A tight-coupling microstrip antenna array beam synthesis method based on physical heuristic condition diffusion model

Abstract

The application discloses a tight-coupling microstrip antenna array beam synthesis method based on a physical heuristic condition diffusion model, and relates to the fields of electromagnetic field numerical modeling and artificial intelligence calculation methods. Specifically, the method comprises the following steps: screening a dominant mode of a microstrip antenna unit; solving a directional diagram distribution of the tight-coupling microstrip antenna array under different excitations, constructing a neural network model for predicting the directional diagram of the tight-coupling microstrip antenna array and training the neural network model; constructing a physical heuristic condition diffusion model for the tight-coupling microstrip antenna array beam synthesis and training the physical heuristic condition diffusion model; applying the trained physical heuristic condition diffusion model to the tight-coupling microstrip antenna array beam synthesis, and according to preset main lobe pointing and sidelobe level indicators, calling the physical heuristic condition diffusion model to gradually denoise from initial Gaussian noise, and finally obtaining an array excitation distribution. The application effectively solves the beam synthesis problem under the strong mutual coupling effect while greatly reducing the data set construction cost and the calculation overhead.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic field numerical modeling and artificial intelligence calculation methods, and more specifically to a beam synthesis method for tightly coupled microstrip antenna arrays based on a physics-inspired conditional diffusion model. Background Technology

[0002] With increasingly scarce spectrum resources and ever-increasing demands for communication bandwidth, tightly coupled microstrip antenna arrays, characterized by ultra-wideband, wide-angle scanning, and high integration, are gradually becoming an important component of modern communication systems. Compared to traditional half-wavelength-pitch arrays, tightly coupled microstrip antenna arrays can integrate more radiating elements, thus providing richer degrees of freedom for beam synthesis. However, the densely distributed array elements exhibit severe electromagnetic coupling. This strong mutual coupling effect causes the active radiation patterns of each element in the array to no longer be independent, but rather to fluctuate drastically with changes in the excitation of surrounding elements. Consequently, traditional beam synthesis methods suffer from serious drawbacks such as coarse accuracy, huge overhead, and lengthy processing time, making it difficult to meet the requirements for efficient beam synthesis.

[0003] Researchers have employed big data-driven neural network models or traditional generative models to solve the beam synthesis problem of tightly coupled microstrip antenna arrays, but significant limitations remain. Existing big data-driven models often treat beam synthesis as a deterministic regression problem, ignoring the ill-conditioned "one-to-many" nature of the electromagnetic inverse problem, thus limiting the model's generalization ability and robustness. Traditional generative models often lack constraints from electromagnetic physics mechanisms, making it difficult to guarantee that the generated excitation accurately reproduces the desired beam. Furthermore, these models heavily rely on training data based on full-wave electromagnetic simulations, and their enormous computational cost becomes a major bottleneck restricting their application.

[0004] Therefore, there is an urgent need to develop an efficient beam synthesis method that fully utilizes the laws of electromagnetic physics and is applicable to tightly coupled microstrip antenna array scenarios. Summary of the Invention

[0005] In view of this, the present invention provides a

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model includes the following steps: Screening the dominant modes of microstrip antenna elements; Solve for the radiation pattern distribution of a tightly coupled microstrip antenna array under different excitations, construct and train a neural network model for predicting the radiation pattern of the tightly coupled microstrip antenna array; A physically inspired conditional diffusion model for beam synthesis of tightly coupled microstrip antenna arrays was constructed and trained. The trained physical heuristic conditional diffusion model is applied to beam synthesis of a tightly coupled microstrip antenna array. Based on the preset main lobe pointing and side lobe level indices, the physical heuristic conditional diffusion model is invoked to gradually de-noise the initial Gaussian noise and finally obtain the array excitation distribution.

[0007] Optionally, the dominant modes of the microstrip antenna elements can be screened, specifically by: constructing the generalized impedance matrix of a single microstrip antenna element using the partial element equivalent circuit method, performing generalized eigenvalue decomposition on it to obtain the characteristic modes and corresponding eigenvalues ​​of the single microstrip antenna element, calculating the modal significance coefficients of each characteristic mode, and determining the dominant mode based on the modal significance coefficients.

