An antenna array performance improvement method based on neural network

Abstract

The application discloses an antenna array performance improvement method based on a neural network and belongs to the technical field of wireless communication technologies.The method uses a greedy algorithm as an iterative framework and embeds a deep neural network as a candidate set generation tool to realize optimization of antenna unit positions.The method uses the powerful non-convex function mapping capability of the neural network to generate an optimized candidate set, combines the greedy algorithm to perform iterative evaluation, and solves the convergence and optimization dilemma faced by the prior art when designing a large-scale array.The method uses a double neural network model for respectively processing group and individual unit optimization, guarantees a minimum spacing constraint of the antenna units, significantly improves design efficiency and optimization performance, and has the characteristics of high efficiency, robustness and suitability for large-scale arrays.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a method for improving the energy harvesting efficiency of a two-dimensional sparse antenna array by integrating neural networks and greedy algorithms. Background Technology

[0002] Far-field microwave power transfer (MPT) technology is of great value for wireless power supply, with its core objective being to achieve efficient power transmission and collection. While tapered amplitude excitation can be used in MPT transmit antenna array design to pursue high beam collection efficiency (BCE), this method often leads to reduced antenna aperture utilization, thus affecting the overall system power transmission efficiency. To overcome this drawback, uniformly spaced antenna arrays (INSAs) have emerged. By optimizing the spatial position of antenna elements rather than the excitation amplitude, and employing a uniform excitation method, INSAs provide a new approach to improving the overall wireless power transmission and reception efficiency of antenna arrays.

[0003] However, in practical integration of INSAs, especially for large-scale arrays to meet the requirements of MPT systems for high efficiency and specific radiation patterns (such as central dense distribution to achieve spatial taper), existing design methods face severe technical challenges. The minimum spacing constraint between elements and the design principle of spatial taper make many swarm intelligence-based optimization algorithms and their individual mutation versions prone to getting caught in a "convergence-optimization dilemma" during the optimization process, where it is difficult to balance convergence speed and global optimization capability; this problem becomes particularly prominent when the array size increases significantly.

[0004] Some constraint methods that rely on specific distance models (such as those based on Chebyshev distance) struggle to effectively guarantee the minimum spacing between antenna elements in the diagonal direction. The optimization process often suffers from low overall computational efficiency due to the large number of repetitive fitness function (BCE) or energy harvesting efficiency (ECE) evaluations. For large-scale arrays, the high computational cost of a single fitness evaluation further exacerbates the slow convergence problem. Existing advanced individual mutation strategies (such as the DE-NEM-CM method combined with differential evolution) may fail to effectively place newly generated elements precisely in the specific locations desired by the MPT application (such as a denser central distribution required for high BCE), potentially leading to instability in the optimization process and a decrease in optimization effectiveness as the array size continues to increase. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for improving antenna array performance based on neural networks. This method can effectively handle minimum spacing constraints, adapt to the design requirements of large-scale arrays, and efficiently guide antenna elements to make reasonable spatial arrangements to maximize performance indicators.

[0006] The technical problem addressed by this invention is solved as follows:

[0007] A method for improving the performance of an antenna array based on a neural network includes the following steps:

[0008] Step S1: Establish an XYZ three-dimensional rectangular coordinate system, mesh the XOY two-dimensional plane space, select the same number of grid points as the number of antenna elements in the two-dimensional sparse antenna array, and initialize the coordinates of the selected grid points as the optimal antenna element position matrix in the XOY two-dimensional plane space.

[0009] Step S2: Based on the current optimal antenna element position matrix, calculate the optimized target performance value of the two-dimensional sparse antenna array. The optimized target performance value corresponding to the current optimal antenna element position matrix is ​​denoted as the optimal optimized target performance value.

[0010] Step S3: Construct a first deep neural network model and a second deep neural network model. The first deep neural network model and the second deep neural network model have the same structure, both including an input layer, a hidden layer and an output layer cascaded in sequence. The hidden layer includes a linear layer and a ReLU activation function cascaded in sequence.

[0011] For the first deep neural network model, the input layer is the expected optimization target performance value of the two-dimensional sparse antenna array, and the output layer is the position change matrix of all antenna elements in the two-dimensional sparse antenna array; for the second deep neural network model, the input layer is the expected optimization target performance value of the two-dimensional sparse antenna array, and the output layer is the position change matrix of any antenna element in the two-dimensional sparse antenna array.

