Rapid simulation solving method for radiation characteristics of large-scale array antenna

Abstract

The invention belongs to the field of electromagnetic numerical methods, and relates to a rapid simulation solving method for radiation characteristics of a large-scale array antenna. In the simulation solution process of the large-scale array antenna, a regional decomposition technology is adopted: firstly, m * n antenna units in the center of the large-scale array antenna are selected as small-scale array antennas; then, establishing a unit model of an antenna array, and performing corresponding simulation solution for a small-scale array antenna according to the arrangement of the array; thirdly, constructing a matrix equation for finite element region decomposition solution, and obtaining a far field of the small-scale antenna array through matrix multiplexing simulation solution; further, a far field of a large-scale array antenna is expanded; and finally, obtaining a radiation far-field parameter result of any amplitude phase distribution by changing feed source parameters of the large-scale array antenna excitation unit according to actual requirements. According to the method, the radiation characteristics of the large-scale array antenna can be quickly simulated and analyzed only by carrying out actual simulation calculation on a small-scale antenna array.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic numerical methods and relates to a fast simulation and solution method for the radiation characteristics of large-scale array antennas. Background Art

[0002] An array antenna is an antenna system composed of multiple antenna elements arranged in a certain pattern. It has advantages such as high gain, high directivity, and flexible beam control, and thus has broad application prospects in fields such as satellite communication technology, radar detection systems, and precise navigation. In the design process of an array antenna, it is first necessary to preliminarily evaluate whether the radiation characteristics of the array antenna meet the index requirements through antenna simulation analysis, and then carry out physical processing and microwave anechoic chamber measurement, and finally complete the design of the array antenna. The use of efficient electromagnetic simulation methods can significantly improve the efficiency of antenna simulation analysis. Therefore, the research on fast solution methods for the radiation characteristics of array antennas is of great significance.

[0003] However, with the development of antenna technology and the increasing demand for antenna performance such as antenna gain, the scale of the antenna array has gradually increased. In practical applications, the scale of the array antenna has increased from hundreds of elements to thousands or even tens of thousands of elements. To ensure accuracy, the full-wave numerical algorithm is mainly used for the simulation analysis of array antennas at present. However, the number of unknowns required for the solution of large-scale antenna arrays is huge, and the solution complexity is very high, resulting in the full-wave numerical algorithm consuming a large amount of computing time and memory, and even being unable to solve.

[0004] Although the use of periodic boundary conditions can approximately simulate an infinite array structure through the simulation of a single antenna element, and can achieve the simulation of large-scale antenna arrays to a certain extent; however, this method ignores the edge effect of the finite array in actual engineering and cannot consider the coupling between elements, resulting in a certain deviation between the results and the actual situation.

[0005] Therefore, how to achieve efficient and high-precision simulation design of large-scale array antennas is a major difficulty in the current research on array antenna simulation technology. Summary of the Invention

[0006] In view of the above problems or deficiencies, to solve the problem that efficient and high-precision simulation design of existing large-scale array antennas cannot be achieved, the present invention provides a method for quickly simulating and solving the radiation characteristics of large-scale array antennas. This method adopts the domain decomposition technique in the simulation and solution process, effectively reducing the simulation memory consumption and improving the solution efficiency. Compared with the existing large-scale antenna array simulation technology, the advantages of the present invention compared with the traditional simulation and solution methods include: 1) Only a small number of modeling operations are required, and there is no need for overall modeling; 2) During the solution process, through matrix reuse, the memory consumption required for simulation and solution is very small; 3) Only a small-scale antenna array needs to be actually simulated and calculated. By performing a certain array expansion derivation on the far-field radiation of the sub-array (small-scale antenna array), the far-field of the large-scale antenna array can be directly obtained, thereby realizing the rapid simulation and analysis of the radiation characteristics of the large-scale array antenna.

[0007] A method for quickly simulating and solving the radiation characteristics of a large-scale array antenna includes the following steps:

[0008] Step 1: For the large-scale antenna array to be simulated and analyzed, extract the small-scale sub-array at its center as the sub-antenna array required for simulation. The small-scale sub-array consists of m×n antenna elements; m≥5, n≥5.

[0009] Step 2: Establish a single antenna element model required for simulation. Assume that the array antenna is arranged in the XOY plane, and the distances between the antenna elements in the x-axis and y-axis directions are d x and d y , respectively. For the remaining array antenna elements, according to the established single antenna element, the information of the sub-antenna array used for simulation calculation is directly obtained by translation through the distance relationship;

[0010] In addition, a vacuum region needs to be constructed around the small-scale sub-array during calculation; for the vacuum region, first automatically generate a single corresponding solid model block, and then directly obtain the relevant calculation information of the remaining vacuum regions by translation through the position relationship of the small-scale sub-array.

