Waveguide array near-field calibration method based on deep learning

Abstract

This invention discloses a deep learning-based near-field calibration method for waveguide arrays, belonging to the field of antenna measurement and array calibration technology. The invention includes: establishing a waveguide array model in electromagnetic simulation software; collecting planar near-field distribution data and corresponding waveguide excitation data under different excitation states to construct a dataset; performing multi-scale feature transformation and preprocessing on the planar near-field distribution data and waveguide excitation data to construct input and output feature tensors; building a deep learning calibration model including a cascaded one-dimensional convolutional neural network, a dual attention mechanism module, a global feature extraction module, and a multi-layer fully connected network; training the model using a progressive training strategy and a weighted combined loss function; inputting the measured near-field data of the array to be calibrated into the trained model to invert the actual excitation; and completing array calibration based on the deviation. This invention does not rely on a precise analytical model, effectively captures mutual coupling effects and phase periodicity, and has advantages such as high inversion accuracy, high computational efficiency, and strong generalization ability. It can be widely applied to waveguide array calibration in fields such as phased array radar and millimeter-wave communication.

Description

Technical Field

[0001] This invention relates to the field of antenna measurement and array calibration technology, and in particular to a waveguide array near-field calibration method based on deep learning. Background Technology

[0002] Array antennas are core components of modern electronic information equipment such as radar, satellite communications, and millimeter-wave systems. Their radiation performance directly determines the system's detection accuracy, signal transmission efficiency, and anti-interference capability. Waveguide arrays, as a preferred type of high-frequency array system, are widely used in phased array radar, millimeter-wave communications, and other fields due to their advantages of high gain, low loss, and compact structure. The amplitude and phase distribution of waveguide excitation are key parameters determining the array's radiation pattern, beam pointing, and sidelobe level.

[0003] During array fabrication and assembly, long-term operation, and complex environmental disturbances, factors such as element position deviations, amplitude and phase errors, and mutual coupling effects can cause the actual excitation to deviate from the ideal design value, thereby leading to array performance degradation. Therefore, accurately acquiring the true excitation information of the waveguide array and completing calibration has become a core requirement for ensuring the stable and efficient operation of the array system.

[0004] Planar near-field measurement technology has become the mainstream method for array antenna performance testing and calibration due to its high measurement accuracy, lack of site limitations, and ability to fully characterize array radiation characteristics. Obtaining the near-field amplitude and phase distribution of the array plane through scanning and then inverting it to obtain waveguide excitation information is an effective approach for waveguide array calibration. Traditional waveguide excitation inversion methods mostly rely on electromagnetic analytical models, using numerical optimization algorithms such as the least squares method and the conjugate gradient method to solve the mapping relationship between the near field and the excitation. However, such methods have the following problems in practical applications: 1. Strong dependence on analytical models: The accuracy of the method is highly dependent on the accuracy of the electromagnetic model, making it difficult to accurately characterize the influence of nonlinear factors such as complex mutual coupling effects, measurement noise, and environmental disturbances on the near-field distribution, resulting in deviations between the inversion results and the actual excitation.

[0005] 2. High computational complexity: Numerical optimization algorithms require multiple iterations to solve the problem. Especially when there are many array elements or dense near-field sampling points, the computational overhead increases significantly, making it difficult to meet the real-time or high-efficiency requirements of engineering applications.

[0006] 3. Poor convergence stability: Due to the influence of initial value selection and the non-convexity of the objective function, traditional optimization algorithms are prone to getting trapped in local optima, and the convergence speed is slow, making it difficult to guarantee the stability and consistency of calibration results.

