Phase-only real-time beam scanning and sidelobe control method based on machine learning

Abstract

The invention discloses an array antenna phase-only real-time beam scanning and side lobe control method based on machine learning. Firstly, array geometry, scanning angles and minor lobe indexes are set; and then, array element excitation phases meeting requirements are rapidly synthesized by using a phase-only fast Fourier FFT (Fast Fourier Transform) algorithm. Constructing a training data set by taking the scanning angle and the minor lobe index as input and the corresponding phase distribution as output; training a neural network by using the data set to obtain a real-time prediction model from initial excitation distribution to accurate excitation distribution; and according to a target expected directional diagram scanning angle and a sidelobe feature, inputting the scanning angle and the sidelobe feature into a neural network to predict and obtain an array element excitation phase so as to realize a real-time phase-only beam and sidelobe control function. Input dimensions are reduced by extracting key features of a directional diagram, data generation is accelerated by means of FFT, real-time performance and precision are both considered, and the method is suitable for fast beam scheduling tasks of various array antennas.

Description

Technical Field

[0001] This invention relates to the field of array antennas, and more specifically, to a machine learning-based method for phase-only real-time beam scanning and sidelobe control of array antennas. Background Technology

[0002] With the rapid development of 5G communication technology and the in-depth advancements in astronomical exploration, aerospace engineering, and military technology, large-scale array antenna technology is increasingly becoming a research hotspot and attracting widespread attention from academia and industry. Phase-only beam scanning technology, by adjusting the phase of array elements while maintaining constant amplitude, rapidly achieves beam direction switching, effectively improving system response speed and hardware feasibility. Furthermore, in modern communication and electronic warfare environments, phase-only beam scanning not only reduces system complexity and power consumption but also enables flexible control of signal direction in dynamic environments, thereby enhancing anti-interference capabilities and resource scheduling efficiency. Therefore, the phase-only real-time beam scanning method for large-scale arrays is of great significance in both academic research and engineering practice.

[0003] Beam scanning and pattern shaping under phase-only constraints have always been a challenge in array antenna research. To address this problem, the academic community has developed various numerical optimization strategies aimed at achieving rapid synthesis of array patterns. Among them, the alternating projection method, due to its simplicity and intuitive structure, has been widely adopted in engineering practice. Mathematical programming techniques such as semidefinite relaxation and sequential convex optimization provide feasibility verification of theoretical solutions and lower bound estimates of performance for phase-only shaping problems. Furthermore, intelligent optimization methods such as genetic algorithms and particle swarm optimization are widely used for scenarios with complex pattern shapes or multi-objective constraints. Although these algorithms have made positive progress in handling non-convex phase-only optimization problems, their high computational cost and slow convergence speed make it difficult to meet the real-time requirements of rapid beam switching in dynamic scenarios. To address these challenges, in recent years, data-driven machine learning methods have been gradually introduced into this field. By constructing end-to-end prediction models through neural networks, rapid estimation of phase-only excitation weights and flexible control of beam direction have been achieved, expanding the solutions for real-time beam scanning.

[0004] Leveraging its strengths in fitting complex nonlinear functions and its strong generalization ability, machine learning technology has been widely applied in various fields such as speech recognition, image processing, and signal processing. In the research of array antenna beam synthesis, neural networks can learn the nonlinear mapping relationship between input and output. After training on high-quality datasets and employing appropriate regularization strategies, they possess the ability to quickly predict array excitation based on design specifications. Introducing machine learning methods into antenna array synthesis can significantly reduce the computational cost of beamforming solutions in large-scale array systems, thereby improving overall beamforming efficiency and engineering practicality.

[0005] Chinese Patent 201811366570.7 discloses a fast beamforming method using phase-weighted only. This method employs a fast beamforming algorithm, first setting the desired beam pattern and initializing the weighting function and phase weighting values. Iteratively updating the phase of each antenna element while keeping the weighted values ​​of other elements unchanged gradually minimizes the beamforming error. In each iteration, the weighting function at discrete angles is updated synchronously, causing the array beam pattern to continuously approximate the desired beam shape, ultimately obtaining an optimized phase-weighted vector, achieving efficient beam control that adjusts only the phase. However, this method still cannot achieve real-time beamforming in terms of efficiency.

