Broadband planar array antenna light-operated beam forming method based on multi-task sparse learning

Abstract

The invention relates to a broadband planar array antenna light-operated beam forming method based on multi-task sparse learning, and the method comprises the steps: deducing an array factor expression of a broadband array as priori knowledge through employing a rectangular planar array antenna; constructing a multi-frequency-point beam joint optimization model of the planar array antenna based on the neural network; based on the priori knowledge, calculating a total loss function of the model by using expected broadband array pattern data and a group inhaul cable regularization method, and training a multi-frequency-spot beam joint optimization model; and based on the trained model, obtaining the optimal array layout and the amplitude and delay distribution of each array element, and calculating to obtain a low-sidelobe directional diagram in which the deflection angle is irrelevant to the frequency. According to the invention, the deflection angle of the array radiation beam is kept constant in a broadband range, and the problem of'beam squint 'of a traditional phased array is solved; and meanwhile, the beam sidelobe level of each frequency point is effectively suppressed, and the grating lobe problem of the uniform array on the broadband is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of broadband array antenna beam technology, and in particular to a method for optically controlled beamforming of broadband planar array antennas based on multi-task sparse learning. Background Art

[0002] To handle the wide instantaneous bandwidth, traditional ultra-wideband phased array designs require each array element to be terminated with microwave RF components such as filters, mixers, and adders, significantly increasing engineering complexity and implementation costs. Furthermore, because phase is a frequency-dependent quantity, the beam direction formed by traditional phased arrays deflects with frequency, resulting in a phenomenon known as "beam squint."

[0003] Microwave photonics technology overcomes some of the limitations of traditional microwave radio frequency systems by converting photoelectricity and transmitting data using optical fiber. It is seen as a possible solution for future communications and radar systems. Optical control is used for broadband array antenna beamforming, replacing traditional electronic phase shifting with true delay technology to form beams with different orientations. This ensures that the beam orientation does not deflect with frequency changes and provides the system with strong anti-interference capabilities. However, during broadband beamforming, the electrical dimensions corresponding to high and low frequency bands differ, making the synthesized beam in the high frequency band prone to grating lobes. Therefore, optimizing the array layout and excitation to reduce the sidelobe levels of beams with different orientations across a wide bandwidth is an urgent issue.

[0004] In the field of machine learning, multi-task learning systematically learns related tasks within a single model. This creates mutual inductive biases between related tasks, leading to knowledge transfer learning. This allows the system to gain more prior knowledge from a limited sample space to guide model training, enhancing the system's learning capabilities. Multi-task sparse learning utilizes a parallel associative sparse learning approach, fully utilizing computing resources and improving the model's operational efficiency. When performing pattern synthesis on a wideband planar array antenna, the broadband task can be split into multiple related single-frequency subtasks for associative learning, enabling rapid completion of the broadband array antenna pattern synthesis task. Summary of the Invention

[0005] The purpose of the present invention is to address the "beam squint" phenomenon of traditional phased array antennas and the problem of grating lobes that are prone to occur in the beamforming problem of broadband array antennas. The present invention proposes a wideband planar array antenna optical control beamforming method based on multi-task sparse learning.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for optically controlled beamforming of wideband planar array antennas based on multi-task sparse learning includes:

[0008] Using rectangular planar array antennas and true delay technology of microwave photonics, the array factor expression of broadband array is derived as the prior knowledge of neural network.

[0009] A neural network-based joint optimization model for multi-frequency spot beams of planar array antennas is constructed, where the model input layer is the desired broadband array pattern data, and the output layer represents the amplitude and delay of the array element excitation.

[0010] Based on the prior knowledge, using the expected broadband array pattern data and the group lasso regularization method, the standard loss function and the sparsity loss function of the model are calculated to train the multi-frequency point beam joint optimization model;

[0011] Based on the trained model, the optimal array layout and the amplitude and delay distribution of each array element are obtained, and a low sidelobe pattern with a deflection angle independent of frequency is calculated.

