A method for designing and optimizing the amplitude and phase of a low-sidelobe large-interval array antenna

Abstract

The present application relates to the field of large-interval array antenna design optimization, and particularly relates to a method for designing and optimizing the amplitude and phase of a large-interval array antenna with low sidelobe. The present application randomly assigns each large-interval array element with an amplitude and a phase value, and sets the range of variation of the amplitude and phase value. This random combination of amplitude and phase can generate a series of large-interval array antenna radiation patterns with different characteristics. These rich radiation pattern data constitute the data set for training the neural network model. Then, the neural network model is trained by using the obtained data set. After the training is completed, the large-interval array antenna radiation pattern with a sidelobe level lower than -20 dB is input into the trained neural network model, and the neural network model outputs the optimized amplitude and phase distribution. The present application is suitable for optimizing the design of a large-interval array antenna.

Description

Technical Field

[0001] This invention relates to the field of large-pitch array antenna design optimization, specifically to a method for optimizing the amplitude and phase of a low-sidelobe large-pitch array antenna. Background Technology

[0002] Large-pitch array antennas, because the element spacing often exceeds a wavelength threshold, frequently exhibit high-level grating lobes in their radiation patterns. This grating lobe phenomenon disperses the energy of the main lobe, leading not only to a decline in gain performance but also potentially interfering with precise beam positioning, thus affecting the overall system performance. In electromagnetic compatibility systems, low-sidelobe antennas significantly reduce the radiation intensity of sidelobes and sidelobes, effectively weakening the sensitivity to external interference sources and greatly enhancing the system's anti-interference resilience. This is of paramount importance for systems that must maintain robust operation in high electromagnetic interference environments.

[0003] Currently, sidelobe suppression techniques for large-pitch array antennas mainly cover the following directions: First, intelligent optimization methods such as genetic algorithms, particle swarm optimization, or differential evolution algorithms are used to optimize the arrangement of array elements. However, these algorithms are relatively time-consuming, and the computation time is positively correlated with the scale and number of optimization problems, limiting their efficiency in practical applications. Second, deterministic numerical methods such as Legendre transformation and degree clipping techniques are used. Although these methods do not have specific restrictions on the spacing between array elements, they may cause serious coupling problems, thus weakening their practical application value. Third, metamaterial technology is combined to artificially control the phase distribution above the array antenna to achieve phase uniformity above the array elements, thereby suppressing grating lobes. Although this method can reduce the grating lobe level to a certain extent, the sidelobe level still falls short of the -20dB standard, failing to fully meet the requirements for low sidelobe levels. Summary of the Invention

[0004] The purpose of this 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, large-pitch array antenna. This method optimizes the amplitude and phase of the large-pitch array antenna while meeting the standard that the sidelobe level is below -20dB.

[0005] The present invention achieves the above objectives by adopting the following technical solution: the present invention provides a method for designing and optimizing the amplitude and phase of a low sidelobe, large-pitch array antenna, comprising:

[0006] S1. Obtain the dataset;

[0007] The center of the large-pitch array is set as the origin of the coordinate system. The large-pitch array is used as the feed source. The coordinate position of each feed source element is located, and the far-field radiation field generated by each element 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. The electric field from the feed source to the metasurface lens array is calculated based on the far-field radiation field of the entire planar array. Then, the phase at the metasurface lens is calculated.

[0008] 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. Then, the radiation pattern of the array antenna is calculated based on the calculated total electric field. Finally, the amplitude and phase values ​​are randomly assigned to each large-pitch array element to generate the corresponding array antenna radiation pattern with different characteristics. The dataset consists of the array antenna radiation patterns with different characteristics.

[0009] S2. Train the neural network model using the acquired dataset;

[0010] S3. Input the radiation pattern of the large-spacing array antenna with a sidelobe level below -20dB into the trained neural network model. The neural network model outputs the optimized amplitude and phase distribution.

[0011] Furthermore, by setting the center of the large-pitch array as the coordinate origin and using the large-pitch array as a feed source, the specific steps for locating the coordinate position of each feed source element include:

[0012] With the center of the large-pitch array set as the origin, and the large-pitch array serving as the feed source, if the feed source array contains N elements along the x-direction and M elements along the y-direction, then the coordinate position of each feed source element is located using the following method:

[0013] ;

[0014] ;

[0015] in, This represents the x-coordinate of the nth element in the feed array along the x-direction. This represents the ordinate of the m-th element in the y-direction of the feed array, and the spacing between the elements in the x-direction is... The spacing in the y-direction is .

