Reverse design method of non-uniformly modulated holographic metasurface antenna based on mixed density network

Abstract

The invention discloses a reverse design method for a non-uniformly modulated holographic metasurface antenna based on a mixed density network (MDN). The method comprises the following steps: firstly, acquiring a voltage standing wave ratio (VSWR) and a far-field pattern of a target antenna, and taking the VSWR and the far-field pattern as a reversely designed target electromagnetic response; inputting the target response into a reverse prediction model constructed by a mixed density network, and obtaining multiple groups of candidate structure parameters required by non-uniform modulation through multi-modal probability distribution output by the model; further selecting an optimal parameter combination according to the similarity between the electromagnetic response corresponding to the candidate parameters and the target response; and finally, the parameters are used for generating the non-uniformly modulated holographic metasurface antenna structure. According to the method, the one-to-many problem in reverse design is solved by using the mixed density network, an automatic design process of target electromagnetic response-non-uniform modulation parameter-antenna structure is realized, and a holographic metasurface antenna structure with high aperture efficiency can be directly obtained.

Description

Technical Field

[0001] This invention relates to the fields of antenna engineering technology and artificial intelligence technology, specifically to a reverse design method for holographic metasurface antennas based on non-uniform modulation of hybrid density networks, which is particularly suitable for high-aperture-efficiency design of holographic metasurface antennas based on automatically generating non-uniform modulation parameters based on the target electromagnetic response. Background Technology

[0002] With the advent of the information age, especially the development of 5G, 6G, and future higher-frequency communication technologies, antennas, as a core component of wireless communication systems, are playing an increasingly important role. Holographic metasurface antennas utilize subwavelength structures to precisely control the phase, amplitude, and propagation direction of electromagnetic waves, achieving highly flexible beam control and efficient radiation characteristics. Compared to traditional antennas, holographic metasurface antennas often employ the same processing techniques and fabrication processes as traditional microstrip antennas, eliminating the need for complex feeding networks. They not only provide higher performance within a smaller size but also possess exceptional design flexibility, adapting to the needs of different frequency bands and application scenarios. However, despite their numerous theoretical advantages, existing design methods still suffer from many problems, particularly in antenna aperture efficiency, polarization control, and optimization algorithms. These methods still rely heavily on electromagnetic simulation calculations and engineering experience, resulting in low design efficiency and complex optimization processes, thus limiting their widespread adoption in practical applications.

[0003] Deep learning, as a multi-layer neural network modeling technique, possesses powerful feature extraction and nonlinear mapping capabilities and has been widely applied in fields such as image recognition, natural language processing, and scientific computing. Deep neural networks can learn complex relationships between inputs and outputs through a large number of samples and provide prediction results with extremely low computational cost during the inference stage. Therefore, it also demonstrates significant advantages in the electromagnetic field, which requires extensive numerical computation or parameter search. In recent years, deep learning has been increasingly applied to antenna design, including rapid prediction of radiation characteristics, structural parameter optimization, and replacement of full-wave simulations. The common approach is to use deep learning to build a forward model, i.e., inputting structural parameters and outputting the antenna's electromagnetic response, thereby significantly reducing the number of full-wave simulations. In addition, some research has explored constructing inverse design models, i.e., directly predicting structural parameters based on the target electromagnetic performance. However, inverse design problems often have a one-to-many mapping characteristic: multiple different antenna structures may produce similar electromagnetic responses, leading to problems such as prediction ambiguity, unstable results, and unrealizable structures in traditional single-value regression networks. Furthermore, deep learning still requires a large amount of high-quality training data. In the case of non-uniform modulation, the cost of generating datasets using full-wave simulation is extremely high. Therefore, how to construct an efficient, stable inverse model that can handle multiple solutions has become a current research hotspot. Summary of the Invention

[0004] Existing holographic metasurface antennas still rely heavily on electromagnetic simulations and manual parameter tuning during the design process. This is especially true when using non-uniform modulation, where the modulation parameters and antenna radiation performance exhibit highly nonlinear coupling, resulting in extremely high optimization complexity. Furthermore, the one-to-many mapping between the target electromagnetic response and structural parameters in reverse engineering makes it difficult for traditional deep learning models to stably predict structural parameters. This leads to non-unique, unstable, or even unrealizable output structures, thus limiting the practical application of reverse engineering methods in the design of high-aperture-efficiency holographic metasurface antennas.

