A sparse subarray array antenna arrangement optimization method
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ROCKET FORCE UNIV OF ENG
- Filing Date
- 2023-04-21
- Publication Date
- 2026-06-09
Smart Images
Figure CN116306315B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of array antenna layout design technology, and relates to a method for optimizing the layout of sparse subarray array antennas. Background Technology
[0002] As the scale of array antennas continues to increase, the problems of high system hardware costs and complex array design are becoming increasingly prominent. Sparse array design is an effective method to reduce the size of the array antenna while maintaining the array aperture. Since the directional beamwidth of the antenna is determined by the array antenna aperture size, the element distribution density can be reduced according to certain rules while keeping the array aperture constant, and the beamwidth of the optimized sparse array and full array are kept approximately equal. Compared to a uniform full array, a non-uniform sparse array has a larger antenna aperture, a narrower main lobe width, and improved angular resolution. However, after sparsification, the element spacing is greater than half a wavelength, and the sparse array has fewer radiating elements than a uniform full array. Under the same antenna aperture, the gain of the sparse array will decrease, the sidelobe level will be higher, and grating lobes may appear. Typically, irregular element arrangement is used to suppress grating lobes, i.e., non-periodic arrangement between elements. Therefore, using random algorithms to reduce and avoid grating lobes for large-spacing array antenna optimization has theoretical significance and practical engineering value. The layout of the array is sparsely optimized using intelligent optimization algorithms. The goal is to achieve a narrow main lobe beamwidth while simultaneously searching for low sidelobe levels and avoiding grating lobes. Optimizing element positions is a nonlinear optimization problem, and intelligent optimization algorithms are often used to address the nonlinear relationships between multiple constraint variables. To improve the computational efficiency of the algorithm, it is common practice to improve individual intelligent optimization algorithms or combine multiple algorithms for optimization.
[0003] The above describes the optimization design of a single array element. Especially in high-dynamic aircraft applications, the limitations of space constraints and real-time algorithm requirements present new challenges and higher demands for array antenna layout optimization. In large-scale array antennas, beamforming requires each radiating element to be combined with an independent transceiver component. Consequently, radar systems will have an array antenna configured with an equal number of control units and receiving channels, increasing both the difficulty of engineering implementation and the computational load. The larger the array antenna and the more elements it contains, the more complex subsequent signal and data processing becomes. To address this issue, a sparse arrangement method for large array subarrays is adopted, i.e., sparse array optimization of the subarrays. Each subarray module is configured with a receiving channel, which significantly reduces the number of transceiver components and other equipment compared to a full array, while also increasing the space available for the equipment. Huang Fei et al.'s "Randomly Displaced Subarray Antenna and Its Optimization Design" applies the PSO algorithm to sparse subarrays and proposes a randomly displaced distribution method. However, this method inevitably suffers from problems, such as getting trapped in local optima, thus failing to achieve a globally optimal array layout. Summary of the Invention
[0004] The purpose of this invention is to propose an optimization method for sparse subarray antenna layout, so as to solve the problem that optimization algorithms in sparse array design are prone to getting trapped in local optimization and are not easy to converge.
[0005] To achieve the above objectives, the present invention employs the following technical solution:
[0006] A method for optimizing the layout of a sparse subarray antenna includes the following steps:
[0007] Step 1: Randomly generate an initial population. Each particle array in the initial population corresponds to a subarray arrangement, i.e., each particle array corresponds to a two-dimensional sparse subarray array. There is no overlap between any two subarrays in the two-dimensional sparse subarray array corresponding to each particle array in the initial population. Assign a random initial velocity to the coordinate point of the subarray corresponding to each particle in the initial population in the y-axis and z-axis directions. Generate a beam pattern pointing to (0,0) for each two-dimensional sparse subarray array corresponding to each particle array, and then obtain the main lobe width in the pitch and azimuth directions. Calculate the fitness value of each particle array in the initial population. Divide the initial population into multiple subgroups on an average basis.