[0016] Furthermore, the calculation of the far-field radiation field generated by each element on the metasurface transmission array specifically includes:

[0017] If a point P on the metasurface transmission array is located relative to a point Q in the feed array... In terms of azimuth, the far-field radiation at point Q can be calculated as follows:

[0018] ;

[0019] in, Let C represent the far-field radiation field produced by the mn-th unit, where C is the unit factor independent of mn. Let be the excitation current of the mn-th unit. Let P be the distance from point P to the feed source. Indicates the pitch angle that controls the light beam. The azimuth angle represents the angle controlling the horizontal rotation of the light beam, j represents the imaginary unit, and k represents the propagation constant of the electromagnetic wave.

[0020] Furthermore, calculating the far-field radiation field of the entire planar array specifically includes:

[0021] The far-field radiation field of the entire planar array is:

[0022] ;

[0023] in, This represents the far-field radiation of the entire planar array, where the column distribution of the planar array is:

[0024] ;

[0025] In the formula, This represents the electric field of the column-distributed elements of a planar array. This represents the amplitude of the array elements arranged along the x-direction. This indicates the phase of the array elements arranged along the x-direction;

[0026] The row-wise distribution of the planar matrix is ​​as follows:

[0027] ;

[0028] In the formula, This represents the electric field of the row-distributed elements of a planar array. This represents the amplitude of the array elements arranged along the y-direction. This indicates the phase of the array elements arranged along the y-direction;

[0029] but:

[0030] .

[0031] Furthermore, the spherical wave emitted by the feed is converted into a plane wave, and the electric field from the feed to the metasurface lens array is calculated based on the far-field radiation field of the entire planar array. The phase calculation at the metasurface lens specifically includes:

[0032] Convert the spherical wave emitted by the feed source into a plane wave:

[0033] On the metasurface transmission array, for a reference point with center coordinates (0,0), and points located at any position on the array... Let R be the straight-line distance from point P to the feed source. At this point, there is a phase difference between point P and the array's geometric center, which is... ;

[0034] A plane wavefront is constructed, and phase compensation is performed at point P. The compensation method is as follows:

[0035] ;

[0036] Substituting the coordinates of point P into the equation, we get:

[0037] , This represents the vertical distance from the feed source to the metasurface transmission array. Indicates the compensation phase. Indicates the wavelength of electromagnetic waves;

[0038] The electric field from the feed source to the metasurface lens array is calculated as follows:

[0039] , This represents the electric field from the feed source to the metasurface lens array. Representing the first and second layers of the metasurface lens array, respectively. Okay, number List;

[0040] Once a reference phase is selected, the required phase at the metasurface lens array is determined. It is derived in the following way:

[0041] .

[0042] Furthermore, based on the phase of the metasurface lens, a metasurface lens array is placed, and the total electric field of the electromagnetic wave emitted from the feed after passing through the metasurface lens array is calculated. Then, based on the calculated total electric field, the radiation pattern of the array antenna is calculated, specifically including:

[0043] If a metasurface lens array contains N1 elements in the x-direction and M1 elements 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:

[0044] , Represents the total electric field;

[0045] The radiation pattern of a large-pitch array antenna is calculated based on the total electric field, as follows:

[0046] , This represents the radiation pattern of the array antenna.

[0047] Furthermore, the trained neural network model includes an input layer, an output layer, and a hidden layer. The input layer receives radiation pattern data from a large-pitch array antenna, while the output layer contains the amplitude and phase distribution of the feed. The neurons in the hidden layer receive the weighted outputs from all neurons in the previous layer and undergo nonlinear transformation using the ReLU activation function. The layer connections in the neural network model are fully connected, meaning that each neuron is connected to all neurons in the next layer via 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.

[0048] In the neural network model, each connection is assigned a weight value, and each neuron has a bias term. During training, the weight values ​​and bias terms are optimized and updated using the backpropagation algorithm and gradient descent method.