[0011] Step 3: For the small-scale array antenna, establish the electromagnetic boundary value problem of finite element domain decomposition and obtain the relevant solution equations;

[0012] Step 4: Perform boundary and excitation processing required for antenna simulation;

[0013] Step 5: Construct the matrix equation for finite element domain decomposition solution by repeating the array structure matrix reuse and solve to obtain the far-field radiation of the small-scale antenna array;

[0014] Step 6: After obtaining the far-fields of each unit of the small-scale array antenna excited separately, further expand it to the far-field of the large-scale array antenna;

[0015] Step 7: According to the simulation requirements, by changing the feed parameters of the excitation units of the large-scale array antenna, the radiation far-field parameters with arbitrary amplitude and phase distributions are obtained.

[0016] When solving the antenna radiation problem of the present invention, first, select the central part of the units of the large-scale array antenna as the sub-antenna array to form a small-scale array antenna. Then, establish the unit model of the antenna array and determine the positional relationship of the units of the small-scale array antenna according to the arrangement of the array; after that, for the small-scale array antenna, establish the electromagnetic boundary value problem of finite element domain decomposition and obtain the relevant solution equations; at the same time, construct the boundaries and excitations required for simulating the array antenna and apply them to the simulation solution. Next, construct the matrix equation for finite element domain decomposition solution and reduce the memory consumption of array antenna simulation through matrix reuse; through simulation solution, obtain the far field of the small-scale antenna array. Finally, after obtaining the far fields of each unit of the small-scale array antenna excited separately, further expand it to the far field of the large-scale array antenna. In addition, according to the actual simulation requirements, by changing the feed parameters of the excitation units of the large-scale array antenna, the radiation far-field parameter results with arbitrary amplitude and phase distributions can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is the flow chart of the present invention;

[0018] Figure 2 is the schematic diagram of the calculation model of the antenna array unit;

[0019] Figure 3 is the schematic diagram of matrix reuse of the repetitive structure

[0020] Figure 4 is the schematic diagram of expanding the small-scale antenna sub-array into a large-scale array antenna. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] The present invention will be further described in detail below with reference to the drawings and embodiments.

[0022] A method for quickly simulating and solving the radiation characteristics of a large-scale array antenna, as Figure 1 shown, the specific process is as follows:

[0023] Step 1: For the large-scale antenna array that needs to be simulated and analyzed, extract the small-scale sub-array at its center, which consists of m×n antenna units (m≥5, n≥5). This small-scale sub-array is the sub-antenna array required for subsequent simulation and solution using the domain decomposition method; and the radiation characteristics of the final large-scale array antenna are calculated according to Step 6 through the simulation results of the small-scale antenna array.

[0024] Step 2: Establish a single antenna element model required for simulation. Assume that the array antenna is arranged in the XOY plane, and the distances between antenna elements in the x-axis and y-axis directions are d x and d y respectively. For the remaining array antenna elements, based on the established single antenna element, the sub-antenna array model information for simulation calculation is directly obtained by translation according to the distance relationship.

[0025] In this embodiment, taking a small-scale antenna array as shown in Figure 2 as an example, first establish a single antenna element model of a large-scale array antenna (such as block 5 shown in Figure 2 ). Assume that the array antenna is arranged in the XOY plane, and the distances between antenna elements in the x-axis and y-axis directions are d x and d y respectively. For the remaining array antenna elements, the sub-antenna array information for simulation calculation is directly obtained by translation according to the distance relationship without complete modeling.

[0026] In addition, when calculating the small-scale sub-array, a vacuum region needs to be constructed around it to ensure the solution accuracy. For the vacuum region, first automatically generate four vacuum model blocks at the four vertices (such as blocks 1, 3, 7, and 9 shown in Figure 2 ), and then generate 4 corresponding solid model blocks for the four sides (such as blocks 2, 4, 6, and 8 shown in Figure 2 ), and directly obtain the relevant calculation information of all vacuum region blocks on the four sides by translation according to the position relationship of the array.