[0008] Step 2: Process each particle array in each subgroup using the PSO algorithm, setting the maximum value for continuous updates of the PSO algorithm to MAX1. During the processing of each particle array using the PSO algorithm, whenever a new particle array is generated, the following procedure is executed:
[0009] (1) Check whether all subarrays corresponding to the current particle array are in the planar constraint region. If they are satisfied, execute (2). If they are not satisfied, execute step 2 again.
[0010] (2) Check whether there is any overlap between any two subarrays in the current particle array. If yes, repeat step 2; otherwise, proceed to step 3.
[0011] Step 3: Generate a beammap pointing to (0,0) from the two-dimensional sparse subarray arrays corresponding to all new particle arrays obtained in Step 2 for the current subgroup. Then, obtain the main lobe widths in the pitch and azimuth directions. Calculate the fitness value of each new particle array. Retain the n particle arrays with smaller fitness values in the current subgroup as new subgroups, and take the smallest fitness value as the optimal fitness value. Determine if there is an optimal fitness value that does not change for more than MAX1 consecutive times. If not, return to Step 2. If it does, it is determined that a local optimum has been reached. At this time, output the particle arrays corresponding to the q smaller fitness values in each subgroup and execute Step 4.
[0012] Step 4: Recombine the particle arrays corresponding to the q smaller fitness values of each subpopulation into a new population. Assign a particle array from the PSO algorithm to a chromosome from the GA algorithm. Then, perform selection, crossover, and mutation operations on each chromosome in the new population sequentially using the GA algorithm. During this process, whenever a new chromosome appears, determine whether there is any overlap between any two subarrays in the two-dimensional sparse subarray array corresponding to the new chromosome. If not, save the new chromosome; if so, repeat the crossover or mutation operation in the GA algorithm until a new chromosome that satisfies the constraint is found and saved.
[0013] Step 5: Generate a beammap pointing to (0,0) from the two-dimensional sparse subarray array corresponding to each new chromosome obtained in Step 4. Then, obtain the main lobe widths in the pitch and azimuth directions, and calculate the fitness value of the new chromosome. Compare it with the current optimal fitness value. If the value is smaller, update the optimal fitness value and reset the counter. If it is not smaller, do not update, and increment the counter by 1. Repeat this process for all new chromosomes obtained in Step 4. If the counter is less than MAX2, return to Step 4 and continue iterative optimization using the GA algorithm. If the counter reaches MAX2, output the chromosomes with smaller fitness values.
[0014] Step 6: Process each chromosome output in Step 5 again using the PSO algorithm. At this time, one particle array of the PSO algorithm corresponds to one chromosome of the GA algorithm, and assign a random velocity to each particle in the y-axis and z-axis directions. Calculate the fitness value for each new particle array generated by the PSO algorithm and compare it with the current optimal fitness value. If it is less, update it; otherwise, do not update it. If the optimal fitness value is not updated for MAX1 consecutive times, output the current optimal fitness value.
[0015] Furthermore, in step 1, each subgroup includes an array of 30 to 50 particles.
[0016] Furthermore, in step 1, the fact that the subarrays within the two-dimensional sparse subarray array do not overlap means that the following equation is satisfied:
[0017] |y m1 -y m2 |>(n1-1)d,or|z m1 -z m2 |>(n2-1)d
[0018] Where m1 and m2 are the indices of any two subarrays in the two-dimensional sparse subarray array; y m1 y m2 The y-coordinates and z-coordinates of subarrays m1 and m2 are respectively. m1 z m2 Let m1 and m2 be the z-axis coordinates of subarrays m1 and m2; d is the spacing between array elements within the subarray, d = λ / 2; n1 and n2 are the number of rows and columns of the subarray, respectively; and λ is the wavelength of the signal transmitted by the array antenna.
[0019] Furthermore, in step 1, the formula for calculating the fitness value of the particle array is as follows:
[0020]
[0021] Where PSLL0 is the PSLL design expectation, WB0 is the main lobe width design expectation, and WB... ⊥ The main lobe width in the azimuth direction, WB / / α1 represents the main lobe width in the pitch direction; α2 and α1 are weighting coefficients, both constants between 0 and 1.
