X-band broadband high-gain radar metasurface antenna and design method thereof

Abstract

The application provides an X-band broadband high-gain radar metasurface antenna and a design method thereof. The metasurface antenna comprises, from top to bottom, a metasurface layer, an intermediate metal layer and a lower microstrip feed line layer. The metasurface layer comprises at least one metasurface unit. An asymmetric chamfer structure is designed on each metasurface unit. A center fork-shaped slot is arranged at the center of each metasurface unit, and four embedded parasitic branches are arranged at four side edges, respectively. Rectangular coupling slots corresponding to each metasurface unit are arranged on the intermediate metal layer. Feed lines corresponding to each metasurface unit are arranged on the lower microstrip feed line layer. The design method provided in the application can improve the design efficiency.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of antenna design and deep learning, specifically to a fully intelligent design method for radar metasurface antennas based on DeepONet operator learning, and an X-band broadband high-gain metasurface radar antenna designed based on this method, which is suitable for high-performance radar systems in fields such as meteorological monitoring and autonomous driving. Background Technology

[0002] Modern radar systems are rapidly evolving towards multi-functional integration, high-resolution imaging, and rapid iterative research and development, placing stringent demands on both electromagnetic performance indicators such as antenna bandwidth and gain, as well as research and design efficiency. Metasurfaces, as a planar realization of electromagnetic metamaterials, allow for precise control of the phase, amplitude, and polarization of electromagnetic waves through periodically arranged subwavelength units. They can effectively broaden the operating bandwidth and improve radiation gain on a low-profile structure, and have now become the mainstream technology for X-band radar antennas.

[0003] Most publicly reported X-band metasurface antennas currently employ a symmetrical square, single-slot simple element structure. This results in limited element adjustability and an inherent performance contradiction between bandwidth, gain, and radiation efficiency. Firstly, the completely symmetrical metallic element has a single current distribution pattern, capable of exciting only a single resonant mode. Lacking the additional tuning freedom provided by the asymmetrical chamfered structure, it cannot flexibly adjust the resonant position to achieve wideband impedance matching, thus limiting its bandwidth expansion capability. Secondly, the lack of a central forked long slot in the element results in a short effective current path, making it difficult to excite multiple adjacent resonant modes and limiting operation to narrowband. Forcibly widening the operating bandwidth directly leads to a significant decrease in in-band gain and radiation efficiency. These inherent defects in the element configuration make it difficult for existing X-band metasurface antennas to simultaneously achieve wideband, high gain, and high radiation efficiency.

[0004] Meanwhile, there is a strong nonlinear coupling between the electromagnetic response of metasurface antennas and the geometric parameters of their elements. A single element typically contains 5 to 8 independent size variables. When simultaneously optimizing multiple indicators such as bandwidth, gain, and efficiency, the parameter design space expands exponentially. Traditional antenna design relies entirely on engineers' experience combined with repetitive parameter scanning, which not only results in long development cycles and high manpower and simulation costs, but also easily converges to local optima in multi-parameter, multi-objective optimization scenarios, making it difficult to obtain a globally optimal structure. This has become a core bottleneck restricting the iterative upgrade of high-performance radar antennas.

[0005] Deep learning, with its superior nonlinear mapping capabilities, has provided a new approach to intelligent antenna design. Models such as fully connected networks and convolutional neural networks have been gradually applied to antenna electromagnetic response prediction and structural optimization. However, existing deep learning solutions still have several engineering shortcomings: most models can only output electromagnetic values ​​at discrete frequencies and cannot fully fit the continuous frequency prediction response curve; for electromagnetic signals with high-frequency oscillation characteristics such as S11, the fitting accuracy of conventional ReLU activation networks cannot meet engineering standards, and spurious oscillations and amplitude deviations are easily generated near the resonant frequency; at the design level, existing research mostly adopts the scheme of directly mapping performance indicators to structural parameters, which is prone to generating physically invalid solutions with size interference and unmanufacturable structures, and lacks an integrated optimization framework that can unify and accommodate multiple engineering constraints such as bandwidth, center frequency, gain, and radiation efficiency.

[0006] In summary, existing X-band metasurface antennas generally suffer from shortcomings in overall performance: traditional designs employing metasurface loading, graded refractive index, and characteristic mode analysis can only optimize bandwidth or gain individually, making it difficult to simultaneously improve the three core performance indicators. This fails to meet the stringent requirements of high-performance radar for the comprehensive electromagnetic performance of antennas. In the forward simulation prediction stage, conventional deep neural network surrogate models have bottlenecks in fitting the accuracy of oscillating frequency domain curves such as S-parameters, and resonant point prediction is prone to distortion, making it difficult for the model's reliability to support high-precision antenna optimization. In the reverse structural optimization stage, existing research mostly focuses on optimizing single indicators such as radar cross-section reduction, beamforming, and polarization control. Multi-objective design methods that can simultaneously constrain the four engineering indicators of target absolute impedance bandwidth, center frequency, minimum in-band gain, and minimum in-band radiation efficiency are extremely rare, and the robustness of existing optimization frameworks in handling multi-constraint global optimization still has significant room for improvement. Summary of the Invention

[0007] The purpose of this invention is to provide an X-band broadband high-gain radar metasurface antenna and its design method. By introducing embedded parasitic stubs, central forked slots, and asymmetric chamfered structures, the structure of the X-band broadband high-gain radar metasurface antenna is optimized. At the same time, a design method based on DeepONet operator learning is provided.