[0005] The purpose of this invention is to provide a reverse design method for holographic metasurface antennas based on non-uniform modulation using a hybrid density network. By constructing a multi-mode reverse prediction model, the method solves the problem of multiple solutions in reverse design. Based on the target VSWR and radiation pattern, the non-uniform modulation parameters a and b are automatically predicted, thereby enabling the rapid generation of high-aperture-efficiency holographic metasurface antenna structures, improving antenna design efficiency and reducing electromagnetic simulation costs.

[0006] To achieve the above objectives, this invention provides a reverse design method for a holographic metasurface antenna based on non-uniform modulation using a hybrid density network, comprising the following steps:

[0007] S1. Obtain target electromagnetic performance indicators: The target electromagnetic performance indicators include the target voltage standing wave ratio (VSWR) curve data and the target far-field radiation pattern data of the antenna to be designed;

[0008] S2. Constructing a reverse design training dataset: Through electromagnetic simulation calculations, a large number of sample pairs containing structural modulation parameters (a,b) and their corresponding VSWR curves and far-field radiation patterns are generated to form a training dataset.

[0009] S3. Constructing a reverse-engineered neural network model: The model adopts a deep neural network architecture, including a multi-head encoder module for extracting VSWR and pattern features respectively, a feature fusion module for integrating features, and a hybrid density network (MDN) module for outputting the probability distribution of parameters.

[0010] S4. Training the reverse design neural network model: Supervised learning training of the model is performed using the training dataset to optimize the model parameters to minimize the negative log-likelihood error between the predicted probability distribution and the true parameter distribution.

[0011] S5. Perform reverse prediction: Input the target electromagnetic performance index from step S1 into the trained neural network model. The model outputs the mixture Gaussian distribution parameters of the structural modulation parameters (a,b), and selects the optimal modulation parameters according to the maximum probability principle.

[0012] S6. Generate holographic modulation distribution: Substitute the predicted optimal modulation parameters into the non-uniform modulation function M(r) to calculate the modulation depth distribution at each point on the aperture surface of the holographic metasurface.

[0013] S7. Constructing the antenna physical structure: Based on the principle of holographic interference, the impedance distribution Zs of the aperture target surface is calculated using the modulation depth distribution M(r), and the geometric dimensions of the metasurface unit are calculated by inversion based on the impedance distribution to construct the final holographic metasurface antenna structure model.

[0014] The reverse design method for holographic metasurface antennas based on hybrid density neural networks, specifically requires the following in step S1: [Details of obtaining target electromagnetic performance indicators are missing from the provided text.]

[0015] The sampling frequency band of the VSWR curve data covers 11GHz to 13GHz, with equal step frequency sampling. The sampling method for the target far-field radiation pattern data is as follows: a fixed azimuth angle phi section is selected, for example, phi = 45°, and equal step angle sampling is performed within the range of elevation angle theta = [0°, 90°]. The collected far-field pattern amplitude data is normalized and mapped to the interval to eliminate the influence of absolute gain value on beam shape feature extraction.

[0016] The reverse design method for holographic metasurface antennas based on hybrid density neural networks, in step S2, defines the non-uniform modulation parameters (a,b) and expresses the non-uniform modulation function M(r) as follows:

[0017]

[0018] Where r represents the radial distance from a point on the aperture plane to the center of the antenna, r max The maximum radius of the holographic metasurface aperture is represented by ; parameter a is the modulation amplitude coefficient, which is used to control the saturation value of the modulation depth on the aperture surface, and the preferred value range is [0.1, 1.0]; when constructing the dataset, discretization sampling is performed within the value range of a and b to generate multiple (a, b) combinations.

[0019] The reverse design method for a holographic metasurface antenna based on a hybrid density neural network, wherein the specific structural features of the reverse-designed neural network model in step S3 include: the multi-head encoder module contains two parallel feature extraction branches: the first encoder branch is configured as a one-dimensional convolutional neural network (1D-CNN), specifically used to process the input VSWR frequency domain sequence and extract impedance bandwidth and matching characteristic features; the second encoder branch is configured as a multilayer perceptron (MLP), specifically used to process the input far-field radiation pattern and extract main lobe width, sidelobe level and beam pointing features; the feature fusion module is configured as a concatenate layer and a subsequent fully connected layer, used to perform dimensional concatenation and nonlinear mapping on the feature vectors output by the first encoder branch and the second encoder branch to generate a latent space feature vector containing multi-physics integrated information of the antenna.