[0012] Optionally, the prior knowledge includes:

[0013] Planar array where the excitation amplitude and delay of the array elements can be separated along the x-axis and y-axis:

[0014]

[0015] in, θ and are the elevation angle and azimuth angle of the array antenna far-field observation point, λ is the wavelength, and a il and τ il The coordinate positions (x i ,y l ) the excitation amplitude and delay of the array element, N x is the number of array elements distributed along the x-axis, N y is the number of array elements distributed along the y-axis, imaginary number, x i is the position parameter of the array element distributed in the x-axis direction, y l is the position parameter of the array element distributed in the y-axis direction, and c is the speed of light;

[0016] Planar arrays where the excitation amplitude and delay of the array elements cannot be separated along the x-axis and y-axis:

[0017]

[0018] Among them, a n and τ n are the excitation amplitude and delay of the nth array element, λ i is the wavelength of the corresponding frequency, N is the number of array elements, x n is the position parameter of the array element distributed in the x-axis direction, y nis the position parameter of the array element distributed in the y-axis direction.

[0019] Optionally, constructing a multi-frequency spot beam joint optimization model based on a neural network planar array antenna includes:

[0020] By utilizing the multi-task sparse learning method to simultaneously optimize the learning characteristics of multiple related tasks, the beam synthesis task of the wideband array antenna is split into multiple frequency point beam synthesis subtasks, and a multi-frequency point beam joint optimization model based on neural network planar array antenna is constructed.

[0021] Optionally, the multi-frequency beam joint optimization model includes an input layer, an output layer and N H hidden layers; the multi-frequency beam joint optimization model takes the expected sidelobe level as input and generates a set of predicted excitation vectors for N array elements;

[0022] The expression of the multi-frequency beam joint optimization model is:

[0023]

[0024] Among them, t is the sampling frequency, F ref(i) is the reference pattern of the ith frequency point, A(u,v,λ i ) is the steering vector of the ith frequency point and the corresponding array element excitation, w is the complex excitation, and C is a complex number set.

[0025] Optionally, training the multi-frequency point beam joint optimization model includes:

[0026] Initialization phase:

[0027] Based on the input sidelobe level value, a set of predicted array element excitations, including amplitude and delay, are output. The excitations are regularized using the group lasso regularization method to obtain the sparsity loss function.

[0028] The network's current predicted stimulus is input into the model's multiple subtask modules to calculate the beam pattern of each frequency point. The pre-provided pattern templates of each frequency point are used to constrain the output pattern at this time to obtain the corresponding standard loss function.

[0029] Based on the sum of the sparsity loss function and the standard loss function, a total loss function is formed, which is used to iteratively decrease in the neural network to make the training converge;

[0030] Backpropagation phase:

[0031] The gradient descent algorithm is used to iteratively update the hidden layer weights and output layer weights of the neural network.

[0032] Optionally, the total loss function is:

[0033]

[0034] Among them, Loss is the total loss function, is the sparsity loss function, is the standard loss function, expressed as: γ is the regularization parameter, v kj is the connection weight between the hidden layer and the output layer, N is the number of array elements, q+1 is the number of neurons in the last hidden layer, g(v kj ) is the weight function.

[0035] The beneficial effects of the present invention are:

[0036] The present invention adopts the true delay technology of microwave photons to replace the traditional phase shift technology, and uses a neural network model based on multi-task sparse learning to establish a mapping relationship between the expected directivity pattern index and the array structure parameters. By dividing the large task of broadband beam synthesis into multiple subtasks of single-frequency beam synthesis, the multiple subtasks are trained jointly. During the training process, the GL regularization method is used to perform sparse optimization on the output layer of the neural network representing the array element excitation, thereby obtaining a sparse layout of the array and realizing broadband array beamforming.

[0037] The method proposed in the present invention ensures that the deflection angle of the array radiation beam remains constant within a wide frequency band, solving the "beam squint" problem of traditional phased arrays; at the same time, it effectively suppresses the beam sidelobe levels at each frequency point, avoiding the problem of grating lobes that are prone to occur in uniform arrays over a wide frequency band. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1 Schematic diagram of a comprehensive model of a broadband planar array antenna based on multi-task sparse learning according to an embodiment of the present invention;

[0040] Figure 2 Schematic diagram of planar array beamforming according to an embodiment of the present invention;

[0041] Figure 3 The sparsely optimized planar array layout and excitation amplitude of the embodiment of the present invention;

[0042] Figure 4 The directional diagram of each frequency point when the optimized planar array beam is pointed at 0° along the x-axis in an embodiment of the present invention;

[0043] Figure 5 This is the directional diagram of each frequency point when the optimized planar array beam is pointed at 30° along the x-axis according to the embodiment of the present invention. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0045] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] This embodiment proposes a method for optically controlled beamforming of a wideband planar array antenna based on multi-task sparse learning, including:

[0047] Step 1. Using rectangular planar array antennas and true delay technology from microwave photonics, derive the array factor expression for the broadband array as prior knowledge for the neural network.

