Method for reconstructing far field pattern of sparse sampling antenna based on neural network and spherical wave mode expansion

Abstract

The method for reconstructing the far-field pattern of a sparse sampling antenna based on a neural network and spherical wave mode expansion includes the following steps: step 1: sparse near-field sampling is performed by using a sparse sampling scheme to obtain near-field data; step 2: the obtained near-field data is subjected to test sample enhancement; step 3: the near-field data is subjected to inverse Fourier transform based on the principle of spherical wave expansion to obtain spherical wave expansion coefficients, and the spherical wave expansion coefficients are calculated; step 4: according to the spherical wave expansion theorem and the calculated spherical wave expansion coefficients, a low-precision far field is calculated; step 5: a neural network is trained, and the antenna is subjected to far-field testing; step 6: the loss function used in the neural network training is subjected to optimization by using a weighted combination; and step 7: a physical model is combined with the neural network to reconstruct the far-field pattern of the antenna to be tested. The far-field pattern of the antenna is quickly reconstructed by sparse sampling of the spherical near-field data, in combination with a physical model and machine learning technology.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of antenna testing, in particular to a sparse sampling antenna far-field pattern reconstruction method based on neural networks and spherical wave mode expansion. BACKGROUND

[0002] The spherical near-field testing scheme of an antenna is widely used for far-field pattern prediction of an antenna. However, as the electrical size of the antenna increases, the measurement time and the number of sampling points of the antenna also increase exponentially, resulting in extremely low testing efficiency of the large-size antenna. Therefore, how to optimize the sampling scheme and algorithm to reduce the number of sampling points and improve the efficiency has become a research hotspot at this stage.

[0003] Existing sampling schemes such as adaptive sampling, random sampling, Igloo sampling, spiral sampling, and optimization algorithms such as compressed sensing, optimal interpolation, spherical multi-level expansion, and mode filtering recursive strategy are limited by the sampling trajectory. The optimization algorithm scheme is affected by the intelligent selection strategy, and usually requires the initial number of samples to be concentrated in the high dynamic change near-field region, and the selection of algorithm parameters directly affects the accuracy of the reconstructed far-field pattern. The algorithm lacks a certain universality.

[0004] In addition, deep learning-based electromagnetic calculation methods have gradually attracted attention, such as U-net neural network for electromagnetic interference diagnosis and antenna array fault detection methods, but these methods require a large amount of training data, and the quality of the undersampling data directly affects the generalization ability of the model. SUMMARY

[0005] In order to overcome the defects existing in the prior art, the present application provides a sparse sampling antenna far-field pattern reconstruction method based on neural networks and spherical wave mode expansion, which realizes the rapid reconstruction of the far-field pattern of the antenna by sparse sampling of the spherical near-field data, combining physical models and machine learning techniques, and finally achieving the rapid reconstruction of the far-field pattern of the antenna with only one-ninth of the number of samples of the traditional method.

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0007] The sparse sampling antenna far-field pattern reconstruction method based on neural networks and spherical wave mode expansion comprises the following steps:

[0008] Step 1: sparse near-field sampling of all sample antennas is performed using a sparse sampling scheme to obtain near-field data;

[0009] Step 2: the near-field data is tested for sample enhancement to obtain enhanced near-field data;

[0010] Step 3: The enhanced near-field data is inversely Fourier transformed based on the spherical wave expansion principle to obtain spherical wave expansion coefficients:

[0011] Step 4: According to the spherical wave expansion theorem and the spherical wave expansion coefficients solved in step 3, a low-precision far field is calculated:

[0012] Step 5: The sample antennas in step 1 are tested in the far field to obtain ideal far-field patterns. The low-precision far field calculated in step 4 is used as input, and the ideal far-field pattern of the sample antenna is used as output to construct and train the neural network.

[0013] Step 6: The loss function used in the training of the neural network is optimized.

[0019] Step 7: The physical model is combined with the neural network to reconstruct the far-field pattern of the antenna to be tested.

