Sparse sampling antenna far-field pattern reconstruction method based on neural network and spherical wave mode expansion

Abstract

The invention discloses a sparse sampling antenna far-field pattern reconstruction method based on a neural network and spherical wave mode expansion. The method comprises the following steps of: 1, performing sparse near-field sampling by adopting a sparse sampling scheme to obtain near-field data; 2, performing test sample enhancement on the acquired near-field data; 3, carrying out the Fourier inversion of the near-field data based on the spherical wave expansion principle, obtaining a spherical wave expansion coefficient, and calculating the spherical wave expansion coefficient; 4, calculating a low-precision far field according to the spherical wave expansion theorem and the solved spherical wave expansion coefficient; 5, generating a neural network for training, and carrying out the far-field test of an antenna; step 6, optimizing a loss function using a weighted combination in neural network training; and 7, combining the physical model with the neural network, and reconstructing a far-field pattern of the antenna to be tested. Sparse sampling is carried out on spherical near-field data, and a physical model and a machine learning technology are combined, so that the far-field directional diagram of the antenna is quickly reconstructed.

Description

Technical Field

[0001] The present invention relates to the technical field of antenna testing, and in particular to a method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave mode expansion. Background Art

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

[0003] Existing sampling schemes include adaptive sampling, random sampling, Igloo sampling, spiral sampling, etc., and optimization algorithms such as compressed sensing, optimal interpolation, spherical multi-level expansion, and pattern filtering-based recursive strategies. Although these non-uniform sampling schemes can reduce the redundant information of traditional uniform sampling, they are limited by the sampling trajectory. The optimization algorithm scheme is limited by the influence of the intelligent selection strategy, and usually requires the initial number of samples to be concentrated in the near-field area with high dynamic changes. The choice of algorithm parameters directly affects the accuracy of reconstructing the far-field directional pattern. The algorithm lacks a certain degree of universality.

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

[0005] In order to overcome the defects of the above-mentioned prior art, the present invention provides a method for reconstructing the far-field radiation pattern of a sparsely sampled antenna based on a neural network and a spherical wave mode expansion. The method sparsely samples the spherical near-field data, combines physical models and machine learning technology, and ultimately achieves rapid reconstruction of the far-field radiation pattern of the antenna with only one-ninth of the sampling number of the traditional method.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] The method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave pattern expansion includes the following steps:

[0008] Step 1: Use a sparse sampling scheme to perform sparse near-field sampling on all sample antennas to obtain near-field data;

[0009] Step 2: Performing test sample enhancement on the near-field data to obtain enhanced near-field data;

[0010] Step 3: Perform inverse Fourier transform on the enhanced near-field data based on the spherical wave expansion principle to obtain spherical wave expansion coefficients:

[0011] Step 4: Calculate the low-precision far field based on the spherical wave expansion theorem and the spherical wave expansion coefficients solved in step 3:

[0012] Step 5: Perform a far-field test on the sample antenna in step 1 to obtain an ideal far-field pattern, use the low-precision far field calculated in step 4 as input, and use the ideal far-field pattern of the sample antenna as output to build and train a neural network;

[0013] Step 6: Optimize the loss function of the weighted combination used in neural network training;

[0014] Step 7: Combine the physical model with the neural network to reconstruct the far-field pattern of the antenna under test.

[0015] In step 1, the sparse sampling scheme is specifically:

[0016] A sparse sampling scheme is used to collect the spherical near-field data of M sample antennas. The traditional Nyquist sampling interval of M antennas is three times the uniform sampling required. Each antenna obtains a set of sparse near-field sampling data, and M antennas obtain M sets of data. The sampling interval in the θ and φ directions based on the Nyquist theorem is Δθ. 1 and Δφ 1 , the sampling interval of this sparse sampling scheme in the θ and φ directions is 3Δθ 1 and 3Δφ 1 The sampling intervals at 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 elevation angle and azimuth angle, respectively.

[0017] The step 2 is specifically as follows:

[0018] The near-field data obtained in step 1 is the radiated near-field of the antenna. The near-field radiated near-field of all antennas in step 1 is rotated by m along the x-axis, y-axis, and z-axis respectively, with the center of the antenna, which is the origin of the coordinates of the near-field spherical sampling. 1 angles, generate samples from different perspectives, and expand the training data from the original M groups of data to 3m 1 M groups of near-field data improve the generalization ability of the model and reduce the risk of overfitting.

[0019] The step 3 is specifically as follows:

[0020] According to the spherical wave mode expansion principle, the near-field data of the 3m1M group in step 2 is subjected to inverse Fourier transform based on the spherical wave expansion principle to obtain the spherical wave expansion coefficients.

