Design optimization method for amplitude and phase of low-sidelobe large-spacing array antenna

Abstract

The invention relates to the field of large-spacing array antenna design optimization, in particular to a low-sidelobe large-spacing array antenna amplitude and phase design optimization method. Amplitude and phase values are randomly distributed for each large-spacing array element, the variation ranges of the amplitude and phase values are set, and a series of large-spacing array antenna radiation patterns with different characteristics can be generated through the random amplitude and phase combination, so that the large-spacing array antenna radiation pattern is more uniform in radiation. The rich radiation pattern data form a training data set of a neural network model, then the neural network model is trained through the obtained data set, and after training is completed, the radiation pattern of the large-spacing array antenna with the sidelobe level lower than-20dB is input into the trained neural network model, so that the radiation pattern of the large-spacing array antenna with the sidelobe level lower than-20dB is obtained. And outputting the optimized amplitude and phase distribution by the neural network model. The method is suitable for optimizing the design of the large-spacing array antenna.

Description

Technical Field

[0001] The present invention relates to the field of design optimization of large-spacing array antennas, and in particular to a design optimization method for amplitude and phase of low-sidelobe large-spacing array antennas. Background Art

[0002] Because the element spacing of widely spaced array antennas often exceeds the threshold of a wavelength, their radiation patterns are often accompanied by high-level grating lobes. This grating lobe phenomenon disperses the energy of the main lobe, not only resulting in a decrease in gain performance but also potentially interfering with the precise positioning of the beam, affecting the overall performance of the system. In electromagnetic compatibility systems, low-sidelobe antennas significantly reduce the radiation intensity of sidelobes and sidelobes, effectively reducing sensitivity to external interference sources and greatly enhancing the system's anti-interference resilience. This is of great importance for systems that must maintain robust operation in high electromagnetic interference environments.

[0003] Currently, sidelobe suppression technologies for large-spacing array antennas primarily focus on the following areas: First, intelligent optimization methods such as genetic algorithms, particle swarm algorithms, or differential evolution algorithms are used to optimize the array element layout. However, these algorithms are relatively lengthy in terms of computational time, and their computational time is positively correlated with the scale and number of optimization problems, limiting their effectiveness in practical applications. Second, deterministic numerical methods such as Legendre transforms and degree clipping techniques are employed. While these methods have no specific restrictions on array element spacing, they can lead to serious coupling issues, thereby diminishing their practical application value. Third, by combining metamaterial technology, the phase distribution above the array antenna is manually manipulated to achieve uniform phase distribution above the elements, thereby suppressing grating lobes. Although this method can reduce the grating lobe level to a certain extent, the sidelobe level still struggles to reach the -20dB standard, failing to fully meet the low sidelobe level requirement. Summary of the Invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a design optimization method for the amplitude and phase of a low-sidelobe and large-spacing array antenna, thereby realizing the design optimization of the amplitude and phase of the large-spacing array antenna and meeting the standard that the sidelobe level is lower than -20dB.

[0005] The present invention adopts the following technical solutions to achieve the above-mentioned purpose. The present invention provides a method for designing and optimizing the amplitude and phase of a low-sidelobe and large-spacing array antenna, comprising: S1. Obtain the dataset; The center of the large-interval array is set as the coordinate origin, the large-interval array is used as a feed source, the coordinate positions of each feed unit are located, the far-zone radiation field generated by each unit on the metasurface transmission array is calculated, and the far-zone radiation field of the entire planar array is calculated; the spherical wave emitted by the feed source is converted into a plane wave, the electric field at the metasurface lens array is calculated according to the far-zone radiation field of the entire planar array, and the phase at the metasurface lens is calculated; The metasurface lens array is placed according to the phase at the metasurface lens, the total electric field of the electromagnetic wave emitted by the feed source after passing through the metasurface lens array is calculated, the radiation pattern of the array antenna is calculated according to the calculated total electric field, and finally the amplitude and phase values of each large-interval array element are randomly allocated to generate array antenna radiation patterns corresponding to different characteristics, and the data set is composed of the array antenna radiation patterns corresponding to different characteristics; S2, training the neural network model through the obtained data set; S3, inputting the large-interval array antenna radiation pattern with a sidelobe level lower than -20 dB into the trained neural network model, and outputting the optimized amplitude and phase distribution by the neural network model.