[0007] In summary, existing waveguide excitation inversion methods based on analytical models have significant shortcomings in terms of accuracy, efficiency, and robustness. There is an urgent need for a new array calibration method that can effectively handle nonlinear mapping relationships and has high accuracy and fast reasoning capabilities. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a deep learning-based near-field calibration method for waveguide arrays, aiming to improve waveguide excitation inversion accuracy, reduce computational complexity, increase calibration efficiency, and achieve good generalization capability for different array configurations.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows: A deep learning-based near-field calibration method for waveguide arrays includes the following steps: Step 1: Establish a waveguide array model in electromagnetic simulation software. By changing the excitation amplitude and phase of each array element, collect multiple sets of planar near-field distribution data under different excitation states and their corresponding waveguide excitation data to construct training datasets and validation datasets. Step 2: Perform feature transformation and preprocessing on the planar near-field distribution data and waveguide excitation data in the training dataset and validation dataset to construct the input feature tensor and the output feature tensor; Step 3: Build a deep learning neural network calibration model for inverting waveguide excitation from planar near-field distribution. The calibration model takes the amplitude and phase data of the planar near-field distribution as input and the excitation amplitude and phase of each element of the waveguide array as output. Step 4: Using the preprocessed training dataset, the calibration model is trained using a progressive training strategy. The loss function is a weighted combination loss function that includes amplitude loss function and phase loss function. The AdamW optimizer is used to update the model parameters to obtain the trained calibration model. Step 5: The measured planar near-field distribution data of the waveguide array to be calibrated is processed by the same feature transformation and preprocessing as in Step 2, and then input into the trained calibration model. The excitation amplitude and phase output by the calibration model are the true excitation obtained by inversion. The array elements are compensated according to the deviation between the true excitation and the ideal excitation to complete the array calibration.

[0010] In the above scheme, step 2, which involves feature transformation and preprocessing of the planar near-field distribution data, specifically includes: For planar near-field amplitude data, multi-scale feature transformations, including number domain transformation, linear domain transformation, power domain transformation and cube root domain transformation, are performed, and the results of multiple transformations are stacked in the feature dimension to construct an amplitude feature tensor. For planar near-field phase data, we perform various feature transformations, including complex domain representation, first-order difference features, second-order difference features, sine and cosine transform features, and phase unwrapping features. We then stack the results of these transformations along the feature dimension to construct a phase feature tensor. The amplitude feature tensor and the phase feature tensor are concatenated along the feature dimension to obtain the complete input feature tensor.

[0011] In the above scheme, the calibration model includes a cascaded one-dimensional convolutional neural network, a dual attention mechanism module, a global feature extraction module, and a multi-layer fully connected network connected in sequence. The cascaded one-dimensional convolutional neural network includes four convolutional layers for hierarchical feature extraction of the input feature tensor. The dual attention mechanism module includes a cascaded multi-head self-attention module and a convolutional block attention module. The multi-head self-attention module captures long-distance dependencies within the waveguide sequence through a multi-head mechanism, effectively modeling the coupling effect between adjacent waveguides. The convolutional block attention module adaptively weights features from both channel and spatial dimensions, enabling the neural network to automatically focus on key features that contribute more to waveguide excitation calibration. The global feature extraction module is used to perform global average pooling, global max pooling, and standard deviation calculation on the feature map output by the attention module, and concatenate the obtained feature vectors to form a comprehensive global feature vector. The multilayer fully connected network is used to predict the excitation amplitude and phase of each array element based on the comprehensive global feature vector regression.

[0012] In a further technical solution, the multi-head self-attention module performs self-attention calculation on the input features to obtain attention-weighted features, adds them to the original input through residual connections, and then performs layer normalization processing.

[0013] In a further technical solution, the convolutional block attention module sequentially includes a channel attention submodule and a spatial attention submodule; The channel attention submodule is used to perform global average pooling and global max pooling on the input features respectively, extract the channel dimension description vector, and then generate channel attention weights after processing by a fully connected layer, and multiply them element-wise with the input features. The spatial attention submodule is used to calculate the average and maximum values ​​of the features after channel attention weighting along the channel dimension, concatenate them, generate spatial attention weights through one-dimensional convolution, and multiply them element-wise with the input feature.

[0014] In a further technical solution, the multilayer fully connected network includes four fully connected layers and an output layer connected in this manner. The activation function of the four fully connected layers adopts the Swish function, and the output layer adopts a linear activation function.

[0015] In the above scheme, the expression for the weighted combination loss function is: ; in, For weighted portfolio loss, For amplitude loss function, For phase loss function, and These are the weighting coefficients for amplitude and phase, respectively.

[0016] In a further technical solution, the amplitude loss function uses mean square error to measure the prediction error of the waveguide excitation amplitude, and its expression is: ; in, For the actual amplitude, The predicted amplitude; K is the number of waveguides. .

[0017] In a further technical solution, the phase loss function uses the minimum angle difference to measure the prediction error of the waveguide excitation phase, and its mathematical expression is: ; in, For the actual phase, The predicted phase; K is the number of waveguides. .