[0008] To achieve the above objectives, this technical solution provides an X-band broadband high-gain radar metasurface antenna, comprising: The layers are designed from top to bottom: a metasurface layer, an intermediate metal layer, and a lower microstrip feed layer. The metasurface layer includes at least one metasurface unit, each metasurface unit is designed with an asymmetric chamfer structure, and each metasurface unit has a central fork-shaped slit in the center and embedded parasitic branches on the four sides respectively. The intermediate metal layer has rectangular coupling slots corresponding to each metasurface unit. The lower microstrip feeder layer has feed lines corresponding to each metasurface unit.

[0009] Compared with existing technologies, this technical solution has the following characteristics and beneficial effects: This design for an X-band broadband high-gain radar metasurface antenna employs a composite configuration of diagonally asymmetrical chamfers, a central forked slot, and four-sided embedded parasitic stubs. The asymmetrical chamfers expand the impedance tuning freedom, the forked slots extend the current path to excite multiple neighboring resonances for broadbanding, and the parasitic stubs enhance multi-mode coupling to simultaneously improve in-band gain and radiation efficiency. Combined with a 4×4 periodic array, the radiation aperture is expanded to raise the peak gain. This results in a high relative bandwidth of 34.84%, a peak gain of 10.43 dBi, and a center frequency efficiency of 89.5%. The efficiency across the entire frequency band is consistently above 70%, exhibiting excellent directional radiation performance. This design overcomes the bottleneck of traditional symmetrical elements where bandwidth, gain, and efficiency are difficult to improve simultaneously, making it suitable for various high-performance X-band radar systems.

[0010] The proposed design method for X-band broadband high-gain radar metasurface antennas utilizes a shared branch network to uniformly encode the geometric parameters of the six-dimensional metasurface unit. Two types of backbone networks, SIREN and ReLU, are used to fit the high-frequency oscillation S11 curve and smooth the gain and efficiency curves, respectively. Curvature smoothing loss is introduced to suppress pseudo-oscillations in the resonant region, enabling precise capture of subtle electromagnetic changes in multi-mode composite units. Shared feature encoding reduces redundant parameter training, and joint training based on total loss establishes the physical correlation between the three types of electromagnetic responses. Compared to traditional single-frequency neural networks and multiple independent DeepONet models, this method significantly improves both continuous frequency domain prediction accuracy and training efficiency.

[0011] Furthermore, this solution embeds the trained DeepONet forward proxy prediction model into the differential evolution algorithm, and combines it with intelligent bandwidth identification, hierarchical penalty mechanism and smooth quadratic penalty function to complete multi-constraint inverse optimization. It reduces the dimensionality of the complex full-frequency response curve to four feature parameters: center frequency, bandwidth, minimum in-band gain and minimum efficiency, which greatly reduces the computational overhead. The hierarchical penalty decouples the constraint conflict between bandwidth expansion and center frequency calibration, and the built-in geometric verification automatically filters physically unrealizable structures. Only four engineering indicators need to be input to output the optimal unit size without manual intervention, compressing the traditional design cycle of several days to minutes, and realizing end-to-end automated global optimization of metasurface antennas. Attached Figure Description

[0012] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1This is a structural diagram of an X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0013] Figure 2 This is a structural diagram of the metasurface layer of an X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0014] Figure 3 This is a structural diagram of the intermediate metal layer of an X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0015] Figure 4 This is a structural diagram of the lower microstrip feed layer of an X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0016] Figure 5 This is a side view of the X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0017] Figure 6 This is a graph of the S11 parameters of an X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0018] Figure 7 This is a gain curve diagram of an X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0019] Figure 8 This is a radiation efficiency curve of an X-band broadband high-gain radar metasurface antenna according to an embodiment of this application.

[0020] Figure 9 This is a three-dimensional far-field radiation pattern of an X-band broadband high-gain radar metasurface antenna at a center frequency of 10.25 GHz, according to an embodiment of this application.

[0021] Figure 10 This is a two-dimensional radiation pattern of the E-plane of an X-band broadband high-gain radar metasurface antenna at a center frequency of 10.25 GHz, according to an embodiment of this application.

