Coaxial antenna with large element spacing and low-frequency four-in-one feed and design method thereof

Abstract

The application provides a large-array-element-spacing and low-frequency four-in-one feeding co-boresight antenna and a design method. Co-boresight dual-frequency units are arranged uniformly in 4*4 to form a basic subarray, and the low-frequency unit is fed by using a four-in-one feeding mode. The initial array surface is provided with sufficient subarray spacing to form an M*N size whole array, the offset of each subarray in the x and y directions is changed by using a global optimization algorithm, and the array surface grating lobes under the high-frequency and low-frequency scanning conditions are optimized. The application designs a low-cost co-boresight array surface by using the large-array-element-spacing and low-frequency four-in-one feeding technology, and the non-periodic arrangement of the subarray level is optimized by using an intelligent algorithm, and the high-gain unit is combined to reduce the far-field energy under the low-frequency four-in-one feeding and high-frequency conditions, so that the grating lobe suppression of the large-array-element-spacing co-boresight working antenna array surface is realized. The application has the advantages of not being limited to the array surface form in the array surface design and strong applicability.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of communication, and further relates to a large-element-spacing and low-frequency four-in-one feeding co-aperture antenna and a design method thereof. The present application can be used to design a large-element-spacing co-aperture antenna array with a low number of channels in a dual-band or multi-band. BACKGROUND

[0002] In the phased array antenna technology, the most important array characteristics are usually high gain and low cost. High gain can improve the monitoring distance of the array, and low cost can save money as much as possible. In order to meet the needs of both, large-element-spacing and co-aperture technology is a more feasible method. Large-element-spacing refers to widening the element spacing to achieve a larger aperture and thus a larger gain with the same number of elements, or a smaller number of elements with the same aperture and thus a lower cost. Co-aperture antenna technology refers to placing multiple antennas of different frequency bands in the same radiation aperture, and through reasonable design, they can work independently without interference with each other, saving space costs. In a stacked array, high-frequency elements can be arranged in a smaller pattern than low-frequency elements to avoid grating lobes, but when the array structure does not allow stacking, the spacing of high-frequency elements and low-frequency elements is the same, which often leads to large-element-spacing in the high-frequency array, which is prone to grating lobes. Sometimes, in order to further reduce the number of channels and lower the cost, the low-frequency elements also use a four-in-one input method. At this time, it is easy to have too long element spacing in both high-frequency and low-frequency, and the periodicity on the array will inevitably cause grating lobes in the array pattern, thereby causing the main beam energy to decrease.

[0003] Chengdu Tianxirixintong Technology Co., Ltd. discloses a co-aperture array antenna in its applied patent document "A co-aperture array antenna and satellite communication terminal" (application 202110085055.7, application publication number CN 112421246 A). The antenna realizes a one-to-one correspondence between four high-frequency elements and one low-frequency element through tight coupling, reducing the spacing between high-frequency elements. Secondly, two adjacent tightly coupled elements form a tightly coupled element group, and the phase centers of each tightly coupled element group are also randomly distributed, thereby breaking the periodicity. The combination of the two makes the dual-frequency co-aperture array antenna not appear grating lobes, achieving the design of the dual-frequency co-aperture array antenna. However, the array still has two shortcomings: first, the array has a large number of elements and channels, the high-frequency element arrangement spacing is 0.73 wavelengths, and the low-frequency element arrangement spacing is 0.5 wavelengths. As the aperture expands, the number of channels required will increase significantly, requiring a higher cost. Second, the array uses four high-frequency elements and one low-frequency element, so it is only suitable for microstrip antenna arrays that can be stacked. When the antenna form changes and cannot be stacked, it cannot guarantee that the high-frequency elements will not appear grating lobes when working. SUMMARY

[0004] The present application aims at the deficiencies of the prior art, and provides a large-element-spacing and low-frequency four-in-one feeding co-boresight antenna and a design method thereof, which are used to solve the problem of high cost caused by large number of elements and channels of a dual-frequency co-boresight array antenna, and the problem of co-boresight antenna design for large-element-spacing which is not suitable for a microstrip antenna array.