[0018] In the above scheme, the progressive training strategy in step 5 includes a basic training stage, a fine training stage, and a fine-tuning optimization stage performed sequentially. In the basic training phase, a learning rate warm-up strategy is used for initial training. In the fine training phase, an early stopping mechanism and an adaptive learning rate decay strategy are introduced for deep training. In the fine-tuning and optimization phase, the parameters of the first few layers of the network are frozen, and only the last few layers are trainable, so as to optimize them with a lower learning rate.

[0019] Through the above technical solution, the waveguide array near-field calibration method based on deep learning provided by the present invention has the following beneficial effects: 1. Eliminate reliance on precise analytical models and improve inversion accuracy. This invention constructs a deep learning neural network to autonomously learn the complex nonlinear mapping relationship between waveguide excitation and planar near-field distribution data directly. It does not rely on an accurate electromagnetic analytical model and can effectively capture the influence of nonlinear factors such as mutual coupling effect and measurement noise, thus significantly improving the accuracy of excitation inversion.

[0020] 2. Reduce computational complexity and improve calibration efficiency. This invention employs a combination of multi-scale feature transformation and cascaded convolutional neural networks to efficiently extract features and perform hierarchical abstract representation of near-field amplitude and phase data. Compared to traditional numerical optimization algorithms that require multiple iterations, this invention only requires one forward inference to obtain the waveguide excitation result after model training, significantly reducing computational complexity and meeting the high efficiency requirements of engineering applications.

[0021] 3. Enhance feature expression capabilities and focus on key information. This invention designs a neural network architecture that integrates residual learning and a dual attention mechanism (multi-head self-attention and convolutional block attention). The convolutional block attention module adaptively weights features from both channel and spatial dimensions, automatically identifying the importance differences between amplitude and phase features, and focusing on key waveguide locations that contribute more to calibration accuracy, thereby further improving calibration precision.

[0022] 4. Optimize phase error measurement and resolve phase entanglement problem. In response to the periodicity of phase data, this invention innovatively introduces "minimum angle difference" as the phase loss function, which avoids the error calculation distortion caused by phase entanglement at the junction of 0° and 360° in traditional mean square error, ensuring that the network can correctly learn the phase coupling relationship between waveguide units and guarantee the pointing accuracy of array beamforming.

[0023] 5. Possesses good generalization ability and engineering applicability. Experimental results show that this invention achieves calibration accuracy of less than 0.5 dB amplitude error and less than 5° phase error on the validation set for two different waveguide array configurations: a one-dimensional linear array with one row and three columns and a two-dimensional planar array with two rows and two columns. This verifies the universality of the method for different array configurations. The method is flexible in implementation and highly applicable, providing significant engineering reference value for the array calibration of phased array antenna systems. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0025] Figure 1This is a schematic diagram of a waveguide array near-field calibration method based on deep learning disclosed in an embodiment of the present invention; Figure 2 This is a data acquisition model for a three-column waveguide array; Figure 3 This is a graph showing the amplitude prediction error distribution of the validation set in Example 1; Figure 4 This is a diagram showing the phase prediction error distribution of the validation set in Example 1; Figure 5 This is a graph showing the amplitude prediction error distribution of the validation set in Example 2; Figure 6 This is a diagram showing the phase prediction error distribution of the validation set in Example 2. Detailed Implementation

[0026] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0027] Example 1 This embodiment provides a waveguide array near-field calibration method based on deep learning, such as... Figure 1 As shown, a waveguide array antenna with one row and three columns is used as a specific application scenario for detailed explanation.

[0028] I. Data Acquisition and Preprocessing First, a waveguide array antenna model with one row and three columns is created in the electromagnetic simulation software FEKO. For example... Figure 2 As shown, the three waveguide array elements are evenly distributed, and the operating frequency of each element is... , wavelength is Array element spacing The distance between the data acquisition plane and the array antenna The sampling plane size is Sampling interval .

[0029] By varying the excitation amplitude and phase of the three array elements, planar near-field distribution data under different excitation states were collected. Each excitation corresponds to one sample, resulting in a total of 4096 samples. For each sample, the amplitude matrix and phase matrix of the planar near-field acquisition point were recorded. Both the amplitude matrix and phase matrix have dimensions of N×M, where N is the total number of samples and M is the number of planar near-field acquisition points. Simultaneously, the corresponding waveguide excitation matrix was recorded. Each sample contains the amplitude and phase information of K waveguide element excitations; in this embodiment, K=3.