[0022] Figure 11 This is a logical diagram of the DeepONet forward proxy prediction model.

[0023] Figure 12 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with one or more embodiments of this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of one or more embodiments of this specification as detailed in the appended claims.

[0025] It should be noted that the steps of the corresponding methods are not necessarily performed in the order shown and described in this specification in other embodiments. In some other embodiments, the methods may include more or fewer steps than described in this specification. Furthermore, a single step described in this specification may be broken down into multiple steps in other embodiments; and multiple steps described in this specification may be combined into a single step in other embodiments.

[0026] Example 1 like Figure 1 and Figure 5 As shown, Figure 1 This solution provides an X-band broadband high-gain radar metasurface antenna, including: The layers are designed from top to bottom: a metasurface layer, an intermediate metal layer, and a lower microstrip feed layer. The metasurface layer includes at least one metasurface unit, each metasurface unit is designed with an asymmetric chamfer structure, and each metasurface unit has a central fork-shaped slit in the center and embedded parasitic branches on the four sides respectively. The intermediate metal layer has rectangular coupling slots corresponding to each metasurface unit. The lower microstrip feeder layer has feed lines corresponding to each metasurface unit.

[0027] It is worth mentioning that the X-band broadband high-gain radar metasurface antenna of this scheme effectively extends the surface current path and excites multiple adjacent resonant modes by introducing embedded parasitic stubs, a central forked slot, and an asymmetric chamfered structure. More specifically, the asymmetric structure on the metasurface unit is used to disrupt the perfectly symmetrical current distribution and introduce additional tuning degrees of freedom, thereby adjusting the resonant position and impedance matching; the central forked slot is used to extend the oblique surface current path and excite multiple adjacent resonant modes, serving the purpose of broadbanding; the embedded parasitic stubs are used to form continuous current channels and parasitic coupling paths, enhancing multimode coupling and improving in-band gain and efficiency.

[0028] In some embodiments, an array of metasurface units are formed on the metasurface layer.

[0029] Preferably, 4 are formed on the metasurface layer. Four-period metasurface units are used to enlarge the equivalent radiation aperture to improve gain.

[0030] Figure 2 This is the structure of the metasurface unit in this scheme, such as... Figure 2 As shown; In some embodiments, each metasurface unit is a square unit with an asymmetric chamfer structure, wherein the asymmetric chamfer structure includes a first chamfer and a second chamfer located at opposite corners of the metasurface unit, and the first chamfer and the second chamfer have different dimensions.

[0031] In some embodiments, the first chamfer and the second chamfer are both isosceles right triangles, and the side lengths of the first chamfer and the second chamfer are different.

[0032] It should be noted that each metasurface unit forms an asymmetric chamfer structure only at one diagonal position.

[0033] In some embodiments, the central forked slit is designed as a symmetrical X-shape, and the center of the central forked slit coincides with the center of the metasurface unit.

[0034] In some embodiments, an embedded parasitic branch is formed on each side of the metasurface unit. Each embedded parasitic branch is rectangular and is formed by a groove extending from the side of the metasurface unit toward the center. In other words, a rectangular embedded parasitic branch is formed by an inward groove on each side of the metasurface unit.

[0035] In some embodiments, the two embedded parasitic branches in opposite positions are symmetrical with respect to the central axis of the metasurface unit, and the central axis of the two embedded parasitic branches in opposite positions coincides with the central axis of the metasurface unit.

[0036] In some embodiments, the central forked slit contacts the embedded parasitic nodes located on the upper and lower sides, but does not contact the embedded parasitic nodes located on the left and right sides.

[0037] Figure 3 This is the structure of the intermediate metal layer in this scheme, such as... Figure 3 As shown; In some embodiments, a rectangular coupling slot is formed at the center of the intermediate metal layer, wherein the rectangular coupling slot is a rectangular slot facing the metasurface unit.

[0038] In some embodiments, the rectangular coupling gap does not contact the sides of the intermediate metal layer, and the rectangular coupling gap is centrally symmetrical with respect to the center point of the intermediate metal layer.

[0039] In some embodiments, a rectangular coupling slot of 14mm × 2mm is formed on the intermediate metal layer.

[0040] Figure 4 This is the structure of the lower microstrip feeder layer in this scheme, such as... Figure 4 As shown: In some embodiments, a feed line connected to the boundary is formed on the lower microstrip feed line layer.

[0041] In some embodiments, an 18.9mm × 1.13mm feed line is formed on the lower microstrip feed line layer, with a 50Ω characteristic impedance matching.

