing of 0.25 wavelengths between the subarray boundary and the subarray grid. The subarray boundary is the location of the boundary array element.

[0042] The spacing between adjacent array elements 1 is optimized using the bat algorithm to obtain the arrangement of the entire array.

[0043] The number of array elements contained in the central subarray 3 and the edge subarray 4 can be the same or different.

[0044] The size of the subarray boundary and the subarray grid is not fixed, and changes with the position of the boundary elements obtained by the bat algorithm.

[0045] The array elements in the central subarray 3 and the edge subarray 4 on the multiple cylindrical reflective surfaces 2 are arranged differently.

[0046] The minimum spacing between adjacent array elements 1 within the central subarray 3 is 0.5 times the wavelength, and the maximum spacing is 0.875 times the wavelength.

[0047] The minimum spacing between adjacent array elements 1 within the edge subarray 4 is 0.75 times the wavelength, and the maximum spacing is 1 times the wavelength.

[0048] This embodiment presents a design method for a subarray-level sparse-inner-dense array antenna based on a cylindrical antenna, comprising the following steps:

[0049] S1. Determine the number of array elements assigned to each cylindrical reflector 2;

[0050] S2. Based on the number of array elements allocated on each cylindrical reflective surface 2, allocate the number of array elements in the central subarray 3 and the edge subarray 4.

[0051] S3. Set the optimization variable of the optimization algorithm to the element spacing. The minimum value of the spacing between adjacent elements of the central subarray 3 is half a wavelength, and the maximum value is 0.875 wavelengths. The minimum value of the spacing between adjacent elements of the edge subarray 4 is 0.75 wavelengths, and the maximum value is 1 wavelength.

[0052] S4. Use the bat algorithm to iteratively optimize the spacing between adjacent array elements in each subarray, and then obtain the array element arrangement in the subarray.

[0053] S5. The arrangement of the obtained central subarray 3 and edge subarray 4 is mirrored and symmetrical, thus obtaining the arrangement of the entire cylindrical reflective surface 2 to the entire array.

[0054] S6. Calculate the radiation pattern of the array, determine the fitness function of the corresponding arrangement, and store the relevant data;

[0055] S7. When the bat algorithm reaches the maximum number of iterations, stop iterating and output the arrangement position and peak sidelobe level corresponding to the current best fitness function.

[0056] Specifically, S1 is:

[0057] The total number of array elements to be installed as needed The number of array elements to be installed on each cylindrical reflector is determined. The preferred number of cylindrical reflectors is 3, but this can be increased or decreased as needed in practical applications. In this invention, the number of array elements on each cylindrical reflector is as follows: , , , That is, the ratio of array elements on different cylindrical reflector surfaces is 1:2:3. In practical applications, the ratio can be adjusted according to the total number of array elements.

[0058] Specifically, S2 is:

[0059] Divide the array elements allocated on each cylindrical reflective surface equally to obtain the total number of array elements contained in the central subarray and the edge subarrays, and then proceed according to... The proportion is allocated to the edge subarray and the central subarray. The central subarray of the first cylindrical reflector contains the following number of elements: The number of elements in the edge subarray is The number of array elements in the central subarray of the second cylindrical reflector is... The number of elements in the edge subarray is The central subarray 1 of the third cylindrical reflector contains the following number of elements: The edge subarray 1 contains the following number of elements: .

[0060] Specifically, S3 is:

[0061] If the spacing between adjacent elements within a subarray is used as the optimization variable, then the number of optimization variables within each subarray is: If the lower boundary of the optimization variable for the central subarray is set to half a wavelength and the upper boundary to 0.875 wavelengths, and the lower boundary of the edge subarray is set to 0.75 wavelengths and the upper boundary to 1 wavelength, then the size of the spacing between adjacent array elements obtained by optimization is within this range, the array elements of the central subarray are more densely arranged, and the array elements of the edge subarray are more sparsely arranged.