[0006] Chinese Patent 202110679734.7 discloses a method and system for synthesizing planar array radiation patterns based on an FFT-based genetic algorithm. This method proposes an FFT-based genetic algorithm for optimizing planar array radiation patterns. An initial population is generated and transformed into amplitude and phase excitation matrices. The radiation pattern is obtained using Fast Fourier Transform (FFT), and selection, crossover, and mutation operations are guided by a fitness function for iterative optimization. Finally, the optimal excitation weights for low-sidelobe beamforming or zeroing the radiation pattern are output, theoretically enabling phase-only array synthesis. This method utilizes FFT to convert the amplitude and phase to and from the antenna radiation pattern, significantly improving computational efficiency. However, the global optimization algorithm itself has limitations; it converges slowly in large-scale beam synthesis and is prone to getting trapped in local optima.

[0007] Chinese Patent 202311314802.5 discloses an antenna pattern prediction method based on a residual convolutional neural network model. This method inputs the amplitude matrix, phase matrix, array arrangement matrix, and predicted frequency of the array antenna excitation into a trained pattern prediction model to obtain the vector of the antenna's radiation pattern. While this method can quickly and accurately obtain the radiation pattern of a phased array antenna at several harmonic frequencies both in and out of band, its accuracy suffers when dealing with full-space three-dimensional pattern prediction problems. The large number of output layers leads to lengthy training times for the neural network and prolonged prediction times, impacting overall accuracy.

[0008] To address the technical problems encountered in the background art described above, this invention proposes a real-time phase-only beam scanning method for array antennas based on machine learning. Summary of the Invention

[0009] To address the aforementioned problems, the present invention aims to propose a machine learning-based real-time phase-only beam scanning method for array antennas. This method is applicable to arrays with arbitrary layouts and can predict the excitation phase distribution of the array in real time based on the desired scanning direction and sidelobe requirements.

[0010] To achieve the above-mentioned technical objectives, the present invention includes the following steps:

[0011] Step 1: Constructing a benchmark dataset

[0012] Based on the given array geometry, the input portion of the benchmark dataset is composed of different desired scan angles and sidelobe control parameters. The FFT phase-only algorithm is then used to synthesize the precise excitation phase distributions corresponding to different scan angles and sidelobe requirements, forming the output portion of the benchmark dataset.

[0013] Step 2: Build and train the machine learning model

[0014] Construct a backpropagation (BP) neural network model, where the input data are the scan angle and sidelobe control, and the output data is the excitation phase. Use the backpropagation algorithm to train the network and obtain the weights and biases of the BP neural network.

[0015] Step 3: Perform stimulus prediction based on the trained machine learning model.

[0016] By inputting the target scanning angle and sidelobe requirements into the trained BP neural network, the precise excitation distribution of the corresponding array units can be obtained in real time.

[0017] Compared with existing technologies, the beneficial effects of this invention are as follows: it proposes to use a BP neural network to fit the nonlinear relationship between the pattern diagnostic index and the excitation phase, which solves the problems of high computational complexity and insufficient real-time performance of phase-only beam scanning and sidelobe control in large-scale antenna arrays. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the method of the present invention;

[0020] Figure 2 This is a schematic diagram of the 256-element 16*16-element planar array layout in an embodiment of the present invention;

[0021] Figure 3 The BP neural network model designed in this embodiment of the invention includes an input layer, hidden layers, an output layer structure, and a number of neurons.

[0022] Figure 4 For performance testing in this embodiment of the invention, the scanning angle is... The target desired power pattern has a maximum sidelobe level of -18.75 dB.

[0023] Figure 5 shows the embodiment of the present invention. Figure 4 The neural network predicts the direction pattern of the target. Detailed Implementation

[0024] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments are not intended to limit the present invention. The present invention mainly introduces a low-complexity real-time beamforming method for array antennas based on feature extraction. The method includes the following steps:

[0025] First, given a The pattern function of a metaplanar array can be expressed as:

[0026]

[0027] in , , It is the observation angle in the global coordinate system. For the first The incentive of each array element Indicates wave number, Indicates the operating wavelength. For the first The position of each array element.

[0028] Next, this patent proposes to solve the phase-only array scanning and sidelobe control problem using Fast Fourier Transform (FFT), collecting the excitation phase distribution that meets the desired requirements. The phase-only array pattern synthesis method based on FFT performs an inverse transform of the desired pattern in the spatial frequency domain to obtain the complex form of the array excitation. While maintaining a constant excitation amplitude, only its phase information is extracted for element feeding, thus achieving phase-only pattern approximation. This method utilizes the fast computation characteristics of FFT and IFFT to effectively improve the computational efficiency of array synthesis, and is particularly suitable for arrays with uniformly arranged elements.