[0030] The collected data undergoes preprocessing, specifically including: For planar near-field amplitude data, given the large dynamic range of amplitude, this invention processes the amplitude data using four feature transformations at different scales: number domain transformation, linear domain transformation, power domain transformation, and root cube domain transformation. The results of these four transformations are then stacked along the feature dimension to construct an amplitude feature tensor. The dimensions are N×M×4.

[0031] For planar near-field phase data, due to the inherent periodicity and entanglement characteristics of the phase, this invention processes the phase data through seven feature transformations: complex domain representation, first-order difference features, second-order difference features, sine and cosine transform features, and phase untangling features. The results of these seven transformations are then stacked along the feature dimension to construct a phase feature tensor. The dimensions are N×M×7.

[0032] The constructed amplitude feature tensor and phase characteristic tensor Concatenate the features along the feature dimension to obtain the complete input feature tensor. The dimension is N×M×11, where 11 is the sum of the 4-dimensional amplitude and 7-dimensional phase features.

[0033] The same method is used to preprocess the amplitude and phase data of the waveguide excitation to construct the output feature tensor. The dimensions are N×K×11.

[0034] II. Constructing a Deep Learning Neural Network Calibration Model The calibration model constructed in this embodiment includes a cascaded one-dimensional convolutional neural network, a dual attention mechanism module, a global feature extraction module, and a multi-layer fully connected network connected in sequence.

[0035] (a) Cascaded one-dimensional convolutional neural networks The input feature tensor has dimensions (N, M, 11), and hierarchical feature extraction is performed through the following four convolutional layers: The first convolutional layer uses 64 convolutional kernels of size 7×11 with a stride of 1, same padding, and ReLU activation. The output feature map has dimensions (N, M, 64). After batch normalization, max pooling with a stride of 2 is performed to reduce the dimensionality, resulting in an output dimension of (N, M / 2, 64).

[0036] The second convolutional layer uses 128 kernels of size 5×64 with a stride of 1, same padding, and ReLU activation. The output dimension is (N, M / 2, 128). A residual learning unit is then embedded, consisting of two convolutional layers. After the first convolutional layer, batch normalization, ReLU activation, and dropout with a dropout rate of 0.1 are performed sequentially. After the second convolutional layer, batch normalization is performed again. Finally, the unit input and output are summed via skip connections. The output is then subjected to max pooling with a stride of 2 for dimensionality reduction, resulting in a dimension of (N, M / 4, 128).

[0037] The third convolutional layer uses 256 kernels of size 3×128 with a stride of 1, same padding, and ReLU activation. The output dimension is (N, M / 4, 256). It embeds the same residual learning units as the second convolutional layer, and the output undergoes max pooling with a stride of 2 to reduce the dimension to (N, M / 8, 256).

[0038] The fourth convolutional layer uses 512 kernels of size 3×256 with a stride of 1, same padding, and ReLU activation. The output dimension is (N, M / 8, 512). Residual learning units are embedded within this layer. No pooling is performed in this layer to preserve the spatial dimension of the feature map.

[0039] (II) Dual Attention Mechanism Module The dual attention mechanism module comprises a cascaded multi-head self-attention module and a convolutional block attention module (CBAM). The multi-head self-attention module captures long-range dependencies within the waveguide sequence through a multi-head mechanism, effectively modeling coupling effects between adjacent waveguides. CBAM attention weights features from both channel and spatial dimensions. Channel attention automatically identifies the importance differences between amplitude and phase features, while spatial attention focuses on key waveguide locations that contribute more to calibration accuracy. The cascaded use of these two attention mechanisms enables the network to accurately locate the core features affecting waveguide excitation from complex near-field distributions, thereby improving calibration accuracy.

[0040] Multi-head self-attention module: Eight attention heads are set, each with a feature dimension of 64. Self-attention is calculated on the input features to obtain attention-weighted features, which are then added to the original input via residual connections and followed by layer normalization. A feedforward network is constructed, first expanding the feature dimension to 1024, then compressing it back to 512, with a Dropout layer of 0.1 inserted in between, followed by another round of residual connections and layer normalization. The output feature map dimension remains (N, M / 8, 512).

[0041] Convolutional Block Attention Module (CBAM): Includes channel attention submodule and spatial attention submodule.

