A sparse antenna array synthesis method based on kernel density estimation
By using kernel density estimation and differential optimization algorithms, the problem of insufficient generalization ability of neural networks in sparse data regions in antenna array optimization is solved, realizing efficient and accurate synthesis of sparse arrays and improving design efficiency and accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANDONG UNIV OF SCI & TECH
- Filing Date
- 2026-01-28
- Publication Date
- 2026-06-12
AI Technical Summary
In existing technologies, neural networks suffer from uneven data distribution, particularly in sparse data regions, resulting in unreliable predictions during antenna array optimization and impacting design efficiency and accuracy.
A sparse antenna array synthesis method based on kernel density estimation is adopted. The initial dataset is obtained through full-wave electromagnetic simulation, a kernel density estimation neural network KDENN is constructed, and the differential optimization algorithm combined with weighted loss and course learning strategy is used to divide the array into sparse and dense subsets for training, and the array element positions are optimized to improve prediction accuracy.
It significantly improves the prediction accuracy and generalization ability of neural networks in sparse data regions, ensures efficient and accurate synthesis of sparse arrays, and reduces computational complexity and time cost.
Smart Images
Figure CN121598548B_ABST
Abstract
Description
Technical Field
[0001] This invention discloses a sparse antenna array synthesis method based on kernel density estimation, belonging to the field of smart antenna design technology. Background Technology
[0002] Antenna array technology is a core foundation in the field of wireless communication. As a key infrastructure for achieving high-speed and reliable connections between the physical world and the digital information space, its development level directly determines the performance of modern communication systems.
[0003] Existing non-uniform array design methods face a key technical challenge in engineering practice: the mutual coupling effect between array elements. The mutual coupling effect refers to the mutual influence between adjacent antenna elements in an array due to electromagnetic field interactions. To overcome the problems caused by the mutual coupling effect, researchers have proposed various technical solutions. The most direct traditional method is to introduce full-wave electromagnetic simulation to calculate the radiation pattern of the active elements after adjusting the position of each array element. Full-wave simulation can accurately solve Maxwell's equations, thus capturing the mutual coupling effect with high precision. However, this method has a fatal flaw: its computational load is extremely large and time-consuming. For an optimization process requiring hundreds or thousands of iterations, calling full-wave simulation to re-evaluate the radiation pattern of all elements in each iteration is prohibitively time-consuming, severely restricting design efficiency. To address the problem of excessive computational overhead in full-wave simulation, in recent years, artificial intelligence technology, especially neural networks, has been introduced into the comprehensive optimization of non-uniform arrays. A typical existing technical solution is to pre-obtain a batch of different array element layouts and their corresponding active radiation pattern data through a finite number of full-wave simulations, forming a training dataset. Then, a neural network model is trained to learn the complex nonlinear mapping relationship between "element position distribution" and "active radiation pattern". Once the model is trained, in the subsequent optimization process, this trained neural network can be used to quickly predict the radiation pattern under any new element layout, thereby replacing the computationally expensive full-wave simulation and greatly improving optimization efficiency.
[0004] While neural network algorithms can capture the complex coupling relationships between array elements to some extent, their performance is highly dependent on the quality of the training data. In the vast feature space of array element locations, the sample data obtained through simulation or experimentation is often uneven. Some regions have densely packed sample points, while others are very sparse. Neural network models perform well in densely data-rich regions and make accurate predictions; however, in sparsely data-rich regions, due to insufficient learning, their predictive generalization ability deteriorates significantly. This means that during optimization, if the algorithm explores a sparse array element layout region, the neural network's predictions may be unreliable, leading the optimization in the wrong direction. Therefore, improving the modeling accuracy of neural networks under uneven data distribution, especially their generalization ability in sparsely data-rich regions, is a core problem that urgently needs to be solved in this field. Summary of the Invention
[0005] The purpose of this invention is to provide a sparse antenna array synthesis method based on kernel density estimation, in order to solve the problem in the prior art of how to improve the modeling accuracy of neural networks under uneven data distribution, especially the generalization ability in sparse data regions.