[0048] Step 2. Construct a multi-frequency spot beam joint optimization model for a planar array antenna based on a neural network, where the model input layer is the desired broadband array pattern data, and the output layer represents the amplitude and delay of the array element excitation;

[0049] Step 3. Based on the prior knowledge, the desired broadband array pattern data and the group Lasso regularization method are used to calculate the standard loss function and sparsity loss function of the model, and the multi-frequency point beam joint optimization model is trained; wherein the desired pattern is equivalent to the template, and the goal of this embodiment is to optimize the desired direction. Figure 1 The prior knowledge is used to generate the current direction map of the network, which is used to generate the standard loss together with the expected direction map.

[0050] Step 4. Based on the trained model, obtain the optimal array layout and the amplitude and delay distribution of each array element, and calculate the low sidelobe radiation pattern with a deflection angle that is independent of frequency.

[0051] This embodiment uses true delay technology of microwave photons to replace traditional phase shifting technology. A mapping relationship between desired pattern indicators and array structure parameters is established using a neural network model based on multi-task sparse learning. The large task of broadband beam synthesis is divided into multiple subtasks of single-frequency beam synthesis. The multiple subtasks are jointly trained. During the training process, the GL regularization method is used to perform sparse optimization on the output layer of the neural network representing the array element excitation, thereby obtaining a sparse layout of the array and realizing broadband array beamforming.

[0052] Specifically, in this embodiment, step 1: using the “true delay” technology of the microwave photonic system to replace the traditional phase shift technology to form a beam whose deflection angle is independent of frequency. Figure 2 As shown, for a x ×N y The directional pattern of the rectangular plane array composed of array elements is expressed as:

[0053]

[0054] In this formula, θ and are the elevation angle and azimuth angle of the array antenna far-field observation point, λ is the wavelength, and a il and τ il The coordinate positions (x i ,y l ) is the excitation amplitude and delay of the array element at .

[0055] For a general inseparable plane matrix, that is, a il and τ il The x-axis and y-axis cannot be separated, so for an N-element planar rectangular array, the more general pattern expression is:

[0056]

[0057] Among them, a n and τ n are the excitation amplitude and delay of the nth array element respectively. The corresponding vector expression is:

[0058] F(u,v,λ i )=A(u,v,λ i )w

[0059] Among them, A(u,v,λ i ) and w are the steering vector and corresponding array element excitation of the ith frequency point, respectively, expressed as:

[0060]

[0061] Furthermore, the multi-frequency spot beam joint optimization model based on neural network planar array antenna is constructed, including:

[0062] By utilizing the multi-task sparse learning method to simultaneously optimize the learning characteristics of multiple related tasks, the beam synthesis task of the wideband array antenna is split into multiple frequency point beam synthesis subtasks, and a multi-frequency point beam joint optimization model based on neural network planar array antenna is constructed.

[0063] The multi-frequency spot beam joint optimization model includes an input layer, an output layer and N H hidden layers; the multi-frequency beam joint optimization model takes the expected sidelobe level as input and generates a set of predicted excitation vectors for N array elements;

[0064] Specifically, in this embodiment, step 2: utilizing a multi-task sparse learning method to simultaneously optimize the learning characteristics of multiple related tasks, the beam synthesis task of a wideband array antenna can be split into multiple frequency-point beam synthesis subtasks. A neural network-based multi-frequency beam joint optimization model for planar array antennas is established, and related subtasks are systematically learned within a single model. This allows for more prior knowledge to be obtained within a limited sample space to guide model training and achieve low-sidelobe beamforming for planar array antennas. The mathematical model for multi-task learning for this problem can be expressed as:

[0065]

[0066] Among them, t is the sampling frequency, F ref(i) is the reference pattern of the ith frequency point.