[0042] The channel attention submodule performs global average pooling and global max pooling on the input features, resulting in two channel description vectors with a dimension of 512. Feature transformation is then performed through two fully connected layers. The first fully connected layer compresses the number of channels to 1 / 8 of the original, i.e., 64 dimensions, using the ReLU activation function; the second fully connected layer restores the original number of channels to 512 dimensions, using the Sigmoid activation function. The outputs of the two branches are summed to obtain the channel attention weights, with a dimension of 512. These reshaped weights are then multiplied element-wise with the original features to achieve feature recalibration in the channel dimension.

[0043] The spatial attention submodule calculates the average and maximum values ​​along the channel dimension, resulting in two spatial feature maps, each with dimensions (N, M / 8, 1). These are then concatenated along the channel dimension to obtain a feature map of dimension (N, M / 8, 2). A 7×1 one-dimensional convolution with one output channel and a sigmoid activation function generates spatial attention weights of dimension (N, M / 8, 1), which are then element-wise multiplied with the input features to enhance the spatial dimension.

[0044] (III) Global Feature Extraction Module Global context information is extracted from the feature map output by the attention module. At this point, the feature map dimension is (N, M / 8, 512). Global average pooling is then performed to obtain the mean feature vector. Global max pooling yields the eigenvector of the maximum value. And calculate the standard deviation along the spatial dimension to obtain the standard deviation eigenvector. The three are then concatenated to form a comprehensive global feature vector. The dimension is 1536.

[0045] (iv) Multi-layer fully connected network A multi-layer fully connected network is constructed for regression prediction, with the following specific structure: The first fully connected layer has 1024 neurons, uses the Swish activation function, has an input dimension of 1536, and an output dimension of 1024. Batch normalization is then performed, followed by Dropout regularization with a dropout rate of 0.3.

[0046] The second fully connected layer has 512 neurons, uses the Swish activation function, has an input dimension of 1024, and an output dimension of 512. Batch normalization is then performed, followed by Dropout with a dropout rate of 0.25.

[0047] The third fully connected layer has 256 neurons, uses the Swish activation function, has an input dimension of 512, and an output dimension of 256. Batch normalization is then performed, followed by Dropout with a dropout rate of 0.2.

[0048] The fourth fully connected layer has 128 neurons, uses the Swish activation function, has an input dimension of 256, and an output dimension of 128. It is then subjected to row-batch normalization and a dropout rate of 0.15.

[0049] Output layer: The number of neurons equals the total dimension of the output features D = K × 11. A linear activation function is used. The input dimension is 128, and the output dimension is K × 11. The predicted value vector is directly output. .

[0050] III. Model Training To address the differences in the physical characteristics of amplitude and phase, a weighted combined loss function is designed, expressed as follows: ; in, For weighted portfolio loss, For amplitude loss function, For phase loss function, and These are the weighting coefficients for amplitude and phase, respectively. In this embodiment, , Simulations using controlled variables verified that when the weights are as described above, the model achieves the optimal balance between amplitude prediction accuracy and phase prediction accuracy.

[0051] The amplitude loss function uses mean square error (MSE) to measure the prediction error of the waveguide excitation amplitude, and its expression is: ; in, For the actual amplitude, The predicted amplitude; K is the number of waveguides. Divide by the number of waveguides This is to eliminate the influence of the number of waveguides on the loss value, so that the loss function values ​​are comparable.

[0052] To address the periodicity of phase data in array calibration, conventional MSE (Minimum Angle Difference) suffers from severe error calculation distortion due to phase entanglement at the 0° and 360° boundary, thus misleading the network's optimization of beam pointing. Therefore, this invention innovatively introduces the "minimum angle difference" as a phase error metric. This loss function accurately reflects the true phase difference at the periodic boundary, enabling the network to correctly learn the phase coupling relationship between waveguide elements and ensuring the pointing accuracy of array beamforming. Its mathematical expression is: ; in, For the actual phase, This is the predicted phase.

[0053] The core of model training is to update the model parameters through the optimizer and minimize the corrected total loss function. Considering the characteristics of this model—deep network, high feature dimension, and large training sample size—the AdamW optimizer is selected. By calculating the first and second moments of the gradient, the learning rate of each parameter is adaptively adjusted. At the same time, a weight decay term is introduced to achieve regularized parameter updates and avoid overfitting caused by excessive weights.