[0020] In step 1, the sparse sampling scheme is as follows:

[0021] The spherical near-field data of M sample antennas is collected using a sparse sampling scheme. Each antenna obtains a set of sparse near-field sampling data at a sampling interval that is three times the traditional Nyquist sampling interval of the M antennas. The sampling interval in the θ and φ directions based on the Nyquist theorem is Δθ1 and Δφ1, and the sampling interval in the θ and φ directions of the sparse sampling scheme is 3Δθ1 and 3Δφ1, respectively. The sampling interval in the θ and φ directions is three times that of the traditional method, and the total number of samples is one-ninth of the Nyquist sampling, i.e., the total number of sampling points is one-ninth of the Nyquist sampling. θ and φ are the elevation and azimuth angles, respectively.

[0022] Step 2 is as follows:

[0023] The near-field data obtained in step 1 is the antenna's radiation near-field. The center of the antenna, which is the coordinate origin of the near-field spherical sampling, is rotated along the x, y, and z axes by m1 angles to generate samples at different viewing angles, expand the training data from the original M groups to 3m1M groups, and improve the generalization ability of the model and reduce the risk of overfitting.

[0024] Step 3 is as follows:

[0025] The 3m1M groups of near-field data in step 2 are inversely Fourier transformed based on the spherical wave expansion principle to obtain spherical wave expansion coefficients [a mn ,b mn ] = IDFT {E(r, θ, φ), n = 1, …, N, m = -n, …, 0, … n}

[0022] Wherein, the number of truncations in the spherical wave expansion coefficient is N = 180 / (3Δθ1), E(r,θ,φ) is the near-field measured by the antenna under test on a sphere of radius r, and a mn and b mn is the spherical wave expansion coefficient; m and n are the modes of spherical wave expansion, n = 1, ..., N, m = -n, ..., 0, ..., n.

[0023] Step 4 specifically involves:

[0024] According to the spherical wave expansion theorem and the spherical wave expansion coefficient α obtained in step 3... mn and b mn Interpolation of the near field of sparse sampling

[0025]

[0026] Among them, M mn and N mn It is a spherical wave generating function. The low-precision far-field sampling intervals in the θ and φ directions are Δθ2 and Δφ2, corresponding to angles θ2 = 0:Δθ2:180° and φ2 = 0:Δφ2:360°, respectively. Δθ2 and Δφ2 are less than 3Δθ1 and 3Δφ1, respectively. The interval is determined according to the final required sampling interval of the antenna far-field.

[0027] The far field converted from sparse sampling is a low-precision far field.

[0028] Step 5 specifically involves:

[0029] Far-field tests are performed on the M antennas in step 1, with sampling intervals of Δθ2 and Δφ2 in the θ and φ directions, respectively. The same angle as in step 2 is used for rotation to obtain the ideal high-precision far-field radiation pattern of 3m1M groups. This data is used as the output of the neural network. The low-precision far-field radiation pattern in step 4 is used as the input of the neural network. The neural network is used to reconstruct and train the low-precision far-field radiation pattern to learn the mapping relationship between it and the ideal far-field radiation pattern. Through the training of the neural network, the final far-field radiation pattern reconstruction result is obtained.

[0030] Step 6 specifically involves:

[0031] In neural network training, a weighted combination loss function is used, with different weight coefficients assigned to each loss function to guide the optimization of the neural network. In the early stage of training, the reconstruction loss is given a larger weight to ensure that the basic generation rules are learned. In the later stage of training, the adversarial loss weight is gradually increased to improve the realism of the generated far-field radiation pattern.

[0032] L total =λ advL adv +λ recon L recon +λ perc L perc

[0033] Among them, L adv ,L recon and L perc These are adversarial loss, reconstruction loss, and other losses, λ adv ,λ recon and λ prec These are the relative contributions of the adversarial control loss, the reconstruction loss, and other losses, with the other losses being selected based on the specific training model.

[0034] Step 7 specifically involves:

[0035] For antennas under test that are not included in the initial sparse sampling in step 1, the physical prior information provided by the spherical wave mode expansion is used to obtain a low-precision far field from the sparse near field obtained by the test according to steps 3 and 4. Then, the low-precision far field is embedded into the neural network that has been trained in step 6 to reconstruct the far field pattern of the antenna under test.