[0005] The idea for achieving the purpose of the present application is that, in view of the above problems, the present application adopts a large-spacing element and low-frequency element four-in-one scheme when designing an antenna array, thereby solving the problem of high cost caused by large number of elements and channels of a dual-frequency co-boresight array antenna. The present application optimizes the non-periodic arrangement of each subarray level by an intelligent algorithm, combines a high-gain element, reduces far-zone energy in the case of low-frequency four-in-one feeding and high-frequency two-in-one feeding, realizes grating lobe suppression of a large-element-spacing co-boresight working antenna array, and solves the problem of co-boresight antenna design for large-element-spacing which is not suitable for a microstrip antenna array.

[0006] The co-boresight antenna of the present application comprises a plurality of subarrays, each of which is composed of 4x4 antenna elements co-boresight antenna elements arranged in a large-element-spacing rectangular grid.

[0007] The steps of the co-boresight antenna design method of the co-boresight antenna of the present application with large-element-spacing and low-frequency four-in-one feeding comprise the following:

[0008] Step 1: Establish an array model

[0009] Two adjacent elements are arranged into a subarray composed of 4x4 antenna elements according to a center spacing d>2r, and a whole array model composed of MxN subarrays is established according to a center spacing D>8r between two adjacent subarrays, where r is the radius of the co-boresight element, and M and N are both integers and cannot be 0 at the same time.

[0010] Step 2: Determine the optimization variable

[0011] Let the offsets of each of the MxN subarrays in the x-axis direction and the y-axis direction be dx and dy, respectively, where dx is a vector with a length of MxN, each element of the vector representing the offset of the corresponding position element in the x-axis direction, and dy is a vector with a length of MxN, each element of the vector representing the offset of the corresponding position element in the y-axis direction; and a vector d is formed by connecting dx and dy as the optimization variable.

[0012] Step 3: Optimize the optimization variable d

[0013] Step 3.1, set the initial parameters of the particle swarm algorithm, the population size NP is the number of particles in each iteration, set to 50, the boundary value is the maximum value of each element when the particle changes, set to D m , D m is greater than D-8r, the maximum flying speed v max is the maximum value of the particle change in each iteration, set to D m / 10; the individual learning factor c1, social factor c2 and inertia factor ω in the particle swarm algorithm are selected as 2, 2 and 0.8 respectively according to the general rule;

[0014] Step 3.2, randomly generate MxNx2 values less than or equal to D m as the initial value of d, repeat this step NP times to get d0, d1, … d NP-1 ;

[0015] Step 3.3, one by one d0, d1, … d NP-1 get MxN sub-array offset in x-axis direction and y-axis direction according to the corresponding relationship described in step 2, and check if there is overlap between the sub-arrays at this time: if there is no overlap between the sub-arrays, the array surface is a realizable array, and the d i corresponding to the offset is taken as an initial particle X i enter the next step; if there is overlap between the sub-arrays, the array surface is not realizable, a new particle is generated and checked for overlap between the sub-arrays until NP particles are reached in the population;

[0016] Step 3.4, according to the conversion relationship described in step 2, obtain the array surface under the corresponding sub-array offset of each particle, calculate the side lobe MSLL1 and MSLL2 of the array surface, evaluate the fitness value of each particle in the initial population according to the fitness calculation formula, obtain the local historical optimal position and the global optimal position, and the fitness function is as follows:

[0017] Value=ω1MSLL1+ω2MSLL2

[0018] Wherein, MSLL1 represents the maximum value of the array surface excluding the main lobe when the array elements are calculated according to the four-in-one feeding mode, and the array surface points to the maximum scanning angle, MSLL2 represents the maximum value of the array surface excluding the main lobe when the array elements are calculated according to the independent feeding mode, and the array surface points to the maximum scanning angle, ω1 and ω2 are weights, representing the contribution degree of high and low frequency side lobes to fitness respectively;

[0019] Step 3.5, according to the local historical optimal position and the global optimal position, the speed and position of each particle are updated from the previous population, and then the corresponding M*N sub-arrays of each new particle are obtained according to the conversion relationship in step 2; the offset of each sub-array in the x-axis direction and the y-axis direction is judged; if any particle has overlapping sub-arrays in the array surface, a new non-overlapping sub-array particle is generated to replace the old particle; if the sub-arrays are all non-overlapping, the function fitness value of each new particle is evaluated, and the historical optimal position of each particle and the global optimal position of the population are updated;

[0020] Step 3.6, repeat step 3.5 until the maximum iteration number is reached or the target fitness value is reached, and the X ibest of the final population is obtained, and the particle with the best fitness value is the global optimal position.