[0020] The reverse design method for a holographic metasurface antenna based on a hybrid density neural network (MDN) is described above. The output layer structure and parameter selection method of the MDN module are as follows:

[0021] The MDN module outputs a set of parameters for a Gaussian mixture model (GMM), specifically including the mixing coefficients α of the K Gaussian components. k The mean vector μk and variance σk or covariance matrix Σ k The mixing coefficients satisfy the normalization constraint:

[0022]

[0023] In step S5, the method for selecting the optimal modulation parameters includes: calculating the mean μk of the Gaussian component with the largest mixing coefficient α_k as the prediction result.

[0024] The reverse design method for holographic metasurface antennas based on hybrid density neural networks, wherein the calculation of the target surface impedance distribution Zs in step S7 can be expressed as:

[0025]

[0026] Where j is the imaginary unit, X is the average surface reactance of the holographic metasurface, M(r) is the non-uniform modulation depth distribution calculated in step S6, and Re represents the operation of taking the real part. Let be the field distribution function of the target radiation beam on the aperture surface; The field distribution function of the reference wave (feed wave) on the aperture surface is given by *, where * denotes conjugate operation; the final steps for constructing the final antenna physical structure model include: establishing a mapping formula between the geometry of the metasurface unit (width of the metasurface unit patch) and the surface impedance value;

[0027] Z s =10.8g 3 +557.6g 2 -1167.2g +792.3g

[0028] Based on the calculated Zs, the specific geometric dimensions of each element on the aperture surface are inverted and calculated.

[0029] Furthermore, a holographic metasurface antenna is constructed to obtain the corresponding structure; its radiation performance can then be verified through simulation to determine whether it meets the target requirements.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] This invention achieves automated acquisition of non-uniform modulation parameters for holographic metasurface antennas by constructing a multi-head coding-fusion-hybrid density network inverse prediction model oriented towards voltage standing wave ratio and radiation pattern targets. This effectively solves the problems of traditional methods, such as reliance on extensive electromagnetic simulations, low optimization efficiency, and difficulty in handling one-to-many mappings in reverse design. This invention can directly predict modulation parameters a and b from the target electromagnetic response and generate a complete non-uniform modulation impedance distribution accordingly. This method reduces reliance on human experience in the design process, significantly improves design efficiency and structural stability, and provides an implementable and scalable intelligent design scheme for the rapid design and engineering application of high-aperture efficiency holographic metasurface antennas. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the overall process of the reverse design method provided by the present invention;

[0033] Figure 2 This invention relates to a physical structure decomposition and unit geometry schematic diagram of a holographic metasurface antenna.

[0034] Figure 3 This is a schematic diagram illustrating the parameter control characteristics of the non-uniform modulation function M(r) and its influence on the holographic impedance distribution.

[0035] Figure 4 It is a two-dimensional holographic impedance distribution map;

[0036] Figure 5 This is a graph showing the mapping relationship between the surface impedance value Zs of a holographic metasurface unit and the geometric gap g between the units;

[0037] Figure 6The figure shows the simulation results of an embodiment of the present invention. Detailed Implementation

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] The design of holographic antennas is inspired by holographic optics. Its core idea is to use surface waves excited by the feed source as a reference wave. The aperture field corresponding to the desired far-field radiation pattern is taken as the target wave. According to the principle of holographic interference, the interference pattern records all the phase and amplitude information of the target wave. In the microwave frequency band, this interference pattern is physically realized as a scalar surface impedance distribution Zs on the aperture surface:

[0040]

[0041] Where j is the imaginary unit, X is the average surface reactance of the holographic metasurface, M(r) is the non-uniform modulation depth distribution calculated in step S6, Re represents the real part operation, and * represents the conjugate operation;

[0042] Field distribution function of the target radiated beam on the aperture surface Field distribution function of the reference wave on the aperture surface

[0043] Traditional holographic antenna designs typically employ uniform modulation M(r) = Const. However, due to the continuous energy leakage of surface waves as they propagate from the center to the edges, the field strength on the aperture surface decays exponentially. This non-uniform aperture field distribution leads to main lobe broadening, gain reduction, and low aperture efficiency.

[0044] This invention introduces a parameterized non-uniform modulation function, such as Figure 3 As shown. This function aims to compensate for the propagation loss of surface waves and increase the radiation intensity at the edges. Its mathematical expression is defined as:

[0045]

[0046] Where r represents the radial distance from a point on the aperture plane to the center of the antenna, r maxThe maximum radius of the holographic metasurface aperture is represented by ; parameter a is the modulation amplitude coefficient, preferably ranging from [0.1, 1.0]. It controls the saturation value of the modulation depth, determining the overall radiation efficiency and dynamic range of impedance variation of the antenna. Its preferred value range is [1.0, 10.0]. It controls the rate at which the modulation depth increases with increasing radius. A larger b results in a faster increase in modulation depth in the central region, suitable for scenarios where energy is mainly concentrated in the center; a smaller b results in a more gradual increase in modulation depth, helping to push energy towards the aperture edge, thereby improving aperture efficiency.