[0012] Step S4: Adjust the current optimal antenna element position matrix according to the position change matrix output by the deep neural network model to obtain the updated antenna element position matrix; calculate the loss function of the deep neural network model based on the updated antenna element position matrix.

[0013] Step S5: Update the first deep neural network model using the loss function Loss1; input the expected optimization target performance value of the two-dimensional sparse antenna array into the updated first deep neural network model to generate the position change matrix of all antenna elements in the two-dimensional sparse antenna array; update the antenna element position matrix according to the generated position change matrix, and calculate the optimization target performance value A' of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix; use the generated position change matrix and the optimization target performance value A' as training samples to train the first deep neural network model;

[0014] Complete the training of the first deep neural network model several times according to the above process, compare the maximum value of the optimization target performance value A' in all training samples with the current optimization target performance value A. If A' > A, update the current optimal antenna element position matrix to the antenna element position matrix corresponding to this training sample, and update the current optimal optimization target performance value to the maximum value of A'.

[0015] Step S6: Traverse all antenna elements in the two-dimensional sparse antenna array to perform a movable distance check; if the movable distance meets the set threshold, mark this antenna element; traverse the marked antenna elements and update the second deep neural network model using the loss function Loss2.

[0016] Input the expected optimization target performance value of the two-dimensional sparse antenna array into the updated second deep neural network model to generate a position change matrix for all antenna elements in the two-dimensional sparse antenna array; update the antenna element position matrix according to the generated position change matrix, and calculate the optimization target performance value A' of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix; use the generated position change matrix and the optimization target performance value A' as training samples to train the second deep neural network model.

[0017] For each marked antenna element, complete the training of the second deep neural network model several times according to the above process, compare the minimum value of the loss function Loss2' corresponding to all training samples with the loss function Loss2 corresponding to the current optimal antenna element position matrix. If Loss2' < Loss2, update the current optimal antenna element position matrix to the antenna element position matrix corresponding to the training sample with the minimum value of the loss function Loss2', and update the current optimal optimization target performance value to the maximum value of A'.

[0018] Step S7: Iteratively execute Step S5 and Step S6 until convergence or the current iteration number reaches the set maximum value, and output the current optimal antenna element position matrix and its corresponding current optimal optimization target performance value.

[0019] Further, in Step S1, during the process of meshing the XOY two-dimensional plane space, the grid period is such that the number of grid points within the array aperture of the two-dimensional sparse antenna array is greater than the number of antenna elements.

[0020] Further, select the energy harvesting efficiency as the optimization target performance value. In Step S2 and Step S4, the array factor pattern AF(u, v) of the two-dimensional sparse antenna array is expressed as:

[0021]

[0022] where θ and These are the elevation and azimuth angles of any point in the XYZ three-dimensional rectangular coordinate system, respectively. θ0 and Here, represents the scanning elevation angle and scanning azimuth angle of the two-dimensional sparse antenna array, respectively; 1 ≤ n ≤ N, where N is the total number of antenna elements in the two-dimensional sparse antenna array, k is the wavenumber, and x... n and y n These are the x and y coordinates of the nth antenna element in the XOY two-dimensional plane space, respectively.

[0023] The energy harvesting efficiency (ECE) of a two-dimensional sparse antenna array is expressed as:

[0024] ECE=APR′BCE

[0025] Where BCE is the beam collection efficiency of the two-dimensional sparse antenna array, and APR is the ratio of the actual input power of the two-dimensional sparse antenna array to the input power of the uniform excitation array.

[0026]

[0027] Among them, a n The normalized excitation amplitude of the nth antenna element;

[0028]

[0029] Wherein, the superscript H represents the conjugate transpose, Ω represents the entire spatial domain in the XYZ three-dimensional rectangular coordinate system, and ψ represents the specified spatial domain range centered on the maximum radiation direction of the two-dimensional sparse antenna array pattern.

[0030] Furthermore, in step S3, the position change matrix refers to the polar coordinate coefficient and polar angle coefficient of the antenna element relative to the origin, established by taking the current coordinate position of the antenna element in the XOY two-dimensional plane space as the origin.