[0022] Furthermore, the check in step 2(1) regarding whether the subarray is within the planar constraint region specifically refers to:
[0023] Determine if all subarrays satisfy 0 ≤ y m ≤Y′,0≤z m ≤Z′, Y′=Y-(n1-1)×d, Z′=Z-(n2-1)d, where, (y m , zm ) represents the coordinates of the m-th subarray, 1≤m≤M, where M is the number of subarrays in the two-dimensional sparse subarray array; Y and Z represent the constraint space range of the two-dimensional sparse subarray array.
[0024] Further, in step 2, the specific operation of (2) is as follows: First, sort the y-coordinates of each subarray by size. Then, starting from the y-coordinate of the second subarray, subtract the y-coordinate of the previous subarray to obtain the distance between the two adjacent subarrays. Record the subarray combinations with a distance less than (n1-1)d. Then verify whether the recorded subarray combinations satisfy |z m1 -z m2 If |>(n2-1)d is not satisfied, it means that there is an overlap and step 2 needs to be executed again. If it is satisfied, save it until all particle arrays in the current subgroup have been processed and proceed to step 3.
[0025] Furthermore, in step 4, the new population comprises an array of 100-200 particles.
[0026] Furthermore, in step 5, the chromosomes with smaller output fitness values are the chromosomes that have smaller output fitness values, which are 20% to 30%.
[0027] Furthermore, the values of MAX1 and MAX2 range from 10 to 30.
[0028] Compared with the prior art, the present invention has the following technical effects:
[0029] 1. Based on the global optimization capability of the GA algorithm and the fast local optimization feature of the PSO algorithm, this invention proposes an improved GA-PSO combined algorithm. By constraining the position of the subarrays, determining whether they are within the array area and whether there is cross-over between subarrays, the optimal sparse array layout result is obtained after multiple iterations.
[0030] 2. This invention improves the robustness of the optimization algorithm by rationally designing the fitness function and utilizing multiple GA-PSO combined iterative cycles, making the solution closer to the true global optimum. The improved GA-PSO combined algorithm is applied to the sparse array optimization design of two-dimensional subarrays, and the beam performance of the optimized array is simulated and verified. Compared with the simulation analysis results of other algorithms, the method of this invention has the lowest convergence fitness function value and the best convergence effect. The sparse optimization result shows the main lobe pointing in the desired direction with no grating lobes, effectively suppressing PSLL of the beam, thereby effectively suppressing grating lobes and high sidelobes, providing theoretical and technical support for engineering design. Attached Figure Description
[0031] Figure 1 It is a diagram of a two-dimensional sparse subarray structure;
[0032] Figure 2 It is a simulation of the fitness function of the optimized array algorithm;
[0033] Figure 3 This is the result of the first simulation experiment for optimizing the array layout;
[0034] Figure 4 This is the result of the second simulation experiment for optimizing the array layout.
[0035] Figure 5 It optimizes the array beam pattern.
[0036] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. Detailed Implementation
[0037] like Figure 1 As shown, suppose M rectangular subarrays of n1×n2 are sparsely arranged on the yoz plane, with the element spacing within the subarrays being d=λ / 2, where λ is the wavelength of the signal transmitted by the array antenna.
[0038] In practical engineering, subarray modules are arranged within a limited space, constrained to a Y×Z range. The subarrays are ensured to be randomly distributed and non-overlapping. The reference element of all subarrays is determined by the element at the lower left corner, i.e., the coordinates (y, y) of the lower left corner element are used to define the reference element. m , z m Let 1 ≤ m ≤ M be the coordinates of the subarray. To ensure that within the constrained space, the coordinates of the reference elements of all subarrays satisfy 0 ≤ y m ≤Y′,0≤z m ≤Z′, where Y′=Y-(n1-1)×d, Z′=Z-(n2-1)×d. In addition, to further expand the array aperture, the main lobe width is introduced into the optimization objective function. Therefore, from the problem model analysis of the optimized array layout, the variable that needs to be optimized is the position of the reference elements of the M subarrays, which can be expressed as:
[0039]
[0040] In the formula, (y m , z m Let be the coordinates of the m-th subarray, in meters. Meanwhile, to ensure that no two subarrays overlap, the following constraints must be satisfied:
[0041] |y m1 -y m2 |>(n1-1)d,or|z m1 -z m2 |>(n2-1)d
[0042] Where m1 and m2 are the numbers of any two subarrays in the two-dimensional sparse subarray array.
