An Adaptive Beamforming Method Based on a First-Order Convolutional Neural Network

Abstract

The present invention provides an adaptive beamforming method based on a first-order convolutional neural network. Aiming at the problems of high computational complexity and slow real-time response in large-array beamforming, the mapping relationship between parameters such as array structure and beam characteristics and sub-array excitation is analyzed, and a method for strengthening the characterization of array element excitation features in the first-order convolutional neural network framework of the adaptive beamforming problem is constructed. The array element excitation is adaptively and real-time predicted through the first-order convolutional neural network, and an ideal beam pattern is generated according to different beamforming beam index requirements to meet the requirements of real-time response scenarios. At the same time, aiming at the problems of large memory occupation and large sample requirements of existing deep learning methods, in order to further improve the accuracy of the neural network in predicting array element excitation on the premise of unchanged sample size, a first-order convolutional layer is connected based on the fully connected layer. By converting low-dimensional features to high-dimensional features, the diversity of features is enriched, the feature mapping ability of the neural network is strengthened, and the diversity characterization of non-linear relationships is realized.

Description

Technical Field

[0001] The present invention relates to array beamforming technology, and particularly to an adaptive beamforming technology based on a neural network. Prior Art

[0002] The purpose of array beamforming is to synthesize radiation patterns with different shapes and directions by controlling the amplitude and phase of element excitations. This technology is widely used in radar, sonar, array antennas, and wireless communication systems. In the past few decades, a large number of beamforming algorithms have been proposed. Existing beamforming methods mainly include evolutionary algorithms (such as genetic algorithms, ant colony algorithms, particle swarm algorithms, etc.), optimization algorithms (such as gradient descent method, Newton's method, quadratic programming method, dual interior point method, etc.), and other numerical methods (such as fast Fourier transform method, matrix pencil method, taper density method, etc.). However, when the array size is large, existing methods also have obvious defects, namely large memory requirements and long calculation time. This makes it increasingly difficult for traditional methods to meet the rapid beamforming requirements of increasingly large-scale array antennas.

[0003] Taking a linear array antenna as an example, the conclusions for planar array antennas or higher-dimensional array antennas can be deduced by analogy. Assuming that the antenna has N elements with isotropic and equally spaced distribution, the far-field radiation f(θ) of the array antenna is:

[0004] f(θ) = a(θ) H w

[0005] where is the array steering vector when the incident signal angle is θ, λ is the wavelength, d is the element spacing, w = [w1, w2,..., w N T is the element excitation, H is the conjugate transpose, T is the transpose.

[0006] The energy radiated by the antenna can be expressed as:

[0007] [ |f(θ)| 2 = w H a(θ)a(θ) H w

[0008] In the form of a real-valued vector, the matrix form of the antenna radiation energy can also be expressed as:

[0009] |f(θ)| 2 = x H A(θ)A(θ) H x = x T Qx

[0010] ​

[0011] Since Q = A(θ) T A(θ) is the real symmetric matrix of the array steering vector matrix A(θ), and x is a real-valued vector, so the following properties can be satisfied:

[0012] x T Qx = Tr(x T Qx) = Tr(Qxx T )

[0013] where Tr(·) is the trace of the matrix, so the radiation energy becomes:

[0014] |f(θ)| 2 = Tr(QX), with X = xx T ∈R 2N×2N

[0015] Existing beamforming methods:

[0016] Taking the semi-definite programming SDR (Semi-Definite Relaxation) algorithm as an example, in the problem of pattern synthesis, the element excitations are often solved according to the power constraint of the array radiation. During this process, subject to the rank-1 constraint, the pattern model X is expressed as:

[0017]

[0018] where C k is the radiation energy constraint when the angle of the incoming wave signal is θ k and Q k is the real symmetric matrix of the array steering vector matrix when the angle of the incoming wave signal is θ k ; however, due to the rank-1 constraint, this model is a non-convex model. The SDR algorithm discards the rank-1 constraint, and this model is converted into a convex problem. The model can be expressed as:

[0019]