[0049] The neural network model uses the Adam optimizer to dynamically adjust the learning rate. It also uses the StepLR learning rate scheduler, which multiplies the learning rate by 0.1 every 10 training epochs to help the model converge better during training.

[0050] The beneficial effects of this invention are as follows:

[0051] This invention introduces a transmission array antenna, where the feed source is precisely equivalent to an ideal current source. At the same time, both the large-pitch array and the metasurface lens array use their geometric centers as reference points to achieve accurate calibration of their position coordinates. This plays a crucial role in the subsequent accurate calculation of the electric field distribution on the metasurface lens array, thereby enabling the accurate simulation of the radiation pattern characteristics of the large-pitch array antenna after loading the metasurface.

[0052] This invention randomly assigns amplitude and phase values ​​to each large-pitch array element, generating corresponding array antenna radiation patterns with different characteristics. The dataset is composed of these array antenna radiation patterns with different characteristics, greatly improving the richness of the dataset.

[0053] This invention trains a neural network model using the acquired dataset. The input layer receives radiation pattern data from the array antenna, while the output layer provides the amplitude and phase distribution of the feed source. Finally, the trained neural network model outputs optimized array antenna amplitude and phase, thus improving computational efficiency.

[0054] The large-pitch feed of this invention employs a uniform array element design with an element spacing exceeding one wavelength, thereby effectively avoiding severe coupling problems. Furthermore, this invention has an extremely wide range of applications, not only suitable for uniform large-pitch arrays but also exhibiting strong adaptability and compatibility for non-uniform array antennas. Attached Figure Description

[0055] Figure 1 This is a flowchart of a method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to an embodiment of the present invention.

[0056] Figure 2 This is a schematic diagram of a large-pitch array antenna loaded with a metasurface lens array provided in an embodiment of the present invention;

[0057] Figure 3 This is a schematic diagram of phase compensation provided in an embodiment of the present invention;

[0058] Figure 4 This is a schematic diagram of the neural network model provided in an embodiment of the present invention;

[0059] Figure 5 This is a schematic diagram comparing the fitting results on the first test set provided in this embodiment of the invention;

[0060] Figure 6 This is a schematic diagram comparing the fitting results on the second test set provided in this embodiment of the invention;

[0061] Figure 7 This is a comparison of the results after fitting the desired result network provided in the embodiments of the present invention. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0063] This invention provides a method for optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna, such as... Figure 1 As shown, it specifically includes:

[0064] S1. Obtaining the dataset;

[0065] For an array antenna system, the electric field intensity at each point on the transmission array is directly affected by the radiation pattern of the feed array. Figure 2This relationship is visually illustrated, 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 noteworthy that the electric field intensity at each element position in the transmission array depends not only on the specific location of that element but also closely related to the electric field distribution of the corresponding element in the feed array.

[0066] To accurately describe this relationship, this invention first sets the center of the array as the origin of the coordinate system. 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.

[0067] ;

[0068] ;

[0069] in, This represents the x-coordinate of the nth element in the feed array along the x-direction. This represents the ordinate of the m-th element in the y-direction of the feed array, and the spacing between the elements in the x-direction is... The spacing in the y-direction is ;

[0070] To accurately calculate the electric field intensity at each element position in the transmission array, this invention makes the following assumption: a specific element P on the transmission array is located exactly relative to a point Q in the feed array. In terms of azimuth. Based on this setting, the electric field strength originating from point Q can be calculated and derived in detail using the following formula.

[0071] ;

[0072] in, Let C represent the far-field radiation field produced by the mn-th unit, where C is the unit factor independent of mn. Let be the excitation current of the mn-th unit. Let P be the distance from point P to the center of the array. Indicates the pitch angle that controls the light beam. The azimuth angle represents the horizontal rotation of the light beam, j represents the imaginary unit, and k represents the propagation constant of the electromagnetic wave.