[0042] As mentioned above, the X-band broadband high-gain radar metasurface antenna designed in this scheme uses a Rogers RO4003C dielectric substrate (ε-coated). =3.55, tanδ=0.0027), with overall dimensions of 30mm×30mm×3.526mm. The X-band center frequency is 10GHz, bandwidth is 3GHz, minimum gain is 7dBi, and minimum efficiency is 70%. Specifically, this X-band broadband high-gain radar metasurface achieves an absolute impedance bandwidth of 3.362GHz in the frequency range of 8.014GHz to 11.376GHz, a relative bandwidth of up to 34.84%, a peak gain of 10.43dBi, a total efficiency of 89.5% at the center frequency, a 3dB beamwidth of 46.9°, and a maximum sidelobe level of -10.9dB.

[0043] Furthermore, the dimensions a of the metasurface elements of the X-band broadband high-gain radar metasurface antenna are set to be between 2 and 7 mm, the side length c1 of the first chamfer is between 0.1 and 2.3 mm, the side length c2 of the second chamfer is between 0.1 and 2.3 mm, the side length a1 of the central forked slit is between 0.2 and 5 mm, the fork angle angle of the central forked slit is between 20 and 70°, and the element spacing d between the metasurface elements is between 0.2 and 8 mm.

[0044] Preferably, the size a of the metasurface element of the X-band broadband high-gain radar metasurface antenna is set to be between 5 mm, the side length c1 of the first chamfer is between 1 mm, the side length c2 of the second chamfer is between 1 mm, the side length a1 of the central forked slit is between 4.4 mm, the fork angle angle of the central forked slit is between 26°, and the element spacing d between the metasurface elements is between 0.3 mm.

[0045] The X-band broadband high-gain radar metasurface antenna designed with the above optimized parameters was subjected to CST full-wave simulation to verify the performance of the final antenna. Figure 6Figure 7 shows a comparison of the S11 parameters of the final antenna and the initial antenna, showing that the bandwidth has been extended from 2.26 GHz to 3.362 GHz; Figure 8 shows a comparison of the gain, showing that the problem of sharp drop in gain after 11 GHz has been solved; Figure 9 shows a comparison of the radiation efficiency, with the efficiency remaining above 70% across the entire frequency band. Figure 9 Figure 10 shows the radiation pattern at the center frequency, demonstrating that the metasurface antenna exhibits excellent directional radiation characteristics.

[0046] Example 2 This solution provides a design method for X-band broadband high-gain radar metasurface antennas. Addressing the challenges of bandwidth expansion and center frequency alignment coupling in multi-objective optimization, and gradient breakage caused by discrete bandwidth extraction, it proposes three core innovations: an intelligent bandwidth identification strategy, a hierarchical penalty mechanism, and a smoothed quadratic penalty function. This enables end-to-end design without manual intervention. Users only need to provide four objectives: center frequency, bandwidth, minimum gain, and minimum efficiency, and the solution will automatically output antenna geometric parameters that meet all design requirements. The design cycle is shortened from several days to minutes.

[0047] Specifically, such as Figure 11 As shown, the design method for an X-band broadband high-gain radar metasurface antenna provided in this scheme includes the following steps: S1: Obtain multiple sets of candidate parameters and set design targets for the X-band broadband high-gain radar metasurface antenna, and normalize the design targets to obtain normalized frequency sampling information. S2: The normalized frequency sampling information and candidate parameters are input into the pre-trained DeepONet forward proxy prediction model, which outputs three types of predicted response curves corresponding to different groups of candidate geometric parameters. The DeepONet forward proxy prediction model includes a branch network and a backbone network. The branch network is used to encode the input candidate geometric parameters to obtain branch feature vectors. The backbone network includes a parallel first branch and a second branch. The first branch is used to generate a first feature vector to characterize the gain response curve and the efficiency response curve based on the normalized frequency sampling information. The second branch is used to generate a second feature vector to characterize the S11 response curve based on the normalized frequency sampling information. The first feature vector and the second feature vector are fused to obtain the backbone feature vector. The branch feature vector is copied and expanded according to the number of frequency points and then multiplied element-wise with the backbone feature vector to obtain the product feature. The product feature is processed to obtain the three types of predicted response curves. S3: Based on the three types of predicted response curves, differential evolution is performed on multiple sets of candidate geometric parameters to obtain the preferred geometric parameters.

[0048] In some embodiments, each set of candidate parameters for an X-band broadband high-gain radar metasurface antenna includes the size a of the metasurface element, the side length c1 of the first chamfer, the side length c2 of the second chamfer, the side length a1 of the central forked slot, the fork angle angle of the central forked slot, and the element spacing d between the metasurface elements.

[0049] It should be noted that the dimension 'a' of the metasurface unit refers to the side length of each metasurface unit. In some embodiments, the metasurface unit is a square with an asymmetrical chamfered structure. The side length 'a1' of the central forked slit refers to the length of each slit, and the forked angle of the central forked slit refers to the smaller included angle between two intersecting slits.