[0021] [a mn ,b mn ]=IDFT{E(r,θ,φ),n=1,…,N,m=-n,…,0,…n}

[0022] Among them, the number of truncation of the spherical wave expansion coefficient is N = 180 / (3Δθ 1 ), E(r,θ,φ) is the near field of the antenna under test on a spherical surface with a radius of r, a mn and b mn is the spherical wave expansion coefficient; m and n are the mode numbers of spherical wave expansion, n = 1, ..., N, m = -n, ..., 0, ..., n.

[0023] The step 4 is specifically as follows:

[0024] According to the spherical wave expansion theorem and the spherical wave expansion coefficient a solved in step 3 mn and b mn Interpolating the sparsely sampled near field

[0025]

[0026] Among them, mn and N mn is the spherical wave generating function, and the sampling interval of the low-precision far field in the θ and φ directions is Δθ 2 and Δφ 2 , corresponding to the angle θ 2 =0:Δθ 2 :180° and φ 2 =0:Δφ 2 :360°, Δθ 2 and Δφ 2 Less than 3Δθ 1 and 3Δφ 1 The interval is determined by the sampling interval of the antenna far field that is ultimately required.

[0027] The far field converted from the sparsely sampled near field is a low-precision far field.

[0028] The step 5 is specifically as follows:

[0029] Perform far-field testing on the M antennas in step 1, with sampling intervals Δθ in the θ and φ directions respectively. 2 and Δφ 2, rotate at the same angle as in step 2 to obtain the ideal high-precision far-field pattern of the 3m1M group. This data is used as the output of the neural network. The low-precision far-field pattern in step 4 is used as the input of the neural network. The neural network is used to reconstruct the low-precision far-field pattern and learn the mapping relationship between it and the ideal far-field pattern. The final far-field pattern reconstruction result is obtained through the training of the neural network.

[0030] The step 6 is specifically as follows:

[0031] A weighted combination of loss functions is used in neural network training. Different weight coefficients are assigned to each loss function to guide the optimization of the neural network. In the early stage of training, a larger weight is given to the reconstruction loss to ensure the learning of basic generation rules. In the later stage of training, the weight of the adversarial loss is gradually increased to improve the realism of the generated far-field directional map.

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

[0033] Among them, L adv ,L recon and L perc They are adversarial loss, reconstruction loss and other losses, λ adv ,λ recon and λ prec They respectively control the relative contributions of adversarial loss, reconstruction loss and other losses. Other losses are selected according to the specific training model.

[0034] The step 7 is specifically as follows:

[0035] For the antenna to be tested that does not belong to 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, and then the low-precision far field is embedded in the neural network that has been trained in step 6 to reconstruct the far-field radiation pattern of the antenna to be tested.

[0036] After the previous neural network training, as long as the sparse near field of the antenna to be tested can be tested, the low-precision far field of the antenna to be tested can be obtained according to steps 3 and 4. The low-precision far field of the antenna to be tested can be directly embedded into the neural network as input through the neural network trained by the sample antenna, and the high-precision far field of the antenna to be tested can be directly obtained.

[0037] The M antennas in step 1 are sample antennas. The sparse near field of the sample antenna 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. After the neural network is trained, the antenna to be tested that is not in the sample only needs to know the sparse near field to obtain the high-precision far field.

[0038] Beneficial effects of the present invention:

[0039] 1. Sparse sampling greatly reduces the number of sampling points required in spherical near-field testing, significantly reduces antenna measurement time and the use of laboratory equipment, and reduces testing costs. This is especially true for electrically large antennas (usually when the characteristic size of an antenna or object is larger than the operating wavelength (λ), it is considered to be electrically large. A stricter definition is when the size exceeds several wavelengths (usually 2λ or more)).

[0040] 2. Calculate the spherical wave expansion coefficient based on the spherical wave expansion, convert the near-field data into far-field information, obtain the spherical wave expansion coefficient through inverse Fourier transform in step 3, and obtain the low-precision far field through formula calculation in step 4; avoid the application of super-resolution network, ensure that the preliminary reconstruction results conform to the physical laws of electromagnetic radiation, and improve the physical rationality of reconstruction.

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

[0042] 4. By combining physical models and data-driven neural network methods, the model can better cope with diverse input conditions in the real world and improve its adaptability to different antenna designs and test conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of the present invention.

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

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

[0046] Figure 4 (a) and Figure 4(b) is a comparison of the reference radiation pattern of the horn antenna and the far-field results obtained by using the traditional fast Fourier transform method and the method proposed in the present invention in the XOZ plane and the YOZ plane. DETAILED DESCRIPTION

[0047] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0048] The present invention proposes a sparse sampling antenna far-field pattern reconstruction method based on neural network and spherical wave mode expansion. The overall process of the method is as follows: Figure 1 As shown:

[0049] Step 1: Use simulation software to obtain sparsely sampled near-field data 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, and the operating frequency range of this group of antennas is 0.1-1.9GHz. The sampling interval of these 508 groups of antennas in the θ and φ directions is approximately 5 degrees based on the Nyquist theorem.