[0073] The far-field radiation field of the entire planar array is:

[0074] ;

[0075] in, This represents the far-field radiation of the entire planar array, where the column distribution of the planar array is:

[0076] ;

[0077] In the formula, This represents the electric field of the column-distributed elements of a planar array. This represents the amplitude of the array elements arranged along the x-direction. This indicates the phase of the array elements arranged along the x-direction;

[0078] The row-wise distribution of the planar matrix is ​​as follows:

[0079] ;

[0080] In the formula, This represents the electric field of the row-distributed elements of a planar array. This represents the amplitude of the array elements arranged along the y-direction. This indicates the phase of the array elements arranged along the y-direction;

[0081] but:

[0082] ;

[0083] Within a specific frequency range, the metasurface lens unit exhibits exceptional phase-independent control capabilities while maintaining a nearly constant amplitude response. The metasurface lens design cleverly leverages the fundamental principle of phase compensation, where the electromagnetic waves emitted by the feed propagate as spherical waves. A crucial step in achieving high-gain beam focusing is the precise control of the metasurface lens unit to convert the spherical waves emitted by the feed into plane waves. For example... Figure 3 As shown: the spherical wave emitted by the feed source is cleverly transformed into a plane wave after being carefully adjusted by the metasurface lens array, thus achieving high-efficiency and high-gain focusing of the beam.

[0084] On the transmission array, for a reference point with center coordinates (0,0), and points located at any position on the array... Let r be the distance from point P to the array center, and R be the straight-line distance from point P to the feed source. At this point, there exists a phase difference between point P and the array's geometric center, denoted as [equation missing]. To construct an ideal plane wavefront, phase compensation is performed at point P, and this compensation amount can be specifically expressed as:

[0085] ;

[0086] Substituting the coordinates of point P into the equation, we get:

[0087] , This represents the vertical distance from the feed source to the metasurface transmission array;

[0088] In this invention, to more quickly determine the phase that the metasurface lens needs to compensate for, the electric field from the feed source to the metasurface lens is calculated. The phase here can be calculated using the following formula:

[0089] , This represents the electric field from the feed source to the metasurface lens array. Representing the first and second layers of the metasurface lens array, respectively. Okay, number List;

[0090] If a reference phase is selected, for example, 0°, then the required phase at the metasurface lens is... It can be calculated using the following formula:

[0091] ;

[0092] By positioning the metasurface lens array according to the above formula, the phase of the feed wave passing through the metasurface lens array remains consistent while the amplitude remains almost unchanged, thus achieving beam focusing. Assuming the metasurface lens array contains N1 elements in the x-direction and M1 elements in the y-direction, the total electric field of the electromagnetic wave emitted by the feed wave after passing through the metasurface lens array can be expressed as:

[0093] ;

[0094] The radiation pattern of the array antenna is calculated based on the total electric field, as follows:

[0095] , This represents the radiation pattern of the array antenna.

[0096] Amplitude and phase values ​​are randomly assigned to each large-pitch array element to generate corresponding array antenna radiation patterns with different characteristics. The dataset consists of the array antenna radiation patterns with different characteristics.

[0097] S2. Train the neural network model using the acquired dataset;

[0098] After obtaining the training dataset, a fully connected network is constructed, where the input and output layers represent the amplitude and phase distribution of the feed source and the radiation pattern of the array antenna, respectively. The dataset is normalized before being fed into the network to accelerate model convergence and improve performance. This neural network uses multiple fully connected layers and batch normalization layers, and enhances the nonlinear representation using the ReLU activation function. A Dropout layer effectively prevents overfitting, and predictions are ultimately made through the output layer. The model is designed to optimize the stability and generalization ability of network training through normalization and regularization, making it suitable for regression prediction problems or other tasks requiring efficient learning.

[0099] Specifically, this invention, combining relevant theoretical knowledge of transmission arrays, performed calculations for a large-pitch array with 8×8 elements, where the element spacing is set to 1.5 wavelengths. For example... Figure 3 As shown, at a position 1.0 wavelength above the large-pitch array, this invention loads a metasurface lens array, the size of which is twice the overall size of the feed source, relative to the distance from the feed source to the metasurface lens. The metasurface lens itself is designed to be 0.25 wavelengths in size, and its placement height is precisely set at one wavelength above the large-pitch feed source. At this location, the entire metasurface lens array reaches a size of 56×56.