[0021] After optimization, the X ibest of the final population is obtained, and the particle with the best fitness value is the global optimal position.

[0022] Compared with the prior art, the present application has the following advantages:

[0023] First, by adopting large element spacing and low-frequency four-in-one feeding technology, the present application overcomes the high cost caused by the large number of elements and channels in the prior art dual-frequency co-caliber array antenna, and has the advantage of low channel number in the same caliber, thereby reducing the cost of the co-caliber array antenna.

[0024] Second, by optimizing the non-periodic arrangement of the sub-array level through an intelligent algorithm, and combining with the high-gain element to reduce the far-zone energy in the low-frequency and high-frequency cases, the present application realizes the grating lobe suppression of the large-element-spacing co-caliber working antenna array, and overcomes the disadvantage of the prior art that is only suitable for microstrip antenna arrays and cannot be used for multi-band large-element-spacing antennas, thereby making the present application have the advantage of not being limited to the array form in array design and strong applicability. DETAILED DESCRIPTION

[0025] Figure 1 is a flowchart of an embodiment of the present application;

[0026] Figure 2 is a schematic diagram of the initial array element of the same surface of the embodiment of the present application and the array after applying large element spacing and low-frequency four-in-one feeding;

[0027] Figure 3 is a structural schematic diagram of the initial array of the embodiment of the present application;

[0028] Figure 4This is a radiation pattern of the initial array plane in two scanning directions according to an embodiment of the present invention; wherein, Figure 4 (a) The beam direction is θ = 10° at high frequencies. The array surface has a radiation pattern in the uv coordinate system where -0.6≤u≤0.6 and -0.6≤v≤0.6. Figure 4 (b) When the beam direction is θ = 10° at high frequencies. The two-dimensional radiation pattern of the array surface on the yoz plane when -30°≤θ≤30°; Figure 4 (c) When the beam direction is θ = 10° at high frequencies. The array surface has a radiation pattern in the uv coordinate system where -0.6≤u≤0.6 and -0.6≤v≤0.6. Figure 4 (d) indicates that the beam direction is θ = 10° at high frequencies. Two-dimensional radiation pattern of the array surface on the yoz plane when -30°≤θ≤30°; Figure 4 (e) indicates that the beam pointing at low frequencies is θ = 10°. The array surface has a radiation pattern in the uv coordinate system where -0.6≤u≤0.6 and -0.6≤v≤0.6. Figure 4 (f) shows the beam pointing at low frequencies when θ = 10°. Two-dimensional radiation pattern of the array surface on the yoz plane when -30°≤θ≤30°; Figure 4 (g) indicates that the beam pointing at low frequencies is θ = 10°. The array pattern of the array in the uv coordinate system under the condition of -0.6≤u≤0.6, -0.6≤v≤0.6; Figure 4 (h) indicates the beam pointing at low frequencies when θ = 10°. The two-dimensional radiation pattern of the array surface on the yoz plane when -30°≤θ≤30°.

[0029] Figure 5 This is a schematic diagram of the optimized array surface according to an embodiment of the present invention;

[0030] Figure 6 This is a radiation pattern of two scanning directions in the optimized array configuration of this invention. Figure 6 (a) is the optimized radiation pattern of 4(a). Figure 6 (b) is Figure 4 (b) Optimized two-dimensional orientation pattern Figure 6 (c) is Figure 4 (c) Optimized radiation pattern Figure 6 (d) is Figure 4 (d) Optimized 2D orientation pattern Figure 6 (e) is Figure 4 (e) Optimized radiation pattern, Figure 6 (f) is Figure 4 (f) Optimized 2D radiation patternFigure 6 (g) is Figure 4 (g) optimized directional pattern, Figure 1 (h) is Figure 2 (h) optimized two-dimensional directional pattern. DETAILED DESCRIPTION

[0031] The implementation steps and effects of the present application are further described below in combination with the drawings and examples.