[0043] Furthermore, to improve the practicality of the array design, the desired PSLL design value is set to PSLL0, and the desired main lobe width design value is set to WB0. The array layout is optimized to make PSLL and WB approach these desired values. Since the radiation pattern in a two-dimensional plane is a three-dimensional pattern, considering that the main lobe width may differ depending on whether it is projected in the azimuth or elevation directions, the squares of the main lobe widths projected in the elevation and azimuth directions are used as the parameters for calculation. WB ⊥ The main lobe width in the azimuth direction, WB / / The main lobe width in the pitch direction is represented by the optimized model as follows:
[0044]
[0045] st0≤y m ≤Y′,0≤z m ≤Z′
[0046] |y m1 -y m2 |>(n1-1)d,or|z m1 -z m2 |>(n2-1)d
[0047] 1≤m1, m2≤M, m1≠m2
[0048] The idea behind this invention is to apply the improved GA-PSO algorithm to solve the above equation for the array optimization problem of a two-dimensional planar sparse subarray array, thereby optimizing the random array arrangement of M n1×n2 subarrays within a given array surface, ensuring that each subarray does not overlap or intersect.
[0049] Based on the above ideas, the sparse subarray antenna array layout optimization method provided by this invention specifically includes the following steps:
[0050] Step 1: Randomly generate an initial population. Each particle array in the initial population corresponds to a subarray arrangement (i.e., each particle array corresponds to a two-dimensional sparse subarray array). There is no overlap between any two subarrays in the two-dimensional sparse subarray array corresponding to each particle array in the initial population (consistent with Equation 1). Assign a random initial velocity to the coordinate point of the subarray corresponding to each particle in the initial population in the y-axis and z-axis directions. Generate a beam pattern pointing to (0,0) for each two-dimensional sparse subarray array corresponding to each particle array. Then obtain the main lobe width in the pitch and azimuth directions. Calculate the fitness value (i.e., fitness value) of each particle array in the initial population according to Equation 2. Divide the initial population into X subgroups (each subgroup includes n particle arrays, n is generally 30 to 50).
[0051] |y m1-y m2 |>(n1-1)d,or|z m1 -z m2 |>(n2-1)d Equation 1
[0052] Where m1 and m2 are the indices of any two subarrays in the two-dimensional sparse subarray array; y m1 y m2 The y-coordinates and z-coordinates of subarrays m1 and m2 are respectively. m1 z m2 Let m1 and m2 be the z-axis coordinates of subarrays m1 and m2; d is the spacing between elements within the subarray, d = λ / 2; n1 and n2 are the number of rows and columns of the subarray, respectively.
[0053]
[0054] Where PSLL0 is the PSLL design expectation, WB0 is the main lobe width design expectation, and WB... ⊥ The main lobe width in the azimuth direction, WB / / α1 represents the main lobe width in the pitch direction; α2 and α1 are weighting coefficients, both constants between 0 and 1.
[0055] Step 2: Process each particle array in each subgroup using the PSO algorithm, setting the maximum value for continuous updates of the PSO algorithm to MAX1. During the processing of each particle array using the PSO algorithm, whenever a new particle array is generated, the following procedure is executed:
[0056] (1) Check whether all subarrays corresponding to the current particle array are within the planar constraint region. If they are, proceed to (2). If not, repeat step 2. Specifically, determine whether all subarrays satisfy 0 ≤ y m ≤Y′,0≤z m ≤Z′, Y′=Y-(n1-1)×d, Z′=Z-(n2-1)×d, where, (y m , z m Let y be the coordinates of the m-th subarray, 1≤m≤M, where M is the number of subarrays in the two-dimensional sparse subarray array; Y and Z are the constraint space ranges of the two-dimensional sparse subarray array.