[0050] Regarding the DeepONet forward proxy prediction model: The branch network of this DeepONet forward proxy prediction model is used to encode the 6-dimensional candidate geometric parameters of the input to extract structural features to obtain the branch feature vector.

[0051] In some embodiments, the branch network includes multiple cascaded coding modules and a fully connected layer, wherein each coding module includes a fully connected layer, a ReLU activation layer, a batch normalization layer, and a Dropout layer connected in sequence.

[0052] In a specific embodiment, the branch network includes three cascaded 512-dimensional encoding modules, which ultimately output a 512-dimensional branch feature vector.

[0053] The backbone network of the DeepONet forward proxy prediction model encodes frequency targets to generate frequency-related features. The backbone network is designed with a first branch and a second branch in parallel. The first branch is specifically designed for smooth curves such as prediction gain and efficiency, while the second branch is specifically designed for high-frequency oscillating curves such as S11.

[0054] In some embodiments, design objectives include center frequency and bandwidth.

[0055] In some embodiments, the design target is normalized to obtain normalized frequency sampling information. That is, the user inputs the design target / performance target, where the center frequency and bandwidth are used to determine the frequency sampling range or frequency coordinates. This scheme normalizes the design target to obtain frequency sampling information which is then input into the backbone network.

[0056] In addition, in some embodiments, the user-input design goals also include minimum gain and minimum efficiency, which are used for subsequent fitness evaluation.

[0057] In some embodiments, the first branch includes a multi-layered cascaded ReLU fully connected layer and a fully connected layer, and the second branch includes a multi-layered cascaded SIREN sine wave layer, wherein the ReLU fully connected layer includes a fully connected layer, a ReLU activation layer, a batch normalization layer, and a Dropout layer connected in sequence. The second branch of this scheme utilizes the natural characterization ability of the sine function for high-frequency signals to capture the fine features of resonance valleys.

[0058] It should be noted that a main feature vector is generated for each frequency point in the design target. Therefore, the branch feature vectors need to be copied and expanded according to the number of frequency points, and then multiplied element-wise with the main feature vector of each frequency point to obtain the product feature. In other words, the dot product of the main feature vector and the branch feature vectors at each frequency point yields the S11, gain, or efficiency response at that frequency point. By traversing all frequency points, the complete S11 response curve, gain response curve, or efficiency response curve can be obtained. In some embodiments, summing along the feature dimension and applying a learnable bias to the product features yields three types of prediction response curves, including the S11 response curve, the gain response curve, or the efficiency response curve.

[0059] It should be noted that the DeepONet forward proxy prediction model is trained using samples with known S11 response curves, gain response curves, or efficiency response curves. Each sample has a defined metasurface unit size a, the side length of the first chamfer c1, the side length of the second chamfer c2, the side length of the central forked slit a1, the fork angle of the central forked slit angle, and the unit spacing d between metasurface units.

[0060] Specifically, this scheme adopts the Latin hypercube sampling method with embedded geometric constraints to generate 3056 sets of valid samples in a six-dimensional parameter space. An automated batch simulation program is developed through Python and CST VBA interface to realize the automatic acquisition, anomaly handling and buffering of S-parameter, gain and radiation efficiency frequency response data, and finally form a high-quality antenna electromagnetic response dataset as a training dataset.

[0061] The DeepONet forward agent prediction model's branch network is jointly trained with two backbone branches. The branch network encodes geometric parameters. The first backbone branch is responsible for gain and efficiency prediction, using gain loss and efficiency loss constraints. The second backbone branch is responsible for S11 prediction, using S11 loss constraints. The branch network parameters are jointly updated by the total loss of the joint gain loss, efficiency loss, and S11 loss.

[0062] Specifically, the total loss function of the DeepONet forward proxy prediction model is expressed as: L_total = L_S11 + L_gain + L_eff; L_S11 = MSE_S11 + 1e-3 L_curv; Where L_gain and L_eff are the mean squared errors after Min-Max normalization, corresponding to the gain loss and efficiency loss constraints; L_curv is the curvature smoothing regularization term of the S11 response curve, MSE_S11 is the MSE loss of the S11 response curve, and L_S11 corresponds to the S11 loss.

[0063] Further:

[0064] Where N_g, N_e, and N_s represent the gain, efficiency, and number of frequency sampling points of the S11 response curve, respectively; This represents the predicted gain value. This represents the true gain value. This represents the predicted efficiency value. This represents the true value of efficiency. This represents the predicted value of S11. denoted as the true value of S11, norm represents the Min-Max normalization based on the upper and lower limits of the training set, and i is the frequency sampling point number.

[0065] The DeepONet positive agent prediction model was trained using the Adam optimizer, along with a learning rate decay and early stopping strategy. All three models achieved stable convergence within 600 iterations.