[0031] Furthermore, in step S4, for the nth antenna element, the updated antenna element position matrix P n '=[x n ',y n '] represents:

[0032]

[0033] Where, x n 'and y n 'Represents the XOY coordinates in the two-dimensional plane space corresponding to the updated antenna element position matrix, x and y respectively. n and y n Represent the XOY coordinates in the two-dimensional plane space corresponding to the current optimal antenna element position matrix; and the actual moving distance of the nth antenna element. The movement distance coefficients in the position change matrix output by the deep neural network model represent the movable distance. min represents taking the minimum value, j∈[1,N],j≠n, d nj d represents the spacing between the nth antenna element and the jth antenna element. cons This represents the minimum spacing between adjacent antenna elements; the actual movement direction of the nth antenna element. Phi represents the movement direction coefficient in the position change matrix output by the deep neural network model. start =0°, Phi end =360°;

[0034] The loss function Loss1 of the first deep neural network model is expressed as:

[0035] Loss1=1-ECE'

[0036] Where ECE' is the energy harvesting efficiency of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix;

[0037] The loss function Loss2 of the second deep neural network model is expressed as:

[0038] Loss2 = c1·Loss1 + c2·Loss dist

[0039] Where c1 and c2 represent Loss1 and Loss respectively. dist The weights; the loss function corresponding to the updated position matrix of a single antenna element. dist Represented as:

[0040]

[0041] Where the nth antenna element is located within the array aperture AP, then let dist _ flag = 0, otherwise let dist _ flag = 1; dist(AP, P n ') represents the minimum distance between the nth antenna element and the AP boundary of the array aperture; ReLU represents the ReLU function, max represents taking the maximum value, dist(P n ',P j ') represents the distance between the nth antenna element and the jth antenna element.

[0042] Furthermore, in steps S5 and S6, the process of updating the deep neural network model using the loss function Loss is represented as follows:

[0043]

[0044] Among them, W i and W i ' represents the model weight matrix before and after the update, respectively, where η is the learning rate; B i and B i ' represents the model bias matrix before and after the update, 1≤i≤N h +1, N h This represents the number of hidden layers.

[0045] Furthermore, in step S6, if the movable distance satisfies Rho... n <0.01*d cons Then mark the antenna element.

[0046] The beneficial effects of this invention are:

[0047] (1) The method described in this invention establishes a deep neural network and utilizes its powerful non-convex function mapping capability to balance the convergence speed and global optimization capability, so that the antenna element position can be optimized to the best.

[0048] (2) The method of the present invention embeds a first deep neural network and a second deep neural network into a greedy algorithm to perform position change operations on all antenna elements and any antenna element respectively, thereby ensuring the minimum spacing constraint of all antenna elements during the optimization process.

[0049] (3) The method described in this invention is applicable to improving the energy harvesting efficiency of large-scale antenna arrays with resolvable apertures such as rectangles or circles. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the initial arrangement position of the antenna array in the XYZ three-dimensional rectangular coordinate system in the method described in the embodiment;

[0051] Figure 2 This is a schematic diagram of the iterative framework of the method for improving the energy harvesting efficiency of a two-dimensional sparse antenna array that integrates neural networks and greedy algorithms as described in the embodiment.

[0052] Figure 3 This is a schematic diagram showing the initial and optimized arrangement positions of the 25 antenna elements in the first quadrant of the XOY plane in the method described in the embodiment.

[0053] Figure 4 The antenna array radiation pattern is calculated using the method described in the embodiment.

[0054] Figure 5 This is a top view of the antenna array in the method described in the embodiment;

[0055] Figure 6 The above are the radiation pattern analysis results and simulation results of the antenna array in the method described in the embodiment, where (a) is the E-plane radiation pattern, (b) is the H-plane radiation pattern, and (c) is the D-plane radiation pattern. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0057] This embodiment provides a neural network-based method for improving antenna array performance. Energy harvesting efficiency is selected as the target performance value for optimization, and it is applicable to MPT transmit antenna array design in the following fields: electric vehicles, drones, and solar satellite wireless power supply. The energy harvesting efficiency of a two-dimensional sparse antenna array is optimized using a method that integrates neural networks and a greedy algorithm. The neural network serves as a candidate set generation tool, and the greedy algorithm serves as an iterative framework. The greedy algorithm iteratively evaluates and selects from the candidate set generated by the neural network, thereby improving the energy harvesting efficiency of the two-dimensional sparse antenna array and enhancing the energy transmission efficiency of the far-field microwave power transmission system.

