Large-scale circular array design method based on uneven sampling and distributed computing

Abstract

The application discloses a large-scale circular array design method based on uneven sampling and distributed calculation. The rotating array configuration utilizes uneven sampling to evaluate the sidelobe performance, obtains a new offspring population under the current mutation probability and the crossover probability, and utilizes the directional diagram distributed calculation to each phi section. The application can realize the accurate calculation of the sidelobe performance of the directional diagram of the circular array under different beam scanning angles, improves the calculation speed in the optimization process under the premise of ensuring the accuracy, increases the probability that the final result is the global optimum, reduces the memory requirement of the computer, and improves the optimization efficiency of the array design. The simulation result shows that the large-scale circular array in the embodiment of the application has the required performance after being designed by using the large-scale circular array design method based on uneven sampling and distributed calculation.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and more specifically relates to a design method for large-scale circular arrays based on non-uniform sampling and distributed computing in the field of antenna technology. This invention can be used to determine the position and number of elements in a large-scale circular array to achieve the desired array antenna performance. Background Technology

[0002] Optimization of array antenna layout refers to achieving superior performance indicators by adjusting the array geometry to meet the system's requirements for the array antenna. For large-scale arrays with power requirements, achieving low sidelobe performance by adjusting the feed amplitude will result in some power loss. To ensure the overall power of the array is maximized, the array element positions are optimized to achieve low sidelobe performance. Large-scale unequal-pitch arrays, as a type of array antenna, have high gain characteristics due to their large number of array elements and are often used in applications such as deep space exploration. These applications often require the array antenna to have beam scanning capabilities. Due to the large scale of the array, achieving beam scanning by adjusting the mechanical structure is time-consuming and labor-intensive; therefore, changing the element feed phase is commonly used to achieve beam scanning.

[0003] Circular arrays, as a common method for realizing unequally spaced array surfaces, have the advantages of having few variables to be optimized, and each... The array elements in the cross-section share the same characteristics. For a circular array design with a given constraint on the maximum sidelobe level, the optimization objective is to minimize the ratio of the maximum sidelobe level to the maximum main lobe level within the wideband scanning angle range of the circular array, given the number of rotations. Due to the non-convexity and non-differentiability of the objective, differential evolution algorithms are commonly used in engineering to solve this problem. For differential evolution algorithms based on population iterative optimization, a large number of array radiation patterns need to be calculated as the optimization process progresses. Calculating the radiation patterns of high-gain, large-scale array antennas requires enormous computational resources, thus consuming significant computational resources and time.

[0004] Harbin Engineering University disclosed a method for optimizing sparsely distributed concentric ring arrays based on dimensionality reduction technology in its patent application "A Dimensionality Reduction Optimization Algorithm for Sparsely Distributed Concentric Ring Arrays" (Application No. 201711134028.4, Authorization Announcement No. CN 107896129 B). This method reduces the dimensionality of the optimization problem, obtaining the relationship between the number of array elements on each ring layer and the ring radius, thus halving the number of variables to be optimized. A novel random search technique is used to find the optimal ring radius, significantly improving the optimization speed. The optimization results are verified through high-density sampling to obtain the final result. However, this method still has three shortcomings: First, when verifying the optimization results through high-density sampling, if the number of array elements is large, a single pattern calculation requires a large amount of computer memory, causing personal computers to be unable to complete the calculation or experience slow calculation speeds due to insufficient memory. Second, it does not consider the antenna beam scanning requirements. When optimizing arrays with beam scanning requirements, it cannot accurately find the maximum sidelobe, leading to a significant difference between the optimized result and the actual result. Thirdly, optimizing only the radius of each ring and calculating the number of array elements on each ring according to the formula is only a feasible result under the current performance constraints, and cannot guarantee that the final array element arrangement is the globally optimal arrangement.

