Rapid approximate analysis method for mutual-coupling-containing pattern of large-scale ultra-wideband heterogeneous array

Abstract

Disclosed in the present application is a rapid approximate analysis method for a mutual-coupling-containing pattern of a large-scale ultra-wideband heterogeneous array. The method comprises the following steps: according to the types of elements used, dividing a heterogeneous array into a plurality of sub-arrays, wherein the types of elements in each sub-array are identical; according to the positions of the elements, classifying the elements in the sub-arrays; selecting representative elements for representing environmentally similar elements, removing rows and columns that do not have the representative elements, and retaining all key features of the heterogeneous array; performing full-wave simulation on a constructed compact representative array, extracting AEPs of all the representative elements, and storing same; and replacing AEPs of the environmentally similar elements with the AEPs of the representative elements, performing approximate computing to obtain patterns of all the sub-arrays, and superimposing the obtained results to obtain a mutual-coupling-containing pattern of the heterogeneous array. The present application can effectively avoid the enormous operational resource overheads of full-wave simulation of a large-scale heterogeneous array, thus greatly reduce the complexity of computing of a mutual-coupling-containing pattern, and can also ensure the accuracy of the obtained mutual-coupling-containing pattern.

Description

Fast approximate analysis method for mutual coupling patterns of large-scale ultra-wideband heterogeneous arrays

[0001] Related applications

[0002] This application claims priority to the Chinese patent application filed with the State Intellectual Property Office on June 28, 2023, with application number 202310774967.4, the entire contents of which are incorporated by reference into this application. Technical Field

[0003] The present application relates to the field of array antennas, and in particular to a method for fast approximate analysis of mutual coupling patterns of large-scale ultra-wideband heterogeneous arrays. Background Art

[0004] In solving most array synthesis problems, the pattern product theorem is typically used to express the array pattern as the product of the element pattern and the array factor. Once the array factor is synthesized to meet design requirements, the array factor is multiplied by the element pattern to obtain the desired array pattern. However, in real environments, element antennas cannot exist in isolation. Surrounding structures absorb and reflect electromagnetic waves, affecting the radiation pattern of the element antenna. Mutual coupling refers to the interaction between the antenna and its surroundings. It primarily consists of three influences: radiation coupling between adjacent elements, coupling with surrounding conductors, and coupling with the array antenna's internal feed network. The presence of mutual coupling can cause deviations between the array pattern calculated using the pattern product theorem and the actual array pattern, resulting in the synthesized array pattern failing to meet radiation performance requirements. Therefore, for heterogeneous arrays with complex mutual coupling effects, it is essential to consider mutual coupling in synthesis and design to improve accuracy.

[0005] For the synthesis of arrays with mutual coupling, theoretically, it is necessary to first obtain the active element pattern (AEP) of each element through full-wave simulation. The AEP is then imported into the synthesis algorithm to obtain the feed excitation amplitude and phase that meet the radiation specifications while accounting for mutual coupling effects. Finally, the AEP is weighted superpositioned with the feed excitation value to obtain the array pattern with mutual coupling. However, if the array has a large number of antenna elements and a wide operating bandwidth, the difficulty of analyzing the pattern with mutual coupling increases dramatically, mainly due to the following reasons: 1) The high complexity of full-wave simulation. The simulation process requires calculating the electromagnetic radiation characteristics of each element in the far field. Due to the large size of the given array and the large number of element characteristic parameters, the computational complexity of the full-wave simulation increases exponentially, and may even make the solution impossible. 2) The large storage capacity of full-wave simulation. The simulation process requires storing the AEP information of each element. Due to the wide bandwidth and high angular resolution of the array pattern, a huge number of pattern sampling points are required, making the storage overhead of full-wave simulation enormous. In summary, it is impractical to directly perform full-wave simulations on large-scale heterogeneous arrays when considering mutual coupling effects. Therefore, it is necessary to develop a fast analysis method for large-scale ultra-wideband heterogeneous arrays with mutual coupling patterns, thereby significantly reducing the required computational time and storage overhead.