[0058] The method described in this embodiment takes improving the energy harvesting efficiency of a two-dimensional sparse antenna array with 100 array elements as an example, and specifically includes the following steps:

[0059] Step S1: As Figure 1 As shown, a three-dimensional Cartesian coordinate system (XYZ) is established, and the two-dimensional XOY plane space is meshed. During the meshing process, the mesh period ensures that the number of meshes within the array aperture is greater than and as close as possible to the number of antenna elements. In this embodiment, considering that the distribution of antenna elements in the two-dimensional sparse antenna array to be optimized has a centrally symmetrical characteristic in the XOY plane, 25 antenna elements are arranged in the first, second, third, and fourth quadrants of the XOY plane coordinate system, and the 100 antenna elements are symmetrically distributed along the X and Y axes. This step simplifies the problem, requiring only the optimization of the position matrix of the 25 antenna elements in the first quadrant.

[0060] Randomly select a number of grid points equal to the number of antenna elements in the two-dimensional sparse antenna array, and initialize the coordinates of the selected grid points as the current optimal antenna element position matrix in the XOY two-dimensional plane space. In this embodiment, the initialization process of the optimal antenna element position matrix of the 25 antenna elements in the XOY two-dimensional plane space is as follows: define the square region formed by (0,0), (0,3.15λ), (3.15λ,0), and (3.15λ,3.15λ) in the XOY coordinate system as the array aperture of the two-dimensional sparse antenna array, denoted as AP; divide AP with a uniform square grid, and the grid spacing is greater than or equal to the minimum allowable spacing d between antenna elements. consThe number of grid points within the AP should be as close to 25 as possible but not less than 25; randomly select 25 grid points within the AP and use their coordinate positions as the current optimal antenna element position matrix for the 25 antenna elements in the first quadrant.

[0061] Step S2: Based on the current optimal antenna element position matrix, calculate the array factor pattern and energy harvesting efficiency of the two-dimensional sparse antenna array. The energy harvesting efficiency corresponding to the current optimal antenna element position matrix is ​​denoted as the optimal energy harvesting efficiency.

[0062] Furthermore, in steps S2 and S4, the array factor pattern AF(u,v) of the two-dimensional sparse antenna array is represented as:

[0063]

[0064] in, θ and These are the elevation and azimuth angles of any point in the XYZ three-dimensional rectangular coordinate system, respectively. θ0 and These represent the scanning elevation and scanning azimuth angles of a two-dimensional sparse antenna array, respectively; 1 ≤ n ≤ 25, k is the wavenumber, and x... n and y n and represent the x and y coordinates of the nth antenna element in the XOY two-dimensional plane space, respectively.

[0065] The energy harvesting efficiency (ECE) of a two-dimensional sparse antenna array is expressed as:

[0066] ECE=APR′BCE

[0067] Where BCE is the beam collection efficiency of the two-dimensional sparse antenna array, and APR is the ratio of the actual input power of the two-dimensional sparse antenna array to the input power of the uniform excitation array.

[0068]

[0069] Among them, a n The normalized excitation amplitude of the nth antenna element;

[0070]

[0071] Wherein, the superscript H represents the conjugate transpose, Ω represents the entire spatial domain in the XYZ three-dimensional rectangular coordinate system, and ψ represents the specified spatial domain range centered on the maximum radiation direction of the two-dimensional sparse antenna array pattern.

[0072] In this embodiment, each antenna element is uniformly excited, so ECE = BCE, and the scanning angle is set to (0,0).

[0073] Step S3: Construct a first deep neural network model and a second deep neural network model. The first deep neural network model and the second deep neural network model have the same structure, both including an input layer, a hidden layer and an output layer cascaded in sequence. The hidden layer includes a linear layer and a ReLU activation function cascaded in sequence.