[0100] This invention utilizes a random function to generate 2000 sets of feed radiation patterns with different amplitude and phase distributions. The amplitude variation range is carefully controlled within (0,1], while the phase variation range fully covers all possibilities in the range [0,360°]. These radiation patterns mainly include data from the E-plane and H-plane, with each plane precisely described using 400 data points. This invention records each set of amplitude, phase, and its corresponding radiation pattern in detail, and divides this data into 1800 training sets, 100 validation sets, and 100 test sets. To facilitate subsequent neural network training, this invention organizes the amplitude and phase data into a 1×128 format, while the radiation pattern data is organized into a 1×800 format. To improve the generality of the dataset and the generalization ability of the network, this invention randomly shuffles the dataset and selects the first 1800 sets as the training set input to the neural network model.

[0101] like Figure 4As shown, in the designed neural network, the input layer receives radiation pattern data, while the output layer represents the amplitude and phase distribution of the feed. Specifically, the input layer contains 800 neurons, and the network architecture embeds three hidden layers, consisting of 1024, 800, and 300 neurons respectively. These hidden layer neurons receive weighted outputs from all neurons in the previous layer and undergo nonlinear transformation using the ReLU activation function, significantly enhancing the network's nonlinear expressive power. The network uses fully connected layers, meaning each neuron is connected to all neurons in the next layer via weights. The output layer contains 128 neurons, corresponding to the network's predictions. These neurons also receive weighted outputs from the last hidden layer and undergo final processing using an activation function. After each hidden layer, a corresponding batch normalization layer is added to normalize the output of the previous hidden layer, accelerating the training process and improving model stability. After each hidden layer (after ReLU activation and before the output layer), a Dropout layer is added, randomly discarding a certain percentage of neuron connections (20% in this case) to prevent overfitting.

[0102] 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 optimized and updated using backpropagation and gradient descent. The neural network model uses mean squared error as the loss function, aiming to minimize the squared error between the predicted and actual values. The optimizer uses the Adam optimizer, and 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 epochs, thus helping the model converge better during training. After sufficient training, the error on the training set eventually stabilized at 0.6, the error on the validation set also stabilized at 0.6, and the error on the test set also stabilized at 0.6.

[0103] S3. Once the error of the neural network model reaches the standard set by this invention, the target radiation pattern (i.e., the pattern with sidelobe levels below -20dB) is used as input to successfully output the amplitude and phase distribution of the large-pitch array elements that meet the requirements. This process can not only quickly find the feed amplitude and phase distribution of low-sidelobe antennas, but is also applicable to non-uniform large-pitch arrays, possessing universality and flexibility.

[0104] To verify the actual performance of the neural network model, this invention randomly selected two sets of data from the test set to test the network's performance. This invention used radiation pattern data as network input and obtained the corresponding amplitude and phase distributions. Then, using the formula for transmission arrays, these amplitude and phase distributions were calculated to obtain the theoretical radiation pattern. The two radiation patterns were compared on the same graph, and the results are as follows... Figure 5 , Figure 6 As shown, it is clear that the network exhibits good performance on the test set.

[0105] To obtain the desired results, this invention generates a radiation pattern with a sidelobe electrical average below -20 dB, processes it, and uses it as input to a neural network model. Next, the output of the neural network is used again to calculate using the formula for a transmission array, and the radiation pattern obtained through theoretical calculation is compared with the given desired radiation pattern. The results are as follows: Figure 7 As shown, it can be clearly seen that although the curve fitted by the neural network differs somewhat from the theoretically calculated image, the curve fitted by the neural network still meets the requirements of this invention, therefore the method is effective. The method of this invention successfully achieves a low sidelobe effect by optimizing the amplitude and phase distribution of the large-pitch array antenna.

[0106] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna, applied to a structure composed 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 origin of the coordinate system. The large-pitch array is used as the feed source. The coordinate position of each feed source element is located, and the far-field radiation field generated by each element 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. The electric field from the feed source to the metasurface lens array is calculated based on the far-field radiation field of the entire planar array. Then, 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. Then, the radiation pattern of the array antenna is calculated based on the calculated total electric field. Finally, the amplitude and phase values ​​are randomly assigned to each large-pitch array element to generate the corresponding array antenna radiation pattern with different characteristics. The dataset consists of the array antenna radiation patterns with different characteristics. S2. Train the neural network model using the acquired dataset; S3. Input the radiation pattern of the large-spacing array antenna with a sidelobe level below -20dB into the trained neural network model. The neural network model outputs the optimized amplitude and phase distribution.