[0008] Optionally, the specific expression for the modal significance coefficient is as follows: ; in, Indicates the first Modal significance coefficients corresponding to each feature pattern Represents the imaginary unit. Indicates the first The feature values ​​corresponding to each feature pattern This indicates the modulo operation.

[0009] Optionally, the neural network model used to predict the radiation pattern of a tightly coupled microstrip antenna array takes the amplitude and phase of the array excitation as input and outputs the array radiation pattern, with the mapping relationship satisfying: ; in, This represents the radiation pattern of a tightly coupled microstrip antenna array. and These represent the normalized amplitude and phase of the antenna array, respectively. These represent the training parameters of the neural network model. This represents the neural network model.

[0010] Optionally, the physical-inspired conditional diffusion model is applied to the beam synthesis task of a tightly coupled microstrip antenna array. Its conditions are set as the main lobe pointing and side lobe level, which are combined with the excitation amplitude and phase distribution of the antenna array at the current time step obtained by gradually denoising Gaussian noise as input, and noise is used as output.

[0011] Optionally, a neural network model for predicting the radiation pattern of a tightly coupled microstrip antenna array is constructed and trained. Specifically, this includes: using the eigenmode method to solve for the radiation pattern of the tightly coupled microstrip antenna array under different excitations, generating an "excitation-radiation pattern" dataset, which is divided into a training set and a test set; constructing a neural network model for predicting the radiation pattern of the tightly coupled microstrip antenna array using a convolutional neural network architecture, with the input set as the normalized amplitude and phase of the excitation, the output set as the array radiation pattern, and the loss function defined as the mean square error between the model output and the dataset; training the neural network model using a backpropagation algorithm, wherein the training learning rate is gradually adjusted according to the number of training rounds.

[0012] Optionally, a physically inspired conditional diffusion model for beam synthesis of tightly coupled microstrip antenna arrays is constructed and trained, specifically including: A training dataset containing excitations and corresponding radiation patterns of a tightly coupled microstrip antenna array is constructed; the radiation patterns corresponding to different excitations are generated using the array factor method, expressed as:

[0013] in, The radiation pattern was obtained using the matrix factor method. It is the radiation pattern of a single antenna element under unit excitation. and They represent the first The excitation amplitude and phase of each antenna element, and They represent the first Each antenna element Coordinates of a plane Represents the wave vector. Indicates the total number of antenna elements. and These are the elevation angle and the azimuth angle, respectively. A composite loss function is constructed that integrates data fitting error and physical constraint; the training of the physical heuristic conditional diffusion model adopts a composite loss function composed of a data fitting loss term and a physical constraint loss term, satisfying the following form:

[0014] in, This represents the total loss function used to train the physically inspired conditional diffusion model. These are the weighting coefficients of the numerical loss function. These are the weighting coefficients of the physical loss function. It is a data fitting loss function that constrains the mean square error between the output noise of the physical heuristic diffusion model and the reference noise data. The physical loss function used to constrain the denoising result of the physically heuristic conditional diffusion model to satisfy the physical coupling law is defined as the input of the excitation amplitude and phase distribution of the antenna array at the current time step to the completed training. The mean squared error between the output pattern of the neural network model and the results in the training dataset.

[0015] Optionally, the weighting coefficients of the physical loss function It has diffusion step size correlation, in When the value is smaller, a larger weight is applied. Approaching total step size A smaller weight is used at times to balance training stability and physical constraints.

[0016] Optionally, the array excitation distribution is obtained by calling the physically inspired conditional diffusion model, specifically including the following steps: Preset a pure Gaussian noise with the same dimension as the array excitation. Its subscript indicates the current time step. The preset main lobe pointing and side lobe level indices are used as conditions for the trained physical heuristic conditional diffusion model, along with... The common input is a pre-trained physics-inspired conditional diffusion model, and the output is the noise corresponding to the current time step. ,pass Obtain the denoising result ;Will Repeat the above steps until the loop reaches... ,at this time This represents the final required array excitation distribution.