[0006] A sparse antenna array synthesis method based on kernel density estimation includes:
[0007] S1. Based on sparse antenna array, the radiation pattern of active element under different array element position distribution is obtained through full-wave electromagnetic simulation. An initial dataset is established based on the distance of the antenna array elements. The initial dataset includes array element position characteristics and radiation characteristics.
[0008] S2. Calculate the kernel density estimate using the radiation characteristics, construct the kernel density estimation neural network KDENN based on the radiation characteristics and kernel density estimate and train it. After training, the KDENN model is obtained.
[0009] S3. Based on the predicted kernel density estimate, set the proportion threshold, divide the initial dataset into sparse subsets and dense subsets, construct two subnetworks with the same structure, and train them as sparse subset processing branches and dense subset processing branches respectively. After training, the dense branch subnetwork and sparse branch subnetwork are obtained.
[0010] S4. Calculate the initial dataset of the antenna array to be synthesized according to step S1. Optimize the element position features of the antenna array to be synthesized using the differential optimization algorithm. Based on the optimized element position features, KDENN model, proportion threshold, sparse subset processing branch, and dense subset processing branch, output the active element direction prediction map of each element. Preset evaluation parameters and evaluate the performance of the current element position based on the active element direction prediction map. Iteratively optimize the element position according to the performance evaluation results and the differential optimization algorithm until the preset evaluation parameters are met, thus obtaining the sparse antenna array synthesis result.
[0011] S1 includes, S1.1, assuming the sparse antenna array is non-uniformly distributed along a preset coordinate axis. Composed of antenna array elements A linear array, forming Each array element sample is input into a full-wave electromagnetic simulation to construct a far-field radiation pattern model of the array that includes mutual coupling effects.
[0012] ;
[0013] In the formula, This is the far-field radiation pattern. For far field to The steering angle of the shaft, For wave number, , For the operating wavelength, The imaginary unit, For the first The complex excitation amplitude of each antenna element The radiation pattern of the active element. For the first The radiation pattern of the active elements of an antenna array. This is the index of the antenna array element. .
[0014] S1 includes, S1.2, taking the reciprocal of the original relative distance between antenna elements as the input of the antenna elements, setting the reciprocal component of the distance between antenna elements and themselves to 0, and denoting the first... Array element position characteristics at each element for:
[0015] ;
[0016] In the formula, The positional characteristics of the array elements For distance, For the first The distance between each antenna element and the current antenna element will Normalization to Interval.
[0017] S1 includes, S1.3, and will Represent it in complex form, After extracting the real and imaginary parts separately, they are concatenated to construct the radial features. :
[0018] ;
[0019] In the formula, For the real part operator, For the imaginary part operator, This represents the number of angle sampling points.
[0020] Will Normalization to interval, and The initial dataset is constructed and used as array element samples.
[0021] S2 includes, S2.1, based on Calculate the kernel density estimate for each array element sample:
[0022] ;
[0023] In the formula, For kernel function, This is a bandwidth parameter used to control the smoothness of the kernel function. For radiation eigenvectors, for The kernel density estimate, For array element sample index, , For the index variable of the summation loop, , for The kernel density estimate, , The dimension for kernel density estimation. ;
[0024] Calculate the kernel density estimate for all array element samples and normalize it.
[0025] S2 includes, S2.2, and For the dataset, Using labels, construct a kernel density estimation neural network (KDENN), train the neural network, and use the mean squared error as a loss function to constrain the KDENN. When the mean squared error reaches the minimum value, output the result and generate the KDENN model. If the mean squared error does not reach the minimum value, return to the neural network training.
[0026] The kernel density estimation neural network KDENN consists of a fully connected layer, a hidden layer, and an output layer connected sequentially. The number of input nodes in the fully connected layer is equal to the number of array elements, and the number of output nodes is 1. The number of hidden layer nodes is 32 or 64, and the hidden layer uses the ReLU activation function. The output layer uses the sigmoid activation function.
[0027] Kernel density estimation neural network KDENN As input, output is the predicted kernel density estimate. .