[0032] Referring to Figure 2 , the implementation steps of the embodiments of the present application are further described.

[0033] The element spacing and array size are designed according to the general common aperture antenna array; then the element spacing of the common aperture antenna array is expanded to three times the original spacing under the same aperture, and the number of elements is reduced to 1 / 9 of the original number; secondly, every 2x2 low-frequency elements are fed by the same channel to realize a four-in-one feeding mode to reduce the number of channels; then 4x4 common aperture elements form a subarray, and the whole array is established according to the requirements, that is, the size of the subarray, the placement mode of the subarray, and the possible offset of the subarray in the x direction and the y direction are determined; the initial parameters of the particle swarm are set, such as the population size, the maximum flying speed, the boundary value, the individual learning factor, the social factor, and the inertia factor; then the high and low frequency grating lobes in several main observation planes are taken into the fitness function, the particle results are evaluated according to the fitness function, and the global optimal position and the local historical optimal position are recorded; the particle speed and position are constantly updated according to the flight experience, the particle fitness is evaluated, and the historical optimal position and the global optimal position are updated until the end condition is met and the results are output.

[0034] In the embodiments of the present application, the element spacing of the array is expanded from 0.73 times the high frequency wavelength to 2.24 times the high frequency wavelength, and the number of elements is reduced to 1 / 9 of the original number. Secondly, every 2x2 low-frequency elements are fed by the same channel to realize a four-in-one feeding mode to reduce the number of channels, and at this time, the same aperture has 5 channels corresponding to 72 channels of 36 high-frequency elements and 36 low-frequency elements under the same aperture as shown in Figure 3 . Figure 3 Each circle in the figure represents a high-low frequency common aperture element.

[0035] In the embodiments of the present application, 4x4 common aperture elements form a subarray, which is arranged into an initial whole array as a basic unit of the initial whole array. In order to optimize later, the spacing between the centers of the subarrays in the initial whole array is slightly larger than the size of a subarray. The schematic diagram of the initial whole array is shown in Figure 4 , which is arranged on the xoy plane and consists of 6 subarrays in the x direction and 10 common subarrays in the y direction, wherein each subarray contains 4x4 elements. Figure 4Each circle represents a high-low frequency co-boresight element. The high frequency element operates at 6GHz with a gain of 16.2dBi, and the low frequency element operates at 2.4GHz with a gain of 9.8dBi. The initial subarray spacing is 508mm, and the element spacing within the subarray is 112mm. The array is required to achieve a maximum scan of 10° in the y direction.

[0036] For the high frequency 6GHz element, the element spacing exceeds two wavelengths. For the low frequency 2.4GHz element, the element spacing is close to one wavelength and it is fed by a four-in-one feed. Therefore, in the initial array with this regular arrangement, there will be certain grating lobes for both high and low frequencies.

[0037] Figure 4 The beam pointing direction patterns of the initial array in the high-low frequency example of the present application in two scanning directions are given. Among them, Figure 4 (a) is the direction pattern of the array in the case of high frequency beam pointing θ = 10°, -0.5≤u≤0.5, -0.5≤v≤0.5 in the uv coordinate system, Figure 4 (b) is the two-dimensional direction pattern of the array in the case of high frequency beam pointing θ = 10°, -30°≤θ≤30° on the yoz plane, Figure 4 (c) is the direction pattern of the array in the case of high frequency beam pointing θ = 10°, -0.5≤u≤0.5, -0.5≤v≤0.5 in the uv coordinate system, Figure 4 (d) is the two-dimensional direction pattern of the array in the case of high frequency beam pointing θ = 10°, -30°≤θ≤30° on the yoz plane. Figure 4 (e) is the direction pattern of the array in the case of low frequency beam pointing θ = 10°, -0.5≤u≤0.5, -0.5≤v≤0.5 in the uv coordinate system, Figure 4 (f) is the two-dimensional direction pattern of the array in the case of low frequency beam pointing θ = 10°, -30°≤θ≤30° on the yoz plane, Figure 5 (g) is the direction pattern of the array in the case of low frequency beam pointing θ = 10°, -0.5≤u≤0.5, -0.5≤v≤0.5 in the uv coordinate system, Figure 6 (h) is the two-dimensional direction pattern of the array in the case of low frequency beam pointing θ = 10°, -30°≤θ≤30° on the yoz plane. The maximum grating lobe of the array is -4.2029dB at high frequency, and the maximum grating lobe of the array is -4.5348dB at low frequency.