[0006] Further, the center of the large-interval array is set as the coordinate origin, the large-interval array is used as a feed source, and the coordinate positions of each feed unit are located, which specifically includes: The center of the large-interval array is set as the coordinate origin, the large-interval array is used as a feed source, and if the feed array contains N units in the x direction and M units in the y direction, the coordinate positions of each feed unit are located by the following method: ; ; wherein, represents the abscissa of the nth unit of the feed array in the x direction, represents the ordinate of the mth unit of the feed array in the y direction, the interval of the array element of the feed array in the x direction is , and the interval in the y direction is .

[0007] Further, the calculation of the far-zone radiation field generated by each unit on the metasurface transmission array specifically includes: If a point P on the metasurface transmission array is located at the azimuth angle relative to a point Q in the feed array, the far-zone radiation field of the Q point can be calculated by the following method: ; wherein, represents the far-zone radiation field generated by the mnth unit, and C is a unit factor independent of mn. is the excitation current of the mn-th unit, is the distance from point P to the feed, denotes the elevation angle of the control light beam, denotes the azimuth angle of the control light beam horizontal rotation, j denotes the imaginary unit, and k denotes the electromagnetic wave propagation constant.

[0008] Further, the calculation of the far-field radiation field of the entire planar array specifically includes: The far-field radiation field of the entire planar array is: ; wherein, denotes the far-field radiation field of the entire planar array, and the column distribution of the planar array is: ; wherein, denotes the electric field of the column-distributed element of the planar array, denotes the amplitude of the element arranged along the x direction, denotes the phase of the element arranged along the x direction; The row distribution of the planar array is: ; wherein, denotes the electric field of the row-distributed element of the planar array, denotes the amplitude of the element arranged along the y direction, denotes the phase of the element arranged along the y direction; then: .

[0009] Further, the conversion of the spherical wave emitted by the feed into a plane wave, the calculation of the electric field of the feed to the super-structured surface lens array according to the far-field radiation field of the entire planar array, and the calculation of the phase at the super-structured surface lens specifically include: The conversion of the spherical wave emitted by the feed into a plane wave is: On the super-structured surface transmission array, a reference point with a center coordinate of (0, 0) and a point P located at any position on the array are defined. The straight-line distance from point P to the feed is R, and at this time, there is a phase difference between point P and the geometric center of the array, which is ; The plane wave front is constructed, and the phase at point P is compensated in the following manner: ; Substitute the coordinates of point P into the formula, and then: , denotes the vertical distance from the feed to the super-structured surface transmission array, denotes a compensation phase, denotes a wavelength of the electromagnetic wave; calculating the electric field of the feed source at the metasurface lens array in the following manner: , denotes the electric field of the feed source at the metasurface lens array, denotes the i-th row and the j-th column of the metasurface lens array, respectively; denotes the i-th row and the j-th column of the metasurface lens array, respectively; denotes the i-th row and the j-th column of the metasurface lens array, respectively; selecting a reference phase, the phase required at the metasurface lens array is obtained in the following manner: .

[0010] Further, according to the phase placement of the metasurface lens at the metasurface lens array, the total electric field of the electromagnetic wave emitted by the feed source after passing through the metasurface lens array is calculated, and the radiation pattern of the array antenna is calculated according to the calculated total electric field, which specifically includes: If the metasurface lens array contains N1 units in the x direction and M1 units in the y direction, the total electric field of the electromagnetic wave emitted by the feed source after passing through the metasurface lens array is represented as: , denotes the total electric field; According to the total electric field, the radiation pattern of the large-interval array antenna is calculated in the following manner: , denotes the radiation pattern of the array antenna.