[0020] In convex optimization theory, minimizing the trace of a matrix is equivalent to minimizing the sum of its eigenvalues and the rank of the matrix. In order to obtain a low-rank solution in the convex optimization model, the method of applying convex relaxation to array synthesis problems disclosed in the reference B. Fuchs, "Application of Convex Relaxation to Array Synthesis Problems," in IEEE Transactions on Antennas and Propagation, vol. 62, no. 2, pp. 634 - 640, Feb. 2014, doi: 10.1109 / TAP.2013.2290797 is cited:

[0021]

[0022] where δ is the regularization constant, I is the eigenmatrix and X 0 = I, X t represents X at the t-th iteration. Express X in the form of eigenvalue decomposition:

[0023]

[0024] where σ1 ≥... ≥ σ 2N are the eigenvalues, and u n is the n-th eigenvector. And the vector is the potential solution of the model, and the element excitation w n of the n-th eigenvalue can be expressed as:

[0025] w n = x(n) + jx(n + N)

[0026] In recent years, with the rapid development of deep learning, due to its excellent offline learning ability, in the field of array antennas and wireless communications, more and more deep learning-based beamforming algorithms have been studied. Existing machine learning-based beamforming methods mainly use fully connected neural networks, radial basis neural networks, and generalized regression neural networks. For different application scenarios, research on array beamforming methods based on a variety of different neural networks has been carried out, including low sidelobe performance, low null performance, wide beamforming ability, adaptive maximum signal-to-noise ratio reception, and beamforming of conformal antennas, etc., and certain progress has been made.

[0027] Relatively speaking, research on beamforming methods based on convolutional neural networks is also less, and convolutional neural networks are rarely used in fitting problems. Although radial basis neural networks and generalized regression neural networks can achieve good performance with only a small number of samples during the training process, during the inference process, the training set will participate in the operation, which will occupy a large amount of hard disk memory and impose a heavy burden on embedded, single-chip microcomputer systems, and FPGAs. Compared with fully connected neural networks, convolutional neural networks can connect similar elements and have excellent feature mapping capabilities, enriching the diversity of features. At the same time, for large array antennas, convolutional kernels have the ability to strengthen the characteristics of neural network regression element excitation, and can achieve higher-precision real-time beamforming compared with other neural networks. Summary of the Invention

[0028] The technical problem to be solved by the present invention is to provide a method for constructing an adaptive beamforming by strengthening the characterization of element excitation features through a convolutional neural network.

[0029] The technical solution adopted by the present invention to solve the above technical problems is an adaptive beamforming method based on a first-order convolutional neural network, including the steps:

[0030] Step 1: Set beam variable parameters, where the beam variable parameters include null directions, the number of nulls, and null widths, and generate corresponding array element excitations through a semidefinite programming algorithm; construct a training set {r, z} from the vector form r of the array steering vector matrix of the null direction that has undergone real and imaginary part separation and normalization processing and the array element excitation z;

[0031] Step 2: Construct a first-order convolutional neural network that realizes the mapping relationship between the array steering vector and the array element excitation; the first-order convolutional neural network is composed of multiple first-order convolutional layers and a fully connected deep neural network; the former is used to enrich the feature dimension of the input data, and the latter predicts the array element excitation based on the data features learned by the former;

[0032] Step 3: Determine the optimal structure of the first-order convolutional neural network, and input the training set to complete the training of the first-order convolutional neural network;

[0033] Step 4: Generate the vector form of the array steering vector matrix according to the required beam variable parameters and input it into the trained first-order convolutional neural network, and then complete beam synthesis according to the array element excitation output from the first-order convolutional neural network.

[0034] Aiming at the problems of high computational complexity and slow real-time response in large array beamforming, the present invention analyzes the mapping relationship between array structures, beam characteristics and other parameters and sub-array excitations, constructs a method for strengthening the characterization of array element excitation features in the first-order convolutional neural network framework of the adaptive beamforming problem, adaptively and real-time predicts the array element excitation through the first-order convolutional neural network, generates an ideal beam pattern according to different beamforming index requirements, and meets the requirements of real-time response scenarios. At the same time, aiming at the problems of large memory occupation and large sample requirements of existing deep learning methods, in order to further improve the accuracy of the neural network in predicting array element excitations on the premise of unchanged sample size, a first-order convolutional layer is connected based on the fully connected layer. By converting low-dimensional features to high-dimensional features, the diversity of features is enriched, the feature mapping ability of the neural network is strengthened, and the diversity characterization of non-linear relationships is realized.

