A method for fast prediction of array active pattern based on multi-scale neighborhood transformer
By using a prediction method based on multi-scale neighborhood Transformer, the geometric relationship between array elements and their neighborhood is extracted and a feature sequence is constructed. End-to-end prediction is then performed using the self-attention mechanism of the Transformer encoder, which resolves the contradiction between computational efficiency, accuracy and generalization ability in existing methods and achieves high-precision and fast array pattern prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2026-01-20
- Publication Date
- 2026-05-29
AI Technical Summary
Existing array pattern prediction methods struggle to balance computational efficiency, modeling accuracy, and generalization ability. In particular, they suffer from large prediction errors in large arrays and complex structures, making it difficult to meet the needs of rapid iterative design.
A prediction method based on multi-scale neighborhood Transformer is adopted. By extracting the geometric relationship between array elements and their neighborhood and constructing feature sequences, the self-attention mechanism of the Transformer encoder is used to perform end-to-end orientation pattern prediction, thereby achieving efficient modeling of the mutual coupling effect between array elements.
It achieves high-precision and fast array pattern prediction, and can complete the prediction of a single array element in milliseconds. It is applicable to various array layouts and breaks through the limitations of traditional methods in terms of application scope.
Smart Images
Figure CN122113580A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to array pattern prediction techniques, and particularly to array active pattern prediction techniques based on multi-scale neighborhood Transformers. Background Technology
[0002] The overall radiation performance of an array antenna is influenced by a variety of factors, including element layout, mutual coupling effect, and excitation parameters. The active element pattern (AEP) characterizes the radiation characteristics of each element in space and is the foundation for the design and optimization of key technologies such as beamforming, pattern synthesis, and interference suppression.
[0003] Currently, array pattern prediction methods are mainly divided into the following three categories:
[0004] 1. Full-wave electromagnetic simulation method
[0005] This type of method directly solves Maxwell's equations using commercial electromagnetic simulation software such as HFSS, CST, and FEKO to obtain an accurate far-field radiation pattern of the array. Its advantages lie in high accuracy and strong physical consistency, accurately reflecting the electromagnetic coupling and radiation characteristics under complex structures. However, the computational complexity of full-wave simulation increases exponentially with the number of array elements. For medium to large arrays (e.g., more than 100 elements), a single simulation often takes several hours to several days. Furthermore, any changes to element position, excitation parameters, or structure require remodeling, meshing, and solving, resulting in extremely low efficiency in parameter scanning and optimization design, making it difficult to meet the needs of rapid iteration in engineering projects.
[0006] 2. Analytical and approximate modeling methods
[0007] This type of method is based on theoretical models such as array factor superposition and mutual coupling correction. It approximates the overall array pattern by templated and extrapolated the radiation patterns of typical array elements (such as corner, edge, and center elements) in a regular array. This method has certain efficiency advantages in small-scale, regular, uniform arrays. However, it assumes that the mutual coupling relationship between array elements is simple and consistent, making it difficult to accurately characterize higher-order mutual coupling and edge effects under irregular layouts, non-uniform excitation, or complex carriers. Once the array structure is disturbed, the prediction error will increase significantly, limiting its applicability and generalization ability.
[0008] 3. Data-driven machine learning methods
[0009] In recent years, with the development of artificial intelligence technology, researchers have attempted to use machine learning models to establish a mapping relationship between array geometric parameters and radiation patterns, in order to improve prediction speed while ensuring accuracy. Common methods currently include:
[0010] K-Nearest Neighbors (KNN) regression: It performs local interpolation prediction based on the distance between samples. It is simple to implement, but it lacks explicit modeling of the physical structure of the array and the global coupling relationship. When the structure is complex or the samples are imbalanced, the prediction error is large, and the inference efficiency decreases linearly with the number of samples.
[0011] Gaussian process regression (GPR): It uses a kernel function to characterize the smooth relationship between input and output, possessing some nonlinear modeling capabilities. However, GPR has high computational complexity (O(N³)) and large memory consumption (O(N²)), making it inefficient when processing high-dimensional radiation pattern outputs. It often requires downsampling and interpolation, sacrificing prediction accuracy. Furthermore, its performance is significantly affected by the kernel function and hyperparameters, and it is not well-suited for complex coupled models.