[0011] Further, the training neural network model includes an input layer, an output layer, and a hidden layer, the input layer receives large-interval array antenna radiation pattern data, the output layer is the amplitude and phase distribution of the feed source, the neurons of the hidden layer receive the weighted output from all neurons of the previous layer and perform nonlinear transformation through the ReLU activation function, the layer connection mode in the neural network model is full connection, that is, each neuron is connected to all neurons of the next layer through weight, after each hidden layer, a corresponding batch normalization layer is added for normalizing the output of the previous hidden layer, and a Dropout layer is added after the ReLU activation and before the output layer to randomly discard a certain proportion of neuron connections.

[0012] Each connection in the neural network model is provided with a weight value, and each neuron has a bias term, and in the training process, the weight value and the bias term are updated by the back propagation algorithm and the gradient descent method.

[0013] The neural network model dynamically adjusts the learning rate using an Adam optimizer.

[0014] The present application has the following advantages: The present application introduces a transmission array antenna, the feed is ingeniously equivalent to an ideal current source, at the same time, the large-interval array and the super-structured surface lens array are both referenced to the geometric center as the reference point, realizing the accurate calibration of the position coordinates, which plays a crucial role in the subsequent accurate calculation of the electric field distribution on the super-structured surface lens array, so that the radiation pattern characteristics of the large-interval array antenna after loading the super-structured surface can be accurately simulated.

[0015] The present application randomly allocates amplitude and phase values to each large-interval array element, generates array antenna radiation patterns with different characteristics, and the data set is composed of the array antenna radiation patterns with different characteristics, greatly improving the richness of the data set.

[0016] The present application trains the neural network model through the obtained data set, the input layer receives the array antenna radiation pattern data, and the output layer is the amplitude and phase distribution of the feed, and finally outputs the optimized array antenna amplitude and phase through the trained neural network model, improving the calculation efficiency.

[0017] The present application adopts a uniform element design for the large-interval feed, and the element spacing is more than one wavelength, thereby effectively avoiding the serious coupling problem. In addition, the application range of the present application is extremely wide, and it is not only suitable for uniform large-interval arrays, but also shows strong adaptability and compatibility for non-uniform array antennas. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a low-sidelobe large-interval array antenna amplitude and phase design optimization method flowchart provided by the embodiment of the present application; Figure 2 is a schematic diagram of a large-interval array antenna loaded with a super-structured surface lens array provided by the embodiment of the present application; Figure 3 is a schematic diagram of phase compensation provided by the embodiment of the present application; Figure 4 is a neural network model schematic diagram provided by the embodiment of the present application; Figure 5 is a fitting effect comparison schematic diagram on the first test set provided by the embodiment of the present application; Figure 6 is a fitting effect comparison schematic diagram on the second test set provided by the embodiment of the present application; Figure 7 This is a comparison of results after network fitting for a given desired result provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0019] To make the objectives, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0020] The present invention provides a design optimization method for the amplitude and phase of a low sidelobe and large spacing array antenna. Figure 1 As shown, specifically including: S1. Dataset acquisition; For an array antenna system, the electric field strength at each point on the transmission array is directly affected by the radiation pattern of the feed array. Figure 2 This relationship is intuitively demonstrated in the figure, where the elements of the feed array are spaced dx in the x-direction and dy in the y-direction, while the elements of the transmission array are spaced dx1 in the x-direction and dy1 in the y-direction. It is worth noting that the electric field strength at each element position in the transmission array depends not only on the specific position of the element but also on the electric field distribution of the element at the corresponding position in the feed array.

[0021] To accurately describe this relationship, the present invention first sets the center of the array as the coordinate origin. Based on this, assuming the feed array contains N elements along the x-direction and M elements along the y-direction, the following mathematical expression is used to precisely locate the coordinate position of each feed element.