[0047] The performance of deep learning models is highly dependent on the quality and coverage of the training data. This embodiment details the forward data generation process for "structural parameters - electromagnetic properties," corresponding to... Figure 1 The data construction part.

[0048] To construct a representative dataset, we need to scan within the feasible region of (a, b). Considering the computational cost of electromagnetic simulation, we adopt constant-step grid sampling.

[0049] Parameter a: Samples within the interval [0.1, 0.8] with a step size of 0.01. Parameter b: Samples within the interval [1.0, 10.0] with a step size of 0.1.

[0050] Automated control is achieved using electromagnetic simulation software (such as ANSYS HFSS) and scripts (such as a Python interface). For each group (ai, bi), the following simulation procedure is executed:

[0051] (1) Impedance distribution generation: Substitute (ai,bi) into the above non-uniform modulation formula to calculate the impedance distribution matrix Zs(x,y) of the full aperture.

[0052] (2) Physical structure mapping: based on Figure 5 The "impedance-geometry" mapping shown converts the impedance value Zs into the specific cell gap g.

[0053] Z s =10.8g 3 +557.6g 2 -1167.2g +792.3g

[0054] (3) Modeling and solving: Automatically generate an antenna array model containing thousands of elements and perform simulation and solving.

[0055] (4) Data extraction: VSWR data was uniformly sampled at 21 frequency points within the range of 11-13 GHz. The far-field gain at the center frequency (12 GHz) was extracted. A phi = 45° section was selected, and samples were taken every 2° within the range of theta = [0°, 90°], for a total of 46 points.

[0056] Raw electromagnetic data has different dimensions and orders of magnitude, and directly inputting it into a neural network can lead to unstable gradient updates. Therefore, rigorous preprocessing is necessary.

[0057] First, for VSWR data, a logarithmic transformation x′=log(x) is used to improve numerical smoothness, making it easier for the network to extract the features of VSWR as a function of frequency.

[0058] Secondly, the directional pattern data needs to be normalized to its maximum value. The normalization method is as follows:

[0059]

[0060] Finally, the output modulation parameter labels (a, b) need to be Z-score normalized, i.e.:

[0061]

[0062] The final dataset consists of triples:

[0063] Figure 1 The deep neural network architecture shown is illustrated. The multi-head feature encoder network input is designed with a dual-stream parallel structure. The VSWR encoder head uses a three-layer 1D-CNN with a MaxPool structure; the pattern encoder head uses an MLP. LeakyReLU is used for all activation functions.

[0064] Next is the feature fusion module, which first integrates the output vectors of the two encoders using a concatenation strategy, and then inputs the concatenated vector into a fully connected layer for nonlinear combination using the LeakyReLu activation function.

[0065] Finally, there is the Mixture Density Network (MDN) output layer: this layer outputs the conditional probability density function parameters, assuming the distribution consists of K Gaussian components. The MDN itself is a fully connected layer, and its output is divided into three parts: the mixing coefficients are processed by the Softmax activation function to ensure the weights sum to 1; the mean vector has no activation function and corresponds to the center of each Gaussian distribution (i.e., possible parameter combinations); the standard deviation is guaranteed to be positive by the Softplus activation function, reflecting the uncertainty of the prediction.

[0066] The loss function is defined as the negative log-likelihood (NLL):

[0067]

[0068] This embodiment describes the operational steps for designing a practical antenna using a trained model:

[0069] S1. Define the target electromagnetic parameters and input the design target according to actual needs.

[0070] S2. MDN inverse inference inputs the target vector into the trained network. After forward propagation, the network outputs a set of GMM parameters.

[0071] S3. Optimal Parameter Decision: Since the output is a multimodal distribution, the optimal modulation parameters are selected based on the principle of maximum probability.

[0072] S4. Holographic impedance distribution calculation: Using the predicted (apred,bpred), substitute them into the holographic formula to calculate the complex impedance Zs at each position (x,y) on the aperture surface.

[0073] S5. Basis for Physical Structure Inversion Figure 5 The Zs-g mapping relationship transforms the impedance distribution into a geometric distribution.