[0028] S3 includes, S3.1, according to Set a percentage threshold, and those exceeding the percentage threshold will be... The corresponding initial dataset is divided into dense subsets, and those smaller than the percentage threshold are... The corresponding initial dataset is divided into sparse subsets;
[0029] Two subnetworks with identical structures are constructed. Dense subsets and coefficient subsets are input into the two subnetworks respectively for neural network training. A weighted loss function constrains the subnetwork, and a course learning strategy is introduced for adaptive training. When the weighted loss function reaches the minimum value, the result is output, and dense branch subnetworks and sparse branch subnetworks are generated. If the weighted loss function does not reach the minimum value, the process returns to neural network training.
[0030] The subnetwork adopts a fully connected network structure, including 5 hidden layers and an output layer. The hidden layers use the ReLU activation function, and the output layer uses the Sigmoid activation function. The subnetwork takes the element position features as input and predicts the orientation map of the active elements. This is the output.
[0031] S3 includes S3.2, constructing a weighted loss function based on the kernel density estimate, and setting the array element sample weights in exponential form. :
[0032] ;
[0033] In the formula, The weight distribution adjustment parameter, For the first The kernel density estimate of each array element sample. It is an exponential function;
[0034] A weighted loss function is established based on absolute error. :
[0035] ;
[0036] In the formula, For the first The true active element radiation pattern of each array element sample This is the radiation pattern of the active cells predicted by the model.
[0037] S3 includes S3.4, which introduces a course learning strategy during the training process of the dual-branch network, based on the training cycle. Linear control of the proportion of training samples in each batch:
[0038] ;
[0039] In the formula, This represents the proportion of samples used for updating network parameters in the current training batch. yes The proportion of samples used in the training batch for updating network parameters. for The period that first reaches 1, and sorted in ascending order according to the current loss function, selects the period with the smallest loss. Each sample is backpropagated to update the network parameters. , For batch size, This is the floor function.
[0040] S4 includes:
[0041] S4.1 Initialize the sparse antenna array to be synthesized ;
[0042] S4.2 Optimization using differential evolution algorithm According to the optimized calculate ,Will Input a KDENN model and output the position of the current element. ;
[0043] S4.3, according to The initial dataset is divided into sparse and dense subsets based on the proportion threshold. The dense and sparse subsets are then input into the dense branch subnetwork and the sparse branch subnetwork, respectively, and the output of each element is... ;
[0044] S4.4, Preset evaluation parameters include preset target array radiation patterns or radiation performance indicators, based on each array element. The array far-field pattern model containing mutual coupling effect is used, and the performance of the current array element position is evaluated according to the preset target array pattern or radiation performance index.
[0045] S4.5 Based on the performance evaluation results, the array element positions are iteratively updated using the differential evolution algorithm until the array far-field radiation pattern meets the target array radiation pattern or radiation performance index, and the corresponding sparse antenna array element position distribution is output.
[0046] Compared with existing technologies, this invention has the following advantages: This invention identifies and focuses on sparse data regions through kernel density estimation, and combines weighted loss and course learning to effectively improve the model's fitting ability and prediction generalization performance in sparse data regions, making the training process more stable and convergent, while avoiding training oscillations or convergence difficulties that may result from directly processing all samples. This invention significantly improves performance in sparse data regions while ensuring learning accuracy in dense data regions, resulting in a higher degree of agreement between the overall array pattern prediction results and the full-wave simulation results, providing a reliable technical means for the accurate and efficient synthesis of sparse arrays. Attached Figure Description
[0047] Figure 1 This is a top view of a sparse microstrip patch antenna array;
[0048] Figure 2 This is a flowchart of the training phase of the method of the present invention;
[0049] Figure 3 This is a flowchart of the array synthesis stage of the present invention;
[0050] Figure 4 This is a graph showing the changes in the mean square error between the original model and the optimized model;
[0051] Figure 5 These are comparison images of the radiation pattern of a sparse microstrip patch antenna array before and after optimization.