2. The method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to claim 1, is characterized in that, The center of the large-pitch array is set as the origin of the coordinate system. The large-pitch array is used as a feed source. The specific steps for locating the coordinate position of each feed source element include: With the center of the large-pitch array set as the origin, and the large-pitch array serving as the feed source, if the feed source array contains N elements along the x-direction and M elements along the y-direction, then the coordinate position of each feed source element is located using the following method: ； ； in, This represents the x-coordinate of the nth element in the feed array along the x-direction. This represents the ordinate of the m-th element in the y-direction of the feed array, and the spacing between the elements in the x-direction is... The spacing in the y-direction is .

3. The method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to claim 2, is characterized in that, The calculation of the far-field radiation field generated by each element on the metasurface transmission array specifically includes: If a point P on the metasurface transmission array is located relative to a point Q in the feed array... In terms of azimuth, the far-field radiation at point Q can be calculated as follows: ； in, Let C represent the far-field radiation field produced by the mn-th unit, where C is the unit factor independent of mn. Let be the excitation current of the mn-th unit. Let P be the distance from point P to the feed source. Indicates the pitch angle that controls the light beam. The azimuth angle represents the angle controlling the horizontal rotation of the light beam, j represents the imaginary unit, and k represents the propagation constant of the electromagnetic wave.

4. The method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to claim 3, is characterized in that, 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: ； in, This represents the far-field radiation of the entire planar array, where the column distribution of the planar array is: ； In the formula, This represents the electric field of the column-distributed elements of a planar array. This represents the amplitude of the array elements arranged along the x-direction. This indicates the phase of the array elements arranged along the x-direction; The row-wise distribution of the planar matrix is ​​as follows: ； In the formula, This represents the electric field of the row-distributed elements of a planar array. This represents the amplitude of the array elements arranged along the y-direction. This indicates the phase of the array elements arranged along the y-direction; but: 。 5. The method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to claim 4, is characterized in that, The spherical wave emitted by the feed is converted into a plane wave. The electric field from the feed to the metasurface lens array is calculated based on the far-field radiation field of the entire planar array. Then, the phase at the metasurface lens is calculated, specifically including: Convert the spherical wave emitted by the feed source into a plane wave: On the metasurface transmission array, for a reference point with center coordinates (0,0), and points located at any position on the array... Let R be the straight-line distance from point P to the feed source. At this point, there is a phase difference between point P and the array's geometric center, which is... ; A plane wavefront is constructed, and phase compensation is performed at point P. The compensation method is as follows: ； Substituting the coordinates of point P into the equation, we get: , This represents the vertical distance from the feed source to the metasurface transmission array. Indicates the compensation phase. Indicates the wavelength of electromagnetic waves; The electric field from the feed source to the metasurface lens array is calculated as follows: , This represents the electric field from the feed source to the metasurface lens array. These represent the first and second layers of the metasurface lens array, respectively. Okay, number List; Once a reference phase is selected, the required phase at the metasurface lens array is determined. It is derived in the following way: 。 6. The method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to claim 5, is characterized in that, The metasurface lens array is placed according to the phase at the metasurface lens. The total electric field of the electromagnetic wave emitted from the feed source after passing through the metasurface lens array is calculated. Then, the radiation pattern of the array antenna is calculated based on the calculated total electric field. Specifically, this includes: If a metasurface lens array contains N1 elements in the x-direction and M1 elements 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: , Represents the total electric field; The radiation pattern of a large-pitch array antenna is calculated based on the total electric field, as follows: , This represents the radiation pattern of the array antenna.

7. The method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to claim 1, characterized in that, The neural network model includes an input layer, an output layer, and hidden layers. The input layer receives radiation pattern data from a large-pitch array antenna, while the output layer displays the amplitude and phase distribution of the feed. The neurons in the hidden layers receive the weighted outputs from all neurons in the previous layer and undergo a nonlinear transformation using the ReLU activation function. The layer connections in the neural network model are fully connected, meaning that each neuron is connected to all neurons in the next layer via 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 method for designing and optimizing the amplitude and phase of a low-sidelobe, large-pitch array antenna according to claim 7, is characterized in that, In the neural network model, each connection is assigned a weight value, and each neuron has a bias term. During training, the weight values ​​and bias terms are optimized and updated using the backpropagation 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 epochs, thereby helping the model converge better during training.

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