[0062] Specifically, S4 is:

[0063] Set the frequency and loudness parameters of the bat algorithm, and use the bat algorithm to iteratively optimize the spacing between adjacent elements in different central and peripheral subarrays.

[0064] Specifically, S5 is:

[0065] Will As the axis of symmetry, The ordinate of the first element of the central subarray 1 (where...) (Wt is the wavelength). The element positions of the central subarray are calculated sequentially based on the optimized element spacing. After obtaining the ordinate of the last element position of the central subarray, this ordinate is increased by half the wavelength to obtain the ordinate of the first element of the edge subarray. The element positions of the edge subarray are then calculated sequentially based on the optimized element spacing.

[0066] Specifically, S6 is:

[0067] Assume the positions of all array elements are represented as follows: , Then, according to the matrix factor calculation formula:

[0068] The array orientation is calculated, where, Polar angle, It is the azimuth angle. The wavelength of electromagnetic waves, The imaginary unit, ( ) represents the position of the nth element;

[0069] The fitness function is set as follows: ,in The magnitude of the array factor in the sidelobe region. This represents the maximum value of the matrix factor modulus, used for normalizing the matrix factor.

[0070] Specifically, S7 is:

[0071] The optimal population in the bat algorithm is selected based on the optimal fitness function. The algorithm stops iterating after reaching the maximum number of iterations and outputs the optimal array arrangement and the optimal fitness value under that arrangement.

[0072] This embodiment uses a total of 96 array elements as an example. These 96 elements are distributed across three cylindrical surfaces (cylindrical reflective surfaces). Each cylinder contains two types of subarrays: a central subarray and an edge subarray. The ratio of the number of array elements on each cylinder is... The ratio of the number of array elements in the central subarray to the number of array elements in the edge subarray is 5:3. Specifically, in this example, the first cylinder contains 16 array elements, with each central subarray containing 5 array elements and each edge subarray containing 3 array elements; the second cylinder contains 32 array elements, with each central subarray containing 10 array elements and each edge subarray containing 6 array elements; and the third cylinder contains 48 array elements, with each central subarray containing 15 array elements and each edge subarray containing 9 array elements.

[0073] The spacing between two adjacent array elements is the optimizable spacing of the array elements, which is also the variable that needs to be optimized later; the subarray boundary is the location of the boundary array elements within the subarray, and the distance between the subarray boundary and the subarray grid is... (in The wavelength of the electromagnetic wave at 750MHz is 0.4m, used to ensure that the spacing between boundary elements of different subarrays is equal to half the wavelength.

[0074] The Bat Algorithm is used to optimize the spacing between adjacent elements within different types of subarrays on different cylinders. The Bat Algorithm is a swarm intelligence optimization algorithm that optimizes iteratively and is suitable for multidimensional and multi-constraint problems. The optimization variable is the spacing between adjacent elements. For the central subarray, the lower boundary of the optimization variable is 0.5 times the wavelength, and the upper boundary is 0.875 times the wavelength. For the edge subarray, the lower boundary is 0.75 times the wavelength, and the upper boundary is 1 times the wavelength. That is, the spacing between adjacent elements within the central subarray is greater than half a wavelength and less than 0.875 times the wavelength; the spacing between adjacent elements within the edge subarray is greater than 0.75 times the wavelength and less than 1 times the wavelength. The elements in the central subarray are more densely packed, while those in the edge subarray are more sparsely packed, and the spacing between adjacent elements is greater than half a wavelength.