[0012] In summary, existing methods struggle to balance computational efficiency, modeling accuracy, and generalization ability: full-wave simulation offers high accuracy but is slow; analytical methods are fast but have a narrow range of applications; and while traditional machine learning methods are effective in some scenarios, they still suffer from high computational complexity, weak physical interpretability, and insufficient ability to model complex coupling and structural changes. Summary of the Invention
[0013] The technical problem to be solved by the present invention is to provide a fast pattern prediction technology that can maintain high accuracy, achieve millisecond-level inference, and adapt to various array layouts, so as to support the agile design and optimization of array antennas in 5G / 6G communication, multi-functional radar, satellite payload and other fields.
[0014] The technical solution adopted by this invention to solve the above-mentioned technical problems is a fast prediction method for array active radiation patterns based on multi-scale neighborhood Transformer, comprising the following steps:
[0015] Includes the following steps:
[0016] S1. Feature Extraction and Sequence Construction: For the target array element in the array, extract its geometric relationship with other array elements in the set neighborhood; convert the geometric relationship into an ordered number of tokens to form a feature representation, and add learnable position embeddings to construct an input feature sequence representing the local mutual coupling environment of the target array element;
[0017] S2. Feature Encoding and Prediction: The input feature sequence is input into the Transformer prediction network; the Transformer prediction network models the dependencies between tokens through the self-attention mechanism of its Transformer encoder, and after feature aggregation, it directly outputs the active element pattern (AEP) prediction result of the target array element through a fully connected layer;
[0018] S3. Array pattern synthesis: Obtain the AEP prediction results corresponding to each array element in the array; based on the spatial position and excitation of each array element, coherently superimpose the AEP prediction results of all array elements to synthesize the total far-field pattern of the array.
[0019] When the array is a linear array, step S1 specifically includes:
[0020] Extract the spacing between the target array element and its M nearest neighboring array elements on the left and right, where M is a positive integer; arrange the spacing in left-right spatial order, and use each spacing as a token to form the feature representation.
[0021] When the array is a planar array, step S1 specifically includes:
[0022] S11. Divide the space around the target array element into four quadrants; select the K nearest neighbor array elements in each quadrant, where K is a positive integer;
[0023] S12. Extract the relative geometric relationship of each neighboring array element relative to the target array element, wherein the relative geometric relationship includes at least Cartesian coordinate offset, Euclidean distance and relative azimuth angle;
[0024] S13. Convert the relative geometric relationship of each neighboring array element into a geometric relationship token;
[0025] S14. Obtain the global and quadrant-specific neighbor count statistics and convert them into independent counting tokens;
[0026] S15. Combine the geometric relationship token and the count token according to a preset rule to form a feature representation, and add a learnable position embedding and a learnable type embedding to form the input feature sequence; the type embedding is used to identify the count token or the geometric relationship token.
[0027] This invention introduces the self-attention mechanism from deep learning, utilizing the Transformer structure to perform multi-scale modeling of the spatial geometric relationships and mutual coupling features of array elements. It adaptively learns the spatial dependencies between array elements from the array's geometric parameters, achieving efficient modeling and end-to-end prediction of complex mutual coupling effects. Thus, it achieves high-precision and rapid prediction of the array radiation pattern without the need for repeated electromagnetic simulations, ultimately yielding the radiation pattern of the entire array.
[0028] The beneficial effects of this invention are:
[0029] 1. High prediction accuracy and strong physical interpretability:
[0030] Compared to existing deep learning-based prediction methods, which often treat the array as a whole and perform end-to-end black-box fitting, these models fail to understand the physical mechanisms of coupling between array elements. This invention achieves physically interpretable modeling through mechanism embedding. It designs a multi-scale neighborhood feature encoding method, decoupling and serializing the complex spatial relationships around array elements into structured tokens. This allows the Transformer prediction network to explicitly learn and model the geometric coupling relationships between array elements. Based on the Transformer's self-attention mechanism, it can explicitly model the spatial geometric relationships and coupling effects between array elements, achieving data-driven learning of the array's electromagnetic coupling behavior. This is equivalent to injecting prior electromagnetic knowledge into the model, making its prediction results not only highly accurate but also physically interpretable. The model's attention weights can directly reflect the coupling strength between array elements, providing an analytical tool for array optimization.