[0006] Patent No. CN201410298622.7 provides a method for analyzing the sidelobe performance of large-scale deformable array antennas based on element mutual coupling. This method utilizes the mutual coupling parameter matrices of the subarrays to construct the overall mutual coupling parameter matrix of the deformable array antenna, analyzing the impact of structural errors and mutual coupling on the antenna's electrical performance. This effectively addresses the difficulty of evaluating the mutual coupling effects of heterogeneous array antennas in existing technologies. However, this mutual coupling analysis method still requires full-wave simulation of the entire array, which consumes significant computational resources for large-scale simulations.

[0007] Patent No. CN202210710497.0 provides a method for rapid and accurate analysis of the vector gain pattern of irregular antenna arrays. This method can quickly and accurately analyze the vector gain pattern of irregular antenna arrays by utilizing regional partitioning and the rotation, interpolation, translation, and projection of the vector active element pattern of representative elements in the irregular antenna array, thereby reducing the computational time of full-wave simulations of large-scale irregular arrays. However, this mutual coupling analysis method is only applicable to general irregular arrays and cannot be used for heterogeneous arrays with complex array structures.

[0008] Summary of the Invention

[0009] The purpose of this application is to overcome the above-mentioned shortcomings of the existing mutual coupling analysis methods, propose a fast analysis method for mutual coupling patterns suitable for large-scale heterogeneous arrays, construct a compact representative array to describe all the key features of the original large-scale heterogeneous array, effectively avoid the huge computing resource overhead of full-wave simulation of large-scale heterogeneous arrays, greatly reduce the complexity of mutual coupling pattern calculation, and at the same time ensure the accuracy of the obtained mutual coupling pattern.

[0010] The method for rapid analysis of mutual coupling patterns of large-scale ultra-wideband heterogeneous arrays of the present application includes the following steps:

[0011] Step 1: Sub-array division of large-scale heterogeneous arrays: Divide the entire large-scale heterogeneous array into multiple sub-arrays according to the unit types used by the heterogeneous array, and the unit types in each sub-array are the same.

[0012] Step 2: Classify large-scale heterogeneous array elements. Based on the location of the array elements, the elements in the sub-array are classified into corner elements, edge elements, and interior elements.

[0013] Step 3: Select representative cells for large-scale heterogeneous arrays. For cells with similar array environments, select the AEP of representative cells for characterization, including corner representative cells, edge representative cells, and interior representative cells.

[0014] Step 4: Compact reorganization of large-scale heterogeneous arrays. Based on the selected representative cells, the large-scale heterogeneous array is compactly reorganized, rows and columns without representative cells are removed, and all key features of the heterogeneous array are retained.

[0015] Step 5: Full-wave simulation of the compact representative array. Perform full-wave simulation on the constructed compact representative array, and extract and store the AEP information of all representative units in the simulation results.

[0016] Step 6: Approximate calculation of the mutual coupling pattern. Replace the AEP of similar units in the array environment with the AEP of the representative unit, and approximate the pattern of all sub-arrays. Then, superimpose the obtained results to obtain the mutual coupling pattern of the large-scale heterogeneous array.

[0017] This application has the following advantages and beneficial effects:

[0018] a) This application divides a large-scale heterogeneous array into sub-arrays and classifies the units within the sub-arrays based on the type of heterogeneous array units and the array position of each unit. This clarifies the composition of each part of the heterogeneous array and guides the selection of representative units.

[0019] b) This application compactly reorganizes large-scale heterogeneous arrays based on representative units, clarifies the basic array structure that describes all key features of the heterogeneous array, and then transforms the full-wave simulation of the large-scale heterogeneous array into the full-wave simulation of the small-scale compact representative array, effectively avoiding the huge computing resource overhead of the full-wave simulation.

[0020] c) This application uses the AEP of a representative unit to replace the AEP of similar units in the array environment, so that the calculation of the mutual coupling pattern can use the pattern product theorem, which greatly reduces the computational complexity.