[0005] Xi'an University of Electronic Science and Technology disclosed a circular array optimization method based on a differential evolution algorithm in its patent application "Design Method of Circular Array Antenna Based on Multi-Objective Discrete Differential Evolution Algorithm" (Application No. 201710299694.7, Publication No. CN 107169181 A). This method obtains a set of optimal dominant solutions by using a multi-objective discrete differential evolution algorithm, and the sampling points are distributed in a high-density and uniform manner during radiation pattern calculation, thus improving the quality of the optimization results. However, this method still has two shortcomings: First, the dense sampling points in the radiation pattern calculation result in excessively long calculation time when used for large-scale circular array optimization design, thus slowing down the optimization speed for large-scale circular array problems. Second, it does not consider the antenna's beam scanning requirements. When optimizing arrays with beam scanning requirements, it cannot accurately find the maximum sidelobe, leading to a significant difference between the optimization results and the actual results. Summary of the Invention

[0006] The purpose of this invention is to address the problems existing in the prior art by providing a large-scale circular array design method based on non-uniform sampling and distributed computing. This method aims to solve the problems of slow optimization speed, inability to consider beam scanning requirements, large memory requirements and slow computing speed of personal computers, and difficulty in ensuring that the final array element arrangement is the globally optimal arrangement in the design of large-scale circular arrays.

[0007] The approach to achieving the invention's objective is as follows: Addressing the aforementioned problems, this invention proposes a method for evaluating sidelobe performance using non-uniform sampling. This method increases the number of pattern sampling points in regions with drastic changes near the main beam, while reducing the number of sampling points in other smooth regions. The sampling point positions need to change randomly throughout the optimization process to prevent the final result from only meeting performance requirements at fixed sampling points. This improves computational speed while maintaining relatively high accuracy, solving the problem of slow optimization speed in large-scale circular array design. The rotating array configuration in this invention directs the main beam within the beam scanning angle range to the Z-axis, simplifying the process of finding the maximum sidelobe and resolving the problem in large-scale circular array design where the inability to accurately find the maximum sidelobe leads to significant discrepancies between optimized and actual results. This invention utilizes distributed pattern calculation for each... A cross section, representing each of the radiation patterns The cross-sections are distributed among different computers for computation, allocating memory and time consumption to different computers, thus solving the problem of personal computers being unable to complete calculations due to insufficient memory or slow calculation speed. This invention obtains a new offspring population under the current mutation and crossover probabilities, adaptively adjusting the mutation and crossover probabilities during the iteration process, reducing the probability of getting trapped in local optima, and solving the problem of not being able to ensure that the final array element arrangement is the globally optimal arrangement.

[0008] To achieve the above objectives, the technical solution adopted in this invention is as follows: using differential evolution algorithm as the core optimization algorithm, rotating array configuration, evaluating sidelobe performance using non-uniform sampling, obtaining a new offspring population under the current mutation and crossover probabilities, and utilizing distributed computation of the radiation pattern for each... Operations such as slicing enable optimized design of the number and position of elements in a circular array with beam scanning requirements, accelerating the optimization process, reducing the probability of getting trapped in local optima, and lowering the demand for computer memory.

[0009] This invention provides a method for designing large-scale circular arrays based on non-uniform sampling and distributed computing, with the following steps:

[0010] Step 1: Randomly generate an initial offspring population based on the value range of the parameter to be optimized;

[0011] Step 2, Rotating array configuration:

[0012] Load the parameters of each individual in the current iteration of the offspring population into the circular array cell arrangement; rotate each array configuration of each individual in the offspring population, and rotate each main beam direction within the beam scanning range to the Z-axis.

[0013] Step 3: Evaluate sidelobe performance using non-uniform sampling:

[0014] For each individual, high-precision random sampling is performed around the Z-axis of each array configuration after rotation, and low-precision random sampling is performed in the other directions. The sampling point positions change randomly with each iteration. The values ​​at each sampling point are calculated to form a radiation pattern. The sidelobe performance of all radiation patterns is evaluated to obtain the sidelobe performance of each individual. The individual with the lowest sidelobe performance in the offspring population of the current iteration is taken as the optimal individual of the current iteration.

[0015] Step 4: Determine whether the sidelobe performance of the best individual in the current iteration is less than the sidelobe constraint. If yes, proceed to step 6; otherwise, proceed to step 5.

[0016] Step 5: Execute the differential evolution algorithm on the current offspring population. After obtaining a new offspring population under the current mutation and crossover probabilities, proceed to step 2.