[0031] 2. Overcoming the inherent constraints of precision and efficiency:
[0032] In multiple experiments, the predicted radiation patterns of this invention showed high agreement with the full-wave simulation results, with significantly lower errors than traditional approximation methods. Furthermore, the lightweight Transformer model can predict the radiation patterns of individual array elements within milliseconds, and the synthesis of the overall array radiation patterns requires only a few milliseconds to tens of milliseconds.
[0033] 3. Strong generalization ability, suitable for complex array structures:
[0034] The effectiveness of existing fast prediction methods heavily relies on the regularity and periodicity of the array. This invention, through multi-scale neighborhood feature extraction and a regional sub-model mechanism, shifts the model's learning basis from being limited to regular array arrangements to focusing on the relative geometric relationship between array elements and their local electromagnetic environment. Therefore, this method can be directly applied to various advanced array configurations (such as sparse arrays and random arrays) with arbitrary element distribution and non-uniform spacing, without requiring retraining or adjustment, thus overcoming the fundamental limitations of traditional methods in terms of application scope. Attached Figure Description
[0035] Figure 1 Feature extraction for linear array input;
[0036] Figure 2 Feature extraction for area array input;
[0037] Figure 3 This is a schematic diagram of a patch antenna element;
[0038] Figure 4 The element position distribution of a 32-element random linear array;
[0039] Figure 5 A comparison of the AEP of the three left elements of a randomly distributed 32-element linear array;
[0040] Figure 6 A comparison of the AEP of the three middle elements of a randomly distributed 32-element linear array;
[0041] Figure 7 A comparison of the AEP of the three elements on the right side of a randomly distributed 32-element linear array;
[0042] Figure 8 Comparison of the predicted radiation pattern and the actual radiation pattern of a 32-element linear array;
[0043] Figure 9 The element position distribution of a 64-element randomly distributed planar array;
[0044] Figure 10 AEP comparison of randomly distributed 64-element area array corner elements;
[0045] Figure 11 AEP comparison of the intermediate elements of a randomly distributed 64-element array;
[0046] Figure 12 AEP comparison of edge elements of a randomly distributed 64-element area array;
[0047] Figure 13 Comparison of randomized 64-element area array radiation patterns;
[0048] Figure 14 Comparison of orientation patterns for different φ-shaped cross-sections. Detailed Implementation
[0049] The method of this invention is divided into two types: linear array pattern prediction model and area array pattern prediction model. Both can be used independently or in combination in multi-level array design.
[0050] Example 1: Pattern Prediction Method for Linear Array Active Elements
[0051] In linear array structures, array elements are arranged at equal or non-equal intervals along a single direction (x-axis), and the coupling relationship between elements mainly depends on the relative spacing and excitation phase distribution. To address this characteristic, this invention proposes a lightweight Transformer prediction network for rapidly predicting the radiation pattern of array elements based on array geometry and excitation parameters.
[0052] The steps for predicting the radiation pattern of a linear array active element are as follows:
[0053] (1) Data input construction:
[0054] Using each element of a randomly distributed N-element linear array as a sample, 100 sets of 17-element linear arrays are constructed. The geometric relationships between their four adjacent elements are extracted. The input feature extraction of the linear array is as follows: Figure 1As shown, the spacing parameters of the two adjacent array elements on the left and right are taken. If there are no array elements, zeros are added to form four tokens as feature representations.
[0055] ;
[0056] Where n is the array element index. The characteristic representation of array element n, It consists of 4 tokens, including the distance between the second element to the left of the element n and the first element to the left. The spacing between the first element to the left of the element n The spacing between the first element to the right of the element n is The distance between the second element to the right of the element n and the first element to the right. , Indicates transpose. Represents the real number field; if there is no array element in the adjacent left or right position, fill with 0. After linear transformation, the data is input into the Transformer encoder to form an input sequence with a shape of [B, 4, 1]. B represents the batch size.