[0038] The large element spacing and the four-in-one low frequency feed of the common aperture antenna design method of the common aperture antenna of the application are used to optimize the non-periodic arrangement of the subarray level.

[0039] Step 1, establish the whole array model:

[0040] According to the spacing of 112 mm between the centers of every two adjacent units, a subarray composed of 4*4 antenna units is arranged, and according to the spacing of 508 mm between the centers of every two adjacent subarrays, a whole array model composed of 6*10 subarrays is established;

[0041] Step 2, determine the optimization variable:

[0042] Let the offsets of the 6*10 subarrays in the x-axis direction and the y-axis direction be dx and dy respectively, wherein dx is a vector with a length of 6*10, each element of the vector represents the offset of the corresponding unit in the x-axis direction; dy is a vector with a length of 6*10, each element of the vector represents the offset of the corresponding unit in the y-axis direction; connect dx and dy to form a vector d as the optimization variable;

[0043] Step 3, optimize the optimization variable d:

[0044] Step 3.1, set the initial parameters of the particle swarm algorithm, the population size NP is the number of particles in each iteration, which is set to 50, the boundary value is the maximum value of each element when the particle changes, which is set to D m , D m is greater than D-8r, the maximum flight speed v max is the maximum value of the particle change in each iteration, which is set to D m / 10; the individual learning factor c1, the social factor c2 and the inertia factor ω in the particle swarm algorithm are selected as 2, 2 and 0.8 respectively according to the general rule;

[0045] Step 3.1, set the initial parameters of the particle swarm algorithm, the population size NP is the number of particles in each iteration, which is set to 50, the boundary value is the maximum value of each element when the particle changes, which is set to 50 mm, the maximum flight speed v max is the maximum value of the particle change in each iteration, which is set to 5 mm; in addition, the individual learning factor c1, the social factor c2 and the inertia factor ω in the particle swarm algorithm are selected as 2, 2 and 0.8 respectively according to the general rule;

[0046] Step 3.2, randomly generate 6*10*2 values less than or equal to 50 mm as the initial value of d, repeat this step NP times to obtain d0, d1, … d NP-1 ;

[0047] Step 3.3, d0, d1, … d NP-1According to the correspondence relationship in step 2, the offsets of the 6x10 sub-arrays in the x-axis direction and the y-axis direction are obtained, and it is checked whether there is an overlap between the sub-arrays at this time. If there is no overlap between the sub-arrays, the array surface is a realizable array surface, and the offset corresponding to the d i As an initial particle X i Enter the next step; if there is an overlap between the sub-arrays, the array surface is not realizable, a new particle is regenerated, and it is checked whether there is an overlap between the sub-arrays until NP particles are reached in the population;

[0048] Step 3.4, according to the conversion relationship in step 2, the array surface corresponding to the offset of each particle is obtained, the side lobe MSLL1 and MSLL2 of the array surface are calculated, the fitness value of each particle in the initial population is evaluated according to the fitness calculation formula, and the local historical optimal position and the global optimal position are obtained. Assuming that the maximum scanning angle of the array surface in the y direction is ±10°, that is, θ=10° in the spherical coordinate system, The fitness function is set as follows:

[0049] Value=ω1MSLL1+ω2MSLL2

[0050] Wherein, MSLL1 is the maximum value of the side lobe of the array surface except the main lobe when the low-frequency array element is calculated according to the four-in-one feeding mode, and the array surface is directed to θ=10°, MSLL2 is the maximum value of the side lobe of the array surface except the main lobe when the high-frequency array element is calculated according to the four-in-one feeding mode, and the array surface is directed to θ=10°, ω1 and ω2 are weights, representing the contribution degree of the high and low frequency side lobes to the fitness.

