Wideband planar array antenna optical beamforming method based on multi-task sparse learning

Abstract

The present application relates to a wideband planar array antenna light-controlled beam forming method based on multi-task sparse learning, comprising: using a rectangular planar array antenna, deriving the array factor expression of the wideband array as prior knowledge; constructing a multi-frequency point beam joint optimization model of the planar array antenna based on a neural network; based on the prior knowledge, using the expected wideband array directional diagram data, and the group lasso regularization method, calculating the total loss function of the model, training the multi-frequency point beam joint optimization model; based on the trained model, obtaining the optimal array layout and the amplitude and delay distribution of each array element, and calculating the low sidelobe directional diagram independent of the deflection angle and frequency. The present application ensures that the deflection angle of the array radiation beam remains constant within the wideband range, solving the "beam squint" problem of the traditional phased array; at the same time, effectively suppressing the beam sidelobe level of each frequency point, avoiding the grating lobe problem that the uniform array is prone to in the wideband.

Description

Technical Field

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

[0002] In designing traditional ultra-wideband phased arrays, to handle the wide instantaneous bandwidth, microwave and radio frequency devices such as filters, mixers, and adders need to be connected to each array element, which greatly increases engineering complexity and implementation cost. In addition, since phase is a frequency-dependent quantity, the beam direction formed by a traditional phased array will deflect with the frequency, resulting in a "beam squinting" phenomenon.

[0003] Microwave photonics technology, through photoelectric conversion and fiber optic data transmission, overcomes some limitations of traditional microwave radio frequency systems and is seen as a potential solution for future communication and radar systems. Applying optical control to broadband array antenna beamforming utilizes true time-delay technology instead of traditional electronic phase-shifting to form beams with different directions, ensuring the beam direction does not deviate with frequency changes and providing strong anti-interference capabilities. However, in broadband beamforming, the electrical dimensions corresponding to high and low frequencies differ, leading to grating lobes in the synthesized beam at high frequencies. Therefore, optimizing the array arrangement and excitation to reduce the sidelobe level of beams with different directions across a wide bandwidth is a pressing issue.

[0004] In the field of machine learning, multi-task learning systematically learns related tasks within a single model. These related tasks can mutually influence each other through inductive bias, leading to knowledge transfer and enabling the system to acquire more prior knowledge from a limited sample space to guide model training, thus enhancing its learning ability. Multi-task sparse learning employs a parallel correlated sparse learning approach, thereby fully utilizing computational resources and improving model efficiency. In the task of pattern synthesis for broadband planar array antennas, the broadband task can be divided into multiple related single-frequency subtasks for correlated learning, thereby quickly completing the broadband array antenna pattern synthesis task. Summary of the Invention

[0005] The purpose of this invention is to address the "beam squinting" phenomenon in traditional phased array antennas and the problem of grating lobes easily occurring in the beamforming of broadband array antennas. This invention proposes a method for optically controlled beamforming of broadband planar array antennas based on multi-task sparse learning.

[0006] To achieve the above objectives, the present invention provides the following solution:

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

[0008] Using a rectangular planar array antenna and employing true time delay technology in microwave photonics, the array factor expression of a wideband array is derived as prior knowledge for a neural network.

[0009] A multi-frequency beam joint optimization model for a planar array antenna based on a neural network is constructed, wherein the input layer of the model 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 desired broadband array pattern data and the group cable regularization method, the standard loss function and sparsity loss function of the model are calculated, and the multi-frequency beam joint optimization model is trained.

[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 deflection angle independent of frequency is calculated.

[0012] Optionally, the prior knowledge includes:

[0013] A planar array whose element excitation amplitude and delay can be separated along the x-axis and y-axis:

[0014]

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

[0016] Planar arrays whose excitation amplitude and delay cannot be separated along the x-axis and y-axis:

[0017]

[0018] Among them, a n and τ n λ represents the excitation amplitude and delay of the nth array element, respectively. i The wavelength corresponds to the frequency, N is the number of array elements, and x n The position parameters of the array elements are distributed along the x-axis, and the y-axis is the position parameter of the array elements. nThe position parameters of the array elements are distributed along the y-axis.

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

[0020] By leveraging the characteristic of multi-task sparse learning methods to simultaneously optimize multiple related tasks, the beam synthesis task of broadband array antennas is decomposed into sub-tasks of beam synthesis at multiple frequency points, and a multi-frequency beam joint optimization model based on neural network planar array antennas is constructed.