[0027] Step 3: For the small-scale array antenna, establish an electromagnetic boundary value problem of finite element domain decomposition and construct relevant solution equations;

[0028] First, assume that there are N non-overlapping sub-regions in the solution domain of the small-scale array antenna, where a single antenna element is located in an independent sub-region (as shown in Figure 2 ). For two adjacent sub-regions i and j, they are connected by the Robin boundary condition. The internal region of sub-region i is represented by Ω i , and Γ ij represents the interface between sub-regions i and j. Then the form of the boundary value problem of this domain decomposition is:

[0029]

[0030] where is the electric field, is the applied current source, ε ri is the relative permittivity of region i, μ ri is the relative permeability of region i, k0 is the vacuum wavenumber, and the symbol is the interface normal vector.

[0031] Then, the finite element weak form is constructed by the Galerkin method, and vector basis functions are used inside the finite element. For testing, basis functions are respectively used at the region interface, i.e., the Robin boundary part. and for testing. It can be obtained that:

[0032]

[0033] where

[0034] Furthermore, by replacing half of the surface integral in (3) with the surface integral in (4), constructing a symmetric form matrix, and combining with (5), the solution equation of the finite element domain decomposition method can be obtained:

[0035]

[0036] Step 4: For small-scale array antennas, perform boundary and excitation processing required for small-scale antenna array simulation;

[0037] During the antenna simulation process, corresponding boundary conditions and excitations need to be set to achieve simulation solution. The boundaries required in antenna simulation include: perfect electric conductor boundary perfect magnetic conductor boundary impedance boundary Z s is the surface impedance), and radiation boundary ( Z0 is the vacuum wave impedance).

[0038] In addition, for the thin-layer medium that is difficult to mesh, the equivalent boundary of multi-layer media needs to be used for solution. Assume there are L layers of thin-layer media, and d l is the thickness of each layer of the medium, and its form is:

[0039]

[0040] Assume that after the multi-layer medium structure is equivalent to an infinitely thin equivalent boundary, the magnetic fields on both sides of the boundary are respectively and Then the relationship between the electric field and magnetic field of this boundary is:

[0041]

[0042] Furthermore, the finite element surface integral formula of the relevant boundary can be expressed as:

[0043]

[0044] In terms of excitation, in order to ensure the solution accuracy, the waveguide port excitation method is adopted in this embodiment (the voltage gap or current feed excitation can also be used). Assume that the feeding excitation electric field on the port is Only considering the main mode excitation, let Z p represent the mode impedance of port p, then the relationship between the electric field and magnetic field at port p is:

[0045]

[0046] The corresponding finite element surface integral form at the port is:

[0047]

[0048] By adding the relevant excitation and boundary of the antenna array simulation to the domain decomposition solution equation (6) established in step 3, the boundary and excitation processing required for the small-scale antenna array simulation is completed.

[0049] Step 5: By repeatedly reusing the array structure matrix, construct and solve the matrix equation for the finite element domain decomposition to obtain the far-field radiation of the small-scale antenna array;

[0050] Write the domain decomposition solution equation (6) in matrix form, let M i represent the finite element domain decomposition submatrix block of sub-region i, G ij represent the submatrix block of the interface part between sub-region i and sub-region j, x represents the unknown electric field to be solved, and y represents the port excitation of the antenna array.

[0051] In addition, assume that there are a total of P antenna excitation units. In order to be able to adjust the amplitude and phase of the feed in real time to obtain the corresponding radiation pattern, it is necessary to solve each port excitation in turn. Therefore, a total of P right-hand sides need to be solved. Then the final matrix form of the finite element domain decomposition solution equation is:

[0052]

[0053] Since the antenna element (single antenna element) has a repetitive structure, the antenna subdomain matrices M i and G ij do not need to be calculated in full, only the matrices with different structures (partial matrices) need to be calculated, and the antenna subdomain matrices with repetitive structures are directly reused. Specifically, as Figure 3 shown, assume an antenna array calculation model with 49 regions. After reuse, when solving the matrix (12), only the matrices corresponding to 9 sub-regions and the connection matrices corresponding to 18 interfaces need to be stored, and there is no need to store all the matrices.

[0054] After that, by solving matrix (12), the electric field solutions in the case of the antenna excitation units being excited respectively are obtained. After obtaining the electric field solutions of matrix (12), the far fields under the excitation of each antenna unit are obtained through near-to-far field extrapolation.

[0055] Let I p represent the amplitude and phase of the antenna unit excitation. Then the total far field distribution of the final small-scale antenna array is:

[0056]

[0057] Step 6: After obtaining the far fields of each unit of the small-scale array antenna under separate excitation, further expand them to the far fields of the large-scale array antenna.

[0058] The far fields of the small-scale antenna array have been obtained in the previous process. This step mainly derives the far fields of the original large-scale array through the far field information of the small-scale array.