[0066] It should be noted that the DeepONet forward surrogate prediction model in this scheme decouples geometric parameter encoding from continuous frequency coordinate encoding, allowing direct learning of the operator mapping from geometric parameters to continuous response curves. The use of branch networks reduces repetitive learning of geometric features and establishes a connection between the three types of response curves under the same geometric representation. For gain and efficiency response curves, the first branch of the ReLU backbone is used to fit and smooth the response; for the S11 response curve, the SIREN backbone is used to capture sharp resonance valleys, while curvature smoothing loss is introduced to suppress spurious oscillations. Therefore, the DeepONet forward surrogate prediction model can maintain better curve consistency and resonance point prediction accuracy across continuous frequencies. Compared to ordinary single-frequency point analysis models such as MLP, this model reduces the reuse of geometric parameters during training, thus reducing training time. Furthermore, it uses the total MSE of continuous frequency points as the loss function. Compared to neural networks using single-frequency point analysis, the predicted frequencies of this model are more continuous and correlated. Compared to building three DeepONet models, this DeepONet forward proxy prediction model not only reduces the number of times geometric parameters are reused, but also trains the backbone and branch networks with different loss functions, simulating the continuity and differences between the S11 response curve, gain curve, and efficiency curve. This makes it easier for the model to learn the physical laws of these three curves, improving the model's accuracy.

[0067] Furthermore, this scheme employs a differential evolution algorithm to perform differential evolution on the three types of predicted response curves of multiple candidate geometric parameters in order to determine the preferred geometric parameters.

[0068] In some embodiments, the three types of predicted response curves of each set of candidate geometric parameters are used as a seed, and all seeds are aggregated to obtain an initial population. Four feature parameters, including center frequency, bandwidth, minimum in-band gain, and minimum in-band efficiency, are extracted from the three types of predicted response curves of each set of candidate geometric parameters. The fitness of each seed is calculated according to a hierarchical penalty mechanism. Based on the fitness, differential evolution mutation, crossover, and selection operations are performed on each seed to obtain the preferred geometric parameters.

[0069] This scheme uses the feature parameter dimensionality reduction method to transform the predicted response curve, including the S11, gain, and efficiency curves, into four feature parameters. The advantage of this is that it can reduce the conventional analysis of 1001 frequency points of curves such as S11 and 16 frequency points each of gain and efficiency to only 4 parameters, which greatly reduces the training time.

[0070] Furthermore, this scheme employs a tiered penalty mechanism to calculate the fitness of each seed, preventing the penalty terms from mutually hindering each other and causing performance to fall short of standards. Simultaneously, by using preset parameter boundaries and a built-in geometric check function, maximum penalty values ​​are returned for physically infeasible parameter combinations, ensuring the engineering feasibility of the optimization results.

[0071] In some embodiments, the hierarchical penalty mechanism is as follows: when the actual bandwidth does not reach the target value, only the penalty for insufficient bandwidth is imposed; when the bandwidth meets the requirements, the center frequency deviation penalty term is activated, and finally, within the selected operating bandwidth, a smooth quadratic penalty is imposed on the parts where the gain and efficiency are lower than the threshold values.

[0072] Generally speaking, the smaller the fitness value, the better. The calculation formula for fitness is as follows: Let the target center frequency be f0, the target bandwidth be B0, the minimum gain be G0, and the minimum efficiency be Eta0; the predicted results of the candidate parameter x are used to extract the actual center frequency f_c(x), the actual bandwidth B(x), the in-band gain G_i(x), and the efficiency Eta_i(x). If the parameter combination does not satisfy the geometric constraints, then F(x)=M, where M is a maximum penalty value. If B(x)<B0, then F(x)=w_b [max(0,(B0 - B(x)) / B0)]^2; B(x)>=B0, then

[0073] where N is the total number of frequency points, F(x) is the fitness, and the weights w_b, w_f, w_g, w_e can be set according to the engineering priorities. f_c(x), B(x), G_i(x), and η_i(x) are the actual center frequency, actual bandwidth, gain at the i-th frequency point in the band, and efficiency corresponding to the candidate parameter x, respectively.

[0074] This scheme sets the size of the initial population to 50, the maximum number of iterations to 300, and enables local optimization to find the optimal geometric parameters.

[0075] Regarding the design method of the X-band broadband high-gain radar metasurface antenna of this scheme, this method upgrades the traditional discrete frequency point prediction to continuous frequency curve prediction through the DeepONet operator learning technology, and at the same time adopts a task-aware dual-backbone model architecture to achieve high-fidelity reconstruction of high-frequency oscillating signals and prediction of the physical relationships of S11, gain, and efficiency, and reduces the reuse of geometric parameters during training, improving the training efficiency.