[0075] After defining the optimizable spacing and number of elements for each type of subarray, the bat algorithm is used to optimize the spacing between adjacent elements in different types of subarrays on each cylinder, thus obtaining the relative positions of each element within the subarray. As the axis of symmetry, Using the ordinate of the first element of the first central subarray as the reference coordinate, the absolute position of the elements in the first central subarray is calculated based on the optimized relative positions between the elements. After obtaining the ordinate of the last element of the first central subarray, this ordinate is increased by half the wavelength to obtain the ordinate of the first element of the first edge subarray. The absolute positions of the elements in the first edge subarray are then calculated sequentially based on the optimized relative positions between the elements. The element positions of the first central and first edge subarrays are then inverted to obtain the element positions of the second central and second edge subarrays. The first and second central subarrays and the first and second edge subarrays are then mirror-symmetric about the array center, thus obtaining the element arrangement of the entire array.

[0076] In this example, the array elements are non-uniformly arranged in the central and peripheral subarrays, and the subarrays of the same type in each cylinder are mirror-symmetric about the center of the cylinder.

[0077] Figure 4 and Figure 5 These are the two-dimensional and three-dimensional radiation patterns of the array antenna in this example. The cylindrical reflector has beam-focusing properties. The east-west direction (E-plane) is a curved cylindrical surface. The sidelobe size of the beam in the E-plane radiation pattern is determined by the electrical dimensions of the cylindrical reflector, while the sidelobe size in the north-south direction (H-plane) radiation pattern is determined by the array structure. The formula for the cylindrical single antenna model used in this example is as follows:

[0078] The basic model of the feed source is:

[0079] ;

[0080] in: Here, FWHM is the beam normalization coefficient, where FWHM is the input parameter representing the full width at half maximum (FWHM) of the beam in rad. When the angular attenuation is... Beam amplitude decays to peak value (-3dB point).

[0081] In the east-west direction, there is a beam focusing effect. Fraunhofer diffraction calculations are then performed on the feed base beam.

[0082] ,

[0083] in: For aperture sampling variables, and angle satisfy ; For the normalized wave number, For the electrical dimensions of the reflector, The length of the curved surface of the reflecting surface. The spatial frequency in the far-field x-direction. This is the Fourier transform operator.

[0084] To achieve amplitude calculation at arbitrary angles, the FFT results are processed. Perform cubic interpolation to obtain a continuous function. ,in Represents a unit vector The projection on the x-axis, i.e. , Polar angle, It is the azimuth angle. This is a cubic interpolation operator.

[0085] Any direction in three-dimensional space is determined by a unit vector. The description is as follows: its projection onto the orthogonal axis is:

[0086] , ;

[0087] Cylindrical single antenna beam = E-plane (x-direction) amplitude × H-plane (y-direction) amplitude:

[0088] .

[0089] The array pattern is then represented by a single antenna beam multiplied by the array factor.

[0090] .

[0091] like Figure 4 Figure 5 As shown, the cylindrical antenna has a narrow east-west beam and a wide north-south beam. Since the feed spacing in the east-west direction is much larger than the wavelength (the feed is installed on the axis of the cylindrical reflector, and the feed spacing in the east-west direction is fixed), the array factor pattern will produce many dense grating lobes in the east-west direction. However, the spacing between these grating lobes and the main lobe is small, so we regard them as the main lobe and focus on the size of the side lobes in the north-south direction.

[0092] Figure 6 For beam pattern in The cross-sectional view shows that the structure in this invention can achieve a grating lobe level of -23.82dB in the north-south direction, which is better than other structures (such as -13dB with uniform spacing at half wavelength and -21.89dB with random array elements arranged under the same parameters using an optimization algorithm).