[0074] For the first deep neural network model, the input layer is the expected energy harvesting efficiency of the two-dimensional sparse antenna array, and the output layer is the position change matrix of all antenna elements in the two-dimensional sparse antenna array; for the second deep neural network model, the input layer is the expected energy harvesting efficiency of the two-dimensional sparse antenna array, and the output layer is the position change matrix of any antenna element in the two-dimensional sparse antenna array.

[0075] The position change matrix refers to the polar radius coefficient and polar angle coefficient of the antenna element relative to the origin, established by taking the current coordinate position of the antenna element in the XOY two-dimensional plane space as the origin.

[0076] In this embodiment, the input layer of both the first and second deep neural network models contains one neuron, which is the desired two-dimensional sparse antenna array ECE; each of the hidden layers of both models contains a linear layer and a ReLU activation function, with the number of neurons in each layer being 16, 32, 64, 128, 128, 64, 32, and 16, respectively; the output layer of the first deep neural network model has 50 neurons, which is the position change matrix of all antenna elements in the two-dimensional sparse antenna array; the output layer of the second deep neural network model has 2 neurons, which is the position change matrix of any antenna element in the two-dimensional sparse antenna array.

[0077] The input layer neurons of the deep neural network model are the desired two-dimensional sparse antenna array ECE0, and the desired ECE0 is set to 100%; the output layer uses the Sigmoid activation function.

[0078] Step S4: Adjust the current optimal antenna element position matrix according to the position change matrix output by the deep neural network model to obtain the updated antenna element position matrix; calculate the loss function of the deep neural network model based on the updated antenna element position matrix.

[0079] Furthermore, in step S4, for the nth antenna element, the updated antenna element position matrix P n '=[x n ',y n '] represents:

[0080]

[0081] Where, x n 'and y n'Represents the XOY coordinates in the two-dimensional plane space corresponding to the updated antenna element position matrix, x and y respectively. n and y n Represent the XOY coordinates in the two-dimensional plane space corresponding to the current optimal antenna element position matrix; and the actual moving distance of the nth antenna element. The movement distance coefficients in the position change matrix output by the deep neural network model represent the movable distance. min represents taking the minimum value, j∈[1,N],j≠n, d nj d represents the spacing between the nth antenna element and the jth antenna element. cons This represents the minimum spacing between adjacent antenna elements; the actual movement direction of the nth antenna element. Phi represents the movement direction coefficient in the position change matrix output by the deep neural network model. start =0°, Phi end =360°.

[0082] The loss function Loss1 of the first deep neural network model is expressed as:

[0083] Loss1=1-ECE'

[0084] Where ECE' is the energy harvesting efficiency of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix.

[0085] The loss function Loss2 of the second deep neural network model is expressed as:

[0086] Loss2 = c1·Loss1 + c2·Loss dist

[0087] Where c1 and c2 represent Loss1 and Loss respectively. dist The weights; the loss function corresponding to the updated position matrix of a single antenna element. dist Represented as:

[0088]

[0089] Where the nth antenna element is located within the array aperture AP, then let dist _ flag = 0, otherwise let dist _ flag = 1; dist(AP, P n ') represents the minimum distance between the nth antenna element and the AP boundary of the array aperture; ReLU represents the ReLU function, max represents taking the maximum value, dist(P n ',P j') represents the distance between the nth antenna element and the jth antenna element.

[0090] Step S5: Update the first deep neural network model using the loss function Loss1; input the desired energy harvesting efficiency of the two-dimensional sparse antenna array into the updated first deep neural network model to generate a position change matrix for all antenna elements in the two-dimensional sparse antenna array; update the antenna element position matrix according to the generated position change matrix, and calculate the energy harvesting efficiency ECE' of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix; use the generated position change matrix and the energy harvesting efficiency ECE' as training samples to train the first deep neural network model. <​​​​​​​​​​​​​​​​​Furthermore, in steps S5 and S6, the process of updating the deep neural network model using the loss function Loss is represented as follows:

[0096]

[0097] Among them, W i and W i ' represents the model weight matrix before and after the update, respectively, where η is the learning rate; B i and B i ' represents the model bias matrix before and after the update, 1≤i≤N h +1, N h This represents the number of hidden layers.

[0098] Step S7: As Figure 2 As shown, steps S5 and S6 are executed iteratively until convergence or the current iteration count reaches the set maximum value, and the current optimal antenna element position matrix and its corresponding current optimal energy harvesting efficiency are output.