[0057] (2) Model structure design:
[0058] The feature representations of array element n, containing four tokens, are input into a Transformer network. The Transformer network employs a three-layer Transformer encoder structure, with each layer containing a multi-head self-attention module, a feedforward network, and a normalization layer. Learnable position embeddings are introduced to model the relative positional relationships of the array elements. After encoding, the encoded results of the four tokens are subjected to mean pooling and mapped to the AEP prediction result of the output array element n through a fully connected layer. Corresponding directional pattern Of the 1801 sampling points, .
[0059] The core architecture of the Transformer prediction network aims to predict data from ordered sequences of element spacing. In this process, mutually coupled features are adaptively extracted and fused, as follows:
[0060] (2.1) Input: The feature representations of array element n are input into the Transformer network, first through a learnable linear layer, which will... Each scalar spacing value is projected into a high-dimensional feature space. Subsequently, a learnable positional embedding is added to each position in the sequence to form the input feature sequence. The positional embedding enables the model to distinguish the sequential relationships of left second neighbor, left first neighbor, right first neighbor, and right second neighbor, which is key to modeling the mutual coupling asymmetry.
[0061] (2.2) Feature Encoding: Transformer Encoder Stack
[0062] The core of processing the input feature sequence is a Transformer encoder stack consisting of L layers (L=3 in this example).
[0063] Each encoder layer performs the following operations sequentially to progressively extract and refine features:
[0064] Multi-head attention module: Taking the output of the previous layer as input, it calculates the association weight between any two tokens in the sequence through a multi-head attention mechanism. This enables the model to automatically identify and focus on the key neighbors that have the greatest impact on the AEP of the predicted target array element, thereby explicitly modeling the spatial dependencies between array elements;
[0065] Residual connections and layer normalization: The output and input of the multi-head attention module are added together by residual, and then layer normalization is performed. This operation stabilizes the training process of the deep network.
[0066] Feedforward network: The normalized features pass through a feedforward network consisting of two layers of linear transformation and GELU activation function, which introduces nonlinear mapping capability into the model.
[0067] Second residual connection and layer normalization: The output of the feedforward network is added to the input of the feedforward network again as a residual, and then subjected to a second layer normalization to obtain the final output of the encoder layer.
[0068] (2.3) Feature aggregation and direction map mapping
[0069] After L layers of encoding, the Transformer encoder stack obtains a feature sequence composed of deeply encoded token features.
[0070] Sequence pooling: To transform the deep-encoded token feature sequence into a fixed-length global feature vector, average pooling is performed on the four deep-encoded token features to obtain the global feature vector.
[0071] Layout pattern regression: The global feature vector is input into a fully connected layer. The number of neurons in this layer is equal to the number of layout pattern sampling points (1801). The predicted array element n is directly output. AEP prediction results of uniform sampling over the domain , n=1,…,N.
[0072] (3) Training and prediction process:
[0073] The Adam optimizer is used for training, with mean squared error (MSE) as the loss function.
[0074] After model training, given the feature representations of the input array elements, the Transformer prediction network can directly predict the AEP (Active Electric Field) of any array element within milliseconds, without needing to perform full-wave simulation again. Furthermore, based on the positional relationships of each array element, the total electric field of the entire linear array can be obtained using the following formula. ;
[0075] ;
[0076] N represents the total number of array elements. Indicates pitch angle, This represents the excitation of array element n. Indicates beam, This represents the distance of array element n relative to the reference array element, i.e., the position of array element n;
[0077] Then obtain the far-field power pattern of the linear array. :
[0078] ;
[0079] in For free space impedance, , This represents the total input power to the array.
[0080] Example 2: Pattern Prediction Method for Active Elements in Area Arrays
[0081] In planar array structures, array elements are distributed across a two-dimensional plane, exhibiting complex mutual coupling relationships with significant directional dependence and regional differences. To address this, Example 2 proposes a Transformer planar array prediction model based on multi-quadrant neighborhood features. This model learns and predicts high-dimensional mutual coupling relationships through quadrant partitioning and neighborhood feature encoding.