[0022] ; ; in, represents the horizontal coordinate of the nth unit of the feed array in the x direction, represents the ordinate of the mth element of the feed array in the y direction, and the spacing of the elements of the feed array in the x direction is , the spacing in the y direction is ; In order to accurately calculate the electric field strength at each element position in the transmission array, the present invention makes the following assumptions: a specific element P on the transmission array is located exactly relative to a point Q in the feed array. Based on this setting, the electric field strength originating from point Q can be calculated and derived in detail using the following formula.

[0023] ; in, E mn (θ, φ) represents the far-field radiation pattern of the mn th element, C is an element factor independent of mn, is the excitation current of the mn th element, is the distance from point P to the center of the array, represents the elevation angle of the control light, represents the azimuth angle of the horizontal rotation of the control light, j represents the imaginary unit, and k represents the propagation constant of the electromagnetic wave; The far-field radiation pattern of the entire planar array is: ; wherein, represents the far-field radiation pattern of the entire planar array, if the column distribution of the planar array is: ; wherein, represents the electric field of the column-distributed element of the planar array, represents the amplitude of the element arranged along the x direction, represents the phase of the element arranged along the x direction; The row distribution of the planar array is: ; wherein, represents the electric field of the row-distributed element of the planar array, represents the amplitude of the element arranged along the y direction, represents the phase of the element arranged along the y direction; then: ; In a specific frequency range, the metasurface lens unit exhibits excellent phase-independent control ability, and in this process, the amplitude response remains nearly constant. The design of the metasurface lens is ingenious according to the basic principle of phase compensation, in which the electromagnetic wave released by the feed propagates in the form of a spherical wave. In order to achieve the effect of high-gain beam focusing, it is crucial to convert the spherical wave originally emitted by the feed into a plane wave through precise control of the metasurface lens unit. As shown in Figure 3 : the spherical wave emitted by the feed is ingeniously converted into a plane wave after careful adjustment of the metasurface lens array, thereby realizing efficient and high-gain focusing of the beam.

[0024] On the transmission array, for a reference point with a center coordinate of (0, 0) and a point P located at any position on the array , the distance from point P to the center of the array is defined as r, and the straight-line distance from point P to the feed is defined as R. At this time, there is a phase difference between point P and the geometric center of the array, which is denoted as In order to construct an ideal plane wave front, the phase at point P is compensated, and the compensation amount can be specifically expressed as: ; Substitute the coordinates of point P into the formula, then: , represents the vertical distance from the feed source to the metasurface lens array; In the present application, in order to determine the phase that needs to be compensated by the metasurface lens more quickly, the present application calculates the electric field at the metasurface lens from the feed source, and the phase here can be calculated by the following formula: , represents the electric field at the metasurface lens array from the feed source, respectively represent the i-th row and j-th column of the metasurface lens array; respectively represent the i-th row and j-th column of the metasurface lens array; Select a reference phase, such as 0°, then the phase required at the metasurface lens can be calculated by the following formula: ; By the above formula, the metasurface lens array is placed, then the phase of the electromagnetic wave transmitted through the metasurface lens array is consistent and the amplitude is almost unchanged, thereby realizing the focusing of the beam. Assuming that the metasurface lens array contains N1 units in the x direction and M1 units in the y direction, then the total electric field of the electromagnetic wave emitted by the feed source after passing through the metasurface lens array can be expressed as: ; According to the total electric field, the radiation pattern of the array antenna is calculated, and the calculation method is as follows: , represents the radiation pattern of the array antenna; Randomly assign amplitude and phase values to each large-interval array element to generate array antenna radiation patterns corresponding to different characteristics, and the data set is composed of the array antenna radiation patterns corresponding to different characteristics.