[0067] Furthermore, training the multi-frequency point beam joint optimization model includes:

[0068] Initialization phase:

[0069] Based on the input sidelobe level value, a set of predicted array element excitations, including amplitude and delay, are output. The excitations are regularized using the group lasso regularization method to obtain the sparsity loss function.

[0070] The network's current predicted stimulus is input into the model's multiple subtask modules to calculate the beam pattern of each frequency point. The pre-provided pattern templates of each frequency point are used to constrain the output pattern at this time to obtain the corresponding standard loss function.

[0071] Based on the sum of the sparsity loss function and the standard loss function, a total loss function is formed;

[0072] Backpropagation phase:

[0073] The gradient descent algorithm is used to iteratively update the hidden layer weights and output layer weights of the neural network.

[0074] Specifically, in this embodiment, step 3: using GL 1 / 2 The regularization method groups and sparses the connection weights between the hidden layer and the output layer of the neural network, thereby sparsely optimizing the output layer neurons that represent the array element excitation and realizing sparse synthesis of the array. Figure 1 As shown in the figure, the proposed neural network model based on multi-task sparse learning consists of an input layer, an output layer and N H The model takes the expected sidelobe level as input and generates a set of predicted excitation vectors for N array elements. Since neurons can only process real data, the output layer neurons representing the array element excitation are divided into two parts, representing the real part and imaginary part of the excitation, so that the output layer of the neural network has 2N neurons. The kth and N+kth neurons in the output layer are used to represent the real part and imaginary part of the kth array element excitation, respectively. The last hidden layer has q+1 neurons, with nodes Indicates a bias with a fixed output value of +1. Let V = (v kj ) 2N×(q+1) The weight matrix connecting the hidden layer and the output layer is represented by arrows of different colors in the figure. If a weight group is optimized to zero by the GL regularizer, both the real and imaginary parts of the corresponding element are zeroed simultaneously, removing the redundant element and achieving sparse array.

[0075] In the initialization phase, N initial array elements are arranged in d c The GL method is used to regularize the excitations and obtain the sparsity loss function, which is expressed as:

[0076]

[0077] Among them, v kj represents the connection weight between the hidden layer and the output layer, g(v kj )=f(v kj )+f(v (N+k)j ), f(α) uses the following expression to alleviate the loss curve oscillation during the convergence process:

[0078]

[0079] The network's current predicted excitation is then input into multiple subtask modules to calculate the beam pattern of each frequency point. The pre-provided pattern templates of each frequency point are used to constrain the output pattern at this time, and the corresponding standard loss function is obtained, which is defined as:

[0080]

[0081] Then, the total loss function is defined as the sum of the standard loss function and the sparsity loss function:

[0082]

[0083] Among them, γ is the regularization parameter.

[0084] In the back propagation phase of the neural network, the gradient descent algorithm is used to iteratively update the weights of each hidden layer and output layer of the neural network. The calculation expressions are as follows:

[0085]

[0086] Where j = 1, 2, ..., q + 1, k = 1, 2, ..., N, and η represents the learning rate.

[0087] Specifically, in this embodiment, step 4: once the multi-task learning model is trained, an array layout and element excitation that meet the target requirements are obtained. The array's directivity pattern satisfies the requirement that the beam scanning angle remains constant within a certain wide frequency band, and the beam sidelobe level at any frequency point is less than the target requirement.

[0088] For an 11×11 rectangular planar array with initial array elements distributed on the xoy plane, the array elements are evenly distributed with a spacing of 0.5λ. The planar array layout obtained after sparse optimization of the proposed model is as follows: Figure 3 As shown in the figure, the normalized excitation amplitude is represented by colors of different depths. The results show that the proposed method can effectively perform sparse optimization on planar array antennas.

[0089] When the beam direction is set to 0° along the x-axis, the optimized directivity diagrams for each frequency point are as follows: Figure 4 As shown, the sidelobe level of each frequency point beam is less than -25dB on average; when the beam pointing is set to 30° along the x-axis, the optimized directivity diagram of each frequency point is as follows Figure 5 As shown, the sidelobe level of each frequency beam is less than -18dB.