[0057] (2) Check if there is any overlap between any two subarrays in the current particle array. If yes, repeat step 2; otherwise, proceed to step 3. Specifically, sort the y-coordinates of each subarray by size. Then, starting from the y-coordinate of the second-ranked subarray, subtract the y-coordinate of the previous subarray from the y-coordinate of the current subarray to obtain the distance between the two adjacent subarrays. Record the subarray combinations with a distance less than (n1-1)d. Then verify whether the recorded subarray combinations satisfy |z m1 -z m2If |>(n2-1)d is not satisfied, it means that there is an overlap and step 2 needs to be executed again. If it is satisfied, save it until all particle arrays in the current subgroup have been processed and proceed to step 3.
[0058] Step 3: Generate a beammap pointing to (0,0) from the two-dimensional sparse subarray arrays corresponding to all new particle arrays obtained in Step 2 for the current subgroup. Then, obtain the main lobe widths in the pitch and azimuth directions. Calculate the fitness value of each new particle array. Retain the n particle arrays with smaller fitness values in the current subgroup as new subgroups, and take the smallest fitness value as the optimal fitness value. Determine if there is an optimal fitness value that does not change for more than MAX1 consecutive times. If not, return to Step 2. If it does, it is determined that a local optimum has been reached. At this time, output the particle arrays corresponding to the q smaller fitness values in each subgroup and execute Step 4.
[0059] Step 4: Recombine the particle arrays corresponding to the q smaller fitness values of each subpopulation into a new population (the new population includes 100-200 particle arrays). Assign one particle array from the PSO algorithm to one chromosome from the GA algorithm. Then, perform selection, crossover, and mutation operations on each chromosome in the new population sequentially using the GA algorithm. During this process, whenever a new chromosome appears, determine whether there is any crossover overlap between any two subarrays in the two-dimensional sparse subarray array corresponding to the new chromosome (meeting Equation 1). If not, save the new chromosome; if so, repeat the crossover or mutation operation in the GA algorithm until a new chromosome that satisfies the constraint is found (the termination condition for the operation in the case of crossover is exhaustion of the number of crossover combinations, and the termination condition for the operation in the case of mutation is reaching the set upper limit of the number of mutations), and save it.
[0060] Selection: Use a roulette wheel strategy; Crossover: Exchange the positions of a selected chromosome with a randomly selected chromosome from the population; Mutation: Randomly select a coordinate position from the selected chromosome and change it to obtain a new coordinate position, and then form a new chromosome.
[0061] Step 5: Generate a beammap pointing to (0,0) from the two-dimensional sparse subarray array corresponding to each new chromosome obtained in Step 4. Then, obtain the main lobe widths in the pitch and azimuth directions, and calculate the fitness value of the new chromosome. Compare it with the current optimal fitness value. If the value is smaller, update the optimal fitness value and reset the counter. If it is not smaller, do not update, and increment the counter by 1. Repeat this process for all new chromosomes obtained in Step 4. If the counter is less than MAX2, return to Step 4 and continue iterative optimization using the GA algorithm. If the counter reaches MAX2, output the chromosomes with smaller fitness values, which are 20% to 30%.
[0062] Step 6: Process each chromosome output in Step 5 again using the PSO algorithm. At this time, one particle array of the PSO algorithm corresponds to one chromosome of the GA algorithm, and assign a random velocity to each particle in the y-axis and z-axis directions. Calculate the fitness value for each new particle array generated by the PSO algorithm and compare it with the current optimal fitness value. If it is less, update it; otherwise, do not update it. If the optimal fitness value is not updated for MAX1 consecutive times, output the current optimal fitness value.
[0063] To demonstrate the feasibility and effectiveness of the method of the present invention, a simulation experiment of two-dimensional planar sparse subarray optimization design was conducted.
[0064] The improved GA-PSO combination algorithm of this invention is extended to optimize two-dimensional subarrays. In the simulation experiment, the radar signal frequency is set to 15GHz, and M=8 subarrays are sparsely optimized and arranged. The 8 subarrays are 6×6 uniform rectangular arrays with an element spacing of d=λ / 2. Each subarray is equipped with a digital-analog channel and is arranged on a two-dimensional plane with a size of 0.31m×0.31m.