[0025] S2, training the neural network model through the obtained data set; ​After obtaining the training dataset, a fully connected network is built, in which the input layer and the output layer are the amplitude and phase distribution of the feed and the radiation pattern of the array antenna respectively. The dataset is first normalized before being put into the network, which can accelerate the model convergence and improve the performance of the model. The neural network uses multiple fully connected layers and batch normalization layers, and enhances the non-linear representation through the ReLU activation function, while effectively preventing overfitting through the Dropout layer. Finally, the prediction is made through the output layer. The design of the model aims to optimize the stability and generalization ability of network training through standardization and regularization methods, and is suitable for regression prediction problems or other tasks that require efficient learning.

[0026] Specifically, the present application combines the relevant theoretical knowledge of the transmission array, and calculates a large-interval array with 8x8 elements, wherein the element interval is set to 1.5 wavelengths. As shown in Figure 3 , at a position 1.0 wavelength above the large-interval array, the present application loads a metasurface lens array, which is twice the size of the entire feed source relative to the distance from the feed source to the metasurface lens. The size of the metasurface lens itself is designed to be 0.25 wavelengths, and its placement height is precisely set at one wavelength above the large-interval feed source . The scale of the entire metasurface lens array reaches 56x56.

[0027] The present application generates 2000 groups of different amplitude and phase distribution of the feed radiation pattern using random functions, wherein the amplitude range is carefully controlled between (0, 1], and the phase range covers all possible values of [0, 360°). These radiation patterns mainly include E-plane and H-plane data, each of which is accurately described by 400 data points. The present application records the amplitude, phase and corresponding radiation pattern of each group in detail, and divides these data into 1800 training sets, 100 validation sets and 100 test sets. In order to facilitate the subsequent training of the neural network, the present application arranges the amplitude and phase data into 1x128 format, and the radiation pattern data into 1x800 format. In order to improve the universality of the dataset and the generalization of the network, the present application randomly shuffles the data, and selects the first 1800 groups as the training set input to the neural network model.

[0028] As Figure 4As shown, in the designed neural network, the input layer receives the radiation pattern data, and the output layer outputs the amplitude and phase distribution of the feed source. Specifically, the input layer contains 800 neurons, and the network architecture is embedded with three hidden layers, which are composed of 1024, 800 and 300 neurons respectively. The neurons of these hidden layers receive the weighted output from all neurons of the previous layer and perform nonlinear transformation through the ReLU activation function, thereby significantly enhancing the nonlinear representation ability of the network. The connection mode of the network layers is full connection, that is, each neuron is connected to all neurons of the next layer through weights. The output layer contains 128 neurons corresponding to the prediction results of the network, which also receive the weighted output from the last hidden layer and undergo final processing through the activation function. After each hidden layer, a corresponding batch normalization layer is added to normalize the output of the previous hidden layer, accelerate the training process and improve the stability of the model. After each hidden layer (after ReLU activation and before the output layer), a Dropout layer is added to randomly discard a certain proportion of neuron connections (20% in this case) to prevent model overfitting.

[0029] Each connection in the neural network model is equipped with a weight value, and each neuron has a bias term. During training, these weights and biases are updated and optimized through the backpropagation algorithm and gradient descent method. The neural network model uses mean square error as the loss function, aiming to minimize the squared error between the predicted value and the actual value. Meanwhile, the optimizer uses the Adam optimizer, and in order to dynamically adjust the learning rate, the model uses the StepLR learning rate scheduler, which multiplies the learning rate by 0.1 every 10 training periods, thereby helping the model better converge during training. After sufficient training, the error on the training set is finally stabilized at 0.6, while the error on the validation set is also stabilized at 0.6, and the error on the test set is also stabilized at 0.6.

[0030] S3, when the error of the neural network model reaches the standard set by the invention, the neural network model is used to successfully output the amplitude and phase distribution of the large-interval array element that meets the requirements, with the target radiation pattern (i.e. the pattern with a side lobe level lower than -20dB) as input. This process not only quickly finds the amplitude and phase distribution of the low side lobe antenna feed source, but also applies to non-uniform large-interval arrays, with universality and flexibility.