[0035] The beneficial effect of the present invention is that it can achieve better quality and faster beamforming. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the present invention;

[0037] Figure 2 is a first-order convolutional operation diagram of the embodiment;

[0038] Figure 3Comparison of the goodness of fit between the existing DNN and the different structures of the 1-D CNN of the present invention;

[0039] Figure 4 Narrow beam null pattern achieved by the embodiment;

[0040] Figure 5 Wide beam null pattern achieved by the embodiment. Detailed implementation manners

[0041] The adaptive beamforming method based on the first-order convolutional neural network provided by this method mainly includes the steps as Figure 1 shown:

[0042] Step 1: Set beam variable parameters (array parameters): The beam variable parameters include null directions, null numbers, and null widths, and corresponding element excitations are generated through the SDR algorithm. Construct a training set: Convert the array steering vector matrix in the null direction into a vector form r′ as the neural network input, and the element excitation z′ as the neural network output. To meet the real-number input requirement of the neural network, the real and imaginary parts of r′ and z′ are separated and normalized to obtain r and z, and the training set {r, z} is constructed.

[0043] Generate the neural network training set through the semi-definite programming (SDR) algorithm. To achieve adaptive beamforming, set the null angles, null numbers, and null widths to generate null intervals as the beam variable parameters of the training set samples.

[0044] For the covariance matrix R of the array steering vector containing N elements:

[0045]

[0046] θ k is the k-th signal angle corresponding to the null interval in the ideal beam pattern. Since the neural network only accepts real-valued inputs, the data of the signal covariance matrix R is decomposed, and its complex values are decomposed into real part Re and imaginary part Im, so that the N×N matrix is converted into a (N 2 -N)×1 vector r′, which is expressed as

[0047] r′ = [Re(R 12 [[ID=X]]), Im(R 12 ),..., Re(R 1N ), Im(R 1N ),..., Re(R (N-1),N ), Im(R (N-1),N )] T

[0048] R (N-1),N is the element in the N-1th row and Nth column of the covariance matrix R;T is the transpose;

[0049] Similarly, for the array element excitation w n (n = 1, …, N), the real part Re and the imaginary part Im are also separated. As the output of the neural network, it is expressed as:

[0050] z′ = [Re(w1), Im(w1),..., Re(w N ), Im(w N )] T

[0051] To converge the input and output ranges within [0, 1], the input and output of the neural network are normalized by the maximum - minimum normalization method.

[0052]

[0053]

[0054] r min and r max are the minimum and maximum values of r′ in the training set respectively. After the above processing, the neural network training set structure {r (d) , z (d)} is obtained, where d = 1, …, D. D is the number of training samples.

[0055] Step 2: Construct a first - order convolutional network for feature mapping to enrich the feature dimensions of the input data. The first - order convolutional network performs feature mapping on the input. A fully - connected deep neural network DNN is connected after the first - order convolutional network to predict the array element excitation, obtaining a first - order convolutional neural network that realizes the mapping relationship between the array steering vector and the array element excitation. The square of the error between the reconstructed actual output and the predicted output is used as the loss function. The optimizer is used to update the network parameters during the back - propagation process to continuously reduce the value of the loss function, making the actual output continuously approach the predicted output, and completing the establishment of the first - order convolutional neural network model.

[0056] The fully - connected DNN includes an input layer, multiple hidden layers, and an output layer, and each layer is composed of a fully - connected neuron structure. Suppose the number of layers of the DNN is N F , and the number of neurons in each layer is n F . Therefore, the output of the p - th fully - connected layer is:

[0057] o [p] = f(W [p] o [p-1] + b [p] )

[0058] where W [p] , b [p]are the weight coefficient and bias coefficient of the p-th layer. o [p] is the output of the p-th layer. f(·) is the activation function. In the embodiments, except for the last layer, the Relu function (Relu(x) = max(0, x)) is adopted to avoid the problem of gradient disappearance. The activation function of the last layer adopts function to control the output range within [0, 1]. Meanwhile, in order to prevent overfitting, a dropout layer is added to the last few hidden layers. The probability of its ineffective units is set to 10%.

[0059] For the deep neural network DNN and the first-order convolutional neural network of the present invention, their training set formats are the same, but the first-order convolutional neural network has one more first-order convolutional layer than the DNN. The input of the first-order convolutional neural network is in vector form, and the convolutional kernel is in vector form.