[0082] The steps for predicting the radiation pattern of an active element in an area array are as follows:
[0083] (1) Construction of multi-quadrant neighborhood features:
[0084] With each array element as the center, the space around it is divided into four quadrants.
[0085] Within each quadrant, select the four nearest neighbors and extract their relative coordinate features, including... , , and ,in, Let n be the horizontal distance between the array element n and its i-th neighbor in quadrant m. Let n be the vertical distance between the array element n and its i-th neighbor located in quadrant m. Let be the Euclidean distance between array element n and its i-th neighbor in quadrant m. Let n be the relative angle between the target element n and its i-th neighbor in quadrant m. Quadrant index. Neighbor number .
[0086] Each quadrant contains 16-dimensional neighbor features, and the four quadrants together form a 64-dimensional feature set.
[0087] (2) Data input construction:
[0088] In each quadrant, the target element n is sorted according to its Euclidean distance to its neighbors, with smaller Euclidean distances ranking higher. The first four neighboring nodes are selected. If there are fewer than four neighboring elements, zeros are added. Figure 2 As shown. Then the geometric relationship of its array element n is represented as follows. for:
[0089] ;
[0090] in, This represents the geometric relationship between array element n and its first four neighbors in quadrant m. Token represents the geometric relationship between array element n and its i-th neighbor in quadrant m.
[0091] In addition, global and quadrant-level counting features of array element n are introduced. :
[0092] ;
[0093] in, The total number of neighboring array elements in the four quadrants is less than or equal to 16; The number of neighboring elements in the first, second, third, and fourth quadrants are respectively, and are less than or equal to 4.
[0094] Using the geometric relationships of array element n and counting features The final feature representation of the 21 tokens of array element n is formed. :
[0095] ;
[0096] The features of the 16 neighbor samples are converted into 16 4-dimensional tokens, and 5 counting tokens are added to represent the number of global neighbors and the number of neighbors in each of the four quadrants, respectively, forming a total of 21 input tokens.
[0097] (3) Transformer prediction network structure
[0098] Input: A global count token plus four quadrant neighbor tokens and their corresponding count tokens. Each token is projected onto a feature representation of the same dimension through an independent linear layer, and learnable location embeddings, as well as type embeddings for count features and geometric relations, are added. The location embeddings are for four categories: quadrant 1, quadrant 2, quadrant 3, and quadrant 4, and the type embeddings are for count features and geometric relations.
[0099] The Transformer prediction network employs a two-layer Transformer encoder, with each layer containing a multi-head self-attention module, a feedforward network, and a normalization layer.
[0100] The outputs of the two-layer Transformer encoder are passed through a single Query Attention Pooling module to obtain global feature representations, which are then used to generate 181×181-dimensional AEP prediction results through linear mapping. .
[0101] The Transformer prediction network supports a warm-start mechanism, which allows training to continue based on the existing optimal weights, thereby improving convergence speed and prediction stability.
[0102] (4) Regional sub-model mechanism
[0103] For a planar array, to characterize the differences in mutual coupling characteristics of array elements in different regions (corners, edges, and center), an input feature sequence based on a four-quadrant neighborhood structure is constructed. This results in the creation of 100 randomly distributed N=17 element planar arrays, where λ is the antenna operating wavelength. Considering the mutual coupling influence of array elements within a radius of 2λ around the extracted array elements, the input feature extraction of a certain array element is as follows: Figure 2 As shown.
[0104] Due to the varying impact of edge effects on the coupling of array elements, the planar array regions are divided into three categories: corner regions, edge regions, and intermediate regions. The square regions with side length 1.5λ at the four corners of the planar array are designated as corner regions; the regions within 1.5λ distances from the four sides of the planar array, excluding the corner regions, are designated as edge regions; and the regions within the planar array outside the corner and edge regions are designated as intermediate regions. Independent models are trained for each of these three regions to capture the mutual coupling characteristics of different spatial regions.
[0105] Based on the location of the center of each array element, the array elements are divided into corner array elements, edge array elements, and middle array elements.