[0017] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model, which has the following beneficial effects: 1. This invention constructs a neural network model for predicting the radiation pattern of tightly coupled microstrip antenna arrays. This model can quickly obtain the array radiation pattern under different excitations, avoiding complex electromagnetic calculations or full-wave simulations, thereby reducing training and prediction costs.

[0018] 2. In constructing the training dataset for the physically inspired conditional diffusion model, this invention adopts the traditional array factor method and introduces physical constraint terms into the conditional diffusion model to ensure that the model can learn the real physical response of the tightly coupled microstrip antenna array considering the coupling effect during the training process, and to ensure that the final generated excitation accurately reproduces the desired beam. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a schematic diagram of a microstrip antenna unit in an embodiment of the present invention; Figure 3 This is a schematic diagram of a tightly coupled microstrip antenna array in an embodiment of the present invention; Figure 4 This is a schematic diagram of the neural network model structure for predicting the radiation pattern of a tightly coupled microstrip antenna array in an embodiment of the present invention; Figure 5 This is a schematic diagram of the convergence result of the neural network model used to predict the radiation pattern of a tightly coupled microstrip antenna array in an embodiment of the present invention; Figure 6 This is a diagram showing the results of the first physically inspired conditional diffusion model in an embodiment of the present invention; Figure 7 This is a diagram showing the results of the second physics-inspired conditional diffusion model in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention constructs a neural network model capable of efficiently and accurately characterizing the strong mutual coupling effect of antenna arrays, enabling rapid prediction of the radiation pattern of tightly coupled microstrip antenna arrays. Furthermore, it employs an array factor method to generate a low-cost dataset, embedding the aforementioned neural network model into the training process of a conditional diffusion model. A composite loss function integrating data fitting error and electromagnetic physical constraints is constructed, ensuring that the conditional diffusion model deeply understands the electromagnetic coupling physical mechanism. Ultimately, this achieves beam synthesis of tightly coupled microstrip antenna arrays under arbitrary target requirements. Compared to big data-driven neural network models or traditional generative models, the method provided by this invention deeply integrates electromagnetic physical mechanisms and the conditional diffusion model. While significantly reducing dataset construction costs and computational overhead, it effectively solves the beam synthesis problem under strong mutual coupling effects, ensuring high consistency between the generated results and full-wave simulation, and possessing good generalization ability. It is applicable to various beam synthesis tasks such as wireless communication, power transmission, and wavefront shaping.

[0023] This invention discloses a beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model, comprising the following steps: Screening the dominant modes of microstrip antenna elements; Solve for the radiation pattern distribution of a tightly coupled microstrip antenna array under different excitations, construct and train a neural network model for predicting the radiation pattern of the tightly coupled microstrip antenna array; A physically inspired conditional diffusion model for beam synthesis of tightly coupled microstrip antenna arrays was constructed and trained. The trained physical heuristic conditional diffusion model is applied to beam synthesis of a tightly coupled microstrip antenna array. Based on the preset main lobe pointing and side lobe level indices, the physical heuristic conditional diffusion model is invoked to gradually de-noise the initial Gaussian noise and finally obtain the array excitation distribution.

[0024] Specifically, according to the invention, the complete implementation embodiments are as follows: Step 1: Construct the generalized impedance matrix of a single microstrip antenna element based on the partial element equivalent circuit method, perform generalized eigenvalue decomposition on it to obtain the characteristic modes of the single microstrip antenna element, and select the dominant mode based on the mode significance coefficient. in, Figure 2 This is a schematic diagram of the microstrip antenna element used in an embodiment of the present invention. First, the generalized impedance matrix of the microstrip antenna element is constructed using the partial element equivalent circuit method. Then, its generalized eigenvalue decomposition is performed to obtain the characteristic modes and corresponding eigenvalues ​​of a single microstrip antenna element. The modal significance coefficients of each characteristic mode are calculated, with the specific expression as follows:

[0025] in, Indicates the first Modal significance coefficients corresponding to each feature pattern Represents the imaginary unit. Indicates the first The feature values ​​corresponding to each feature pattern This indicates a modulus operation. The dominant mode must be selected if its modality significance coefficient is greater than or equal to 1. .