[0052] Figure 6 This is the amplitude prediction diagram of the array element's radiation pattern for the first array element;
[0053] Figure 7 This is the amplitude prediction diagram of the array element's radiation pattern for the second array element;
[0054] Figure 8 This is the amplitude prediction diagram of the array element's radiation pattern for the third array element;
[0055] Figure 9 This is the amplitude prediction diagram of the array element's radiation pattern for the fourth array element;
[0056] Figure 10 This is the amplitude prediction diagram of the array element's orientation pattern for the fifth array element. Detailed Implementation
[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.
[0058] A sparse antenna array synthesis method based on kernel density estimation includes:
[0059] S1. Based on sparse antenna array, the radiation pattern of active element under different array element position distribution is obtained through full-wave electromagnetic simulation. An initial dataset is established based on the distance of the antenna array elements. The initial dataset includes array element position characteristics and radiation characteristics.
[0060] S2. Calculate the kernel density estimate using the radiation characteristics, construct the kernel density estimation neural network KDENN based on the radiation characteristics and kernel density estimate and train it. After training, the KDENN model is obtained.
[0061] S3. Based on the predicted kernel density estimate, set the proportion threshold, divide the initial dataset into sparse subsets and dense subsets, construct two subnetworks with the same structure, and train them as sparse subset processing branches and dense subset processing branches respectively. After training, the dense branch subnetwork and sparse branch subnetwork are obtained.
[0062] S4. Calculate the initial dataset of the antenna array to be synthesized according to step S1. Optimize the element position features of the antenna array to be synthesized using the differential optimization algorithm. Based on the optimized element position features, KDENN model, proportion threshold, sparse subset processing branch, and dense subset processing branch, output the active element direction prediction map of each element. Preset evaluation parameters and evaluate the performance of the current element position based on the active element direction prediction map. Iteratively optimize the element position according to the performance evaluation results and the differential optimization algorithm until the preset evaluation parameters are met, thus obtaining the sparse antenna array synthesis result.
[0063] S1 includes, S1.1, assuming the sparse antenna array is non-uniformly distributed along a preset coordinate axis. Composed of antenna array elements A linear array, forming Each array element sample is input into a full-wave electromagnetic simulation to construct a far-field radiation pattern model of the array that includes mutual coupling effects.
[0064] ;
[0065] In the formula, This is the far-field radiation pattern. For far field to The steering angle of the shaft, For wave number, , For the operating wavelength, The imaginary unit, For the first The complex excitation amplitude of each antenna element The radiation pattern of the active element. For the first The radiation pattern of the active elements of an antenna array. This is the index of the antenna array element. .
[0066] S1 includes, S1.2, taking the reciprocal of the original relative distance between antenna elements as the input of the antenna elements, setting the reciprocal component of the distance between antenna elements and themselves to 0, and denoting the first... Array element position characteristics at each element for:
[0067] ;
[0068] In the formula, The positional characteristics of the array elements For distance, For the first The distance between each antenna element and the current antenna element will Normalization to Interval.
[0069] S1 includes, S1.3, and will Represent it in complex form, After extracting the real and imaginary parts separately, they are concatenated to construct the radial features. :
[0070] ;
[0071] In the formula, For the real part operator, For the imaginary part operator, This represents the number of angle sampling points.
[0072] Will Normalization to interval, and The initial dataset is constructed and used as array element samples.
[0073] S2 includes, S2.1, based on Calculate the kernel density estimate for each array element sample:
[0074] ;
[0075] In the formula, For kernel function, This is a bandwidth parameter used to control the smoothness of the kernel function. For radiation eigenvectors, for The kernel density estimate, For array element sample index, , For the index variable of the summation loop, , for The kernel density estimate, , The dimension for kernel density estimation. ;
[0076] Calculate the kernel density estimate for all array element samples and normalize it.
[0077] S2 includes, S2.2, and For the dataset, Using labels, construct a kernel density estimation neural network (KDENN), train the neural network, and use the mean squared error as a loss function to constrain the KDENN. When the mean squared error reaches the minimum value, output the result and generate the KDENN model. If the mean squared error does not reach the minimum value, return to the neural network training.
[0078] The kernel density estimation neural network KDENN consists of a fully connected layer, a hidden layer, and an output layer connected sequentially. The number of input nodes in the fully connected layer is equal to the number of array elements, and the number of output nodes is 1. The number of hidden layer nodes is 32 or 64, and the hidden layer uses the ReLU activation function. The output layer uses the sigmoid activation function.