[0036] After the preceding neural network training, as long as the sparse near field of the antenna under test can be tested, the low-precision far field of the antenna under test can be obtained according to steps 3 and 4. By directly embedding the low-precision far field of the antenna under test into the neural network as input through the neural network already trained on the sample antenna, the high-precision far field of the antenna under test can be obtained directly.

[0037] In step 1, the M antennas are sample antennas. The sparse near field of the sample antennas is used to calculate the low-precision far field. The low-precision far field and the high-precision far field are used to train the neural network. Once the neural network is trained, the antennas under test that are not in the sample only need to know the sparse near field to obtain the high-precision far field.

[0038] The beneficial effects of this invention are:

[0039] 1. Sparse sampling significantly reduces the number of sampling points required in spherical near-field testing, substantially reducing antenna measurement time and the amount of laboratory equipment used, thus lowering testing costs. This is especially true for electrically large antennas (generally, an antenna or object is considered electrically large when its characteristic size is larger than the operating wavelength (λ). A more stringent definition is when the size exceeds several wavelengths (usually 2λ or greater).

[0040] 2. Based on the spherical wave expansion, the spherical wave expansion coefficient is calculated, and the near-field data is converted into far-field information. Step 3 obtains the spherical wave expansion coefficient through inverse Fourier transform, and step 4 calculates the low-precision far-field through formula. This avoids the application of super-resolution networks, ensures that the preliminary reconstruction results conform to the physical laws of electromagnetic radiation, and improves the physical rationality of the reconstruction.

[0041] 3. By rotating the antenna radiation pattern at different angles to expand the data, the diversity of training data is significantly increased, which helps the model learn input patterns from different perspectives, reduces the model's dependence on specific data directions, and thus reduces the risk of overfitting.

[0042] 4. By combining physical models with data-driven neural network methods, the model can better cope with diverse input conditions in the real world, improving its adaptability to different antenna designs and testing conditions. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention.

[0044] Figure 2 It is the model structure of Conditional Generative Adversarial Network (CGAN).

[0045] Figure 3 (a) and Figure 3 (b) is a comparison of the reference radiation pattern of the single-cone antenna with the far-field results obtained by the traditional fast Fourier transform method and the method proposed in this invention in the XOZ and YOZ planes.

[0046] Figure 4 (a) and Figure 4 (b) is a comparison of the reference radiation pattern of the horn antenna with the far-field results obtained by the traditional fast Fourier transform method and the method proposed in this invention in the XOZ and YOZ planes. Detailed Implementation

[0047] The present invention will now be described in further detail with reference to the accompanying drawings.

[0048] This invention proposes a far-field pattern reconstruction method for sparsely sampled antennas based on neural networks and spherical wave mode expansion. The overall process of this method is as follows: Figure 1 As shown:

[0049] Step 1: Use simulation software to acquire near-field data from sparse sampling of 508 antennas. E(r, θ , φ )(The sampling interval in the θ and φ directions is 15 degrees, θ = 0:15:180°, φ = 0:15:360°), the spherical sampling radius r is 1.6m, the operating frequency range of this group of antennas is 0.1-1.9GHz, and the sampling interval in the θ and φ directions of these 508 groups of antennas is approximately 5 degrees based on the Nyquist theorem.

[0050] Step 2: Rotate the antenna from Step 1 by 45 degrees along the x-axis, y-axis, and z-axis respectively, and finally obtain 3556 sets of near-field data.

[0051] Rotating 45 degrees around the x-axis from the origin gives one set of data, and rotating 90 degrees around the x-axis from the origin gives another set of data. The original data set was 508 sets. Rotating around the three axes, the total number of sets is 508 * 3 * 2 = 3556.

[0052] Step 3: Use inverse Fourier transform to calculate the spherical wave expansion coefficient α of the 3556 sets of near-field data E(r,θ,φ) from Step 2. mn and b mn , m and n are the modes of the spherical wave expansion, and the corresponding number of spherical wave truncations is N = 180 / 15 = 12. Then, low-precision far-field data E(θ2,φ2) is obtained through interpolation using spherical wave expansion techniques, where M... mn and N mn It is a spherical wave generating function. The sampling intervals Δθ2 and Δφ2 of the low-precision far-field data in the θ and φ directions are 2 degrees, corresponding to angles θ2=0:2:180° and φ2=0:2:360°.