[0054] To address the training characteristics of deep neural networks and the task requirements of solving waveguide excitations using planar near-field distribution, a progressive training strategy is adopted to improve the model's convergence performance and generalization ability.

[0055] (1) Basic training phase: The training rounds are set to 50, and the batch size is 32. A learning rate warm-up strategy is adopted, with the learning rate set to [value missing] for the first 10 rounds. The last 40 rounds were restored to Monitor the validation set loss during training.

[0056] (2) Fine-tuning training phase: The training epochs are set to 50, and the batch size is 16. An early stopping mechanism is introduced: training is terminated and the optimal weights are restored when the validation set loss does not decrease for 50 consecutive epochs. Simultaneously, an adaptive learning rate decay strategy is adopted: when the validation set loss does not improve for 15 consecutive epochs, the current learning rate is multiplied by a decay factor γ = 0.5, with a minimum learning rate limit of [missing value]. The model weights are saved for each round of validation set loss improvement.

[0057] (3) Fine-tuning and optimization stage: Freeze the parameters of the first L-10 layers of the network, keeping only the last 10 layers trainable. Recompile the model and set the learning rate to... The training rounds are 30, the batch size is 8, and the early stopping and learning rate decay mechanisms are continued to be applied.

[0058] IV. Model Validation and Application 4096 near-field data points and their corresponding stimuli were collected as the training set. Twenty sets of randomly generated stimuli signals were used as the target output for the validation set. Planar near-field values ​​under these 20 different stimuli were collected as the input for the validation set. The amplitude prediction results are as follows: Figure 3 As shown, the phase prediction results are as follows: Figure 4 As shown, the target upper and lower limits represent the maximum allowable errors in amplitude and phase during array calibration applications, and WG1 represents the first waveguide element of the waveguide array, and so on. Figure 3 and Figure 4 As can be seen, the amplitude error is controlled within ±0.5dB, and the phase error is controlled within ±5°.

[0059] V. Array Calibration For the waveguide array to be calibrated, its planar near-field distribution data is collected. After undergoing the same feature transformation and preprocessing as the training data, it is input into the trained calibration model. The excitation amplitude and phase output by the model are the inverted true excitations. Compensation is then performed on each array element based on the deviation between the true excitation and the ideal excitation to complete the array calibration.

[0060] Example 2 This embodiment is basically the same as Embodiment 1, except that the waveguide array configuration is a two-row, two-column two-dimensional area array. The training samples are 6561, and the validation samples are 20. The amplitude prediction results are as follows: Figure 5 As shown, the phase prediction results are as follows: Figure 6 As shown, the target upper and lower limits are the maximum allowable errors for amplitude and phase in array calibration applications, WG1 represents the first waveguide element of the waveguide array, and so on.

[0061] from Figure 5 and Figure 6 It can be seen that for a two-dimensional waveguide array with two rows and two columns, the calibration scheme of the present invention can also control the amplitude error within ±0.5dB and the phase error within ±5°, which verifies that the method of the present invention has good generalization ability and universality for different array configurations.

[0062] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A waveguide array near-field calibration method based on deep learning, characterized in that, Includes the following steps: Step 1: Establish a waveguide array model in electromagnetic simulation software. By changing the excitation amplitude and phase of each array element, collect multiple sets of planar near-field distribution data under different excitation states and their corresponding waveguide excitation data to construct training datasets and validation datasets. Step 2: Perform feature transformation and preprocessing on the planar near-field distribution data and waveguide excitation data in the training dataset and validation dataset to construct the input feature tensor and the output feature tensor; Step 3: Build a deep learning neural network calibration model for inverting waveguide excitation from planar near-field distribution. The calibration model takes the amplitude and phase data of the planar near-field distribution as input and the excitation amplitude and phase of each element of the waveguide array as output. Step 4: Using the preprocessed training dataset, the calibration model is trained using a progressive training strategy. The loss function is a weighted combination loss function that includes amplitude loss function and phase loss function. The AdamW optimizer is used to update the model parameters to obtain the trained calibration model. Step 5: The measured planar near-field distribution data of the waveguide array to be calibrated is processed by the same feature transformation and preprocessing as in Step 2, and then input into the trained calibration model. The excitation amplitude and phase output by the calibration model are the true excitation obtained by inversion. The array elements are compensated according to the deviation between the true excitation and the ideal excitation to complete the array calibration.