[0106] (5) Training and prediction process:
[0107] The mean squared error (MSE) is used as the loss function, and the AdamW optimizer is employed for training. After training, by inputting information about the surrounding elements of the array, the AEP prediction result for any array element can be predicted directly within milliseconds. , Since this is the azimuth angle, there's no need to perform a full-wave simulation again. The corresponding region model is automatically selected based on the array element's location, yielding all the necessary parameters. Then, using the positions of the array elements, the total electric field of this planar array is calculated using the following formula. :
[0108] ;
[0109] , These represent the positions of array element n relative to the reference array element in terms of horizontal and vertical distances, respectively.
[0110] The far-field power pattern of the planar array can then be obtained using the following formula. This enables accurate prediction of the radiation pattern of a planar array with arbitrary distribution. For free space impedance, , This represents the total input power to the array.
[0111] ;
[0112] Performance analysis of the invention:
[0113] Regarding AEP prediction for linear arrays, this invention uses the AEP of a 17-element randomly distributed linear array with an element spacing greater than 0.6 wavelengths and less than 1.5 wavelengths as training samples. The radiation pattern of each active element is obtained through full-wave simulation software. The algorithm of this invention is used for training, and a linear array is randomly generated. Actual experimental simulations demonstrate that this algorithm can accurately predict the AEP of a linear array with arbitrary element distribution and can quickly calculate the far-field radiation pattern of a larger number of randomly distributed linear arrays.
[0114] Regarding AEP prediction for area arrays, this invention uses the AEP of elements in a 17-element randomly distributed area array with an element spacing greater than 0.6 wavelengths as training samples. The radiation pattern of each active element is obtained through full-wave simulation software. The algorithm of this invention is used for training, and the area array is randomly generated. Actual experimental simulations demonstrate that this algorithm can accurately predict the AEP of an area array with arbitrary element distribution and quickly calculate a larger number of randomly distributed area array far-field radiation patterns.
[0115] To facilitate changing the position of the array elements, a back-feed configuration is used in this design. In HFSS, the antenna elements used in both linear and area arrays are as follows: Figure 3 As shown, the antenna substrate is Rogers 5880 with a thickness of 0.508 mm and a dielectric constant of 2.2; the metal patch is 8.3 mm long and 6.2 mm wide; the feed point is located at the middle of the long side and 1 / 4 of the width of the wide side, and the antenna operates at 15 GHz. To verify the rationality of this design, an arbitrarily distributed 32-element linear array is first constructed, and the element positions of this linear array are distributed as follows: Figure 4 As shown. The method proposed in this design predicts the AEP (Aspect-Effect Perimeter) of the left, middle, and right sides of a 32-element linear array as follows. Figure 5 , Figure 6 , Figure 7 As shown. Figure 8 To predict the gain of the 32-element linear array and compare it with the actual gain of the HFSS.
[0116] To verify the rationality of this design's prediction of the power pattern of a random array, a 64-element array with an arbitrary distribution is first established. The element positions of this array are distributed as follows: Figure 9 As shown. The AEP of a 64-element area array corner elements, center elements, and edge elements is predicted using the method proposed in this design. Figure 10 , Figure 11 , Figure 12 As shown. Figure 13 To predict the far-field radiation pattern of a 64-element array and compare it with the actual HFSS radiation pattern. Figure 14 Comparison of the radiation patterns of this array in the φ=90° and φ=0° sections.
Claims
1. A fast prediction method for array active radiation patterns based on multi-scale neighborhood Transformer, characterized in that, Includes the following steps: S1. Feature Extraction and Sequence Construction: For the target array element in the array, extract its geometric relationship with other array elements in the set neighborhood; convert the geometric relationship into an ordered number of tokens to form a feature representation, and add learnable position embeddings to construct an input feature sequence representing the local mutual coupling environment of the target array element; S2. Feature Encoding and Prediction: The input feature sequence is input into the Transformer prediction network; the Transformer prediction network models the dependencies between tokens through the self-attention mechanism of its Transformer encoder, and after feature aggregation, it directly outputs the active element pattern (AEP) prediction result of the target array element through a fully connected layer; S3. Array pattern synthesis: Obtain the AEP prediction results corresponding to each array element in the array; based on the spatial position and excitation of each array element, coherently superimpose the AEP prediction results of the active element patterns of all array elements to synthesize the total far-field pattern of the array.