[0090] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for optically controlled beamforming of wideband planar array antennas based on multi-task sparse learning, characterized in that: include: Using rectangular planar array antennas and true delay technology of microwave photonics, the array factor expression of broadband array is derived as the prior knowledge of neural network. A neural network-based joint optimization model for multi-frequency spot beams of planar array antennas is constructed, where the model input layer is the desired broadband array pattern data, and the output layer represents the amplitude and delay of the array element excitation. Based on the prior knowledge, using the expected broadband array pattern data and the group lasso regularization method, the standard loss function and the sparsity loss function of the model are calculated to train the multi-frequency point beam joint optimization model; Based on the trained model, the optimal array layout and the amplitude and delay distribution of each array element are obtained, and a low sidelobe pattern with a deflection angle independent of frequency is calculated.

2. The method for optically controlled beamforming of a wideband planar array antenna based on multi-task sparse learning according to claim 1, characterized in that: The prior knowledge includes: Planar array where the excitation amplitude and delay of the array elements can be separated along the x-axis and y-axis: in, θ and are the elevation angle and azimuth angle of the array antenna far-field observation point, λ is the wavelength, and a il and τ il The coordinate positions (x i ,y l ) the excitation amplitude and delay of the array element, N x is the number of array elements distributed along the x-axis, N y is the number of array elements distributed along the y-axis, imaginary number, x i is the position parameter of the array element distributed in the x-axis direction, y l is the position parameter of the array element distributed in the y-axis direction, and c is the speed of light; Planar arrays where the excitation amplitude and delay of the array elements cannot be separated along the x-axis and y-axis: Among them, a n and τ n are the excitation amplitude and delay of the nth array element, λ i is the wavelength of the corresponding frequency, N is the number of array elements, x n is the position parameter of the array element distributed in the x-axis direction, y n is the position parameter of the array element distributed in the y-axis direction.

3. The optical beamforming method for wideband planar array antenna based on multi-task sparse learning according to claim 1, characterized in that: The construction of a multi-frequency spot beam joint optimization model based on a neural network planar array antenna includes: By utilizing the multi-task sparse learning method to simultaneously optimize the learning characteristics of multiple related tasks, the beam synthesis task of the wideband array antenna is split into multiple frequency point beam synthesis subtasks, and a multi-frequency point beam joint optimization model based on neural network planar array antenna is constructed.

4. The optical beamforming method for wideband planar array antenna based on multi-task sparse learning according to claim 1, characterized in that: The multi-frequency spot beam joint optimization model includes an input layer, an output layer and N H hidden layers; the multi-frequency beam joint optimization model takes the expected sidelobe level as input and generates a set of predicted excitation vectors for N array elements; The expression of the multi-frequency beam joint optimization model is: Among them, t is the sampling frequency, F ref(i) is the reference pattern of the ith frequency point, A(u,v,λ i ) is the steering vector of the ith frequency point and the corresponding array element excitation, w is the complex excitation, and C is a complex number set.

5. The optical beamforming method for wideband planar array antenna based on multi-task sparse learning according to claim 1, characterized in that: Training the multi-frequency point beam joint optimization model includes: Initialization phase: Based on the input sidelobe level value, a set of predicted array element excitations, including amplitude and delay, are output. The excitations are regularized using the group lasso regularization method to obtain the sparsity loss function. The network's current predicted excitation is input into multiple subtask modules in the model to calculate the beam pattern at each frequency point. The output pattern is constrained using the pre-provided expected wideband array pattern data to obtain the corresponding standard loss function. Based on the sum of the sparsity loss function and the standard loss function, a total loss function is formed, which is used to iteratively decrease in the neural network to make the training converge; Backpropagation phase: The gradient descent algorithm is used to iteratively update the hidden layer weights and output layer weights of the neural network.

6. The optical beamforming method for wideband planar array antenna based on multi-task sparse learning according to claim 5, characterized in that: The total loss function is: Among them, Loss is the total loss function, is the sparsity loss function, is the standard loss function, expressed as: γ is the regularization parameter, v kj is the connection weight between the hidden layer and the output layer, N is the number of array elements, q+1 is the number of neurons in the last hidden layer, g(v kj ) is the weight function.

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