[0059] For the small-scale antenna array m×n (in this embodiment, both m and n are odd numbers and m = n = 5, so that the small-scale antenna array is completely centered relative to the large-scale array antenna and the accuracy is higher), the array of the large-scale array antenna for which the far fields need to be solved is M×N (M>m, N>n). According to the principle of the active pattern, the active patterns of the central part of the large-scale array are basically the same. Therefore, through the sub-array expansion method, the central unit of the small-scale array antenna is copied and expanded as the central part units of the large-scale array antenna, and the edge units are used as the edge units of the large-scale array antenna, expanding from m×n to M×N; the specific expansion method is as in this embodiment Figure 4 shown: expanding 5×5 to M×N, and this method is also applicable when the number of rows and columns is different.

[0060] Through the above method, the far fields of the final large-scale array antenna can be obtained using the far fields of the small-scale sub-array antenna Let m and n be the row number (x-axis direction) and column number (y-axis direction) of the small-scale antenna array for which the far field distribution has been solved respectively. The specific calculation method is:

[0061]

[0062] Through this method, the far fields of the large-scale array can be directly obtained only through a small amount of calculation.

[0063] Step 7: According to the simulation requirements, by changing the feed parameters of the excitation units of the large-scale array antenna, the radiation far field parameters with any amplitude and phase distribution are obtained.

[0064] The array antenna can obtain the corresponding beam pointing by adjusting the excitation amplitude and phase distribution of each antenna element. According to the simulation requirements, by modifying the feed excitation I of the large-scale array antenna ij (amplitude and phase markers of the excitation unit (i,j)), substituting into (14) can recalculate the far field by superposition, and quickly obtain the radiation characteristics of the large-scale array under different excitation amplitude and phase conditions.

[0065] As can be seen from the above embodiments, the present invention adopts the domain decomposition technique in the simulation solution process of the large-scale array antenna: First, select m×n antenna elements at the center of the large-scale array antenna as a small-scale array antenna; Then, establish the unit model of the antenna array, and according to the arrangement of the array, establish the electromagnetic boundary value problem of finite element domain decomposition for the small-scale array antenna, construct the corresponding boundary and excitation, and then apply it to the simulation solution; Next, construct the matrix equation for finite element domain decomposition solution, and reduce the memory consumption of the array antenna simulation through matrix reuse, and obtain the far field of the small-scale antenna array through simulation solution; After obtaining the far fields of each unit of the small-scale array antenna excited separately, expand it to the far field of the large-scale array antenna. Finally, according to the actual simulation requirements, by changing the feed parameters of the excitation unit of the large-scale array antenna, the radiation far field parameter results with arbitrary amplitude and phase distributions are obtained. The present invention only needs to perform actual simulation calculations on a small-scale antenna array, and through sub-array expansion, the far field of the large-scale antenna array can be directly obtained, thereby realizing the rapid simulation analysis of the radiation characteristics of the large-scale array antenna.

Claims

1. A method for quickly simulating and solving the radiation characteristics of a large-scale array antenna, comprising the following steps: Step 1: For the large-scale antenna array to be simulated and analyzed, extract the small-scale sub-array at its center as the sub-antenna array required for simulation. The small-scale sub-array consists of m×n antenna elements; m≥5, n≥5; Step 2: Establish a single antenna element model required for simulation. Assume that the array antennas are arranged in the XOY plane, and the distances between antenna elements in the x-axis and y-axis directions are d x and d y , respectively. For the remaining array antenna elements, according to the established single antenna element, the sub-antenna array information for simulation calculation is directly obtained by translation based on the distance relationship; In addition, a vacuum region needs to be constructed around the small-scale sub-array during calculation; for the vacuum region, first automatically generate a single corresponding solid model block, and then directly obtain the relevant calculation information of the remaining vacuum regions through translation according to the positional relationship of the small-scale sub-array; Step 3: For the small-scale array antenna, establish the electromagnetic boundary value problem of finite element domain decomposition and obtain the relevant solution equations; Step 4: For the small-scale array antenna, perform the boundary and excitation processing required for antenna simulation; Step 5: By repeatedly reusing the array structure matrix to construct the matrix equation for finite element domain decomposition solution and solve to obtain the far-field radiation of the small-scale antenna array; Step 6: After obtaining the far fields of each unit of the small-scale array antenna excited separately, further expand it to the far field of the large-scale array antenna; Step 7: According to the simulation requirements, by changing the feed parameters of the excitation units of the large-scale array antenna, obtain the radiation far-field parameters with arbitrary amplitude and phase distributions.