[0026] Step 2: Based on the feature-mode method, solve for the radiation pattern distribution of the tightly coupled microstrip antenna array under different excitations, generate multiple training datasets containing array excitations and corresponding radiation patterns, and construct a neural network model for predicting the radiation pattern of the tightly coupled microstrip antenna array. Train the neural network model using the backpropagation algorithm, wherein the training learning rate is gradually adjusted according to the number of training epochs; in, Figure 3 This is a schematic diagram of the microstrip antenna array used in an embodiment of the present invention. The array is uniformly distributed across... On a plane, direction and The number of antenna elements in each direction is set to 12, therefore the total number of antennas in the array is 144. The antenna elements are in... direction and The spacing in all directions is set to ,in The wavelength is used. Based on this array embodiment, the eigenmode method is employed to solve for the radiation patterns of the tightly coupled microstrip antenna array under different excitations, generating 10,000 sets of "excitation-radiation pattern" datasets, which are divided into training and testing sets in a 7:3 ratio. Furthermore, a neural network model based on a convolutional neural network architecture is constructed, such as... Figure 4 As shown, its input is set as the normalized amplitude and phase of the excitation, and its output is set as the array pattern. The mapping relationship satisfies:

[0027] in, This indicates the array pattern. and These represent the normalized amplitude and phase of the antenna array, respectively. These represent the training parameters of the neural network model. This represents the neural network model. The loss function of this model is defined as the model output. The mean squared error between the neural network model and the dataset's orientation graph is used to train the neural network model using the backpropagation algorithm. The gradient descent capability of the neural network at different stages is controlled by dynamically adjusting the learning rate, thereby improving the network's learning time and accuracy. The formula is as follows:

[0028] in, The model represents the first time. t The learning rate of the step. This is the initial learning rate. It is the attenuation factor. It is the decay step size.

[0029] Step 3: Construct a physical heuristic conditional diffusion model for beam synthesis of tightly coupled microstrip antenna arrays. The model takes the main lobe pointing and side lobe level as conditions, and combines them with the excitation amplitude and phase distribution of the antenna array at the current time step obtained by gradually denoising Gaussian noise as input, and noise as output. The physically inspired conditional diffusion model is specifically expressed in mathematical form as follows:

[0030] in, This indicates that the physically inspired conditional diffusion model is at time step [missing information]. Output at time and These are the pitch and azimuth angles corresponding to the main lobe, respectively. Sidelobe level, For time steps The array excitation distribution at that time, This represents the physical heuristic conditional diffusion model.

[0031] Step 4: Generate a training dataset containing the excitation of a tightly coupled microstrip antenna array and its corresponding radiation pattern based on the array factor calculation method; construct a composite loss function that integrates data fitting error and physical law constraints; and train the physical heuristic conditional diffusion model using the backpropagation algorithm. This involves constructing a training dataset containing excitations and corresponding radiation patterns for a tightly coupled microstrip antenna array. 20,000 radiation patterns corresponding to different excitations are generated using the array factor method. This result ignores strong inter-element coupling effects, and the expression is:

[0032] in, The radiation pattern was obtained using the matrix factor method. It is the radiation pattern of a single antenna element under unit excitation. and They represent the first The excitation amplitude and phase of each antenna element, and They represent the first Each antenna element Coordinates of a plane Represents the wave vector. Indicates the total number of antenna elements. and These are the pitch angle and the azimuth angle, respectively.