[0029] First, we introduce the two-dimensional discrete Fourier transform (2D-DFT) and its inverse transform (2D-IDFT). Given two-dimensional data... Its size is M*N, and its two-dimensional DFT is defined as follows:

[0030]

[0031] in, It is the imaginary unit. , The corresponding two-dimensional IDFT definition is as follows:

[0032]

[0033] Now let's analyze the computational complexity of DFT and IDFT, each The calculation requires MN complex multiplications and additions, for a total of MN complex multiplications. Therefore, the computational complexity is O(n). When M and N are large, the computational complexity increases very rapidly. To address this issue, the FFT algorithm is introduced to accelerate the computation.

[0034] If 2D-FFT is used, it can be equivalent to first performing an N-point 1D-FFT on each row, and the computational complexity of this step is O(n). Then perform an M-point 1D-FFT on each column. The computational complexity of this step is O(n). The total complexity is calculated as follows The complexity of FFT increases relatively slowly with the increase of sequence length, which makes large-scale array analysis possible.

[0035] For a rectangular M*N uniform planar array in the XOY plane, with element spacing dx along the X-axis and element spacing dy along the Y-axis, the array factor of this array in uv space is:

[0036]

[0037] in, The excitation for the mn-th element includes excitation amplitude and phase information. The wave number in space, Let u and v be the wavelengths at the antenna's operating frequency.

[0038]

[0039] in and These are the azimuth and elevation angles, respectively. and These represent the beam pointing angles of the focused beam. Under the premise of uniform sampling, compare matrix factors There is a two-dimensional Fourier transform relationship between the excitation and the stimulus:

[0040]

[0041] Accelerating 2D-DFT using FFT allows for rapid calculation of matrix factors. Get motivated Or by incentives Obtain the array factor .

[0042] The array synthesis algorithm based on iterative Fourier transform can be applied to low sidelobe control of planar arrays. The algorithm's iterative process is based on an alternating projection framework, using FFT and IFFT to replace the forward and backward accumulation processes during iteration, thus reducing computational complexity. Given a defined pattern scanning angle and sidelobe constraints, the array pattern is adjusted according to the target pattern in each iteration. The adjusted pattern is then back-calculated to obtain the corresponding excitation. Forward projection uses IFFT to solve for the pattern from the excitation, while backward projection uses FFT to solve for the element excitation from the pattern. The main flow of the FFT-based phase-only beam scanning and sidelobe control method is as follows:

[0043] Step 1: Set initial stimuli The amplitude is 1, and the phase is the desired scan angle. Compensation phase;

[0044] Step 2: Incentives The initial radiation pattern is derived in the forward direction using a 2D-IFFT (inverse Fourier transform) with K1*K2 sampling points. The number of sampling points K1*K2 must be greater than the number of array units M*N.

[0045] Step 3: In the radiation map Find the sidelobe region, set the amplitude value in this region that is greater than the target sidelobe constraint (SLT) to a fixed value (SSL), and keep the phase unchanged. In this iteration, obtain the corrected radiation pattern. Typically, SSL is slightly less than SLT, for example, SSL = SLT - 3dB.

[0046] Step 4: Analyze the corrected radiation pattern Using a 2D-FFT with M*N sampling points, the excitation after the iteration is derived by backwards while retaining the first M*N sampling points.

[0047] Step 5: For the phase-only synthesis problem, the iterative excitation... The amplitude is set to be the same as the initial stimulus;

[0048] Step 6: Repeat steps 2 to 5. The termination condition can be that the direction pattern meets the expected requirements or the number of iterations reaches the upper limit.

[0049] Next, we will collect [the data]. Each pattern is given a scanning angle and sidelobe indices. ,in , Indicates the first Desired beam scanning angle and sidelobe parameters .

[0050] Regarding the above Given a scanning angle and sidelobe index for a given radiation pattern, an array synthesis algorithm using phase-only iterative Fourier transform is employed to obtain a precise excitation phase distribution dataset. This precise excitation phase matrix can then be expressed as:

[0051]

[0052] in This represents the array excitation phase that satisfies the k-th given scan angle and sidelobe index of the radiation pattern:

[0053]

[0054] A backpropagation (BP) neural network mainly consists of four layers: one input layer, one output layer, and two hidden layers. Its training process can be divided into two main stages: the first stage is forward propagation, which moves the error from the input layer through the hidden layers to the output layer; the second stage is backward propagation, which moves the error from the output layer to the hidden layers and back to the input layer. Backpropagation is the core component of the BP neural network, allowing for the sequential adjustment of weights and biases between the three layers.

[0055] Before training a backpropagation (BP) neural network, the network needs to be initialized. Assume the number of nodes in the input layer is... The number of nodes in the hidden layer is The number of output layer nodes is The weights from the input layer to the hidden layer are The bias from the input layer to the hidden layer is The weights from the hidden layer to the output layer are The bias from the hidden layer to the output layer is The learning rate is The activation function is The sigmoid function is generally used: By introducing nonlinear functions through activation functions, neural networks can fit nonlinear data.