[0031] In order to verify the actual effect of the neural network model, the application randomly selects two groups of data on the test set to test the network effect. The application takes the radiation pattern data as the network input, and obtains the corresponding amplitude and phase distribution. Then, the amplitude and phase distribution are calculated by using the formula of the transmission array, and the theoretical radiation pattern is obtained. The two patterns are compared in the same figure, and the results are shown in Figure 5 , Figure 6 It can be clearly seen that the network shows good performance on the test set.

[0032] In order to obtain the expected result, the application generates a radiation pattern with a side lobe average of less than-20dB, and processes it as the input of the neural network model. Then, the output of the neural network is calculated again by using the formula of the transmission array, and the radiation pattern obtained by theoretical calculation is compared with the given expected pattern. The results are shown in Figure 7 It can be clearly seen that although the curve fitted by the neural network has a certain gap with the theoretically calculated picture, the curve fitted by the neural network also meets the requirements of the application, so the method is effective. The method of the application successfully realizes the effect of low side lobe by optimizing the amplitude and phase distribution of the large-interval array antenna.

[0033] The above is only the preferred embodiment of the application, and it should be understood that the application is not limited to the form disclosed herein, and should not be considered as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified by the above teaching or related technical or knowledge within the scope of the concept described herein. The modification and change made by the person skilled in the art without departing from the spirit and scope of the application shall be within the protection scope of the appended claims of the application.

Claims

1. A design optimization method for the amplitude and phase of a low-sidelobe, large-pitch array antenna, applied to a structure consisting of a large-pitch array antenna and a metasurface lens array, characterized in that: include: S1. Obtain the dataset; The center of the large-pitch array is set as the coordinate origin, and the large-pitch array is used as the feed source. The coordinate position of each feed source unit is located, and the far-field radiation field generated by each unit on the metasurface transmission array is calculated. Then, the far-field radiation field of the entire planar array is calculated. The spherical wave emitted by the feed source is converted into a plane wave. Based on the far-field radiation field of the entire planar array, the electric field from the feed source to the metasurface lens array is calculated, and then the phase at the metasurface lens is calculated. The metasurface lens array is placed according to the phase at the metasurface lens, and the total electric field of the electromagnetic wave emitted by the feed source after passing through the metasurface lens array is calculated. The radiation pattern of the array antenna is then calculated based on the calculated total electric field. Finally, amplitude and phase values ​​are randomly assigned to each large-spaced array element to generate corresponding array antenna radiation patterns with different characteristics. The data set consists of the array antenna radiation patterns with different characteristics. S2. Train the neural network model using the acquired data set; S3. Input the radiation pattern of the widely spaced array antenna with a sidelobe level lower than -20 dB into the trained neural network model, and the neural network model outputs the optimized amplitude and phase distribution.

2. The design optimization method for amplitude and phase of a low sidelobe and large spacing array antenna according to claim 1, characterized in that: The center of the large-pitch array is set as the coordinate origin, and the large-pitch array is used as the feed source. The coordinate position of each feed source unit is specifically located as follows: Set the center of the large-pitch array as the coordinate origin, and use the large-pitch array as the feed source. If the feed source array contains N units along the x-direction and M units along the y-direction, the coordinate position of each feed source unit is located using the following method: ； ； in, represents the horizontal coordinate of the nth element of the feed array in the x direction, represents the ordinate of the mth element of the feed array in the y direction, and the spacing of the elements of the feed array in the x direction is , the spacing in the y direction is .

3. The design optimization method for amplitude and phase of a low sidelobe and large spacing array antenna according to claim 2, characterized in that: Calculating the far-zone radiation field generated by each element in the metasurface transmission array specifically involves: If a point P on the metasurface transmission array is located exactly relative to a point Q in the feed array, In azimuth, the far-field radiation field at point Q can be calculated as follows: ； in, represents the far-field radiation generated by the mnth unit, C is a unit factor that is independent of mn, is the excitation current of the mnth unit, is the distance from point P to the feed source, Indicates the pitch angle of the light. represents the azimuth angle that controls the horizontal rotation of light, j represents the imaginary unit, and k represents the propagation constant of electromagnetic waves.