[0053] [a mn ,b mn ]=IDFT{E(r,θ,φ),n=1,…,N,m=-n,…,0,…n}

[0054]

[0055] Step 4: The low-precision far-field data E(θ2,φ2) from Step 3 is a complex number. The real and imaginary parts of E(θ2,φ2) are used as inputs to the neural network. Simultaneously, the real and imaginary parts of the ideal far-field pattern E2(θ2,φ2) generated by the simulation software are used as the outputs of the neural network. To ensure consistency in data processing, the input and output data grid sizes are the same.

[0056] To facilitate network training and accelerate convergence, the input and output data are normalized at both ends of the network to limit their range to [-1, 1].

[0057] The specific steps for normalization are as follows:

[0058] (1) Determine the maximum and minimum values ​​of the data: First, calculate the maximum (max) and minimum (min) values ​​in the dataset.

[0059] (2) Using the linear transformation formula, normalize each data point x in the dataset using the following formula:

[0060]

[0061] Where x' is the normalized data. This formula is applied to all data points in the dataset to ensure that the normalized data is within the interval [-1, 1]. This normalization method can effectively scale the data, making it suitable for further processing and analysis.

[0062] Step 5. The neural network used in this example is a conditional generative adversarial network, such as... Figure 2 As shown, this conditional generative adversarial network consists of an input layer, an output layer, convolutional layers, normalization layers, activation functions, merging operations, and deconvolutional layers. Figure 2 The functions of each part of the conditional generative adversarial network are as follows:

[0063] (1) Input layer: The real and imaginary parts of low-precision far-field data E(θ2,φ2) with an input size of 91×181 are used to represent the input features.

[0064] (2) Output layer: Generate the real and imaginary parts of the ideal far-field pattern E2(θ2,φ2) with the same size of 91×181, representing the output features, which correspond to the input features.

[0065] (3) Convolutional layer: used to extract input features step by step. The convolution operation reduces the size of the feature map and increases the number of channels layer by layer by setting the kernel size and stride. The feature map size is reduced from 91×181 to 3×5, and the number of channels is increased from 64 to 512. Each convolutional layer is followed by a normalization layer and an activation function.

[0066] (4) Normalization layer: to accelerate the training process and improve model stability, making the input distribution of each layer more stable.

[0067] (5) Activation function: introduces nonlinearity into the network, thereby enhancing the expressive power of the model.

[0068] (6) Deconvolutional layer: used to map low-dimensional features back to high-dimensional space, thereby generating an output that matches the input conditions.

[0069] (7) Merging operation: Merge the condition information with the intermediate feature map in the generation process to ensure the consistency between the generation result and the condition information.

[0070] This structural design enables conditional generative adversarial networks to effectively generate high-quality samples under given conditions. The accompanying diagram provides a more intuitive understanding of the connections between the components and the flow of information.

[0071] In this architecture, a weighted combination loss function is used to guide the network optimization process.

[0072] Specifically, the loss function consists of three parts: adversarial loss, reconstruction loss, and perceptual loss, each assigned different weights.

[0073] L total =λ adv L adv +λ recon L recon +λ perc L perc

[0074] Among them, L adv ,L recon and L perc These are adversarial loss, reconstruction loss, and other losses, λ adv ,λ recon and λ prec These represent the relative contributions of the adversarial loss, reconstruction loss, and other losses, respectively. In this example, the other loss is chosen as the perceptual loss. Hyperparameters are used to control the relative weights of the adversarial loss, reconstruction loss, and perceptual loss. These weight coefficients can be fine-tuned based on experimental results. Initially, λ... adv ,λ recon and λ prec The values ​​were assigned to 0.2, 0.6, and 0.2 respectively. To ensure the generator could stably learn the basic generation rules in the early stages of training, a larger weight was assigned to the reconstruction loss in the early stages; while in the later stages of training, when the loss function L... total As the value tends to stabilize, gradually increase the weight of the loss mitigation factor, λ. adv Increasing from 0.2 to 0.5, λ recon The value was reduced from 0.6 to 0.3, thereby improving the realism and detail quality of the generated far-field samples.