[0099] In this embodiment, the positions of the 25 antenna elements in the first quadrant represented by the final optimal antenna element position matrix are as follows: Figure 3 As shown, its corresponding array radiation direction Figure 4 As shown, a simulation is established in the full-wave simulation software as follows: Figure 5 The antenna array model shown has the following radiation pattern results: Figure 6 As shown, Figure 6 (a) is the orientation pattern of plane E. Figure 6 (b) is the H-plane radiation pattern. Figure 6 (c) shows the D-plane radiation pattern, with an energy harvesting efficiency of 91.58%.

Claims

1. A method for improving the performance of an antenna array based on a neural network, characterized in that, Includes the following steps: Step S1: Establish an XYZ three-dimensional rectangular coordinate system, mesh the XOY two-dimensional plane space, select the same number of grid points as the number of antenna elements in the two-dimensional sparse antenna array, and initialize the coordinates of the selected grid points as the optimal antenna element position matrix in the XOY two-dimensional plane space. Step S2: Based on the current optimal antenna element position matrix, calculate the optimized target performance value of the two-dimensional sparse antenna array. The optimized target performance value corresponding to the current optimal antenna element position matrix is ​​denoted as the optimal optimized target performance value. Step S3: Construct a first deep neural network model and a second deep neural network model. The first deep neural network model and the second deep neural network model have the same structure, both including an input layer, a hidden layer and an output layer cascaded in sequence. The hidden layer includes a linear layer and a ReLU activation function cascaded in sequence. For the first deep neural network model, the input layer is the expected optimization target performance value of the two-dimensional sparse antenna array, and the output layer is the position change matrix of all antenna elements in the two-dimensional sparse antenna array; for the second deep neural network model, the input layer is the expected optimization target performance value of the two-dimensional sparse antenna array, and the output layer is the position change matrix of any antenna element in the two-dimensional sparse antenna array. Step S4: Adjust the current optimal antenna element position matrix based on the position change matrix output by the deep neural network model to obtain the updated antenna element position matrix; Based on the updated antenna element position matrix, calculate the loss function of the deep neural network model; Step S5: Update the first deep neural network model using the loss function Loss1; input the expected optimization target performance value of the two-dimensional sparse antenna array into the updated first deep neural network model to generate the position change matrix of all antenna elements in the two-dimensional sparse antenna array; update the antenna element position matrix according to the generated position change matrix, and calculate the optimization target performance value A' of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix. The generated position change matrix and the optimized target performance value A' are used as training samples to train the first deep neural network model; The first deep neural network model is trained several times according to the above process. The maximum value of the optimized target performance value A' in all training samples is compared with the current optimal optimized target performance value A. If A'>A, the current optimal antenna element position matrix is ​​updated to the antenna element position matrix corresponding to the training sample, and the current optimal optimized target performance value is updated to the maximum value of A'. Step S6: Traverse all antenna elements in the two-dimensional sparse antenna array and check the movable distance; if the movable distance meets the set threshold, mark the antenna element; traverse the marked antenna elements and update the second deep neural network model using the loss function Loss2; Input the expected optimized target performance value of the two-dimensional sparse antenna array into the updated second deep neural network model to generate a position change matrix for all antenna elements in the two-dimensional sparse antenna array; update the antenna element position matrix according to the generated position change matrix, and calculate the optimized target performance value A' of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix; Use the generated position change matrix and the optimized target performance value A' as training samples to train the second deep neural network model; For each marked antenna element, complete several trainings of the second deep neural network model according to the above process, and compare the minimum value of the loss function Loss2' corresponding to all training samples with the loss function Loss2 corresponding to the current optimal antenna element position matrix. If Loss2' < Loss2, update the current optimal antenna element position matrix to the antenna element position matrix corresponding to the training sample with the minimum value of the loss function Loss2', and update the current optimal optimized target performance value to the maximum value of A'; Step S7: Iteratively execute Step S5 and Step S6 until convergence or the current iteration number reaches the set maximum value, and output the current optimal antenna element position matrix and its corresponding current optimized target performance value.