[0021] d) This application uses multiple representative units, including corner representative units, edge representative units, and internal representative units, rather than a single representative unit, which can better characterize the complex mutual coupling of heterogeneous arrays, thereby ensuring high accuracy of approximate calculations for heterogeneous arrays containing mutual coupling patterns. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The drawings described herein are used to provide a further understanding of the embodiments of the present application, constitute a part of the present application, and do not constitute a limitation of the embodiments of the present application. In the drawings:

[0023] FIG1 is a flow chart of the method of the present application;

[0024] FIG2 is a schematic diagram of a large-scale ultra-wideband heterogeneous array model of the present application;

[0025] FIG3 is a schematic diagram of a representative unit of a large-scale ultra-wideband heterogeneous array of the present application;

[0026] FIG4 is a schematic diagram of the large-scale ultra-wideband heterogeneous array of the present application for eliminating non-critical feature rows;

[0027] FIG5 is a schematic diagram of a large-scale ultra-wideband heterogeneous array of the present application with non-critical feature columns eliminated, that is, a schematic diagram of a small-scale compact representative array of a large-scale ultra-wideband heterogeneous array. DETAILED DESCRIPTION

[0028] Before describing any embodiment of the present application in detail, it should be understood that the application of the present application is not limited to the details of the structure shown in the following description or the drawings. The present application may adopt other embodiments and may be implemented or executed in various ways. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative improvements are within the scope of protection of this application.

[0029] A large-scale ultra-wideband heterogeneous array refers to an antenna array composed of a large number (usually hundreds, thousands or even more) of antenna units of different types and performances, which can cover a very wide operating frequency band.

[0030] As shown in Figure 1, this application includes the following steps:

[0031] 1) Sub-array division of large-scale heterogeneous arrays;

[0032] For ultra-wideband applications, large-scale heterogeneous arrays usually need to use multiple antenna units operating in specific frequency bands to give full play to the advantages of each type of unit. In addition, to improve aperture efficiency and array gain, the sub-arrays of heterogeneous arrays are usually arranged in a uniform spacing. According to the type of unit used, the entire large-scale heterogeneous array can be divided into multiple sub-arrays, and the unit type in each sub-array is the same. After the sub-array division, the array pattern of the heterogeneous array can be expressed as

[0033] Where θ is the zenith angle, is the azimuth angle, f is the operating frequency, represents the array pattern of the kth sub-array, and K is the total number of sub-arrays. The array pattern of the kth sub-array can be expressed as

[0034] Among them, S (k) represents the unit number set of the kth subarray, w n represents the excitation of the nth unit, β=2πf / c represents the wave number in free space at the frequency f, and c is the propagation speed of the wave in free space. represents the position vector of the nth unit on the XOY plane (the plane in the Cartesian coordinate system), represents the propagation vector, It represents the AEP of the nth unit operating at frequency f.

[0035] 2) Classification of large-scale heterogeneous array units;

[0036] In the divided sub-array, according to the location of the array element, it can be divided into corner elements (Corner-located Element), edge elements (Edge-located Element) and internal elements (Inside-located Element), which correspond to the element set C (k) 、E (k) and I (k) , and there are and C (k) ∪E (k) ∪I (k) =S (k)

[0037] Then, the array pattern of the kth subarray can be further written as

[0038] 3) Selection of representative units for large-scale heterogeneous arrays;

[0039] The array environment in which a cell resides determines its mutual coupling and platform effects, directly impacting its AEP characteristics. In a uniformly spaced array, many cells share similar array environments and therefore similar AEPs. Therefore, it is possible to replace the AEPs of cells with similar array environments with the AEPs of representative cells, thereby accelerating array pattern calculation using the pattern product theorem. Representative cells corresponding to corner cells, edge cells, and interior cells are referred to as corner representative cells, edge representative cells, and interior representative cells, respectively. For corner cells, the array environments of each cell vary significantly, making it difficult to select a representative cell for unified representation. Therefore, the corner representative cell is typically the corner cell itself. For edge cells, the array environments vary significantly from edge to edge, but the array environments of cells within each edge region are relatively similar. Therefore, edge representative cells can be used for unified representation. For interior cells, the array environments of all cells are relatively similar, so internal representative cells can be used for unified representation. It is recommended to select the central cell in each region as the representative cell, and to place representative cells in the same row or column whenever possible to facilitate subsequent compact reorganization of large-scale heterogeneous arrays.

[0040] 4) Compact reorganization of large-scale heterogeneous arrays;

[0041] Selecting representative cells for a large-scale heterogeneous array establishes the array's basic "skeleton," the fundamental array structure that describes all key features of the large-scale heterogeneous array. Without missing any key features, the large-scale heterogeneous array can be compactly reorganized. The rows and columns containing the representative cells are called the key feature rows and columns of the heterogeneous array. First, rows that are not key features of the heterogeneous array are removed; second, columns that are not key features of the heterogeneous array are removed. This process results in a compact representative array that retains all key features of the large-scale heterogeneous array.