[0051] Each particle individual is represented by a one-dimensional vector x for its spatial position, and another vector v for its spatial moving direction and distance. For example, the position vector of the i-th particle at the t-th iteration can be represented as The velocity vector can be represented as Therefore, until the t-th generation, the position of the particle i with the best fitness searched is recorded as Also known as the local historical optimal position, recorded as Pbest i (t). The global optimal position experienced by all particles in the population, including particle i, is recorded as Gbest(t), and when calculating based on the minimization optimization problem, Gbest(t) can be calculated as:

[0052] Gbest(t)=min{pbest1(t),pbest2(t),…,pbest NP (t)}.

[0053] Step 3.5, update the velocity and position of each particle from the local history optimal position and the global optimal position according to the last population. Secondly, get the MxN sub-arrays corresponding to each new particle according to the conversion relationship described in step 2. Determine whether the sub-arrays overlap in the x-axis direction and the y-axis direction. When the actual sub-array designed according to the offset of a certain particle exists overlap, the method of randomly generating a new particle is used to correct. If the sub-arrays corresponding to each new particle do not overlap, evaluate the function fitness value of each particle, and update the history optimal position of each particle and the global optimal position of the population. The particle velocity vector and position vector at the i+1 generation can be calculated by the following formula:

[0054]

[0055] Too large and too small velocity will make the particle exceed the problem solving space, so the boundary processing of velocity and position is needed, that is, the velocity exceeding the upper limit is reset to the maximum velocity value, and the position exceeding the upper limit is reset to the boundary value.

[0056] Step 3.6: repeat step 3.5 until the maximum number of iterations is reached or the target fitness value is reached. The final population obtained is preferred, and the particle with the best fitness value is taken as the final result, that is, the offset of each sub-array in the x and y directions is obtained, and the final optimized array surface is designed according to the offset. The schematic diagram of the array surface after optimization in the embodiment of the present application is shown in Figure 6 .

[0057] Figure 4 The directional diagram of two scanning directions in the array surface after optimization in the embodiment of the present application is shown in Figure 6 (a) is Figure 4 (a) the directional diagram after optimization, Figure 6 (b) is Figure 4 (b) the two-dimensional directional diagram after optimization, Figure 6 (c) is Figure 4 (c) the directional diagram after optimization, Figure 6 (d) is Figure 4 (d) the two-dimensional directional diagram after optimization, Figure 6 (e) is Figure 4 (e) the directional diagram after optimization, Figure 6 (f) is Figure 4 (f) the two-dimensional directional diagram after optimization, Figure 6 (g) is Figure 4 (g) the directional diagram after optimization, Figure 6 (h) is ​ (h) the two-dimensional directional diagram after optimization.

[0058] By searching ​The maximum value of the side lobe of the medium-high frequency and low frequency three-dimensional directional diagram can be obtained, the maximum grating lobe of the array surface is-13.5735 dB at high frequency, and the maximum grating lobe of the array surface is-9.6033 dB at low frequency.

[0059] From the low channel number design result of the present application for the common aperture array antenna, it can be seen that the designed array surface utilizes the low frequency four-in-one feeding and large array element spacing, greatly reduces the number of channels, and simultaneously utilizes the subarray level non-periodic arrangement and high gain unit, optimizes the grating lobe generated due to the four-in-one feeding and large array element spacing.

[0060] The above description is only one example of the present application and does not constitute any limitation on the present application. Any person skilled in the art can think of possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the idea of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, which does not depart from the content of the technical solutions of the present application, shall belong to the protection scope of the technical solutions of the present application.