2. The waveguide array near-field calibration method based on deep learning according to claim 1, characterized in that, Step 2 involves feature transformation and preprocessing of the planar near-field distribution data, specifically including: For planar near-field amplitude data, multi-scale feature transformations, including number domain transformation, linear domain transformation, power domain transformation and cube root domain transformation, are performed, and the results of multiple transformations are stacked in the feature dimension to construct an amplitude feature tensor. For planar near-field phase data, we perform various feature transformations, including complex domain representation, first-order difference features, second-order difference features, sine and cosine transform features, and phase unwrapping features. We then stack the results of these transformations along the feature dimension to construct a phase feature tensor. The amplitude feature tensor and the phase feature tensor are concatenated along the feature dimension to obtain the complete input feature tensor.

3. The waveguide array near-field calibration method based on deep learning according to claim 1, characterized in that, The calibration model includes a cascaded one-dimensional convolutional neural network, a dual attention mechanism module, a global feature extraction module, and a multi-layer fully connected network connected in sequence. The cascaded one-dimensional convolutional neural network includes four convolutional layers for hierarchical feature extraction of the input feature tensor. The dual attention mechanism module includes a cascaded multi-head self-attention module and a convolutional block attention module. The multi-head self-attention module captures long-distance dependencies within the waveguide sequence through a multi-head mechanism, effectively modeling the coupling effect between adjacent waveguides. The convolutional block attention module adaptively weights features from both channel and spatial dimensions, enabling the neural network to automatically focus on key features that contribute more to waveguide excitation calibration. The global feature extraction module is used to perform global average pooling, global max pooling, and standard deviation calculation on the feature map output by the attention module, and concatenate the obtained feature vectors to form a comprehensive global feature vector. The multilayer fully connected network is used to predict the excitation amplitude and phase of each array element based on the comprehensive global feature vector regression.

4. The waveguide array near-field calibration method based on deep learning according to claim 3, characterized in that, The multi-head self-attention module performs self-attention calculation on the input features to obtain attention-weighted features, which are then added to the original input through residual connections and subsequently subjected to layer normalization.

5. The waveguide array near-field calibration method based on deep learning according to claim 3, characterized in that, The convolutional block attention module includes a channel attention submodule and a spatial attention submodule in sequence; The channel attention submodule is used to perform global average pooling and global max pooling on the input features respectively, extract the channel dimension description vector, and then generate channel attention weights after processing by a fully connected layer, and multiply them element-wise with the input features. The spatial attention submodule is used to calculate the average and maximum values ​​of the features after channel attention weighting along the channel dimension, concatenate them, generate spatial attention weights through one-dimensional convolution, and multiply them element-wise with the input feature.

6. The waveguide array near-field calibration method based on deep learning according to claim 3, characterized in that, The multilayer fully connected network includes four fully connected layers and an output layer connected in this way. The activation function of the four fully connected layers is the Swish function, and the output layer uses a linear activation function.

7. The waveguide array near-field calibration method based on deep learning according to claim 1, characterized in that, The expression for the weighted combination loss function is: ； in, For weighted portfolio loss, For amplitude loss function, For phase loss function, and These are the weighting coefficients for amplitude and phase, respectively.

8. The waveguide array near-field calibration method based on deep learning according to claim 7, characterized in that, The amplitude loss function uses mean square error to measure the prediction error of the waveguide excitation amplitude, and its expression is: ； in, For the actual amplitude, The predicted amplitude; K is the number of waveguides. .

9. A waveguide array near-field calibration method based on deep learning according to claim 7, characterized in that, The phase loss function uses the minimum angle difference to measure the prediction error of the waveguide excitation phase, and its mathematical expression is: ； in, For the actual phase, The predicted phase; K is the number of waveguides. .

10. The waveguide array near-field calibration method based on deep learning according to claim 1, characterized in that, The progressive training strategy in step 5 includes a basic training phase, a fine training phase, and a fine-tuning and optimization phase performed sequentially. In the basic training phase, a learning rate warm-up strategy is used for initial training. In the fine training phase, an early stopping mechanism and an adaptive learning rate decay strategy are introduced for deep training. In the fine-tuning and optimization phase, the parameters of the first few layers of the network are frozen, and only the last few layers are trainable, so as to optimize them with a lower learning rate.

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