[0042] 5) Full-wave simulation of compact representative arrays;

[0043] A full-wave simulation is performed on a small, compact representative array of a large-scale heterogeneous array. The AEP information of all representative elements in the simulation results is extracted and stored, including the AEPs of corner, edge, and interior representative elements. Full-wave simulation of a compact representative array effectively avoids the enormous computational overhead of directly performing a full-wave simulation of the entire large-scale ultra-wideband heterogeneous array.

[0044] 6) Including approximate calculation of mutual coupling pattern;

[0045] Based on the AEP information of the representative unit, the AEP of the similar units in the array environment is replaced by the AEP of the representative unit, and the array pattern of all sub-arrays is calculated by the following approximate expression:

[0046] in, is the AEP of the representative unit of the p-th edge of the k-th sub-array, is the unit set of the p-th edge of the k-th sub-array (i.e. is the AEP of the representative unit in the kth subarray. Obviously, the approximate calculation process of the subarray array pattern can use the pattern product theorem, which greatly reduces the computational complexity. Finally, the array patterns of all subarrays are superimposed to obtain the mutual coupling pattern of the entire large-scale heterogeneous array, that is,

[0047] Example:

[0048] The large-scale ultra-wideband heterogeneous array shown in Figure 2 consists of two nested sub-arrays, represented by light gray and dark gray respectively. The light gray sub-array contains 108 units, and the dark gray sub-array contains 144 units, for a total of 252 units. The units are classified according to their location within the sub-array. The corner units are located at the vertices of the sub-array array surface, and the areas where the edge units and internal units are located are marked in Figure 3 (edge ​​unit area and internal unit area). The representative corner unit is set to the corner unit itself, and one representative unit is set in both the edge unit area and the internal unit area. The representative unit is set based on the principle of "being located in the center of the area and in the same row and column as much as possible". The selection result is shown in Figure 3. Based on the representative units in Figure 3, the given large-scale heterogeneous array is compactly reorganized. First, the non-critical feature rows are eliminated, as shown in Figure 4. Second, the non-critical feature columns are eliminated, resulting in a compact representative array, as shown in Figure 5. The resulting compact representative array retains all key features of the given large-scale heterogeneous array, requiring only 21 light-gray elements and 16 dark-gray elements, for a total of 37 elements, representing only 14.7% of the original large-scale heterogeneous array. A full-wave simulation was performed on the resulting compact representative array to extract the AEP information of all representative elements. The representative AEPs were used to replace the AEPs of the elements in the corresponding region, and the array patterns of all subarrays were approximated. The resulting patterns were then superimposed to obtain the mutual coupling-inclusive pattern of the given large-scale heterogeneous array.

[0049] As can be seen from Figures 2 and 5, the scale of the obtained compact representative array is much smaller than the scale of the given heterogeneous array. Therefore, the computing resources required for the full-wave simulation of the compact representative array are much less than the computing resources required for the full-wave simulation of the entire large-scale heterogeneous array. At the same time, due to the introduction of the replacement of the representative unit AEP, the calculation of the mutual coupling pattern can use the pattern product theorem, thereby greatly reducing the computational complexity. In summary, compared with no approximation, that is, directly simulating the full wave of the large-scale ultra-wideband heterogeneous array and superimposing the calculation of the mutual coupling pattern, the proposed method can significantly reduce the computing resource overhead and computational complexity. In addition, compared with the use of a single representative unit, the proposed method uses multiple representative units to more accurately describe the real mutual coupling effect and is more suitable for large-scale heterogeneous arrays with complex geometric structures. Although the addition of representative units will, to a certain extent, expand the scale of the compact representative array and thereby increase the computational complexity of the full-wave simulation, this part of the computing resource overhead is necessary to ensure the accuracy of the obtained mutual coupling pattern.