2. The method as described in claim 1, characterized in that, When the array is a linear array, step S1 specifically includes: Extract the spacing between the target array element and its M nearest neighbor array elements on the left and right, where M is a positive integer; arrange the spacing in left-right spatial order, and use each spacing as a token to form the feature representation.
3. The method as described in claim 1, characterized in that, The feature representation is as follows: ； Where n is the element index, n=1,…,N, The characteristic representation of array element n, It consists of 4 tokens, including the spacing between the second leftmost element adjacent to element n. The spacing between the first element to the left of the element n The spacing between the first element to the right of the element n is The spacing of the second element to the right adjacent to element n , Indicates transpose. Represents the real number field; if there is no array element in the adjacent left or right position, fill with 0.
4. The method as described in claim 3, characterized in that, In step S3, the total far-field pattern of the linear array Synthesize using the following formula: ； N represents the total number of array elements, and n is the array element index. Indicates pitch angle, , This represents the excitation of array element n. Indicates the operating wavelength. Indicates wave number, , This represents the distance of array element n relative to the reference array element; This is to output the AEP prediction result for array element n.
5. The method as described in claim 1, characterized in that, When the array is a planar array, step S1 specifically includes: S11. Divide the space around the target array element into four quadrants; select the K nearest neighbor array elements in each quadrant, where K is a positive integer; S12. Extract the relative geometric relationship of each neighboring array element relative to the target array element, wherein the relative geometric relationship includes at least Cartesian coordinate offset, Euclidean distance and relative azimuth angle; S13. Convert the relative geometric relationship of each neighboring array element into a geometric relationship token; S14. Obtain the global and quadrant-specific neighbor count statistics and convert them into independent counting tokens; S15. Combine the geometric relationship token and the count token according to a preset rule to form a feature representation, and add a learnable position embedding and a learnable type embedding to form the input feature sequence; the type embedding is used to identify the count token or the geometric relationship token.
6. The method as described in claim 5, characterized in that, Where K=4, the feature representation for: ； in, The total number of neighboring array elements in the four quadrants is less than or equal to 16; The number of neighboring elements in the first, second, third, and fourth quadrants are respectively, and are less than or equal to 4; This represents the geometric relationship between array element n and its first four neighbors in quadrant m. Quadrant Index Neighbor Index , Let token represent the geometric relationship between array element n and its i-th neighbor in quadrant m. Let n be the horizontal distance between the array element n and its i-th neighbor in quadrant m. Let n be the vertical distance between the array element n and its i-th neighbor located in quadrant m. Let be the Euclidean distance between array element n and its i-th neighbor in quadrant m. Let n be the relative azimuth angle between the target element n and the i-th neighbor in quadrant m.
7. The method as described in claim 4 or 5, characterized in that, Before feature encoding and prediction, there is also a region segmentation model step: classifying the array elements in the planar array into corner array elements, edge array elements, or middle array elements according to the location of the center of the array elements; training independent Transformer prediction networks for different types of array elements; and selecting the corresponding Transformer prediction network according to the type of the target array element when executing step S2. Where λ is the antenna operating wavelength, the square regions with a side length of 1.5λ at the four corners of the planar array are called corner regions, the parts within a distance of 1.5λ from the four sides of the planar array but excluding the corner regions are called edge regions, and the areas outside the corner and edge regions within the planar array are called middle regions; each array element is classified into corner array elements, edge array elements, and middle array elements according to the type of region where its center is located.
8. The method as described in claim 1, characterized in that, In step S3, the total far-field pattern of the planar array Synthesize using the following formula: ； Where N represents the total number of array elements, and n is the array element index. Indicates pitch angle, It is the azimuth angle. This represents the excitation of array element n. Indicates the operating wavelength. Indicates wave number, ; To output the AEP prediction results for array element n, , These represent the horizontal and vertical distances of array element n relative to the reference array element, respectively.
9. The method as described in claim 1, characterized in that, Step S3 also includes determining the total far-field pattern of the array. Obtain the far-field power pattern of the array. : When the array is a linear array ; When the array is a planar array ; Indicates pitch angle, It is the azimuth angle. For free space impedance, This represents the total input power to the array.