[0076] Testing with a test set yielded predictive MSE values ​​as low as 0.011, 0.008, and 0.009 for the S11, gain, and efficiency curves, respectively, resolving the issue of insufficient prediction accuracy of traditional neural networks near the resonant point. Furthermore, this scheme utilizes a dimensionality-reduction feature parameter method to summarize the complex S11, gain, and efficiency curves into four feature parameters, significantly reducing the time required for reverse engineering. Through an improved differential evolution algorithm and a hierarchical penalty mechanism, the contradiction between bandwidth expansion and center frequency alignment is effectively decoupled, enabling end-to-end reverse engineering without manual intervention. The design cycle has been shortened from several days to minutes.

[0077] Example 3 This embodiment also provides an electronic device, see reference. Figure 12 It includes a memory 402 and a processor 401, the memory 402 storing a computer program and the processor 401 being configured to run the computer program to perform the steps in any of the above embodiments of the design method for an X-band broadband high-gain radar metasurface antenna.

[0078] Specifically, the processor 401 may include a central processing unit (CPU), or an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0079] The memory 402 may include a large-capacity memory 402 for data or instructions. The memory 402 can be used to store or cache various data files that need to be processed and / or communicated, as well as possible computer program instructions executed by the processor 401.

[0080] The processor 401 reads and executes the computer program instructions stored in the memory 402 to implement any of the X-band broadband high-gain radar metasurface antenna design methods in the above embodiments.

[0081] Optionally, the electronic device may further include a transmission device 403 and an input / output device 404, wherein the transmission device 403 is connected to the processor 401 and the input / output device 404 is connected to the processor 401.

[0082] The transmission device 403 can be used to receive or send data via a network. Specific examples of the network described above may include wired or wireless networks provided by the communication provider of the electronic device. In one example, the transmission device includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device 403 may be a Radio Frequency (RF) module used for wireless communication with the Internet.

[0083] Input / output device 404 is used to input or output information. In this embodiment, the input information may be candidate parameters, etc., and the output information may be preferred geometric parameters, etc.

[0084] Optionally, in this embodiment, the processor 401 can be configured to perform the following steps via a computer program: S1: Obtain multiple sets of candidate parameters and set design targets for the X-band broadband high-gain radar metasurface antenna, and normalize the design targets to obtain normalized frequency sampling information. S2: The normalized frequency sampling information and candidate parameters are input into the pre-trained DeepONet forward proxy prediction model, which outputs three types of predicted response curves corresponding to different groups of candidate geometric parameters. The DeepONet forward proxy prediction model includes a branch network and a backbone network. The branch network is used to encode the input candidate geometric parameters to obtain branch feature vectors. The backbone network includes a parallel first branch and a second branch. The first branch is used to generate a first feature vector to characterize the gain response curve and the efficiency response curve based on the normalized frequency sampling information. The second branch is used to generate a second feature vector to characterize the S11 response curve based on the normalized frequency sampling information. The first feature vector and the second feature vector are fused to obtain the backbone feature vector. The branch feature vector is copied and expanded according to the number of frequency points and then multiplied element-wise with the backbone feature vector to obtain the product feature. The product feature is processed to obtain the three types of predicted response curves. S3: Based on the three types of predicted response curves, differential evolution is performed on multiple sets of candidate geometric parameters to obtain the preferred geometric parameters.

[0085] It should be noted that the specific examples in this embodiment can refer to the examples described in the above embodiments and optional implementations, and will not be repeated here.

[0086] Generally, various embodiments can be implemented in hardware or dedicated circuitry, software, logic, or any combination thereof. Some aspects of the invention can be implemented in hardware, while others can be implemented by firmware or software executed by a controller, microprocessor, or other computing device, but the invention is not limited thereto. Although various aspects of the invention may be shown and described as block diagrams, flowcharts, or using some other graphical representation, it should be understood that, by way of non-limiting example, these blocks, apparatuses, systems, techniques, or methods described herein can be implemented in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0087] Embodiments of the present invention can be implemented by computer software, which may be executable by a data processor of a mobile device, such as a processor entity, or by hardware, or by a combination of software and hardware. Computer software or programs (also referred to as program products), including software routines, applets, and / or macros, can be stored in any device-readable data storage medium, and they include program instructions for performing specific tasks. A computer program product may include one or more computer-executable components configured to perform embodiments when the program is run. One or more computer-executable components may be at least one piece of software code or a portion thereof. Additionally, it should be noted that any block in the logical flow of the figures may represent a program step, or interconnected logical circuitry, blocks and functions, or a combination of program steps and logical circuitry, blocks and functions. The software may be stored on physical media such as memory chips or blocks of storage implemented within a processor, magnetic media such as hard disks or floppy disks, and optical media such as, for example, DVDs and their data variants, CDs, etc. The physical medium is a non-transient medium.