4. The design optimization method for amplitude and phase of a low sidelobe and large spacing array antenna according to claim 3, characterized in that: Calculating the far-zone radiation field of the entire planar array specifically includes: The far-zone radiation field of the entire planar array is: ； in, Represents the far-zone radiation field of the entire planar array. If the column distribution of the planar array is: ； Where, represents the electric field of the column-distributed elements of the planar array, represents the amplitude of the array elements arranged along the x direction, represents the phase of the array elements arranged along the x direction; The row distribution of a plane array is: ； Where, represents the electric field of the row-distributed elements of the planar array, represents the amplitude of the array elements arranged along the y direction, represents the phase of the array elements arranged along the y direction; but: 。 5. The design optimization method for amplitude and phase of a low sidelobe and large spacing array antenna according to claim 4, characterized in that: The spherical wave emitted by the feed source is converted into a plane wave. The electric field from the feed source to the metasurface lens array is calculated based on the far-field radiation field of the entire plane array. The phase at the metasurface lens is then calculated. Specifically, the following steps are involved: Convert the spherical wave emitted by the feed into a plane wave: On the metasurface transmission array, for the reference point with the center coordinate (0,0), and any point located at the array , define the straight-line distance from point P to the feed as R. At this time, there is a phase difference between point P and the geometric center of the array, which is ; Construct a plane wavefront and compensate the phase at point P as follows: ； Substituting the coordinates of point P, we get: , represents the vertical distance from the feed source to the metasurface transmission array, represents the compensation phase, Indicates the wavelength of electromagnetic waves; Calculate the electric field from the feed source to the metasurface lens array as follows: , represents the electric field fed to the metasurface lens array, They represent the first Row, No. List; Select a reference phase, then the phase required at the metasurface lens array is It is derived as follows: 。 6. The design optimization method for amplitude and phase of a low sidelobe and large spacing array antenna according to claim 5, characterized in that: The metasurface lens array is placed according to the phase of the metasurface lens, the total electric field of the electromagnetic wave emitted by the feed source after passing through the metasurface lens array is calculated, and the radiation pattern of the array antenna is calculated based on the calculated total electric field. Specifically, the following steps are performed: If the metasurface lens array contains N1 units in the x-direction and M1 units in the y-direction, the total electric field of the electromagnetic wave emitted by the feed after passing through the metasurface lens array can be expressed as: , represents the total electric field; The radiation pattern of the large-spacing array antenna is calculated based on the total electric field. The calculation method is as follows: , Represents the radiation pattern of the array antenna.

7. The design optimization method for amplitude and phase of a low sidelobe and large spacing array antenna according to claim 1, characterized in that: The neural network model includes an input layer, an output layer and a hidden layer. The input layer receives the radiation pattern data of the large-spacing array antenna, and the output layer is the amplitude and phase distribution of the feed source. The neurons in the hidden layer receive the weighted outputs from all neurons in the previous layer and perform nonlinear transformation through the ReLU activation function. The layer connection mode in the neural network model is fully connected, that is, each neuron is connected to all neurons in the next layer through weights. After each hidden layer, a corresponding batch normalization layer is added to normalize the output of the previous hidden layer. After ReLU activation, a Dropout layer is added before the output layer to randomly discard a set proportion of neuron connections.

8. The design optimization method for amplitude and phase of a low sidelobe and large spacing array antenna according to claim 7, characterized in that: Each connection in the neural network model is set with a weight value, and each neuron has a bias term. During the training process, the weight value and bias term are optimized and updated through the back propagation algorithm and gradient descent method; The neural network model uses the Adam optimizer to dynamically adjust the learning rate; The neural network model uses the StepLR learning rate scheduler, which multiplies the learning rate by 0.1 every 10 training cycles to help the model converge better during training.

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