[0093] Figure 7The average convergence curves are obtained by running the structure of this invention and other common structures independently five times using the same optimization algorithm parameters. 163248 represents the number of array elements contained on different cylinders, which are 16, 32, and 48 respectively; central symmetry means that the array elements on each column of cylinders are mirror-symmetric about the array center; "centrally dense and laterally sparse" refers to the structure in this invention example, where the number of array elements in the central subarray is greater and more densely arranged than the array elements in the edge subarray; "centrally sparse and laterally dense" refers to the structure opposite to this invention example, where the ratio of the number of array elements in the central subarray to the number of array elements in the edge subarray is 3:5, the lower boundary of the optimizable spacing of the central subarray elements is 0.75 times the wavelength, the upper boundary is 1 times the wavelength, and the lower boundary of the optimizable spacing of the edge subarray elements is 0. The structure has four optimization parameters: 5 times the wavelength and an upper boundary of 0.875 times the wavelength, meaning the number of elements in the central subarray is less and sparser than those in the edge subarrays; a uniform distribution structure where the ratio of elements in the central subarray to those in the edge subarrays is 1:1, with the lower boundary of the optimizable spacing between elements in the central subarray being 0.5 wavelengths and the upper boundary being 1 wavelength, and the lower boundary of the optimizable spacing between elements in the edge subarrays being 0.5 times the wavelength and the upper boundary being 1 wavelength; and a fully random distribution where no subarrays are defined and the position of each element in each column is randomly determined by the optimization algorithm, with the spacing between adjacent elements being greater than or equal to 0.5 times the wavelength. As shown in the figure, the structure corresponding to this invention not only achieves better grating lobe suppression than other structures after 300 iterations, but also has significantly better initial solutions and convergence speeds in the early stages of iteration, verifying the superiority of the structure of this invention.

[0094] Table 1 compares the peak sidelobe level and redundancy of the best results obtained by running the proposed structure and other structures five times under the same optimization algorithm parameters. Redundancy is an indicator for evaluating antenna structures, referring to the ratio of the total number of baselines to the number of independent baselines in the antenna structure. Generally, the lower the redundancy, the fewer redundant baselines in the antenna structure, and the better the antenna structure. Too many redundant baselines will lead to an increase in the peak sidelobe level of the antenna pattern, but in practical applications, an appropriate number of redundant baselines helps to reduce instrument noise. As shown in the table, the structure with the lowest redundancy is the fully random structure without subarrays, followed by the outer sparse and inner dense structure of the proposed invention (i.e., a centrally symmetric, middle-dense, and side-sparse structure), verifying that the proposed invention has good effects in terms of redundancy and peak sidelobe level suppression.

[0095] Table 1 Comparison of Peak Sidelobe Level and Redundancy

[0096] Structure (16-32-48) Number of independent baselines Total number of baselines Redundancy (total number of baselines / number of independent baselines) PSLL Centrally symmetrical, dense in the middle and sparse on the sides 3605 4560 1.265 -23.82 Centrally symmetrical with sparse center and dense side 3596 4560 1.268 -19.28 Centrally symmetric and uniformly distributed 3584 4560 1.272 -23.22 Fully random distribution 4537 4560 1.005 -21.89

[0097] Figure 8The diagram shows the structure obtained by expanding the array size to 192 elements using the method of this invention. In this example, the array elements are divided into two columns, each containing 96 elements. Each column has a central subarray with 30 elements and an edge subarray with 18 elements. The lower boundary of the optimizable spacing between the central subarray elements is 0.5 times the wavelength, and the upper boundary is 0.875 times the wavelength. The lower boundary of the optimizable spacing between the edge subarray elements is 0.75 times the wavelength, and the upper boundary is 1 times the wavelength. The bat algorithm is used to optimize the spacing between adjacent elements in the central and edge subarrays of each column, resulting in the array arrangement shown in the diagram.

[0098] Figure 9 , Figure 10 The above example structure is shown in the orientation patterns in a two-dimensional plane and three-dimensional space. Figure 11 For beam pattern in The cross-sectional image shows that the north-south grating lobe level reaches -19.69dB, maintaining a good grating lobe suppression effect.