[0088] Those skilled in the art should understand that the technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0089] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A metasurface antenna for X-band broadband high-gain radar, characterized in that, include: The layers are designed from top to bottom: a metasurface layer, an intermediate metal layer, and a lower microstrip feed layer. The metasurface layer includes at least one metasurface unit, each metasurface unit is designed with an asymmetric chamfer structure, and each metasurface unit has a central fork-shaped slit in the center and embedded parasitic branches on the four sides respectively. The intermediate metal layer has rectangular coupling slots corresponding to each metasurface unit. The lower microstrip feeder layer has feed lines corresponding to each metasurface unit.

2. The X-band broadband high-gain radar metasurface antenna according to claim 1, characterized in that, The asymmetric chamfer structure includes a first chamfer and a second chamfer located at opposite corners of the metasurface unit, and the first chamfer and the second chamfer have different dimensions.

3. The X-band broadband high-gain radar metasurface antenna according to claim 1, characterized in that, The central fork-shaped slot is designed as a symmetrical X shape, and the center of the central fork-shaped slot coincides with the center of the metasurface unit.

4. The X-band broadband high-gain radar metasurface antenna according to claim 1, characterized in that, Each embedded parasitic branch is formed by slotting from the edge of the metasurface unit towards the center. The two embedded parasitic branches in opposite positions are symmetrical with respect to the central axis of the metasurface unit, and the central axis of the two embedded parasitic branches in opposite positions coincides with the central axis of the metasurface unit. The central forked slit is in contact with the embedded parasitic branches located on the upper and lower sides, but is not in contact with the embedded parasitic branches located on the left and right sides.

5. A design method for designing the X-band broadband high-gain radar metasurface antenna according to any one of claims 1 to 4, characterized in that, include: S1: Obtain multiple sets of candidate parameters and set design targets for the X-band broadband high-gain radar metasurface antenna, and normalize the design targets to obtain normalized frequency sampling information. S2: The normalized frequency sampling information and candidate parameters are input into the pre-trained DeepONet forward proxy prediction model, which outputs three types of predicted response curves corresponding to different groups of candidate geometric parameters. The DeepONet forward proxy prediction model includes a branch network and a backbone network. The branch network is used to encode the input candidate geometric parameters to obtain branch feature vectors. The backbone network includes a parallel first branch and a second branch. The first branch is used to generate a first feature vector to characterize the gain response curve and the efficiency response curve based on the normalized frequency sampling information. The second branch is used to generate a second feature vector to characterize the S11 response curve based on the normalized frequency sampling information. The first feature vector and the second feature vector are fused to obtain the backbone feature vector. The branch feature vector is copied and expanded according to the number of frequency points and then multiplied element-wise with the backbone feature vector to obtain the product feature. The product feature is processed to obtain the three types of predicted response curves. S3: Based on the three types of predicted response curves, differential evolution is performed on multiple sets of candidate geometric parameters to obtain the preferred geometric parameters.

6. The design method for an X-band broadband high-gain radar metasurface antenna according to claim 5, characterized in that, include: For each set of candidate parameters for the X-band broadband high-gain radar metasurface antenna, the metasurface element size, the side length of the first chamfer, the side length of the second chamfer, the side length of the central forked slot, the fork angle of the central forked slot, and the element spacing between metasurface elements are included.

7. The design method for an X-band broadband high-gain radar metasurface antenna according to claim 5, characterized in that, The branch network includes multiple cascaded coding modules and fully connected layers. Each coding module includes a fully connected layer, a ReLU activation layer, a batch normalization layer, and a Dropout layer connected in sequence. The first branch includes multiple cascaded ReLU fully connected layers and fully connected layers. The second branch includes multiple cascaded SIREN layers, where the ReLU fully connected layers include a fully connected layer, a ReLU activation layer, a batch normalization layer, and a Dropout layer connected in sequence.

8. The design method for an X-band broadband high-gain radar metasurface antenna according to claim 5, characterized in that, The DeepONet forward agent prediction model's branch network is jointly trained with two main branches. The branch network encodes geometric parameters. The first main branch is responsible for gain and efficiency prediction, using gain loss and efficiency loss constraints. The second main branch is responsible for S11 prediction, using S11 loss constraints. The branch network parameters are jointly updated by the total loss of the joint gain loss, efficiency loss, and S11 loss.

9. The design method for an X-band broadband high-gain radar metasurface antenna according to claim 5, characterized in that, The three types of predicted response curves for each set of candidate geometric parameters are used as a seed, and all seeds are aggregated to obtain an initial population. Four feature parameters, including center frequency, bandwidth, minimum in-band gain, and minimum in-band efficiency, are extracted from the three types of predicted response curves for each set of candidate geometric parameters. The fitness of each seed is calculated according to a hierarchical penalty mechanism. Based on the fitness, differential evolution mutation, crossover, and selection operations are performed on each seed to obtain the optimal geometric parameters.

10. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to execute the design method for an X-band broadband high-gain radar metasurface antenna as described in any one of claims 5 to 9.

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