Claims

1. A fast approximate analysis method for large-scale ultra-wideband heterogeneous arrays with mutual coupling patterns, characterized in that: The steps include: Step 1: Divide the entire large-scale heterogeneous array into multiple sub-arrays according to the unit type used by the heterogeneous array, and the unit type in each sub-array is the same; Step 2: Classify the cells in the subarray into corner cells, edge cells and internal cells according to the location of the array cells; Step 3: For cells with similar array environments, select the AEP of representative cells to characterize, including corner representative cells, edge representative cells, and internal representative cells; Step 4: Based on the selected representative units, the large-scale heterogeneous array is compactly reorganized, rows and columns without representative units are removed, and all key features of the heterogeneous array are retained; Step 5: Perform full-wave simulation on the constructed compact representative array, extract and store the AEP information of all representative units in the simulation results; Step 6: Replace the AEP of similar units in the array environment with the AEP of the representative unit, and approximately calculate the directional patterns of all sub-arrays. Then superimpose the obtained results to obtain the mutual coupling directional pattern of the large-scale heterogeneous array.

2. The method for rapid approximate analysis of mutual coupling patterns of large-scale ultra-wideband heterogeneous arrays according to claim 1 is characterized in that: In step 1 and step 2, the heterogeneous array is divided into sub-arrays and the units in the sub-arrays are classified to clarify the composition of each part of the heterogeneous array. At the same time, a standardized mathematical model is established. The directional pattern of the heterogeneous array and its sub-arrays can be specifically expressed as Where θ is the zenith angle, is the azimuth, f is the operating frequency, S (k) The singleton representing the kth subarray The element number set, K is the total number of sub-matrices, w n represents the excitation of the nth unit, β = 2πf / c represents the wave number in free space at the frequency f, c is the propagation speed of the wave in free space, represents the position vector of the nth unit on the XOY plane, represents the propagation vector, represents the AEP of the nth unit working at frequency f, represents the directional pattern of the subarray, represents the directional pattern of the heterogeneous array as a whole; after dividing the units in the subarray into corner units, edge units and internal units, the subarray directional pattern can be expressed as Among them C (k) 、E (k) and I (k) They are the corner cell set, the edge cell set, and the interior cell set.

3. The fast approximate analysis method of large-scale ultra-wideband heterogeneous arrays containing mutual coupling patterns according to claim 1 is characterized in that: In step 3, multiple representative units are set up for characterization of corner units, edge units, and internal units, rather than using a single representative unit, so that the complex mutual coupling of heterogeneous arrays can be characterized more accurately.

4. The method for rapid approximate analysis of mutual coupling patterns of large-scale ultra-wideband heterogeneous arrays according to claim 1 is characterized in that: In step 4, the given heterogeneous array is compactly reorganized based on the selected representative units, and the rows and columns without representative units are removed to obtain the basic array structure that describes all key features.

5. The method for rapid approximate analysis of mutual coupling patterns of large-scale ultra-wideband heterogeneous arrays according to claim 1 is characterized in that: Performing full-wave simulation on the compact representative array in step 5 can effectively avoid the huge computational resource overhead of full-wave simulation on the entire large-scale heterogeneous array, and still obtain the necessary key characteristic information of the heterogeneous array, namely, the AEP information of the representative unit.

6. The method for rapid approximate analysis of mutual coupling patterns of large-scale ultra-wideband heterogeneous arrays according to claim 1 is characterized in that: In step 6, the AEP of similar units in the array environment is replaced by the AEP of the representative unit, and the directional patterns of all subarrays are calculated using the following approximate expression: Where θ is the zenith angle, is the azimuth, f is the operating frequency, w n represents the excitation of the nth unit, β = 2πf / c represents the wave number in free space at the frequency f, c is the propagation speed of the wave in free space, represents the position vector of the nth unit on the XOY plane, represents the propagation vector, represents the AEP of the nth unit working at frequency f, is the AEP of the representative unit of the pth edge of the kth subarray, is the unit set of the p-th edge of the k-th sub-array, that is, P is the total number of edges, is the AEP of the representative unit in the kth sub-array, C (k) 、E (k) and I (k) They are the corner unit set, the edge unit set and the internal unit set respectively. The mutual coupling directional pattern of the heterogeneous array is obtained by superimposing the obtained results. Due to the introduction of the replacement of the representative unit AEP, the calculation process uses the directional pattern product theorem, which greatly reduces the complexity of the calculation of the mutual coupling directional pattern.

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