[0033] A composite loss function is constructed that integrates data fitting error and physical constraint. The training of the physical heuristic conditional diffusion model employs a composite loss function consisting of a data fitting loss term and a physical constraint loss term, satisfying the following form:

[0034] in, This represents the total loss function used to train the physically inspired conditional diffusion model. These are the weighting coefficients of the numerical loss function. These are the weighting coefficients of the physical loss function. It is a data fitting loss function that constrains the mean square error between the output noise of the physical heuristic diffusion model and the reference noise data. The physical loss function used to constrain the denoising result of the physically heuristic conditional diffusion model to satisfy the physical coupling law is defined as the input of the excitation amplitude and phase distribution of the antenna array at the current time step to the completed training. The mean squared error between the output pattern of the neural network model and the results in the training dataset. Furthermore, the weight coefficients of the physical loss function. It has diffusion step size correlation, and this coefficient is in When the value is smaller, a larger weight is applied. Approaching total step size When a smaller weight is used, in order to balance training stability and physical constraints, the specific expression is as follows:

[0035] in, To train the total stride length.

[0036] Step 5: Apply the trained physical heuristic conditional diffusion model to beam synthesis of a tightly coupled microstrip antenna array. Based on the preset main lobe pointing and side lobe level indices, call the physical heuristic conditional diffusion model to gradually de-noise from the initial Gaussian noise, and finally obtain the array excitation distribution. Verify the array pattern under this excitation distribution using full-wave simulation.

[0037] The process of obtaining the array excitation distribution by calling the physically inspired conditional diffusion model includes:

[0038] First, a pure Gaussian noise with the same dimension as the array excitation is preset. Its subscript indicates the current time step. The preset main lobe pointing and side lobe level indices are used as conditions for the trained physical heuristic conditional diffusion model, along with... The common input is a pre-trained physics-inspired conditional diffusion model, and the output is the noise corresponding to the current time step. ,pass Obtain the denoising result .Will Repeat the above steps until the loop reaches... ,at this time This represents the final required array excitation distribution. Based on the obtained array excitation distribution... The array pattern was obtained through full-wave software simulation, and the desired beam pattern was verified.

[0039] Figure 1 The overall flowchart of the present invention is shown. Figure 2 This is a schematic diagram of a microstrip antenna element selected in an embodiment of the present invention. Figure 3 This is a schematic diagram of a tightly coupled microstrip antenna array selected in an embodiment of the present invention. Figure 4 This is a schematic diagram of the neural network model structure used in this invention to predict the radiation pattern of a tightly coupled microstrip antenna array. Figure 5 The image shows the convergence curve of the neural network model used to predict the radiation pattern of a tightly coupled microstrip antenna array in this embodiment of the invention. It can be seen that the model has a good convergence effect. Figure 6 In this invention, the beam synthesis result diagram is generated by calling the trained physical heuristic conditional diffusion model, wherein the target... The target main lobe is set to , = Ultimately, the array pattern main lobe obtained based on the physically inspired conditional diffusion model remains stable. , = And the side lobes are It meets the preset indicators. Figure 7 In this invention, the beam synthesis result diagram is generated by calling the trained physical heuristic conditional diffusion model, where the target and... Figure 6 The results are consistent, differing only in the initial Gaussian noise. After gradual denoising, the array excitation and corresponding radiation pattern still meet the preset specifications, with the main lobe of the array radiation pattern remaining constant. , = And the side lobes are It meets the preset indicators.

[0040] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0041] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model, characterized in that, Includes the following steps: Screening the dominant modes of microstrip antenna elements; The radiation pattern distribution of a tightly coupled microstrip antenna array under different excitations is solved based on the feature mode method. A neural network model for predicting the radiation pattern of a tightly coupled microstrip antenna array is constructed and trained. A physically inspired conditional diffusion model for beam synthesis of tightly coupled microstrip antenna arrays is constructed and trained, specifically including: A training dataset containing excitations and corresponding radiation patterns of a tightly coupled microstrip antenna array is constructed; the radiation patterns corresponding to different excitations are generated using the array factor method, expressed as: in, The radiation pattern was obtained using the matrix factor method. It is the radiation pattern of a single antenna element under unit excitation. and They represent the first The excitation amplitude and phase of each antenna element, and They represent the first Each antenna element Coordinates of a plane Represents the wave vector. Indicates the total number of antenna elements. and These are the elevation angle and the azimuth angle, respectively. A composite loss function is constructed that integrates data fitting error and physical constraint; the training of the physical heuristic conditional diffusion model adopts a composite loss function composed of a data fitting loss term and a physical constraint loss term, satisfying the following form: in, This represents the total loss function used to train the physically inspired conditional diffusion model. These are the weighting coefficients of the numerical loss function. These are the weighting coefficients of the physical loss function. It is a data fitting loss function that constrains the mean square error between the output noise of the physical heuristic diffusion model and the reference noise data. The physical loss function used to constrain the denoising result of the physically heuristic conditional diffusion model to satisfy the physical coupling law is defined as the input of the excitation amplitude and phase distribution of the antenna array at the current time step to the completed training. The mean squared error between the output pattern of the neural network model and the results in the training dataset. The weighting coefficient of the physical loss function It has diffusion step size correlation, in Hourly weighting is used to determine the maximum weight. Approaching total step size Smaller weights are used to balance training stability and physical constraints. The trained physical heuristic conditional diffusion model is applied to beam synthesis of a tightly coupled microstrip antenna array. Based on the preset main lobe pointing and side lobe level indices, the physical heuristic conditional diffusion model is invoked to gradually de-noise the initial Gaussian noise and finally obtain the array excitation distribution.