[0060] Input vector is first input into the first-order convolutional network. One first-order convolutional operation uses 3 convolutional kernels with a size of 3×1, the number of output channels is 3, the stride is set to 1, and the padding method is set to valid. The first-order convolutional network is composed of more than 2 first-order convolutional layers.

[0061] The convolutional operation of the q-th filter in the l-th first-order convolutional layer is as Figure 2 shown, and has the following parameters:

[0062] Input vector: where represents the data size of the output of the (l - 1)-th first-order convolutional layer, [l-1] represents the (l - 1)-th first-order convolutional layer, M [l-1] represents the output vector length of each channel of the (l - 1)-th first-order convolutional layer, represents the number of output channels of the (l - 1)-th first-order convolutional layer, C [l-1] is the input vector of the l-th first-order convolutional layer from the output of the previous layer l - 1;

[0063] Parameters of the first layer (l = 1): C [0] = r, M [0] = N×(N - 1), [0] represents the initial quantity; r is the vector form of the array steering vector matrix of the set null direction;

[0064] Parameters of the filter: Output length v [l] = 3. v [l] is the length of each channel vector in each filter of the l-th layer, and q is the serial number variable of the filter;

[0065] Step size: ξ, Figure 2 The step size of the first-order convolution operation in

[0066] Output vector: The output vector of the previous layer is used as the input of this layer. The output is obtained by element multiplication of the input and the filter parameters and then summation.

[0067] Its matrix calculation representation is:

[0068]

[0069] where m represents the m-th element of the output vector, m = 1,..., M [l] and represents the q-th filter of the l-th layer, i and k represent the size of the filter, i is the length of the filter, and k is the number of channels of the filter; represents the input vector of the l-th layer, and ξ(m - 1)+i represents the element at the ξ(m - 1)+i-th position corresponding to the input vector in the q-th filter of the l-th layer;

[0070] The activation function is set to the ReLU function, and the output vector O of the l-th layer [l] after passing through the activation function f is used as the input vector C of the (l + 1)-th layer [l] .

[0071] Figure 2 In [l-1] each channel vector in q,[l] [[ID=X]]three elements are multiplied by the convolution kernel and summed to obtain the corresponding element in O

[0072] The first-order convolutional neural network is a regression model. In regression problems, the feature maps at each position have a great impact on the result. Therefore, the pooling layer is not considered for dimensionality reduction operations to prevent information loss.

[0073] The loss function is set to the square of the error between the actual output z act and the predicted output z pre , that is, the mean squared error.

[0074]

[0075] The optimizer is set to the Adam optimizer, and the network parameters are continuously optimized by minimizing the loss function through the backpropagation algorithm. Thus, the construction of the neural network is completed.

[0076] Step 3: Optimize the network structure by analyzing the influence of structural parameters such as the number of neural layers and neurons in the neural network on the performance of the neural network. Take the number of layers of the deep neural network and the number of neurons in each hidden layer as structural variables to analyze the optimal structure, and obtain the optimal number of neurons in each hidden layer and the number of network layers of the deep neural network. Put the deep neural network with the optimal structure into the first-order convolutional neural network to analyze the mathematical relationship between the goodness of fit of the first-order convolutional neural network and the number of neural network layers, and obtain the optimal network structure.

[0077] To verify the effectiveness of the present invention under adaptive beamforming, the comparative experiment mainly includes the comparison between existing machine learning and the 1D CNN of the embodiment method. The machine learning method adopted by the existing neural network is the deep neural network DNN algorithm in Z. Zhao, H. Zhao, and M. Zheng. Real-time phase-only nulling based on deep neural network with robustness. IEEE Access, 7: 142287–142294, 2019.

[0078] All simulations are implemented based on a 30-element half-wavelength equally-spaced linear array. The neural network parameters in the simulation are shown in Table 1.

[0079] Table 1 Neural network parameter settings

[0080]

[0081] During the training process of the neural network, the number of neural network layers and the number of neurons have a significant impact on the performance of the neural network. To obtain the optimal network structure, define the goodness of fit GOF as an evaluation function to analyze the fitting performance of the neural network:

[0082]

[0083] where is the average value of the predicted output. It can be found that when the neural network output z act is closer to z pre the goodness of fit value R 2 is closer to 1. Therefore, the neural network structure has a great influence on the goodness of fit.