[0017] Step 6, use distributed computing of the directional graph for each section:

[0018] The parameters of the current optimal individual are loaded into a large-scale circular array with 50 or more elements, and the radiation pattern is distributedly computed to obtain the parameters of each individual. Cut surface, all The cross-sectional composite radiation pattern is used to calculate the beamwidth, sidelobes, and gain, thus completing the design of this large-scale circular array.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] First, due to the rotating array configuration in this invention, all main beams within the beam scanning angle range are oriented towards the Z-axis, and are only used in each of the radiation patterns. Finding the maximum sidelobe on the cross-section simplifies the process of finding the maximum sidelobe in a beam scanning array and enables accurate calculation of the sidelobe performance of the pattern under different beam scanning angles of a circular array.

[0021] Second, this invention utilizes non-uniform sampling to evaluate sidelobe performance. High-precision random sampling is performed in directions within a region of dramatic change around the Z-axis, while low-precision random sampling is performed in other directions. The sampling point positions change randomly with each iteration, preventing the final result from meeting performance requirements only at fixed sampling points, thereby improving computational speed while ensuring accuracy.

[0022] Third, this invention generates a new offspring population under the current mutation and crossover probabilities. By adaptively adjusting the appropriate mutation and crossover probabilities for different optimization problems and different optimization stages, a higher-quality offspring population is generated. This improves global convergence while maintaining optimization speed, increasing the probability of convergence to the global optimum.

[0023] Fourth, in this invention, distributed computing based on directional graphs is used for each... Cross-section. Each of the orientation patterns The cross-sections are distributed to different computers for distributed fine-grained computing, allocating memory and time consumption to different computers. Multiple computers perform parallel computing, reducing computing time and memory consumption of a single computer, lowering the memory requirements of the computers, and improving the efficiency of array design optimization. Attached Figure Description

[0024] Figure 1 This is a flowchart of the present invention;

[0025] Figure 2 This is a schematic diagram of the large-scale circular array of the present invention;

[0026] Figure 3 This is a schematic diagram of the array configuration after rotation according to the present invention;

[0027] Figure 4 This is a schematic diagram of the coarse and fine calculation regions used in the present invention to evaluate the performance of sidelobes using non-uniform sampling;

[0028] Figure 5 This invention utilizes distributed computing of directional graphs for each Cross-section diagram

[0029] Figure 6 This is the two-dimensional radiation pattern obtained after optimization of the large-scale circular array in this invention. Detailed Implementation

[0030] The present invention will now be further described with reference to the accompanying drawings and embodiments.

[0031] Reference Figure 1 The specific steps for implementing the present invention will be further described below.

[0032] Step 1: Based on experience in designing large-scale circular arrays, set the parameter range for the radius and number of elements of each layer of the circular array. Randomly sample within the range of each parameter to obtain a set of sampling points for that parameter. The number of sampling points for each parameter is set to 5 times the number of parameters. Randomly select an unselected sampling point from the sampling point set for each parameter to form a sample. Each sample serves as an individual in the initial offspring population.

[0033] Reference Figure 2 The large-scale circular array in this invention will be further described below.

[0034] Figure 2 This is a schematic diagram of the large-scale circular array of the present invention. Figure 2Each black square in the diagram represents an array element. The horizontal axis (x) represents the horizontal distance from the array center, and the vertical axis (y) represents the vertical distance from the array center; both distances are in millimeters. In the embodiments of this invention, the final circular array is required to operate at a frequency of f0, with a value ranging from [10GHz, 20GHz]. The sidelobe level must be less than -20dB and as low as possible, and the gain must be greater than a given gain index (Gain), with a value ranging from [30dBi, 40dBi]. The main beam scanning angle θ∈[θ1, θ2] θ2 and θ1 are the upper and lower limits of the range of the main beam scanning angle θ. θ1 is set to 0°, and the value range of θ2 is [30°, 90°]. and Main beam scanning angle The upper and lower limits of the range of variation, angles Set to 0° The value range is [45°, 180°].

[0035] Step 2: Load the parameters of each individual in the offspring population into the circular array cell arrangement.

[0036] Load the parameters of each individual in the current iteration of the offspring population into the circular array cell arrangement. Rotate each individual in the offspring population for each array configuration, using the negative Z-axis of the Cartesian coordinate system as the reference direction, and rotate clockwise around the Z-axis. degrees, rotating clockwise by θ around the Y-axis. B Degrees, rotate the main beam to the Z-axis direction, The spherical coordinate direction of the main beam is used to preserve the array configuration after rotation. Figure 3 This is a schematic diagram of the rotated array configuration in an embodiment of the present invention. Figure 3 The lower right coordinate axis represents the horizontal distance of each point from the center of the ring, the lower left coordinate axis represents the vertical distance of each point from the center of the ring, and the left coordinate axis represents the vertical height distance of each point from the center of the ring. The unit of distance is millimeters. Figure 3 The black dashed lines in the diagram indicate the direction of the main beam, and each black square represents an antenna element. Figure 3 As can be seen, although the direction of the main beam deviates from the axis of the circular array, it points to the Z-axis after rotation.