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

[0022] The expression for the multi-frequency beam joint optimization model is as follows:

[0023]

[0024] Where t is the number of frequency points sampled, F ref(i) Let A(u,v,λ) be the reference radiation pattern for the i-th frequency point. i ) represents the steering vector and corresponding array element excitation at the i-th frequency point, w represents the complex excitation, and C represents the set of complex numbers.

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

[0026] Initialization phase:

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

[0028] The current prediction stimulus of the network is input into multiple sub-task modules in the model to calculate the beam pattern at each frequency point. The output beam pattern is constrained by the pre-provided beam pattern templates at each frequency point to obtain the corresponding standard loss function.

[0029] The sum of the sparse loss function and the standard loss function constitutes the total loss function, which is used for iterative descent in the neural network to bring the training to convergence.

[0030] Backpropagation phase:

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

[0032] Optionally, the total loss function is:

[0033]

[0034] Where Loss is the total loss function. For sparsity loss function, The standard loss function is expressed as: γ is the regularization parameter, v kj The connection weights between the hidden layer and the output layer are given by N, where N is the number of array elements, q+1 is the number of neurons in the last hidden layer, and g(v) is the connection weight between the hidden layer and the output layer. kj ) is the weighting function.

[0035] The beneficial effects of this invention are as follows:

[0036] This invention uses true time delay technology of microwave photonics to replace traditional phase shifting technology. It establishes a mapping relationship between desired radiation pattern indicators and array structure parameters using a neural network model based on multi-task sparse learning. By dividing the large task of broadband beamforming into multiple sub-tasks of single-frequency beamforming, and training multiple sub-tasks together, the GL regularization method is used to perform sparse optimization on the output layer of the neural network representing array element excitation during the training process, thereby obtaining the sparse layout of the array and realizing broadband array beamforming.

[0037] The method proposed in this invention ensures that the deflection angle of the array radiation beam remains constant over a wide frequency range, solving the "beam squinting" problem of traditional phased arrays; at the same time, it effectively suppresses the beam sidelobe level at each frequency point, avoiding the problem of grating lobes that easily occur in uniform arrays over a wide frequency range. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments 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.

[0039] Figure 1 This is a schematic diagram of a broadband planar array antenna synthesis model based on multi-task sparse learning, according to an embodiment of the present invention.

[0040] Figure 2 This is a 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 are shown in this embodiment of the invention.

[0042] Figure 4 This is a radiation pattern of each frequency point when the optimized planar array beam pointing along the x-axis is 0°, according to an embodiment of the present invention.

[0043] Figure 5 The optimized planar array beam pointing at each frequency point is shown in the embodiment of the present invention when the beam pointing is 30° along the x-axis. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be 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 broadband planar array antenna based on multi-task sparse learning, including:

[0047] Step 1. Using a rectangular planar array antenna and employing the true time delay technique of microwave photonics, derive the array factor expression of the wideband array as prior knowledge for the neural network;

[0048] Step 2. Construct a multi-frequency beam joint optimization model for a planar array antenna based on a neural network. The input layer of the model 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, using the desired broadband array pattern data and the group cable regularization method, calculate the standard loss function and sparsity loss function of the model, and train the multi-frequency beam joint optimization model; wherein, the desired pattern is equivalent to a template, and the goal of this embodiment is to optimize the desired pattern. Figure 1 The desired orientation pattern is used to generate the current orientation pattern of the network, which, together with the desired orientation pattern, generates the standard loss.

[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 pattern where the deflection angle is independent of the frequency.

[0051] This embodiment uses true time delay technology of microwave photonics to replace the traditional phase shifting technology. It uses a neural network model based on multi-task sparse learning to establish a mapping relationship between the desired radiation pattern index and the array structure parameters. By dividing the large task of broadband beamforming into multiple sub-tasks of single-frequency beamforming, the multiple sub-tasks are trained together. 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 the sparse layout of the array and realizing broadband array beamforming.