[0084] In the neural network structure analysis simulation, take the point null as an example to analyze the optimal network structure, and the obtained optimal structure is also applicable to the wide null problem. In the structure comparison, the deep neural network takes the number of neurons n f and the number of layers N fTo analyze the goodness of fit for variables. The goodness of fit of the deep neural network DNN and the first-order convolutional neural network 1DCNN is as follows Figure 3 shown

[0085] It can be seen from the figure that the deep neural network can obtain a higher GOF value when the number of neurons in the fully connected layer is 600. When the number of hidden layers of the neural network is greater than 4, the GOF value does not continue to increase, indicating that the goodness of fit and the number of neural network layers are not linearly proportional. Thus, the optimal structure of the deep neural network includes 4 hidden layers, 600 neurons in the fully connected layer, and its goodness of fit value is 0.999932. On this basis, the number of neurons in the fully connected layer in the first-order convolutional neural network is set to 600. Similarly, it can be seen from the figure that the optimal structure of the first-order convolutional network consists of 2 first-order convolutional layers and a DNN with 1 input layer, 4 hidden layers, and 1 output layer, and its goodness of fit is 0.999990.

[0086] Input the training set into the network with the optimal structure to complete the training of the first-order convolutional neural network.

[0087] Step 4: After determining the optimal structure of the first-order convolutional neural network, calculate the array steering vector matrix according to the beam variable parameters, convert it into a vector form, and then input it into the neural network to quickly obtain the element excitation and synthesize the ideal pattern.

[0088] Neural network performance evaluation:

[0089] After determining the optimal neural network structure, compare the test set losses of the deep neural network DNN and the first-order convolutional neural network 1-DCNN of the present invention. The test set loss is an important evaluation function for the generalization ability of the neural network. If the difference between the test set loss and the training set loss is too large, it means that the neural network has overfitting and poor generalization ability. Therefore, the smaller the test set loss, the better the generalization ability of the neural network. The test set losses of the neural network are shown in Table 2.

[0090] Table 2 Comparison of neural network test set losses

[0091]

[0092] It can be found from the table that for both the point null and wide null models, the test set loss of 1-D CNN is much smaller than that of DNN, which means that 1-D CNN has better learning ability and generalization ability than DNN. Then, DNN and 1-D CNN are used to generate the radiation patterns for different null directions, null numbers, and null widths. First, the adaptive beamforming of the neural network in the narrow null model is simulated. In Case 1, the number of narrow nulls is set to 1 and the null direction is 47°. In Case 2, the number of narrow nulls is set to 2 and the null directions are -48° and 50° respectively. According to its beam parameters, the array steering vector matrix is generated and transformed into a vector to be input into the neural network, so as to output the element excitation. The radiation patterns for realizing the narrow nulls are as shown in Figure 4 .(a), Figure 4 .(b). It can be found that in both figures, the radiation pattern curves synthesized by the element excitations obtained by 1-D CNN coincide better with the radiation pattern curves synthesized by the SDR algorithm. The null levels synthesized by 1-D CNN can generally reach -80 dB, while in Figure 4 .(b), the null level synthesized by DNN can only reach -60 dB. At the same time, in the null directions of the synthesized radiation patterns, in Figure 4 .(a), the null angle error of DNN reaches more than 1°, on the contrary, the null angle error of 1-D CNN is controlled within the range of 0.5°, which is much smaller than the error of DNN. It can be concluded that in the narrow null model, whether analyzed from the depth of the null level or the null direction, the radiation pattern synthesized by 1-D CNN is closer to the ideal beam radiation pattern.

[0093] After that, the adaptive beamforming of the neural network algorithm in the wide null model is simulated. In Case 3, the number of nulls is set to 2, the null angles are -41° and 34°, and the null width is 28°. In Case 4, the number of nulls is set to 2, the null angles are -33° and 32°, and the null width is 6°. The radiation patterns for realizing the wide nulls are as shown below. In Figure 5 .(a) and Figure 5 .(b), it can be found that regardless of the value of the null width, 1-D CNN remains at about -50 dB under the specified null width, while looking at DNN trained with the same number of samples, the null level often exceeds -40 dB, which has a large difference from the null level of the radiation pattern synthesized by the actual SDR algorithm. Therefore, in the wide null model, the fitting performance of 1-D CNN is better than that of DNN.