2. The beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model according to claim 1, characterized in that, The process of selecting the dominant modes of a microstrip antenna element includes: constructing the generalized impedance matrix of a single microstrip antenna element using the partial element equivalent circuit method, performing generalized eigenvalue decomposition on it to obtain the characteristic modes and corresponding eigenvalues ​​of the single microstrip antenna element, calculating the mode significance coefficients of each characteristic mode, and determining the dominant mode based on the mode significance coefficients.

3. The beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model according to claim 2, characterized in that, The specific expression for the modal significance coefficient is: ； in, Indicates the first Modal significance coefficients corresponding to each feature pattern Represents the imaginary unit. Indicates the first The feature values ​​corresponding to each feature pattern This indicates the modulo operation.

4. The beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model according to claim 1, characterized in that, The neural network model used to predict the radiation pattern of a tightly coupled microstrip antenna array takes the amplitude and phase of the array excitation as input and outputs the array radiation pattern. The mapping relationship satisfies: ； in, This represents the radiation pattern of a tightly coupled microstrip antenna array. and These represent the normalized amplitude and phase of the antenna array, respectively. These represent the training parameters of the neural network model. This represents the neural network model.

5. The beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model according to claim 1, characterized in that, The physical-inspired conditional diffusion model is applied to the beam synthesis task of a tightly coupled microstrip antenna array. Its conditions are set as the main lobe pointing and side lobe level, which are combined with the excitation amplitude and phase distribution of the antenna array at the current time step obtained by gradually denoising Gaussian noise as input, and noise is used as output.

6. The beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model according to claim 1, characterized in that, A neural network model for predicting the radiation pattern of a tightly coupled microstrip antenna array is constructed and trained. Specifically, this includes: using the eigenmode method to solve for the radiation pattern of the tightly coupled microstrip antenna array under different excitations, generating an "excitation-radiation pattern" dataset, which is divided into training and testing sets; constructing a neural network model for predicting the radiation pattern of the tightly coupled microstrip antenna array using a convolutional neural network architecture, with the input set as the normalized amplitude and phase of the excitation, and the output set as the array radiation pattern, the loss function defined as the mean square error between the model output and the dataset; and training the neural network model using the backpropagation algorithm, where the training learning rate is gradually adjusted according to the number of training epochs.

7. The beam synthesis method for tightly coupled microstrip antenna arrays based on a physically inspired conditional diffusion model according to claim 1, characterized in that, The process of obtaining the array excitation distribution by invoking the physical heuristic conditional diffusion model includes the following steps: Preset a pure Gaussian noise with the same dimension as the array excitation. Its subscript indicates the current time step. The preset main lobe pointing and side lobe level indices are used as conditions for the trained physical heuristic conditional diffusion model, along with... The common input is a pre-trained physics-inspired conditional diffusion model, and the output is the noise corresponding to the current time step. ,pass Obtain the denoising result ;Will Repeat the above steps until the loop reaches... ,at this time This represents the final required array excitation distribution.

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