[0050] Step 2: Rotate the antenna in step 1 by 45 and 90 degrees along the x-axis, y-axis, and z-axis, respectively, and finally obtain 3556 sets of near-field data.

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

[0052] Step 3: Use the inverse Fourier transform to calculate the spherical wave expansion coefficient a of the 3556 sets of near-field data E(r,θ,φ) in step 2 mn and b mn , m and n are the mode numbers of spherical wave expansion, and the corresponding spherical wave expansion truncation number is N = 180 / 15 = 12. Then the low-precision far-field data E(θ 2 ,φ 2 ), where M mn and N mn is the spherical wave generating function, and the sampling interval Δθ of the low-precision far-field data in the θ and φ directions is 2 and Δφ 2 is 2 degrees, corresponding to the angle θ 2 =0:2:180° and φ 2 =0:2:360°.

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

[0054]

[0055] Step 4: Convert the low-precision far-field data E(θ 2 ,φ 2 ) is a complex number, E(θ 2 ,φ 2 ) are used as the input of the neural network. At the same time, the ideal far-field pattern E generated by the simulation software 2 (θ 2 ,φ 2 ) is used as the output of the neural network. To ensure the consistency of data processing, the input and output data grid sizes are the same.

[0056] In order 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 of normalization are as follows:

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

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

[0060]

[0061] Where x' is the normalized data. This formula is used for 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 to make 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 in Figure 1. The conditional generative adversarial network consists of an input layer, an output layer, a convolutional layer, a normalization layer, an activation function, a merging operation, and a deconvolutional layer. Figure 2 The functions of each part of the conditional generative adversarial network are:

[0063] (1) Input layer: Input low-precision far-field data E(θ) with a size of 91×181 2 ,φ 2 ), representing the input features.

[0064] (2) Output layer: Generates an ideal far-field pattern E with the same size of 91×181 2 (θ 2 ,φ 2 ), representing the output features, corresponding to the input features.

[0065] (3) Convolutional layer: used to gradually extract input features. 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 step size. 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 speed up the training process and improve the stability of the model, making the input distribution of each layer more stable.

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

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

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

[0070] This structural design enables the conditional generative adversarial network to effectively generate high-quality samples under given conditions. The connection relationship and information flow of each part can be more intuitively understood by combining the attached figure.

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

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

[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 They are adversarial loss, reconstruction loss and other losses, λ adv ,λ recon and λ precThey control the relative contributions of adversarial loss, reconstruction loss and other losses respectively. Other losses are selected as perceptual loss in this example. Hyperparameters are used to control the relative weights of adversarial loss, reconstruction loss and perceptual loss respectively. These weight coefficients can be tuned according to experimental results. adv ,λ recon and λ prec The values ​​are assigned to 0.2, 0.6 and 0.2 respectively. In order to ensure that the generator can stably learn the basic generation rules in the early stage of training, a larger weight is given to the reconstruction loss in the early stage of training; in the later stage of training, when the loss function L total When it tends to be stable, gradually increase the weight of the adversarial loss, λ adv From 0.2 to 0.5, λ recon From 0.6 to 0.3, thus improving the fidelity and detail quality of generated far-field samples.

[0075] Step 6: Figure 3 This is the simulation result of a monoconical antenna, which is not included in the test data set for neural network training. The antenna operates at 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, the traditional fast Fourier transform method and the proposed neural network-based method are used for near-field to far-field conversion, and the sparse sampling interval of the near field is 15 degrees. Figure 3 (a) and Figure 3 (b) is a comparison of the reference far-field pattern of the monoconical antenna, and the far-field results on the XOZ and YOZ planes using the traditional method and the proposed method. The results show that the proposed method has good effectiveness. The far-field pattern generated by the proposed method is highly consistent with the reference pattern, accurately capturing the main lobe and side lobe characteristics, while the traditional method shows obvious deviations in the side lobe region. Although this antenna does not appear in the training set, the proposed method is still able to reconstruct complex radiation patterns with high fidelity.

[0076] Step 7: To verify the robustness of the proposed algorithm, a horn antenna operating at 4-6 GHz was actually tested in a 23-probe spherical near-field chamber with a sparse near-field sampling interval of 15 degrees. The frequency band of the antenna exceeds the range of 0.1-2 GHz in the test set. The reference pattern was obtained by three times oversampling (sampling interval of 5 degrees) in the near-field test. Figure 4 (a) and Figure 4 (b) Comparison of the reference and the directional maps reconstructed based on fast Fourier transform and neural network in the XOZ and YOZ planes.

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

[0078] Despite these potential sources of error, the neural network-based approach significantly outperforms traditional methods in reconstructing far-field patterns from sparse near-field measurement data. Its ability to generalize to frequencies outside the training range, combined with its superior performance in capturing complex radiation signatures, makes it a powerful solution for far-field reconstruction.