[0065] During the simulation, the simulation beam direction was set to (0°, 0°), the angular resolution to 0.1°, and the positioning accuracy of the array elements to 0.5mm. Algorithm parameters were set to MAX1 = 25 and MAX2 = 15; the initial population size was 100, X = 4, and the number of iterations was 200. In the GA algorithm, the selection probability was set to 0.2, the crossover probability to 0.8, and the mutation probability to 0.15. In the PSO algorithm, the inertia weight was set to 0.8, the positive learning factor to 0.2, and the maximum constrained particle movement distance in each iteration was set to 8d.
[0066] MAX1 and MAX2 are determined based on experience. Smaller values result in faster convergence, but it is difficult to guarantee convergence to the optimal value; larger values result in slower convergence, but are closer to the optimal value. Generally, values between 10 and 30 are selected.
[0067] from Figure 2 It can be seen that the GA algorithm has a slow convergence speed and has not reached the optimal solution; the PSO algorithm converges the fastest, but gets stuck in local optimization and has not obtained the optimal solution; the improved GA-PSO combination method of this invention has the best convergence effect.
[0068] Figure 3 , Figure 4 The results of two simulation experiments were obtained by optimizing the improved GA-PSO combination method of this invention.
[0069] in:
[0070] Figure 3 The reference position coordinates for the sparse optimization design are:
[0071]
[0072] Figure 4 The reference position coordinates for the sparse optimization design are:
[0073]
[0074] The DBF algorithm was validated using the results of the first optimization, such as... Figure 5 As shown, Figure 5 The main lobe of the radiation pattern points to (0°, 0°), verifying the effectiveness of the optimized array arrangement.
Claims
1. A method for optimizing the arrangement of sparse subarray antennas, characterized in that, Specifically, the steps include the following: Step 1: Randomly generate an initial population. Each particle array in the initial population corresponds to a subarray arrangement, that is, each particle array corresponds to a two-dimensional sparse subarray array. There is no overlap between any two subarrays in the two-dimensional sparse subarray array corresponding to each particle array in the initial population. And assign a random initial velocity to the coordinate point of the subarray corresponding to each particle in the initial population in the y-axis and z-axis directions. Generate a beammap pointing to (0,0) for each two-dimensional sparse subarray corresponding to each particle array, then obtain the main lobe widths in the pitch and azimuth directions, and calculate the fitness value of each particle array in the initial population; divide the initial population into multiple subgroups on an average basis. Step 2: Process each particle array in each subgroup using the PSO algorithm, setting the maximum value for continuous updates of the PSO algorithm to MAX1. During the processing of each particle array using the PSO algorithm, whenever a new particle array is generated, the following procedure is executed: (1) Check whether all subarrays corresponding to the current particle array are in the planar constraint region. If they are satisfied, execute (2). If they are not satisfied, execute step 2 again. (2) Check whether there is any overlap between any two subarrays in the current particle array. If yes, repeat step 2; otherwise, proceed to step 3. Step 3: Generate a beammap pointing to (0,0) from the two-dimensional sparse subarray arrays corresponding to all new particle arrays obtained in Step 2 for the current subgroup. Then, obtain the main lobe widths in the pitch and azimuth directions. Calculate the fitness value of each new particle array. Retain the n particle arrays with smaller fitness values in the current subgroup as new subgroups, and take the smallest fitness value as the optimal fitness value. Determine if there is an optimal fitness value that does not change for more than MAX1 consecutive times. If not, return to Step 2. If it does, it is determined that a local optimum has been reached. At this time, output the particle arrays corresponding to the q smaller fitness values in each subgroup and execute Step 4. Step 4: Recombine the particle arrays corresponding to the q smaller fitness values of each subpopulation into a new population. Assign a particle array in the PSO algorithm to a chromosome in the GA algorithm. Then, perform selection, crossover, and mutation operations on each chromosome in the new population sequentially using the GA algorithm. During this process, whenever a new chromosome appears, determine whether there is any overlap between any two subarrays in the two-dimensional sparse subarray array corresponding to the new chromosome. If not, save the new chromosome. If it exists, repeat the crossover or mutation operation in the GA algorithm until a new chromosome that satisfies the constraint is found and saved. Step 5: Generate a beammap pointing to (0,0) from the two-dimensional sparse subarray array corresponding to each new chromosome obtained in Step 4. Then, obtain the main lobe widths in the pitch and azimuth directions, and calculate the fitness value of the new chromosome. Compare it with the current optimal fitness value. If the value is smaller, update the optimal fitness value and reset the counter. If it is not smaller, do not update, and increment the counter by 1. Repeat this process for all new chromosomes obtained in Step 4. If the counter is less than MAX2, return to Step 4 and continue iterative optimization using the GA algorithm. If the counter reaches MAX2, output the chromosomes with smaller fitness values. Step 6: Process each chromosome output in Step 5 again using the PSO algorithm. At this time, one particle array of the PSO algorithm corresponds to one chromosome of the GA algorithm, and assign a random velocity to each particle in the y-axis and z-axis directions. Calculate the fitness value for each new particle array generated by the PSO algorithm and compare it with the current optimal fitness value. If it is less, update it; otherwise, do not update it. If the optimal fitness value is not updated for MAX1 consecutive times, output the current optimal fitness value.