2. The method for improving antenna array performance based on neural networks according to claim 1, characterized in that, In Step S1, during the gridification process of the XOY two-dimensional plane space, the grid period is such that the number of grid points within the array aperture of the two-dimensional sparse antenna array is greater than the number of antenna elements.

3. The method for improving antenna array performance based on neural networks according to claim 1, characterized in that, Select the energy harvesting efficiency as the optimized target performance value. In Steps S2 and S4, the array factor pattern AF(u, v) of the two-dimensional sparse antenna array is expressed as: in, θ and These are the elevation and azimuth angles of any point in the XYZ three-dimensional rectangular coordinate system, respectively. θ0 and Here, represents the scanning elevation and scanning azimuth angles of the two-dimensional sparse antenna array, respectively; 1 ≤ n ≤ N, where N is the total number of antenna elements in the two-dimensional sparse antenna array, k is the wavenumber, and x... n and y n These are the x and y coordinates of the nth antenna element in the XOY two-dimensional plane space, respectively. The energy harvesting efficiency ECE of the two-dimensional sparse antenna array is expressed as: ECE = APR × BCE where, BCE is the beam harvesting efficiency of the two-dimensional sparse antenna array, and APR is the ratio of the actual input power of the two-dimensional sparse antenna array to the input power of the uniformly excited array; Among them, a n The normalized excitation amplitude of the nth antenna element; where, the superscript H represents the conjugate transpose, Ω represents the entire spatial domain in the XYZ three-dimensional rectangular coordinate system, and ψ represents the specified spatial domain range centered on the maximum radiation direction of the pattern of the two-dimensional sparse antenna array.

4. The method for improving antenna array performance based on neural networks according to claim 1, characterized in that, In Step S3, the position change matrix refers to establishing a polar coordinate system with the current coordinate position of the antenna element itself in the XOY two-dimensional plane space as the origin, and the radial coefficient and polar angle coefficient of the updated coordinate position of the antenna element relative to the origin.

5. The method for improving antenna array performance based on neural networks according to claim 3, characterized in that, In step S4, for the nth antenna element, the updated antenna element position matrix P n '=[x n ',y n '] represents: Where, x n 'and y n 'Represents the XOY coordinates in the two-dimensional plane space corresponding to the updated antenna element position matrix, x and y respectively. n and y n Represent the XOY coordinates in the two-dimensional plane space corresponding to the current optimal antenna element position matrix; and the actual moving distance of the nth antenna element. The movement distance coefficients in the position change matrix output by the deep neural network model represent the movable distance. min represents taking the minimum value, j∈[1,N],j≠n, d nj d represents the spacing between the nth antenna element and the jth antenna element. cons This represents the minimum spacing between adjacent antenna elements; the actual movement direction of the nth antenna element. Phi represents the movement direction coefficient in the position change matrix output by the deep neural network model. start =0°, Phi end =360°; The loss function Loss1 of the first deep neural network model is expressed as: Loss1 = 1 - ECE' where, ECE' is the energy harvesting efficiency of the two-dimensional sparse antenna array corresponding to the updated antenna element position matrix; The loss function Loss2 of the second deep neural network model is expressed as: Loss2=c1·Loss1+c2·Loss dist Where c1 and c2 represent Loss1 and Loss respectively. dist The weights; the loss function corresponding to the updated position matrix of a single antenna element. dist Represented as: Where the nth antenna element is located within the array aperture AP, then let dist _ flag = 0, otherwise let dist _ flag = 1; dist(AP, P n ') represents the minimum distance between the nth antenna element and the AP boundary of the array aperture; ReLU represents the ReLU function, max represents taking the maximum value, dist(P n ',P j ') represents the distance between the nth antenna element and the jth antenna element.

6. The method for improving antenna array performance based on neural networks according to claim 5, characterized in that, In Steps S5 and S6, the process of updating the deep neural network model using the loss function Loss is expressed as: Among them, W i and W i ' represents the model weight matrix before and after the update, respectively, where η is the learning rate; B i and B i ' represents the model bias matrix before and after the update, 1≤i≤N h +1, N h This represents the number of hidden layers.

7. The method for improving antenna array performance based on neural networks according to claim 1, characterized in that, In step S6, if the movable distance satisfies Rho n <0.01*d cons Then mark the antenna element.

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