[0079] Kernel density estimation neural network KDENN As input, output is the predicted kernel density estimate. .
[0080] S3 includes, S3.1, according to Set a percentage threshold, and those exceeding the percentage threshold will be... The corresponding initial dataset is divided into dense subsets, and those smaller than the percentage threshold are... The corresponding initial dataset is divided into sparse subsets;
[0081] Two subnetworks with identical structures are constructed. Dense subsets and coefficient subsets are input into the two subnetworks respectively for neural network training. A weighted loss function constrains the subnetwork, and a course learning strategy is introduced for adaptive training. When the weighted loss function reaches the minimum value, the result is output, and dense branch subnetworks and sparse branch subnetworks are generated. If the weighted loss function does not reach the minimum value, the process returns to neural network training.
[0082] The subnetwork adopts a fully connected network structure, including 5 hidden layers and an output layer. The hidden layers use the ReLU activation function, and the output layer uses the Sigmoid activation function. The subnetwork takes the element position features as input and predicts the orientation map of the active elements. This is the output.
[0083] S3 includes S3.2, constructing a weighted loss function based on the kernel density estimate, and setting the array element sample weights in exponential form. :
[0084] ;
[0085] In the formula, The weight distribution adjustment parameter, For the first The kernel density estimate of each array element sample. It is an exponential function;
[0086] A weighted loss function is established based on absolute error. :
[0087] ;
[0088] In the formula, For the first The true active element radiation pattern of each array element sample This is the radiation pattern of the active cells predicted by the model.
[0089] S3 includes S3.4, which introduces a course learning strategy during the training process of the dual-branch network, based on the training cycle. Linear control of the proportion of training samples in each batch:
[0090] ;
[0091] In the formula, This represents the proportion of samples used for updating network parameters in the current training batch. yes The proportion of samples used in the training batch for updating network parameters. for The period that first reaches 1, and sorted in ascending order according to the current loss function, selects the period with the smallest loss. Each sample is backpropagated to update the network parameters. , For batch size, This is the floor function.
[0092] S4 includes:
[0093] S4.1 Initialize the sparse antenna array to be synthesized ;
[0094] S4.2 Optimization using differential evolution algorithm According to the optimized calculate ,Will Input a KDENN model and output the position of the current element. ;
[0095] S4.3, according to The initial dataset is divided into sparse and dense subsets based on the proportion threshold. The dense and sparse subsets are then input into the dense branch subnetwork and the sparse branch subnetwork, respectively, and the output of each element is... ;
[0096] S4.4, Preset evaluation parameters include preset target array radiation patterns or radiation performance indicators, based on each array element. The array far-field pattern model containing mutual coupling effect is used, and the performance of the current array element position is evaluated according to the preset target array pattern or radiation performance index.
[0097] S4.5 Based on the performance evaluation results, the array element positions are iteratively updated using the differential evolution algorithm until the array far-field radiation pattern meets the target array radiation pattern or radiation performance index, and the corresponding sparse antenna array element position distribution is output.
[0098] The following explanation, in conjunction with the accompanying drawings, will provide further details. Figure 1 The sparse microstrip patch antenna array shown employs an irregular rectangular microstrip patch design. Its main body has a top width of 38.39 mm and a side length of 29.77 mm. To achieve high performance, a hybrid structure of multiple stubs and slots is integrated at the bottom edge of the patch. This includes a matching stub on each side, 5.445 mm wide, for impedance matching and bandwidth widening; a slender coupling stub in the center, 3.11 mm wide, for enhancing feed coupling and frequency fine-tuning; and tuning slots with a depth of 5 mm formed between the stubs to disturb surface current and lower the resonant frequency, thereby achieving antenna miniaturization and performance optimization.
[0099] like Figure 2 and Figure 3 As shown, the sparse antenna array synthesis method based on kernel density estimation provided by this invention includes two parts: a training phase and an array synthesis phase. The specific process is as follows.