Claims

1. A sparse sampling antenna far-field pattern reconstruction method based on neural network and spherical wave mode expansion, characterized in that: The steps include: Step 1: Use a sparse sampling scheme to perform sparse near-field sampling on all sample antennas to obtain near-field data; Step 2: Performing test sample enhancement on the near-field data to obtain enhanced near-field data; Step 3: Perform inverse Fourier transform on the enhanced near-field data based on the spherical wave expansion principle to obtain spherical wave expansion coefficients: Step 4: Calculate the low-precision far field based on the spherical wave expansion theorem and the spherical wave expansion coefficients solved in step 3: Step 5: Perform a far-field test on the sample antenna in step 1 to obtain an ideal far-field pattern, use the low-precision far field calculated in step 4 as input, and use the ideal far-field pattern of the sample antenna as output to build and train a neural network; Step 6: Optimize the loss function of the weighted combination used in neural network training; Step 7: Combine the physical model with the neural network to reconstruct the far-field pattern of the antenna under test.

2. The method for reconstructing far-field patterns of sparsely sampled 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: A sparse sampling scheme is used to collect the spherical near-field data of M sample antennas. The sampling is uniformly performed at three times the traditional Nyquist sampling interval requirement of M antennas. Each antenna obtains a set of sparse near-field sampling data, and M antennas obtain M sets of data. Based on the Nyquist theorem, the sampling intervals in the θ and φ directions are Δθ1 and Δφ1. The sampling intervals in the θ and φ directions of this sparse sampling scheme are 3Δθ1 and 3Δφ1. The sampling intervals in θ and φ are three times that of the traditional method, respectively. 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 method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave mode expansion according to claim 2, characterized in that: The step 2 is specifically as follows: The near-field data obtained in step 1 is the radiated near-field of the antenna. With the center of the antenna, all the radiated near-fields of the antenna in step 1 are rotated by m1 angles along the x-axis, y-axis, and z-axis respectively to generate samples under different viewing angles and expand the training data from the original M groups of data to 3m1M groups of near-field data.

4. The method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave mode expansion according to claim 3, characterized in that: The step 3 is specifically as follows: According to the spherical wave mode expansion principle, the near-field data of the 3m1M group in step 2 is subjected to inverse Fourier transform based on the spherical wave expansion principle to obtain the spherical wave expansion coefficients. [a mn ,b mn ]=IDFT{E(r,θ,φ),n=1,…,N,m=-n,…,0,…n} Among them, the truncation number of the spherical wave expansion coefficient is N = 180 / (3Δθ1), E(r,θ,φ) is the near field of the antenna under test on a sphere with a radius of r, and a mn and b mn is the spherical wave expansion coefficient; m and n are the mode numbers of spherical wave expansion, n = 1, ..., N, m = -n, ..., 0, ..., n.

5. The method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave mode expansion according to claim 4, characterized in that: The step 4 is specifically as follows: According to the spherical wave expansion theorem and the spherical wave expansion coefficient a solved in step 3 mn and b mn Interpolating the sparsely sampled near field Among them, mn and N mn It is the spherical wave generating function. The sampling intervals of the low-precision far field in the θ and φ directions are Δθ2 and Δφ2, corresponding to the angles θ2=0:Δθ2:180° and φ2=0:Δφ2:360°. Δθ2 and Δφ2 are less than Δθ1 / 3 and Δφ1 / 3, respectively.

6. The method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave mode expansion according to claim 5, characterized in that: The step 5 is specifically as follows: Perform far-field tests on the M antennas in step 1, with sampling intervals of Δθ2 and Δφ2 in the θ and φ directions respectively. Use the same angle as in step 2 to rotate and obtain 3m1M groups of ideal high-precision far-field patterns. This data is used as the output of the neural network. The low-precision far-field patterns in step 4 are used as the input of the neural network. The neural network is used to reconstruct the low-precision far-field patterns and learn the mapping relationship between them and the ideal far-field patterns. The final far-field pattern reconstruction result is obtained through neural network training.

7. The method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave mode expansion according to claim 6, characterized in that: The step 6 is specifically as follows: In the neural network training, a weighted combination of loss functions 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 They are adversarial loss, reconstruction loss and other losses, λ adv ,λ recon and λ prec They respectively control the relative contributions of adversarial loss, reconstruction loss and other losses. Other losses are selected according to the specific training model.

8. The method for reconstructing far-field patterns of sparsely sampled antennas based on neural networks and spherical wave mode expansion according to claim 7, characterized in that: The step 7 is specifically as follows: For the antenna to be tested that does not belong to 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, and then the low-precision far field is embedded in the neural network that has been trained in step 6 to reconstruct the far-field radiation pattern of the antenna to be tested.

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