[0074] S6. Modeling and Verification: Automated modeling is performed using Python scripts, and verification simulations are conducted in HFSS.

[0075] Figure 6 This diagram illustrates the three-dimensional radiation pattern, maximum radiation pattern, and voltage standing wave ratio (VSWR) of an embodiment of the present invention. The radiation pattern shows that at 12 GHz, the motherboard's radiation direction (θ, φ) is (33°, 45°), the gain is 18.31 dBi, the VSWR is less than 2 in the range of 11.2 GHz to 13.11 GHz, and the aperture efficiency is 43.56%.

[0076] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. After reading the above content, various modifications and substitutions of the present invention will be obvious to those skilled in the art. Therefore, any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A holographic metasurface antenna inverse design method based on a hybrid density neural network, characterized in that, The method comprises the following steps: S1, obtaining target electromagnetic performance indicators: the target electromagnetic performance indicators include target voltage standing wave ratio (VSWR) curve data and target far-field radiation pattern data of an antenna to be designed; S2, constructing a reverse design training data set: a large number of sample pairs containing structure modulation parameters (a, b) and corresponding VSWR curves and far-field patterns are generated through electromagnetic simulation calculation to form a data set for training; S3, constructing a reverse design neural network model: the model adopts a deep neural network architecture, including a multi-head encoder module for extracting VSWR and pattern features respectively, a feature fusion module for integrating features, and a mixture density network (MDN) module for outputting parameter probability distribution; S4, training the reverse design neural network model: the model is supervised learning trained by using the training data set, and the model parameters are optimized to minimize the negative log-likelihood error between the predicted probability distribution and the real parameter distribution; S5, performing reverse prediction: the target electromagnetic performance indicators in step S1 are input into the trained neural network model, the model outputs the mixture Gaussian distribution parameters of the structure modulation parameters (a, b), and the optimal modulation parameters are selected according to the maximum probability principle; S6, generating a holographic modulation distribution: the optimal modulation parameters predicted are substituted into the non-uniform modulation function M(r) to calculate the modulation depth distribution of each point on the aperture surface of the holographic metasurface; S7, constructing an antenna physical structure: based on the holographic interference principle, the modulation depth distribution M(r) is used to calculate the target surface impedance distribution Zs of the aperture surface, and the geometric size of the metasurface unit is calculated according to the impedance distribution inversion to construct the final holographic metasurface antenna structure model.

2. The holographic metasurface antenna inverse design method based on a hybrid density neural network according to claim 1, characterized in that, In step S2, the non-uniform modulation parameters (a, b) are defined and the expression of the non-uniform modulation function M(r) is as follows: wherein r represents the radial distance from a point on the aperture plane to the center of the antenna, r max represents the maximum radius of the holographic metasurface aperture; the parameter a is a modulation amplitude coefficient for controlling the saturation value of the modulation depth on the aperture plane, and the value range is preferably [0.1, 1.0]; when constructing the data set, discretization sampling is performed within the value range of a and b to generate multiple sets of (a, b) combinations.

3. The holographic metasurface antenna inverse design method based on hybrid density neural network according to claim 1, characterized in that, In step S3, the specific structure of the reverse design neural network model includes: the multi-head encoder module (Multi-head Encoder) contains at least two parallel feature extraction branches: the first encoder branch is configured as a one-dimensional convolutional neural network (1D-CNN) and is specially used for processing the input VSWR frequency domain sequence to extract impedance bandwidth and matching characteristic features; the second encoder branch is configured as a multi-layer perceptron (MLP) and is specially used for processing the input far-field pattern to extract main lobe width, side lobe level and beam pointing features; the feature fusion module (Feature Fusion Module) is configured as a connection layer (Concatenate Layer) and a subsequent fully connected layer, which is used for dimension splicing and nonlinear mapping of the feature vectors output by the first encoder branch and the second encoder branch to generate an implicit space feature vector containing multi-physical field comprehensive information of the antenna.

4. The holographic metasurface antenna inverse design method based on a hybrid density neural network according to claim 4, characterized in that, The output layer structure and parameter selection method of the hybrid density network (MDN) module are as follows: the MDN module outputs a set of parameters of a Gaussian mixture model (GMM), specifically including the mixing coefficients α of K Gaussian components. k mean vector μ k and variance σ k Or the covariance matrix Σk, wherein the mixing coefficients satisfy the normalization constraint: In step S5, the method of selecting the optimal modulation parameters includes: calculating the mean μk of the Gaussian component with the maximum mixing coefficient α_k as the prediction result.

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