[0052] Specifically, in this embodiment, step 1: The "true time delay" technology of a microwave photonic system is used instead of the traditional phase-shifting technology to form a beam whose deflection angle is independent of frequency. For example... Figure 2 As shown, for a given N = N x ×N y The radiation pattern expression of a rectangular planar array composed of array elements is:

[0053]

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

[0055] For a typical non-separable planar matrix, i.e., a il and τ il Since it cannot be separated along the x-axis and y-axis, the more general expression for the pattern of an N-element planar rectangular array is:

[0056]

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

[0058] F(u,v,λ i )=A(u,v,λ i )w

[0059] Where A(u,v,λ) i ) and w are the steering vector and corresponding array element excitation at the i-th frequency point, respectively, expressed as:

[0060]

[0061] Furthermore, the construction of a multi-frequency beam joint optimization model based on a neural network planar array antenna includes:

[0062] By leveraging the characteristic of multi-task sparse learning methods to simultaneously optimize multiple related tasks, the beam synthesis task of broadband array antennas is decomposed into sub-tasks of beam synthesis at multiple frequency points, and a multi-frequency beam joint optimization model based on neural network planar array antennas is constructed.

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

[0064] Specifically, in this embodiment, step 2: Utilizing the characteristic of multi-task sparse learning to simultaneously optimize and learn multiple related tasks, for the beam synthesis task of a broadband array antenna, it can be broken down into multiple frequency-point beam synthesis sub-tasks. A multi-frequency-point beam joint optimization model based on a neural network for planar array antennas is established, and related sub-tasks are systematically learned within a single model. This allows for the acquisition of more prior knowledge in a limited sample space to guide model training, achieving low sidelobe beamforming of the planar array antenna. The mathematical model for multi-task learning in this problem can be expressed as:

[0065]

[0066] Where t is the number of frequency points sampled, F ref(i) This is the reference radiation pattern for the i-th frequency point.

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

[0068] Initialization phase:

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

[0070] The current prediction stimulus of the network is input into multiple sub-task modules in the model to calculate the beam pattern at each frequency point. The output beam pattern is constrained by the pre-provided beam pattern templates at each frequency point to obtain the corresponding standard loss function.

[0071] The total loss function is formed by the sum of the sparse loss function and the standard loss function.

[0072] Backpropagation phase:

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

[0074] Specifically, in this embodiment, step 3: using GL 1 / 2 Regularization methods group and sparsify the connection weights between the hidden and output layers of a neural network, thereby sparsely optimizing the output layer neurons representing array element excitations and achieving sparse synthesis of the array. For example... Figure 1 As shown, the proposed neural network model based on multi-task sparse learning consists of an input layer, an output layer, and N... H The model consists of 2N hidden layers. It takes the desired sidelobe level as input and generates a set of predicted activation vectors for N array elements. Since neurons can only process real-valued data, the output layer neurons representing the element activations are divided into two parts, representing the real and imaginary parts of the activation, resulting in 2N neurons in the output layer. The k-th and (N+k)-th neurons in the output layer represent the real and imaginary parts of the k-th element activation, respectively. The last hidden layer has q+1 neurons. This indicates a bias with a fixed output value +1. Let V = (v kj ) 2N×(q+1) This represents the weight matrix connecting the hidden layer and the output layer. Weight grouping is represented by arrows of different colors in the diagram. If a weight group is optimized to zero by the GL regularizer, then the real and imaginary parts of the corresponding array element are simultaneously reduced to zero, thus removing the redundant array element and achieving array sparsity.

[0075] During the initialization phase, N initial array elements are set to d. c The elements are evenly spaced on the xoy plane. During the forward pass of the neural network, based on the input sidelobe levels, a set of predicted element excitations, including amplitude and delay, are output. The excitations are regularized using the GL method to obtain a sparsity loss function, expressed as:

[0076]

[0077] Among them, v kj G(v) represents the connection weight between the hidden layer and the output layer. kj )=f(v kj )+f(v (N+k)j The following expression is used to mitigate the oscillation of the loss curve during the convergence process:

[0078]

[0079] Subsequently, the network's current prediction stimulus is input into multiple sub-task modules to calculate the beam pattern at each frequency. The output beam pattern is then constrained using pre-provided frequency pattern templates to obtain the corresponding standard loss function, defined as:

[0080]

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

[0082]

[0083] Where γ is the regularization parameter.

[0084] During the backpropagation phase of the neural network, the gradient descent algorithm is used to iteratively update the weights of each hidden layer and the weights of the output layer. 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 can be obtained. The radiation pattern of the array satisfies the requirement that the beam scanning angle remains constant within a certain wide bandwidth, and the average electrical charge of the beam sidelobes at any frequency is less than the target requirement.