[0094] From the performance analysis of the neural network in the above narrow null model and wide null model, it can be concluded that compared with the DNN, the pattern curve implemented by the 1-D CNN is closer to the pattern curve implemented by the SDR algorithm, which means that the 1-D CNN has better fitting ability in adaptive beamforming. It should be noted that the neural network algorithm only takes less than 0.01 s to obtain the array element excitation, while the SDR algorithm takes 1.2 s to obtain the array element excitation after 5 iterations, which is much longer than the time taken by the neural network algorithm.

Claims

1. An adaptive beamforming method based on a first-order convolutional neural network, characterized in that It includes the following steps: Step 1: Set beam variable parameters, where the beam variable parameters include null directions, null numbers, and null widths, and generate corresponding array element excitations through a semidefinite programming algorithm; construct a training set {r, z} from the vector form r of the array steering vector matrix of the null direction that has undergone real and imaginary part separation and normalization processing and the array element excitation z; Step 2: Construct a first-order convolutional neural network that realizes the mapping relationship between the array steering vector and the array element excitation; the first-order convolutional neural network is composed of multiple first-order convolutional layers and a fully connected deep neural network. The multiple first-order convolutional layers are used to enrich the feature dimensions of the input data, and the fully connected deep neural network is used to predict the array element excitation based on the data features learned by the former; Step 3: Determine the optimal structure of the first-order convolutional neural network, and input the training set to complete the training of the first-order convolutional neural network; Step 4: Generate the vector form of the array steering vector matrix according to the required beam variable parameters and input it into the trained first-order convolutional neural network, and then complete beamforming according to the array element excitation output from the first-order convolutional neural network; Among them, in the l-th first-order convolutional layer, there are the following operations: Input vector: where represents the data size of the output of the (l-1)-th first-order convolutional layer, [l-1] represents the (l-1)-th first-order convolutional layer, M [l-1] represents the length of the output vector of each channel of the (l-1)-th first-order convolutional layer, represents the number of output channels of the (l-1)-th first-order convolutional layer, C [l-1] is the input vector of the l-th first-order convolutional layer from the output of the previous layer l-1; Output vector: The output vector of the previous layer serves as the input to this layer. The output is obtained by multiplying the input element-wise with the filter parameters and then summing them up. Its matrix calculation is expressed as: where m represents the m-th element of the output vector, m = 1, ..., M [l] and represents the q-th filter of the l-th layer, i and k represent the size of the filter, i is the length of the filter, and k is the number of channels of the filter; represents the input vector of the l-th layer, and ξ(m - 1)+i represents the element corresponding to the ξ(m - 1)+i-th position of the input vector input into the q-th filter of the l-th layer; The activation function is set to the ReLU function, and the output vector O of the l-th layer [l] After passing through the activation function f, it serves as the input vector C of the (l + 1)-th layer [l] ; The optimal structure of the first-order convolutional neural network is: the multiple first-order convolutional layers are composed of 2 first-order convolutional layers, and the fully connected deep neural network is composed of 1 input layer, 4 hidden layers, and 1 output layer.

2. The method according to claim 1, wherein Each pair of r, w in the training set is: Among them, r′ is the vector form of the array steering vector matrix of the null direction after separating the real part Re and the imaginary part Im, and r min , r max are respectively the minimum value and the maximum value among all r′; z′ is the element excitation z′ after separating the real part Re and the imaginary part Im; z min , z max are respectively the minimum value and the maximum value among all the generated z′; r′=[Re(R 12 ),Im(R 12 ),...,Re(R 1N ),Im(R 1N ),...,Re(R (N-1),N ),Im(R (N-1),N )] T ; z′ = [Re(w1), Im(w1),..., Re(w N ), Im(w N )] T ; R is the covariance matrix of the array steering vectors of N array elements, R (N-1),N is the element in the Nth column and the (N - 1)th row of the covariance matrix R; w n is the element excitation of the nth antenna, where n = 1, …, N; T is the transpose.

3. The method according to claim 1, wherein The number of neurons in each hidden layer in the optimal structure of the first-order convolutional neural network is 600.

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