[0075] Step 6: Figure 3 These are simulation results for a single-cone antenna, which was not included in the test dataset used for neural network training. The antenna operates at a frequency of 1 GHz, and the minimum spherical radius surrounding the antenna is 0.75 m (2.5 times the wavelength). According to the sampling theorem, the minimum spherical sampling interval should be 6.92 degrees. In the simulation, both the traditional Fast Fourier Transform method and the proposed neural network-based method were used for near-field and far-field conversion, with a sparse sampling interval of 15 degrees in the near field. Figure 3 (a) and Figure 3(b) compares the reference far-field pattern of the monoconical antenna with the far-field results in the XOZ and YOZ planes using both the conventional and proposed methods. The results demonstrate the effectiveness of the proposed method. The far-field patterns generated by the proposed method closely match the reference pattern, accurately capturing both the main lobe and side lobe features, while the conventional method exhibits significant deviations in the side lobe region. Although this antenna was not present in the training set, the proposed method still manages to reconstruct complex radiation patterns with high fidelity.

[0076] Step 7: To verify the robustness of the proposed algorithm, a horn antenna operating in the 4-6 GHz range was tested in a 23-probe spherical near-field anechoic chamber. The antenna's sparse near-field sampling interval was 15 degrees, and its frequency band exceeded the test set range of 0.1-2 GHz. The reference radiation pattern was obtained by triple oversampling (sampling interval of 5 degrees) during the near-field test. Figure 4 (a) and Figure 4 (b) The results of the reference and the orientation patterns based on fast Fourier transform and neural network reconstruction in the XOZ and YOZ planes were compared.

[0077] The results demonstrate several advantages of the proposed method: in both planes, the proposed method is closer to the reference mode compared to traditional methods. This shows that conditional generative adversarial networks exhibit excellent generalization capabilities to unknown frequencies, even when the antenna operates far beyond the network's training set. Horn antennas operate over a wide frequency range, and near-field data may contain subtle variations that are difficult for neural networks to fully capture, especially when trained over a narrower frequency range. These variations can lead to slight inaccuracies in reconstructing detailed features of the far-field radiation pattern.

[0078] Despite these potential sources of error, neural network-based methods significantly outperform traditional methods in reconstructing far-field patterns from sparse near-field measurements. Their ability to generalize to frequencies beyond the training range, coupled with their superior performance in capturing complex radiometric features, makes them a powerful solution for far-field reconstruction.

Claims

1. A method for reconstructing the far-field radiation pattern of a sparsely sampled antenna based on neural networks and spherical wave mode expansion, characterized in that, Includes the following steps; Step 1: Use a sparse sampling scheme to perform sparse near-field sampling on all sample antennas to obtain near-field data; Step 2: Perform test sample enhancement on the near-field data to obtain enhanced near-field data; Step 3: Perform an inverse Fourier transform on the enhanced near-field data based on the principle of spherical wave expansion to obtain the spherical wave expansion coefficients: Step 4: Calculate the low-precision far field using the spherical wave expansion theorem and the spherical wave expansion coefficients obtained in Step 3: Step 5: Perform far-field testing on the sample antenna from Step 1 to obtain the ideal far-field radiation pattern. Use the low-precision far-field calculated in Step 4 as input and the ideal far-field radiation pattern of the sample antenna as output to construct and train the neural network. Step 6: Optimize the loss function used in the weighted combination during neural network training; Step 7: Combine the physical model with the neural network to reconstruct the far-field radiation pattern of the antenna under test; Step 5 specifically involves: Far-field tests are performed on the M antennas in step 1, with sampling intervals of Δθ2 and Δφ2 in the θ and φ directions, respectively. The same angle as in step 2 is used for rotation to obtain the ideal high-precision far-field radiation pattern of 3m1M groups. This data is used as the output of the neural network. The low-precision far-field radiation pattern in step 4 is used as the input of the neural network. The neural network is used to reconstruct and train the low-precision far-field radiation pattern to learn the mapping relationship between it and the ideal far-field radiation pattern. Through the training of the neural network, the final far-field radiation pattern reconstruction result is obtained. Step 7 specifically involves: For antennas under test that are not included in the initial sparse sampling in step 1, the physical prior information provided by the spherical wave mode expansion is used to obtain a low-precision far field from the sparse near field obtained by the test according to steps 3 and 4. Then, the low-precision far field is embedded into the neural network that has been trained in step 6 to reconstruct the far field pattern of the antenna under test.