[0088] For an initial array of 11×11 rectangular planar elements distributed uniformly at intervals of 0.5λ on the xoy plane, the resulting planar array layout after sparse optimization using the proposed model is as follows: Figure 3 As shown, the normalized excitation amplitude is represented by colors of different depths. The results demonstrate that the proposed method can effectively perform sparse optimization for planar array antennas.

[0089] The optimized beam pattern at each frequency point is set to 0° along the x-axis, as shown below. Figure 4 As shown, the sidelobe electrical average of the beam at each frequency is less than -25dB; the optimized radiation pattern at each frequency when the beam pointing is set to 30° along the x-axis is shown in the figure. Figure 5 As shown, the sidelobe electrical average of each frequency beam is less than -18dB.

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

Claims

1. A method for optically controlled beamforming of a broadband planar array antenna based on multi-task sparse learning, characterized in that, include: Using a rectangular planar array antenna and employing true time delay technology in microwave photonics, the array factor expression of a wideband array is derived as prior knowledge for a neural network. A multi-frequency beam joint optimization model for a planar array antenna based on a neural network is constructed, wherein the input layer of the model is the desired broadband array pattern data, and the output layer represents the amplitude and delay of the array element excitation. The construction of a multi-frequency beam joint optimization model based on a neural network planar array antenna includes: By leveraging the characteristic of multi-task sparse learning to simultaneously optimize multiple related tasks, the beam synthesis task of broadband array antennas is decomposed into sub-tasks of beam synthesis at multiple frequency points, and a multi-frequency beam joint optimization model based on neural network planar array antennas is constructed. Based on the prior knowledge, using the desired broadband array pattern data and the group cable regularization method, the standard loss function and sparsity loss function of the model are calculated, and the multi-frequency beam joint optimization model is trained. Training the multi-frequency beam joint optimization model includes: Initialization phase: Based on the input sidelobe level values, a set of predicted array element excitations, including amplitude and delay, are output. The excitations are regularized using the group-law regularization method to obtain the sparsity loss function. The network's current prediction stimulus is input into multiple sub-task modules in the model to calculate the beam pattern at each frequency point. The output beam pattern is constrained using the pre-provided expected broadband array pattern data to obtain the corresponding standard loss function. The sum of the sparse loss function and the standard loss function constitutes the total loss function, which is used for iterative descent in the neural network to bring the training to convergence. Backpropagation phase: The gradient descent algorithm is used to iteratively update the weights of each hidden layer and the weights of the output layer in the neural network. The overall loss function is: in, For the total loss function, For sparsity loss function, The standard loss function is expressed as: , and w The first i The steering vector at each frequency point and the corresponding array element excitation. , , θ and These are the elevation and azimuth angles of the far-field observation point of the array antenna, respectively. The wavelength corresponding to the frequency. t The number of frequency points sampled. For the first i Reference radiation pattern at each frequency point For regularization parameters, The connection weights between the hidden layer and the output layer. The number of array elements. q +1 represents the number of neurons in the last hidden layer. For weighting functions; 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 deflection angle independent of frequency is calculated.

2. The method for optically controlled beamforming of a broadband planar array antenna based on multi-task sparse learning according to claim 1, characterized in that, The prior knowledge includes: A planar array whose element excitation amplitude and delay can be separated along the x-axis and y-axis: in, and These are the coordinate positions. The excitation amplitude and delay of the array element, The number of array elements is distributed along the x-axis. The number of array elements is distributed along the y-axis. j It is an imaginary number. The position parameters of the array elements are distributed along the x-axis. The position parameters of the array elements are distributed along the y-axis. The speed of light; Planar arrays whose excitation amplitude and delay cannot be separated along the x-axis and y-axis: in, and The first n The excitation amplitude and delay of each array element The position parameters of the array elements are distributed along the x-axis. The position parameters of the array elements are distributed along the y-axis.

3. The method for optically controlled beamforming of a broadband planar array antenna based on multi-task sparse learning according to claim 1, characterized in that, The multi-frequency beam joint optimization model includes an input layer, an output layer, and... NH The multi-frequency beam joint optimization model uses the desired sidelobe level as input to generate a set of predicted levels. N The excitation vector of each array element; The expression for the multi-frequency beam joint optimization model is as follows: Where C is the set of complex numbers.

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