[0100] Training phase process description: (e.g.) Figure 2As shown, during the training phase, multiple sets of geometric distribution structures for sparse antenna arrays are first generated. Based on these geometric distributions, a full-wave electromagnetic simulation of the sparse antenna arrays is performed, extracting the active element radiation patterns of each array element in the array environment. Simultaneously, array element position feature vectors are constructed based on the spatial distance relationships between array elements, and these vectors, along with the radiation features, constitute the initial dataset. Subsequently, the distribution density value of the radiation features is calculated using the kernel density estimation method. Based on the calculated kernel density estimates, a kernel density estimation neural network (KDENN) is trained to predict the corresponding kernel density estimates based on the array element geometric features. After training, the KDENN model is saved. Furthermore, a percentage threshold for the kernel density estimates is set, and the initial dataset is divided into sparse and dense subsets according to this threshold. Based on the kernel density estimates, a percentage threshold of 75% is set, classifying samples with KDE values in the top 75% (high value range) as the dense subset and samples with KDE values in the bottom 75% (low value range) as the sparse subset. For sparse and dense subsets respectively, sparse and dense subnetworks with consistent structures are constructed. During training, a weighted loss function and a course learning strategy are introduced to train these subnetworks (for sparse subnetworks). Set to 0.5, dense subnetwork (Set to -0.5), and save the corresponding sub-network model after training.
[0101] Array synthesis phase process description: (e.g.) Figure 3 As shown, in the array synthesis stage, the element positions of the sparse antenna array to be synthesized are first initialized, and the element geometric features are constructed based on the current element positions. These element geometric features are input into the kernel density estimation neural network (KDENN) stored during the training phase, and the kernel density estimate corresponding to the current element position is output. Based on the comparison between the kernel density estimate and a preset proportion threshold, a sparse sub-network or a dense sub-network is selected to predict the AEP (Active Element Pattern) of each element at the current element position. Based on the predicted active element patterns of each element, an array far-field pattern model incorporating mutual coupling effects is constructed, and the performance of the array far-field pattern is evaluated or compared with the target array pattern. If the array far-field pattern corresponding to the current element position does not meet the preset array synthesis target, the element positions are updated using an optimization algorithm, and the above element geometric feature construction step is returned to continue the next round of element position optimization; until the array far-field pattern meets the array synthesis target, the corresponding sparse antenna array element position distribution is output, completing the synthesis design of the sparse antenna array.
[0102] Taking a 10-element sparse microstrip patch antenna array as an example, different combinations of element spacing are randomly generated. The initial learning rate for network training is set to 0.001, and the learning rate is reduced to 75% of its original value whenever the training loss stops decreasing; the batch size is set to 16, and the number of training iterations for sparse and dense neural networks is set to 600.
[0103] In the original model, the average loss of the neural network is high without data partitioning, and the pattern loss converges to [value missing] after 300 training epochs. After introducing kernel density estimation partitioning and independent training, the mean squared error (MSE) was analyzed as a function of the kernel density estimate. The mean squared error of the data after training with the sparse model was... The mean square error of the dense model is Compared to sparse data without partitioning, the mean squared error decreased by 72.2%, without affecting dense datasets. Under the condition of training accuracy, the accuracy of sparse data is improved after training with neural networks. This improvement verifies the effectiveness of the kernel density estimation method in balancing data distribution.