[0099] The foregoing has shown and described the main features and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

[0100] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A subarray-level sparse-outer-dense-inner array antenna based on a cylindrical antenna, characterized in that, include: The array elements (1) are distributed on multiple cylindrical reflective surfaces (2) according to a preset ratio. Edge subarrays (4) are set at both ends of the cylindrical reflective surfaces (2), and a central subarray (3) is set between two edge subarrays (4). The central subarray (3) and the edge subarrays (4) are mirror symmetrical about the center of the array. Both the central subarray (3) and the edge subarray (4) contain subarray grids and subarray boundaries. There is a spacing of 0.25 wavelengths between the subarray boundaries and the subarray grids. The subarray boundaries are the locations of the boundary array elements. The spacing between adjacent array elements (1) is optimized using the bat algorithm to obtain the arrangement of the entire array.

2. The subarray-level sparse-inner-dense array antenna based on a cylindrical antenna according to claim 1, characterized in that, The number of array elements contained in the central subarray (3) and the edge subarray (4) can be the same or different.

3. The subarray-level sparse-inner-dense array antenna based on a cylindrical antenna according to claim 1, characterized in that, The size of the subarray boundary and the subarray grid is not fixed, and changes with the position of the boundary elements obtained by the bat algorithm.

4. The subarray-level sparse-inner-dense array antenna based on a cylindrical antenna according to claim 1, characterized in that, The array elements in the central subarray (3) and the edge subarray (4) on the multiple cylindrical reflective surfaces (2) are arranged differently.

5. A subarray-level sparse-inner-dense array antenna based on a cylindrical antenna according to any one of claims 1-4, characterized in that, The minimum spacing between adjacent array elements (1) within the central subarray (3) is 0.5 times the wavelength, and the maximum spacing is 0.875 times the wavelength.

6. A subarray-level sparse-inner-dense array antenna based on a cylindrical antenna according to any one of claims 1-5, characterized in that, The minimum spacing between adjacent array elements (1) within the edge subarray (4) is 0.75 times the wavelength, and the maximum spacing is 1 times the wavelength.

7. A design method for a subarray-level sparse-outer-dense-inner array antenna based on a cylindrical antenna, characterized in that, Includes the following steps: S1. Determine the number of array elements assigned to each cylindrical reflector (2); S2. Based on the number of array elements allocated on each cylindrical reflective surface (2), allocate the number of array elements in the central subarray (3) and the edge subarray (4); S3. Set the optimization variable of the optimization algorithm as the element spacing. The minimum value of the spacing between adjacent elements of the central subarray (3) is half a wavelength, and the maximum value is 0.875 times the wavelength. The minimum value of the spacing between adjacent elements of the edge subarray (4) is 0.75 times the wavelength, and the maximum value is 1 wavelength. S4. Use the bat algorithm to iteratively optimize the spacing between adjacent array elements in each subarray, and then obtain the array element arrangement in the subarray. S5. The arrangement of the obtained central subarray (3) and edge subarray (4) is mirrored to obtain the arrangement of the entire cylindrical reflective surface (2) to the entire array. S6. Calculate the radiation pattern of the array, determine the fitness function of the corresponding arrangement, and store the relevant data; S7. When the bat algorithm reaches the maximum number of iterations, stop iterating and output the arrangement position and peak sidelobe level corresponding to the current best fitness function.

8. The design method of a subarray-level sparse-inner-dense array antenna based on a cylindrical antenna according to claim 7, characterized in that, Specifically, S4 is: Set the frequency and loudness parameters of the bat algorithm, and use the bat algorithm to iteratively optimize the spacing between adjacent array elements in different central subarrays (3) and edge subarrays (4).

9. The design method of a subarray-level sparse-inner-dense array antenna based on a cylindrical antenna according to claim 7, characterized in that, Specifically, S6 is: Assume the positions of all array elements are represented as follows: , Then, according to the matrix factor calculation formula: The array orientation is calculated, where, Polar angle, It is the azimuth angle. The wavelength of electromagnetic waves, The imaginary unit, ( ) represents the position of the nth array element; The fitness function is set as follows: ,in The magnitude of the array factor in the sidelobe region. This represents the maximum value of the matrix factor modulus, used for normalizing the matrix factor.

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