2. The rapid simulation and solution method for the radiation characteristics of the large-scale array antenna according to claim 1, characterized in that The specific content of Step 3 is as follows: First, assume that there are N non-overlapping sub-regions in the solution domain of the small-scale array antenna, N = m × n, where a single antenna element is located in an independent sub-region. Robin boundary conditions are used to connect between two adjacent sub-regions i and j, and the internal region of sub-region i is represented by Ω i is denoted, and Γ ij denotes the interface between sub-regions i and j. Then the form of the boundary value problem for this domain decomposition is as follows: wherein is the electric field, is the externally applied current source, ε ri is the relative permittivity of region i, μ ri is the relative permeability of region i, and k0 is the wavenumber in vacuum, the symbol is the normal vector of the interface; Then, the finite element weak form is constructed by the Galerkin method, and vector basis functions are used inside the finite element for testing. On the regional interface, i.e., the Robin boundary part, basis functions and are used for testing; it can be obtained that: Among them Furthermore, replace half of the surface integral in (3) with the surface integral in (4), construct a symmetric matrix, and combine it with (5) to obtain the solution equation of the finite element domain decomposition method:

3. The rapid simulation and solution method for the radiation characteristics of the large-scale array antenna according to claim 1, characterized in that, The specific content of Step 4 is as follows: The boundaries required in antenna simulation include: perfect electric conductor boundary perfect magnetic conductor boundary impedance boundary Z s is the surface impedance, and radiation boundary Z0 is the vacuum wave impedance; In addition, for thin-layer media where it is difficult to divide the grid, the equivalent boundary of multi-layer media is used for solution. Assuming there are L thin-layer media, d l is the thickness of each layer of medium, and its form is: Assume that after the multi-layer dielectric structure is equivalent to an infinitely thin equivalent boundary, the magnetic fields on both sides of the boundary are respectively and Then the relationship between the electric field and the magnetic field of this boundary is: Furthermore, the finite element surface integral formula for the relevant boundary can be expressed as: In addition, in terms of excitation, the waveguide port excitation method is adopted; assuming that the feeding excitation electric field on the port is Only the main mode excitation is considered. Let Z p represent the mode impedance of port p, then the relationship between the electric field and magnetic field at port p is: The finite element surface integral form at the corresponding port is: By adding the relevant excitations and boundaries of the antenna array simulation to the domain decomposition solution equation (6) established in Step 3, complete the boundary and excitation processing required for the small-scale antenna array simulation.

4. The rapid simulation solution method for the radiation characteristics of the large-scale array antenna according to claim 1, wherein The specific content of Step 5 is as follows: The region decomposition solution equation (6) is written in matrix form, and let M i represent the finite element region decomposition submatrix block of the part of sub-region i, and G ij represent the submatrix block of the interface part between sub-region i and sub-region j. x represents the unknown electric field to be solved, and y represents the port excitation of the antenna array; In addition, assuming that there are a total of P antenna excitation units, in order to be able to adjust the feed amplitude and phase in real time to obtain the corresponding radiation pattern, it is necessary to solve each port excitation in turn. Therefore, a total of P right-hand sides need to be solved, and the final matrix form of the finite element domain decomposition solution equation is: Since the antenna unit has a repetitive structure, the antenna sub-domain matrices M i and G ij do not need to be fully calculated. Only the matrices with different structures are calculated, and the antenna sub-domain matrices with repetitive structures are directly reused; After that, by solving matrix (12), the electric field solutions in the case of the antenna excitation units being excited respectively are obtained; after obtaining the electric field solutions of matrix (12), through near - far field extrapolation, the far fields under the excitation of each antenna unit respectively are obtained. Let I p represent the amplitude and phase of the antenna unit excitation, then the total far - field distribution of the final small - scale antenna array is as follows:

5. The rapid simulation solution method for the radiation characteristics of the large-scale array antenna according to claim 1, characterized in that The specific content of Step 6 is as follows: For the m×n array of the small-scale array antenna, the array of the large-scale array antenna for which the far field needs to be solved is M×N, where M>m and N>n; according to the principle of the active radiation pattern, through the sub-array expansion method, copy and expand the central unit of the small-scale array antenna as the central part units of the large-scale array antenna, and let the edge part units be the edge units of the large-scale array antenna, expanding from m×n to M×N; Through the above method, the far field of the final large-scale array antenna is obtained from the far field of the small-scale sub-array antenna Let m and n be the row number in the x-axis direction and the column number in the y-axis direction of the small-scale antenna array whose far-field distribution has been solved respectively. The specific calculation method is as follows: Finally, directly obtain the far field of the large-scale array.

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