[0104] exist Figure 4 The data records the changes in the mean squared error of the original model and the model (dense branch subnetwork and sparse branch subnetwork) during training. As the values gradually converge through training of the neural network, by introducing kernel density estimation, the optimized model reduces the mean square error on sparse data to less than 1% compared to the original model, effectively alleviating the training bias caused by uneven data distribution. Figure 5 The results of array radiation patterns of a sparse antenna array optimized for low sidelobes under different model conditions are presented, including the prediction results of the original neural network model, the prediction results of the model optimized with kernel density estimation, and the reference radiation pattern obtained from full-wave electromagnetic simulation. As can be seen from the figures, compared with the original model without kernel density estimation optimization, the optimized model exhibits higher prediction accuracy in main lobe pointing, sidelobe level, and overall waveform consistency. Its radiation pattern shape is also closer to the full-wave simulation results, indicating that the kernel density estimation method can effectively alleviate the model bias introduced by uneven distribution of training data. Furthermore, considering the symmetry of the array element positions, only the first 5 elements are used for radiation pattern amplitude prediction, and the results of the original model, the optimized model, and the full-wave simulation are compared. The results for the first to fifth elements are shown in the figures below. Figure 6 , Figure 7 , Figure 8 , Figure 9 and Figure 10As shown, after introducing kernel density estimation optimization, the model prediction results can more accurately characterize the amplitude variation trend of the array element radiation pattern, and the agreement with the full-wave simulation results is significantly improved. The above results show that the radiation pattern predicted by the model after kernel density estimation optimization is superior to the original model in both accuracy and consistency, and has a higher agreement with the full-wave simulation results, proving the effectiveness of the method presented in this study.
[0105] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A sparse antenna array synthesis method based on kernel density estimation, characterized in that, include: S1. Based on sparse antenna array, the radiation pattern of active element under different array element position distribution is obtained through full-wave electromagnetic simulation. An initial dataset is established based on the distance of the antenna array elements. The initial dataset includes array element position characteristics and radiation characteristics. S2. Calculate the kernel density estimate using the radiation characteristics, construct the kernel density estimation neural network KDENN based on the radiation characteristics and kernel density estimate and train it. After training, the KDENN model is obtained. S3. Based on the predicted kernel density estimate, set the proportion threshold, divide the initial dataset into sparse subsets and dense subsets, construct two subnetworks with the same structure, and train them as sparse subset processing branches and dense subset processing branches respectively. After training, the dense branch subnetwork and sparse branch subnetwork are obtained. S4. Calculate the initial dataset of the sparse antenna array to be synthesized according to step S1. Optimize the element position characteristics of the antenna array to be synthesized using the differential optimization algorithm. Based on the optimized element position characteristics, KDENN model, proportion threshold, sparse subset processing branch, and dense subset processing branch, output the active element direction prediction map of each element. Preset evaluation parameters and evaluate the performance of the current element position based on the active element direction prediction map. Iteratively optimize the element position according to the performance evaluation results and the differential optimization algorithm until the preset evaluation parameters are met, thus obtaining the sparse antenna array synthesis result.
2. The sparse antenna array synthesis method based on kernel density estimation according to claim 1, characterized in that, S1 includes S1.1, setting the sparse antenna array as a linear array composed of a plurality of antenna elements unevenly distributed along a preset coordinate axis S1.2, obtaining a plurality of element samples, inputting the element samples into full-wave electromagnetic simulation, and constructing an array far-field pattern model containing mutual coupling effects ； wherein is a far field pattern, is a far field to is a steering angle of an axis, is a wave number, , is an operating wavelength, is an imaginary unit, is a complex excitation amplitude of an antenna array element, is an active element pattern, is an active element pattern of an antenna array element, is an index of an antenna array element, .
3. The sparse antenna array synthesis method based on kernel density estimation according to claim 2, characterized in that, S1 includes, S1.2, taking the reciprocal of the original relative distance between antenna elements as the input of the antenna elements, setting the reciprocal component of the distance between antenna elements and themselves to 0, and denoting the first... Array element position characteristics at each element for: ； In the formula, For the positional characteristics of array elements, For distance, For the first The distance between each antenna element and the current antenna element will Normalization to Interval.
4. The sparse antenna array synthesis method based on kernel density estimation according to claim 3, characterized in that, S1 includes, S1.3, and will Represent it in complex form, After extracting the real and imaginary parts separately, they are concatenated to construct the radial features. : ； In the formula, For the real part operator, For the imaginary part operator, This represents the number of angle sampling points. Will Normalization to interval, and The initial dataset is constructed and used as array element samples.
5. The sparse antenna array synthesis method based on kernel density estimation according to claim 4, characterized in that, S2 includes, S2.1, based on Calculate the kernel density estimate for each array element sample: ； In the formula, For kernel function, This is a bandwidth parameter used to control the smoothness of the kernel function. For radiation eigenvectors, for The kernel density estimate, For array element sample index, , For the index variable of the summation loop, , for The kernel density estimate, , The dimension for kernel density estimation. ; Calculate the kernel density estimate for all array element samples and normalize it.