[0056] For a neural network that has undergone the above initialization, the output of the hidden layer and the input of the output layer are... The output of the output layer is ,get Then we can output according to the expected results. Calculation error ,in , , , .

[0057] The backpropagation process of a BP neural network updates the network's weights and biases based on the error between the network's output and the desired output, aiming to minimize the error function.

[0058]

[0059] Gradient descent can be used to update the weights from the hidden layer to the output layer.

[0060]

[0061]

[0062] Weight update from input layer to hidden layer:

[0063]

[0064] in:

[0065]

[0066]

[0067] The updated formula is:

[0068]

[0069] Similarly, using gradient descent to update the bias, the formula for updating the bias from the hidden layer to the output layer is as follows:

[0070]

[0071]

[0072] Bias update from input layer to hidden layer:

[0073]

[0074] in:

[0075]

[0076]

[0077] The updated formula is:

[0078]

[0079] Based on the collected data samples, a benchmark dataset for model training and evaluation was constructed. On this basis, a machine learning model based on a backpropagation (BP) neural network was designed and trained. The training process mainly includes key steps such as data preprocessing, setting the neural network structure and parameters, and model training and parameter tuning.

[0080] Data preprocessing stage: The benchmark dataset is randomly divided into training, validation, and test sets according to a preset ratio. The training set is used to fit the neural network model, the validation set is used to adjust and optimize the parameters during training, and the test set is used to evaluate the generalization performance of the model after training is completed.

[0081] Backpropagation (BP) Neural Network Structure and Parameter Settings: The BP neural network mainly consists of three layers: one input layer, one output layer, and one hidden layer. The number of neurons in the input and output layers is determined by the number of indicators and the number of array elements, respectively, with 3 and M*N neurons. The number of neurons in the hidden layer is set based on the actual model fitting results. The activation function for the hidden layer is the sigmoid function.

[0082]

[0083] This function converges faster than the Sigmoid function, and its approximate saturation region covers a wider range. The purelin function is used as the activation function for the output layer. This function is often used for function approximation problems in neural networks.

[0084] Neural Network Training and Parameter Tuning: The training of a BP neural network includes two processes: forward propagation and error backpropagation. This patent selects the Scaled Conjugate Gradient (SCG) algorithm as the error backpropagation algorithm. This algorithm combines the fast convergence and adaptive step size adjustment mechanism of the conjugate gradient method, effectively avoiding the objective function from getting trapped in local minima, and significantly reducing the number of iterations required for training, thereby improving training efficiency. Compared with the traditional gradient descent method, the SCG algorithm does not rely on manually setting the learning rate, but instead uses the approximate information of the Hessian matrix to scale and adjust the search direction, avoiding frequent line search operations and accelerating the optimization process while ensuring numerical stability. In addition, the SCG algorithm can adaptively adjust the step size according to the local curvature of the error surface, avoiding the oscillation or convergence stagnation problems common in gradient methods. It is particularly suitable for neural network structures with a large number of parameters and complex error surfaces, and shows higher training accuracy and stronger generalization ability in practical applications.

[0085] In training a backpropagation (BP) neural network, the weights and biases are first randomly initialized. The output of the neural network is calculated using sample data from the training set through forward propagation. The mean squared error (MSE) is used as the loss function to measure the difference between the predicted and accurate activation of the neural network. The loss function LS can be expressed as:

[0086]

[0087] In the loss function LS, To predict incentives, For precise excitation, the maximum number of epochs during neural network training is no less than 2000, while the learning rate is controlled between 0.001 and 0.005 to ensure system stability. After training, a validation set is used to test the performance of the obtained neural network model. Once the BP neural network model meets the performance requirements, the desired radiation pattern scanning angle and sidelobe index are input into the neural network model, allowing for real-time prediction of the array excitation phase required to achieve the desired radiation pattern.