2. The sparse subarray antenna array layout optimization method as described in claim 1, characterized in that, In step 1, each subgroup consists of 30 to 50 particle arrays.
3. The sparse subarray antenna array layout optimization method as described in claim 1, characterized in that, In step 1, the fact that the subarrays within the two-dimensional sparse subarray array do not overlap means that the following equation is satisfied: |y m1 -y m2 |>(n1-1)d,or|z m1 -z m2 |>(n2-1)d where m1 and m2 are the indices of any two subarrays in the two-dimensional sparse subarray array; y m1 y m2 The y-coordinates and z-coordinates of subarrays m1 and m2 are respectively. m1 z m2 Let m1 and m2 be the z-axis coordinates of subarrays m1 and m2; d is the spacing between array elements within the subarray, d = λ / 2; n1 and n2 are the number of rows and columns of the subarray, respectively; and λ is the wavelength of the signal transmitted by the array antenna.
4. The sparse subarray antenna array layout optimization method as described in claim 1, characterized in that, In step 1, the formula for calculating the fitness value of the particle array is as follows: Where PSLL0 is the PSLL design expectation, WB0 is the main lobe width design expectation, and WB... ⊥ The main lobe width in the azimuth direction, WB / / α1 represents the main lobe width in the pitch direction; α2 and α1 are weighting coefficients, both constants between 0 and 1.
5. The sparse subarray antenna array layout optimization method as described in claim 3, characterized in that, The check in step 2(1) regarding whether the subarray is within the planar constraint region specifically refers to: Determine if all subarrays satisfy 0 ≤ y m ≤Y′,0≤z m ≤Z′, Y′=Y-(n1-1)×d, Z′=Z-(n2-1)×d, where, (y m , z m ) represents the coordinates of the m-th subarray, 1≤m≤M, where M is the number of subarrays in the two-dimensional sparse subarray array; Y and Z represent the constraint space range of the two-dimensional sparse subarray array.
6. The sparse subarray antenna array layout optimization method as described in claim 3, characterized in that, In step 2, the specific operation of (2) is as follows: First, sort the y-coordinates of each subarray by size. Then, starting from the y-coordinate of the second subarray, subtract the y-coordinate of the previous subarray to obtain the distance between the two adjacent subarrays. Record the subarray combinations with a distance less than (n1-1)d. Then, verify whether the recorded subarray combinations satisfy |z m1 -z m2 If |>(n2-1)d is not satisfied, it means that there is an overlap and step 2 needs to be executed again. If it is satisfied, save it until all particle arrays in the current subgroup have been processed and proceed to step 3.
7. The sparse subarray antenna array layout optimization method as described in claim 1, characterized in that, In step 4, the new population consists of an array of 100-200 particles.
8. The sparse subarray antenna array layout optimization method as described in claim 1, characterized in that, In step 5, the chromosomes with smaller output fitness values are the 20% to 30% of chromosomes with smaller output fitness values.
9. The sparse subarray antenna array layout optimization method as described in claim 1, characterized in that, The values of MAX1 and MAX2 range from 10 to 30.