6. The sparse antenna array synthesis method based on kernel density estimation according to claim 5, characterized in that, S2 includes, S2.2, and For the dataset, Using labels, construct a kernel density estimation neural network (KDENN), train the neural network, and use the mean squared error as a loss function to constrain the KDENN. When the mean squared error reaches the minimum value, output the result and generate the KDENN model. If the mean squared error does not reach the minimum value, return to the neural network training. The kernel density estimation neural network KDENN consists of a fully connected layer, a hidden layer, and an output layer connected sequentially. The number of input nodes in the fully connected layer is equal to the number of array elements, and the number of output nodes is 1. The number of hidden layer nodes is 32 or 64, and the hidden layer uses the ReLU activation function. The output layer uses the sigmoid activation function. Kernel density estimation neural network KDENN As input, output is the predicted kernel density estimate. .
7. The sparse antenna array synthesis method based on kernel density estimation according to claim 6, characterized in that, S3 includes, S3.1, according to Set a percentage threshold, and those exceeding the percentage threshold will be... The corresponding initial dataset is divided into dense subsets, and those smaller than the percentage threshold are... The corresponding initial dataset is divided into sparse subsets; Two subnetworks with identical structures are constructed. Dense subsets and coefficient subsets are input into the two subnetworks respectively for neural network training. A weighted loss function constrains the subnetwork, and a course learning strategy is introduced for adaptive training. When the weighted loss function reaches the minimum value, the result is output, and dense branch subnetworks and sparse branch subnetworks are generated. If the weighted loss function does not reach the minimum value, the process returns to neural network training. The subnetwork adopts a fully connected network structure, including 5 hidden layers and an output layer. The hidden layers use the ReLU activation function, and the output layer uses the Sigmoid activation function. The subnetwork takes the element position features as input and predicts the orientation map of the active elements. This is the output.
8. The sparse antenna array synthesis method based on kernel density estimation according to claim 7, characterized in that, S3 includes S3.2, constructing a weighted loss function based on the kernel density estimate, and setting the array element sample weights in exponential form. : ； In the formula, The weight distribution adjustment parameter, For the first The kernel density estimate of each array element sample. It is an exponential function; A weighted loss function is established based on absolute error. : ； In the formula, For the first The true active element radiation pattern of each array element sample This is the radiation pattern of the active cells predicted by the model.
9. The sparse antenna array synthesis method based on kernel density estimation according to claim 8, S3 includes, S3.4, introducing a course learning strategy during the training process of the dual-branch network, according to the training cycle. Linear control of the proportion of training samples in each batch: ； In the formula, This represents the proportion of samples used for updating network parameters in the current training batch. yes The proportion of samples used in the training batch for updating network parameters. for The period that first reaches 1, and sorted in ascending order according to the current loss function, selects the period with the smallest loss. Each sample is backpropagated to update the network parameters. , For batch size, This is the floor function.
10. A sparse antenna array synthesis method based on kernel density estimation according to claim 9, characterized in that, S4 include: S4.1 Initialize the sparse antenna array to be synthesized ; S4.2 Optimization using differential evolution algorithm According to the optimized calculate ,Will Input a KDENN model and output the position of the current element. ; S4.3, according to The initial dataset is divided into sparse and dense subsets based on the proportion threshold. The dense and sparse subsets are then input into the dense branch subnetwork and the sparse branch subnetwork, respectively, and the output of each element is... ; S4.4, Preset evaluation parameters include preset target array radiation patterns or radiation performance indicators, based on each array element. The array far-field pattern model containing mutual coupling effect is used, and the performance of the current array element position is evaluated according to the preset target array pattern or radiation performance index. S4.5 Based on the performance evaluation results, the array element positions are iteratively updated using the differential evolution algorithm until the array far-field radiation pattern meets the target array radiation pattern or radiation performance index, and the corresponding sparse antenna array element position distribution is output.