[0088] The specific implementation of the low-complexity real-time beamforming technology for array antennas based on feature extraction proposed in this invention can be further given through the following simulation examples and results:

[0089] In this simulation example, consider a minimum element spacing of an array composed of ideal point sources operating at 15 GHz. The basic layout of the 16*16 regular planar array priced at 256 yuan is as follows: Figure 2 As shown. Next, a dataset was generated based on the desired power pattern scanning angle and sidelobe control. The dataset covers a φ=0° profile pattern with a scanning angle θ ranging from [-20°, 20°, @0.2°] and a sidelobe level ranging from [-20dB, -15dB, @0.2dB]. The precise excitation phase distribution was obtained using a phase-only iterative Fourier algorithm, resulting in 5226 sets of sample data. The dataset was randomly divided in a ratio of 0.76:0.09:0.15, with 3972 sets (76%) as the training set, 470 sets (9%) as the validation set, and 784 sets (15%) as the test set. A BP neural network was trained using an Intel i7-13700kf@3.6GHz processor and 32GB RAM. After multiple experiments, the number of neurons in the hidden layer was determined to be [256, 64], with a learning rate of 0.004. The network structure is shown below. Figure 3As shown.

[0090] Select a set of test samples, and their expected pattern scanning angle The desired radiation pattern under a target with a maximum sidelobe level of -18.75 dB. Figure 5 (a) shows the predicted orientation pattern obtained by the BP neural network model. Figure 5 (a) shows the radiation pattern obtained using phase-only FFT. The comparison shows that the main lobe shape of the predicted radiation pattern is consistent with the expected radiation pattern, and the sample MSE value is... The sidelobe level increased by 1.3 dB, and the prediction time was 0.0017 s, indicating good prediction performance. Table 1 shows multiple test results, revealing good agreement on sidelobe level prediction, with the MSE of all test samples being less than [value missing]. The maximum sidelobe level error does not exceed 1.3dB, and the prediction time does not exceed 0.002s. These results verify the effectiveness of this technique. The trained BP neural network has low complexity and extremely high excitation prediction efficiency, making it suitable for real-time beamforming of array antennas.

[0091] Table 1. Prediction results of the BP neural network model

[0092]

Claims

1. A machine learning-based method for phase-only real-time beam scanning and sidelobe control of an array antenna includes the following steps: 1) Based on the preset array geometry, a sample dataset is generated by combining the scanning angle of the desired power pattern and the sidelobe control requirements; an iterative Fourier transform algorithm based on phase constraints is used to obtain the accurate excitation phase distribution that meets the target pattern performance index; different scanning angles and sidelobe control parameters are used as input datasets, and the corresponding calculated accurate phase distribution of the array is used as output datasets, thereby constructing a benchmark dataset for training machine learning models. 2) Construct an error backpropagation (BP) neural network model. The core optimization method of the BP neural network is to continuously adjust the weights to minimize the loss function through gradient descent and backpropagation. Its input is different desired scanning angles and their corresponding sidelobe feature requirements, and the output is the accurate excitation phase distribution of the corresponding desired power pattern. Optimize the structural parameters of the BP neural network using the scaling conjugate gradient algorithm until the preset convergence or stopping conditions are met. 3) By inputting the target scanning angle and sidelobe features into the trained BP neural network model, the precise excitation phase distribution of the corresponding array unit can be predicted in real time, thereby achieving fast phase-only beam scanning and sidelobe control.

2. The method for phase-only real-time beam scanning and sidelobe control of an array antenna based on machine learning according to claim 1, characterized in that... This method can predict and obtain the required array excitation phase distribution in real time based on the index characteristics of the target desired power pattern, thereby enabling flexible and rapid beam scanning and sidelobe adjustment.

3. The method for phase-only real-time beam scanning and sidelobe control of an array antenna based on machine learning according to claim 1, characterized in that... Step 1: The array synthesis algorithm based on iterative Fourier transform can be applied to low sidelobe control of planar arrays. This algorithm uses FFT and IFFT to replace the forward and backward accumulation processes in the iteration process, thus significantly reducing computational complexity. Given a clear target pattern scanning angle and sidelobe constraints, the current array pattern is aligned with the target pattern in each iteration. Then, the updated excitation phase distribution is obtained through reverse calculation. Specifically, the forward projection process uses IFFT to derive the pattern from the excitation, while the backward projection process uses FFT to inversely solve the array element excitation from the pattern. The conversion formula between the pattern and the excitation is as follows: ； ； in for Array factor in space, For the first The incentive of each array element Indicates wave number, The element spacing along the X-axis is dx, and the element spacing along the Y-axis is dy.

4. The real-time phase-only beam scanning and sidelobe control method for array antennas based on machine learning as described in claim 1, wherein the array synthesis algorithm based on iterative Fourier transform can be applied to low sidelobe control tasks of planar arrays. The iterative process of this algorithm is built upon the Alternating Projection (AP) framework. The iterative formula of the Alternating Projection method can be expressed as follows: ； in Represents the pattern function. Represents the number of iterations. For the projection operator from the expected set to the feasible set, The projection operator from the feasible set to the desired set.

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