2. The far-field radiation pattern reconstruction method for sparse sampling antennas based on neural networks and spherical wave mode expansion according to claim 1, characterized in that, In step 1, the sparse sampling scheme is specifically adopted as follows: A sparse sampling scheme is used to collect near-field data from M sample antennas on a spherical surface. Uniform sampling is performed at three times the traditional Nyquist sampling interval required by the M antennas. Each antenna acquires one set of sparse near-field sampling data, and the M antennas acquire M sets of data. Let... Based on the Nyquist theorem, the sampling intervals in the θ and φ directions are Δθ1 and Δφ1, respectively. The sparse sampling scheme has sampling intervals of 3Δθ1 and 3Δφ1 in the θ and φ directions, respectively. The sampling intervals in θ and φ are three times that of the traditional method, and the total number of samples is one-third squared, that is, the total number of sampling points is one-ninth of that based on Nyquist sampling. θ and φ are the pitch angle and azimuth angle, respectively.

3. The far-field radiation pattern reconstruction method for sparse sampling antennas based on neural networks and spherical wave mode expansion according to claim 2, characterized in that, Step 2 specifically involves: The near-field data obtained in step 1 is the antenna's radiated near-field. Rotate all the antenna radiated near-field data in step 1 around the center of the antenna by rotating them by m1 angles along the x-axis, y-axis, and z-axis respectively to generate samples from different perspectives. Expand the training data from the original M sets of data to 3m1M sets of near-field data.

4. The far-field radiation pattern reconstruction method for sparsely sampled antennas based on neural networks and spherical wave mode expansion according to claim 3, characterized in that, Step 3 specifically involves: Using the principle of spherical wave mode expansion, the near-field data of the 3m1M group in step 2 are subjected to inverse Fourier transform based on the principle of spherical wave expansion to obtain the spherical wave expansion coefficients. [a mn ,b mn ]=IDFT{E(r,θ,φ),n=1,…,N,m=-n,…,0,…n} Wherein, the number of truncations in the spherical wave expansion coefficient is N = 180 / (3Δθ1), E(r,θ,φ) is the near-field measured by the antenna under test on a sphere of radius r, and a mn and b mn is the spherical wave expansion coefficient; m and n are the modes of spherical wave expansion, n = 1, ..., N, m = -n, ..., 0, ..., n.

5. The far-field radiation pattern reconstruction method for sparse sampling antennas based on neural networks and spherical wave mode expansion according to claim 4, characterized in that, Step 4 specifically involves: According to the spherical wave expansion theorem and the spherical wave expansion coefficient α obtained in step 3... mn and b mn Interpolation of the near field of sparse sampling Among them, M mn and N mn It is a spherical wave generating function with low-precision far-field sampling intervals of Δθ2 and Δφ2 in the θ and φ directions, corresponding to angles θ2=0:Δθ2:180° and φ2=0:Δφ2:360°, where Δθ2 and Δφ2 are less than Δθ1 / 3 and Δφ1 / 3, respectively.

6. The far-field radiation pattern reconstruction method for sparse sampling antennas based on neural networks and spherical wave mode expansion according to claim 1, characterized in that, Step 6 specifically involves: In neural network training, a weighted combination loss function is used, and different weight coefficients are assigned to each loss function to guide the optimization process of the neural network. L total =λ adv L adv +λ recon L recon +λ perc L perc Among them, L adv ,L recon and L perc These are adversarial loss, reconstruction loss, and other losses, λ adv ,λ recon and λ prec These are the relative contributions of the adversarial control loss, the reconstruction loss, and other losses, with the other losses being selected based on the specific training model.

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