[0037] Step 3: Evaluate the sidelobe performance using non-uniform sampling.

[0038] For each array configuration after rotation, high-precision random sampling is performed around the Z-axis for each individual array, while low-precision random sampling is performed in the remaining directions. The sampling point positions change randomly with each iteration, and the values ​​at each sampling point are calculated to form a radiation pattern. The sidelobe performance f is then calculated based on the radiation pattern of the array configuration corresponding to each main beam direction.

[0039]

[0040] Where θ represents the angle between the main scanning beam of the array and the Z-axis of the array normal. This indicates the angle between the main scanning beam of the array and the X-axis of the array configuration. Indicates the main beam scanning direction is The maximum main lobe level of the time pattern, Indicates the main beam scanning direction is The direction is the maximum sidelobe level of the radiation pattern, S represents the beam scanning area, and max represents the maximum value operation.

[0041] The individual with the lowest sidelobe performance in the current iteration's offspring population is taken as the optimal individual for the current iteration.

[0042] Figure 4 This is a schematic diagram illustrating the coarse and fine calculation regions for the fast radiation pattern calculation sidelobe performance evaluation in this embodiment of the invention. The horizontal axis u represents the value after normalizing the horizontal distance from the array center to -1 to +1, and the vertical axis v represents the value after normalizing the vertical distance from the array center to -1 to +1. Figure 4 The dark gray area near the main beam direction is the region of drastic pattern changes. The pattern fluctuates drastically in this area. High-precision sampling in this area can avoid missing radiation angles that do not meet performance requirements. The remaining light gray area is far from the main beam direction and changes more gently. Low-precision random sampling in this area can significantly reduce the calculation time without reducing the calculation accuracy.

[0043] Calculate the orientation pattern based on the sampling points.

[0044] Step 4: Determine whether the sidelobe performance of the best individual in the current iteration is less than the judgment index set by the designer in the range of [-50, -20] dB. If yes, proceed to step 6; otherwise, proceed to step 5.

[0045] Step 5: Execute the differential evolution algorithm on the current offspring population. In the initial iteration, set the initial mean mutation value. and initial cross mean Both are set to 0.5. The adaptive iteration count i = 0 is set, and the mutation probability F and crossover probability CR are both set to 0.5. The current mutation probability and crossover probability are added to the mutation database and crossover database, respectively. If the sidelobe performance of the optimal individual remains unchanged after 10 consecutive iterations, the adaptive iteration count i = i + 1 is set. The current mean mutation value is calculated according to the following formula. and cross means

[0046]

[0047]

[0048] Here, mF is an individual randomly selected from the variation database, and mCR is an individual randomly selected from the crossover database. It is the mean of the mutations from the previous iteration. The crossover mean is the value of the previous iteration, and r is a random number between 0 and 1. Calculate the mutation probability F and crossover probability CR of the current iteration according to the following formula:

[0049]

[0050]

[0051] Here, `rand(A,B)` generates a random number based on a normal distribution with mean A and standard deviation B. The current mutation probability `F` and crossover probability `CR` are added to the mutation database and crossover database, respectively. The database capacity is capped at 50. Once the capacity is reached, the mutation probability `F` and crossover probability `CR` added to the database randomly replace an existing individual in either the current mutation or crossover database. After obtaining a new offspring population under the current mutation and crossover probabilities, step 2 is executed.

[0052] Step 6, use distributed computing of the directional graph for each section.

[0053] The parameters of the current optimal individual are loaded into a large-scale circular array of elements with a number of elements greater than or equal to 50, at fixed angular intervals. Divide the directional pattern into multiple Cross-section. Then, for each The aspect is distributed across different computers for distributed computing, with only one aspect being computed at a time. The cross-section calculates the results and saves them in an external document. A tangent refers to a plane in a given spherical coordinate system. Angle, θ is the plane encompassed by the angle as it changes from 0° to 180°.