Claims

1. A common-aperture antenna design method with large element spacing and low-frequency four-in-one feed, comprising multiple subarrays, characterized in that, Each subarray consists of 4×4 common-aperture antenna elements uniformly distributed in a large-element-gap rectangular grid. Each common-aperture element includes one high-frequency high-gain element and one low-frequency high-gain element. The low-frequency element is fed using a four-in-one feeding method. The array grating lobes are suppressed through aperiodic subarray-level arrangement. The steps of this design method include the following: Step 1, establish the array model: Arrange the antenna elements into a subarray of 4×4 with a center-to-center distance of d>2r between every two adjacent elements. Establish an array model consisting of M×N subarrays with a center-to-center distance of D>8r between every two adjacent subarrays. r is the radius of the common aperture element. M and N are both integers and not both 0. Step 2, determine the optimization variables: Let the offsets of each of the M×N subarrays in the x-axis and y-axis directions be dx and dy, respectively, where dx is a vector of length M×N, and each element of the vector represents the offset of the corresponding unit in the x-axis direction; dy is a vector of length M×N, and each element of the vector represents the offset of the corresponding unit in the y-axis direction; dx and dy are concatenated to form a vector d as the optimization variable; Step 3, optimize the optimization variable d: Step 3.1: Set the initial parameters for the particle swarm optimization algorithm. The population size NP is the number of particles in each iteration, set to 50. The boundary value is the maximum value of each element when the particle changes, set to D. m D m Greater than D-8r, maximum flight speed v max Let D be the maximum change of the particle in each iteration. m / 10; The individual learning factor c1, social factor c2, and inertia factor ω in the particle swarm optimization algorithm are selected as 2, 2, and 0.8 respectively, according to general rules; Step 3.2: Randomly generate M×N×2 numbers whose absolute values ​​are less than or equal to D. m The value of is used as the initial value of d, and this step is repeated NP times to obtain d0, d1, ... d NP-1 ; Step 3.3, sequentially assign d0, d1, ... d NP-1 Following step 2, the relationship between the optimization variables is determined to obtain the offsets of each of the M×N subarrays in the x-axis and y-axis directions. It is then checked whether the array faces overlap between the subarrays: if there is no overlap, the array face is a realizable array face, and the corresponding d-axis offset is calculated. i As an initial particle X i Proceed to the next step; if there is overlap between subarrays, the array is unrealizable. Regenerate new particles and check for overlap between subarrays until there are NP particles in the population. Step 3.4: Obtain the array surface for each particle under the subarray offset condition according to the transformation relationship described in Step 2, calculate the sidelobes MSLL1 and MSLL2 of the array surface, evaluate the fitness value of each particle in the initial population according to the fitness calculation formula, and obtain the local historical best position and the global best position. The fitness function is as follows: Value = ω1MSLL1 + ω2MSLL2 Where MSLL1 represents the maximum value of the array lobes other than the main lobe when the array points to the maximum scanning angle, when the array elements are calculated using the four-in-one feeding method at low frequencies; MSLL2 represents the maximum value of the array lobes other than the main lobe when the array points to the maximum scanning angle, when the array elements are calculated using the independent feeding method at high frequencies; ω1 and ω2 are weights, representing the contribution of high and low frequency sidelobes to fitness, respectively. Step 3.5: Based on the local historical best position and the global best position, update the velocity and position of each particle from the previous population. Then, according to the transformation relationship described in Step 2, obtain the offset of each of the M×N subarrays corresponding to each new particle in the x-axis and y-axis directions. Determine whether the subarrays overlap: if the subarrays overlap under any particle's corresponding array, then randomly generate a new particle with non-overlapping subarrays to replace the old particle; if the subarrays do not overlap, evaluate the function fitness value of each new particle and update the historical best position of each particle and the global best position of the population. Step 3.6: Repeat step 3.5 until the maximum number of iterations is reached or the target fitness value is reached. For all particles in the final population, select the particle with the best fitness value, which is the globally optimal position X. ibest As the final optimization result; After optimization, the array surface under the subarray offset condition corresponding to Xibest is obtained by determining the relationship of the optimization variables as described in step 2. This is then substituted into the final array surface, and the grating lobe value is obtained under the scanning condition of the array surface at this time.

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