[0054] Figure 5 This invention utilizes distributed computing of directional graphs for each A schematic diagram of the cross-section. Figure 5 The black arrow in the diagram represents the X-axis, and the dark gray cross line represents the Z-axis. The positive direction of the Z-axis is from the paper outwards. Looking at the diagram from the positive Z-axis direction, we get the gray circular area shown in the diagram. θ represents the angle between any angle in the radiation pattern and the X-axis, with a minimum of 0° and a maximum of 360°. θ represents the angle between any angle in the radiation pattern and the Z-axis. Figure 5 In the medium gray circular area, the farther away from the center, the larger the angle θ, ranging from a minimum of 0° to a maximum of 180°. (The intervals are set at fixed angles.) Divide the directional pattern into And multiple Cut the surface. Take each The aspect is distributed across different computers for distributed computing, with only one aspect being computed at a time. The cross-section stores the calculation results in an external document. In all... After the section calculation is completed, each section is read into a computer. External document of the section. Merge all. The cross-section yields the three-dimensional total radiation pattern of the array antenna, and the beamwidth and sidelobe level are evaluated for all... Gain is obtained by sectional distributed integration, thus completing the design of a large-scale circular array.

[0055] Reference Figure 6 The performance of the large-scale circular array finally obtained in the embodiments of the present invention will be further described.

[0056] Figure 6 This is the two-dimensional radiation pattern obtained after optimization of the large-scale circular ring array of the present invention. Wherein, Figure 6 (a) is the two-dimensional radiation pattern of the xoz plane when the main beam scanning angle is (0°, 0°). Figure 6 (b) is the two-dimensional radiation pattern of the yoz plane when the main beam scanning angle is (0°, 0°). Figure 6 (c) is the two-dimensional radiation pattern of the xoz plane when the main beam scanning angle is (20°, 45°). Figure 6 (d) is the two-dimensional radiation pattern of the yoz plane when the main beam scanning angle is (20°, 45°). Figure 6 (e) is the two-dimensional radiation pattern of the xoz plane when the main beam scanning angle is (30°, 45°). Figure 6 (f) is the two-dimensional radiation pattern of the yoz plane when the main beam scanning angle is (30°, 45°).

[0057] Figure 6In all radiation patterns, the horizontal axis represents angle θ, in degrees, and the vertical axis represents sidelobe level, in dB. Figure 6 The maximum sidelobe electrical average in all given radiation patterns is less than -20 dB. The radiation patterns of the large-scale circular array obtained from simulation experiments show that the maximum sidelobe is less than -20 dB and the minimum gain is greater than 40 dBi in the full-beam scanning region, which meets the design requirements of the embodiments of the present invention.

Claims

1. A design method for large-scale circular arrays based on non-uniform sampling and distributed computing, characterized in that, A rotating array configuration is used to evaluate sidelobe performance using non-uniform sampling. Under the current mutation and crossover probabilities, a new offspring population is obtained, and each offspring is computed using a pattern-distributed computation. Cross-section; the steps of this design method are as follows: Step 1: Randomly generate an initial offspring population based on the value range of the parameter to be optimized; Step 2, Rotating array configuration: Load the parameters of each individual in the current iteration of the offspring population into the circular array cell arrangement; rotate each array configuration of each individual in the offspring population, and rotate each main beam direction within the beam scanning range to the Z-axis. Step 3: Evaluate sidelobe performance using non-uniform sampling: For each individual, high-precision random sampling is performed around the Z-axis of each array configuration after rotation, and low-precision random sampling is performed in the other directions. The sampling point positions change randomly with each iteration. The values ​​at each sampling point are calculated to form a radiation pattern. The sidelobe performance of all radiation patterns is evaluated to obtain the sidelobe performance of each individual. The individual with the lowest sidelobe performance in the offspring population of the current iteration is taken as the optimal individual of the current iteration. Step 4: Determine whether the sidelobe performance of the best individual in the current iteration is less than the sidelobe constraint. If yes, proceed to step 6; otherwise, proceed to step 5. Step 5: Execute the differential evolution algorithm on the current offspring population. After obtaining a new offspring population under the current mutation and crossover probabilities, proceed to step 2. Step 6, use distributed computing of the directional graph for each section: The parameters of the current optimal individual are loaded into a large-scale circular array with a number of elements greater than or equal to 50, and the radiation pattern is distributedly computed to obtain the parameters of each individual. Cut surface, all The cross-sectional composite radiation pattern is used to calculate the beamwidth, sidelobes, and gain, thus completing the design of this large-scale circular array.

2. The large-scale circular array design method based on non-uniform sampling and distributed computing according to claim 1, characterized in that, The range of values ​​for the parameters to be optimized in step 1 refers to setting the range of parameters for the radius of each ring and the number of elements based on the design experience of large-scale ring arrays. Random sampling is performed within the range of each parameter to obtain the set of sampling points for that parameter. The number of sampling points for each parameter is set to 5 times the number of parameters.

3. The large-scale circular array design method based on non-uniform sampling and distributed computing according to claim 1, characterized in that, The random generation of the initial offspring population mentioned in step 1 means that an unselected sampling point is randomly selected from the sampling point set of each parameter to form a sample, and each sample is an individual in the initial offspring population.

4. The large-scale circular array design method based on non-uniform sampling and distributed computing according to claim 1, characterized in that, Step 2, which describes rotating each main beam direction within the beam scanning range to the Z-axis, means setting the negative coordinate axis as the reference direction and rotating clockwise around the Z-axis. degrees, rotating clockwise by θ around the Y-axis. B Degrees, rotate the main beam to the Z-axis direction, The spherical coordinate direction of the main beam is used to preserve the array configuration after rotation.

5. The large-scale circular array design method based on non-uniform sampling and distributed computing according to claim 1, characterized in that, Step 3, which involves evaluating the sidelobe performance of all patterns to obtain the sidelobe performance of each individual pattern, refers to calculating the sidelobe performance f based on the pattern of the array configuration corresponding to each main beam direction, as follows: Where θ represents the angle between the main scanning beam of the array and the Z-axis of the array normal. This indicates the angle between the main scanning beam of the array and the X-axis of the array configuration; Indicates the main beam scanning direction is The maximum main lobe level of the time pattern, Indicates the main beam scanning direction is The direction is the maximum sidelobe level of the radiation pattern, S represents the beam scanning area, and max represents the maximum value operation.

6. The large-scale circular array design method based on non-uniform sampling and distributed computing according to claim 1, characterized in that, The sidelobe constraint mentioned in step 4 is a judgment index set by the designer within the range of [-50, -20] dB.

7. The large-scale circular array design method based on non-uniform sampling and distributed computing according to claim 1, characterized in that, The mutation probability and crossover probability described in step 5 are characterized in that, in the first iteration, an initial mutation mean is set. and initial cross mean Both are set to 0.

5. The adaptive iteration count i = 0 is set, and the mutation probability F and crossover probability CR are both set to 0.

5. The current mutation probability and crossover probability are added to the mutation database and crossover database, respectively. In subsequent iterations, if the sidelobe performance of the best individual remains unchanged after 10 consecutive iterations, the adaptive iteration count i = i + 1 is set, and the current mean mutation value is calculated according to the following formula. and cross means Where mF represents an individual randomly selected from the variation database, and mCR represents an individual randomly selected from the crossover database. This represents the mean variation of the previous iteration. Let F represent the crossover mean of the previous iteration, and r represent a random number between 0 and 1. Calculate the mutation probability F and crossover probability CR of the current iteration using the following formula. Where rand(A,B) means generating a random number based on a normal distribution with mean A and standard deviation B, adding the current mutation probability F and crossover probability CR to the mutation database and crossover database respectively, and setting the capacity limit of the mutation database and crossover database to 5 to 10 times the number of variables to be optimized. After reaching the capacity limit, the mutation probability F and crossover probability CR entering the database randomly replace one of the existing individuals in the current mutation database and crossover database.

8. The large-scale circular array design method based on non-uniform sampling and distributed computing according to claim 1, characterized in that, Step 6 describes using distributed computation of the directional graph for each A cross section refers to a section spaced at a fixed angle. Divide the directional pattern into multiple Cut the surface, and then do each The aspect is distributed across different computers for distributed computing, with only one aspect being computed at a time. The cross section stores the calculation results in an external document, in all... After the section calculation is completed, each section is read into a computer. External document of the section; merge all The cross-section yields the three-dimensional total radiation pattern of the array antenna, and the beamwidth and sidelobe level are evaluated for all... Gain is obtained by cross-sectional distributed integration.

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