Broadband signal DOA estimation method based on deep convolutional neural networks

Abstract

This invention discloses a broadband signal DOA estimation method based on a deep convolutional neural network. First, based on the array structure of a uniform linear array and spatial target information, a mathematical model of the array under multiple snapshots of the broadband signal is calculated. Then, the array received data matrix at the reference frequency point after focusing is calculated. A sparse representation model of the broadband signal covariance matrix is ​​established. This sparse representation model is preprocessed to obtain a pseudospectral of the network input space. A deep convolutional neural network model for DOA estimation is built and trained. Finally, test samples are input into the trained deep convolutional neural network model to calculate the broadband signal DOA estimate. This invention achieves high-precision, high-resolution, and high-efficiency broadband signal DOA estimation performance.

Description

Technical Field

[0001] This invention belongs to the field of radar signal technology, specifically relating to a broadband signal DOA estimation method based on deep convolutional neural networks. Background Technology

[0002] With the continuous development of radar communication technology, the application scope of array direction finding systems is becoming increasingly wide. At the same time, the signal environment is becoming more complex, and narrowband signals are no longer sufficient to meet current application requirements. During signal transmission, broadband signals, due to their larger relative bandwidth, can transmit more information and have stronger anti-interference capabilities. This is very beneficial for target detection, parameter estimation, and feature extraction. Therefore, broadband signals are increasingly being used in radar and communication systems.

[0003] In the field of wideband signal DOA estimation, a common method is frequency domain processing. This method decomposes the received data of the wideband signal into multiple narrowband components of different frequencies using Discrete Fourier Transform, and then processes them using incoherent or coherent subspace algorithms. Experimental results show that the coherent subspace algorithm outperforms the incoherent subspace algorithm.

[0004] The development of deep learning technology has provided a new approach to DOA estimation, no longer relying on model building but rather being data-driven. It can extract features from large amounts of data samples and train a network to learn the mapping relationship between data and DOA, which can be achieved through classification and regression methods. However, most existing deep learning-based DOA estimation methods are designed for narrowband signals. When dealing with multi-band broadband signals, the input dimension of the network increases, and the amount of parameter computation also increases, increasing the computational complexity of DOA estimation. Summary of the Invention

[0005] The purpose of this invention is to provide a broadband signal DOA estimation method based on deep convolutional neural networks to achieve high-precision, high-resolution, and high-efficiency broadband signal DOA estimation performance.

[0006] The technical solution adopted in this invention is a broadband signal DOA estimation method based on deep convolutional neural networks, which is implemented according to the following steps:

[0007] Step 1: Based on the array structure of the uniform linear array and the spatial target information, calculate the array mathematical model under multiple snapshots of the broadband signal;

[0008] Step 2: Calculate the array received data matrix at the reference frequency after focusing;

[0009] Step 3: Establish a sparse representation model of the broadband signal covariance matrix;

[0010] Step 4: Preprocess the sparse representation model of the broadband signal covariance matrix to obtain the pseudospectral of the network input space;

[0011] Step 5: Build and train a deep convolutional neural network model for DOA estimation;

[0012] Step 6: Input the test samples into the trained deep convolutional neural network model to calculate the estimated DOA value of the broadband signal.

[0013] The invention is further characterized in that,

[0014] Step 1 is implemented in the following steps:

[0015] Step 1.1: Based on the array structure of the uniform linear array and the spatial target information, calculate the echo signal x received by the m-th array element at time t. m (t):

[0016]

[0017] Among them, s k (t) represents the k-th wideband signal, k = 1, 2, ..., K, where K represents the number of signal sources, τ m,k = (m-1)dsinθ k / c indicates source s k (t) represents the time delay difference relative to the reference element when reaching the m-th element, where M represents the number of elements, and θ k Let n be the direction of arrival of the k-th broadband signal, c be the electromagnetic wave propagation speed, d be the element spacing, and n be the direction of arrival. m (t) represents the Gaussian white noise on the m-th element, with a mean of 0 and a variance of .

[0018] Step 1.2: Perform a Discrete Fourier Transform on the array echo signal obtained in Step 1.1 to obtain the single-shot frequency f. j The mathematical model for a point broadband signal is:

[0019] x(f j )=A(f j ,θ)s(f j )+n(f j ), j=1,2,…,J

[0020] Where x(f) j )=[x1(f j ),x2(f j ),…,x M (f j )] T ,s(f j )=[s1(f j ),s2(fj ),…,s K (f j )] T and n(f j )=[n1(f j ),n2(f j ),…,n M (f j )] T They are frequencies f j Discrete Fourier transforms of the array echo signal, target signal, and noise signal, assuming that the noise in each sub-band is independent, and J represents the number of sub-bands, (·) T This is a transpose operation;

[0021] θ = [θ1, θ2, ..., θ K ],A(f j ,θ)=[a(f j ,θ1),…,a(f j ,θ K )]∈C M×K For frequency f j The array manifold matrix of points, Represents angle θ k The guide vector;

[0022] Step 1.3: Based on the single-shot frequency f obtained in Step 1.2 j The mathematical model of a broadband signal divides a fixed time interval into L equally spaced segments, and then performs a discrete Fourier transform on each segment to obtain the frequency f of each beat. j The mathematical model for a point-based broadband signal array is:

[0023] X(f j )=A(f j ,θ)S(f j )+N(f j ), j=1,2,…,J

[0024] Where X(f) j )=[x1(f j ),x2(f j ),…,x L (f j )]∈C M×L It is the array receiving data matrix, x l (f j )=[x l (1,f j ),x l (2,f j ),…,x l (M,f j )] represents frequency fj The frequency domain data of the l-th snapshot of the point, l = 1, 2, ..., L, S(f j )=[s1(f j ),s2(f j )...,s L (f j )]∈C K×L It is a signal waveform matrix, s l (f j )=[s1(f j ),…,s K (f j )] T Represents frequency f j The signal vector of the l-th snapshot of the point;

[0025] N(f j )=[n1(f j ),n2(f j ...,n L (f j )]∈C M×L It is a noisy data matrix;

[0026] n l (f j )=[n l (1,f j ),n l (2,f j ),…,n l (M,f j )] represents the frequency point f j The noise vector at the l-th snapshot, where L represents the frequency domain snapshot number.

[0027] Step 2 is implemented in the following steps:

[0028] Step 2.1: Based on the frequency f obtained in Step 1.3, take multiple shots at the same frequency f. j A mathematical model of a broadband signal at a point assumes that the signal and noise are uncorrelated, and that the noise from different channels is also uncorrelated, thus obtaining the frequency f. j The covariance matrix R corresponding to the point j for:

[0029]

[0030] in, Let I be the signal covariance matrix, and let I denote the identity matrix. H This represents the conjugate transpose operation;

[0031] Step 2.2: Set the lowest frequency point of the broadband signal as the reference frequency point f0;

[0032] Step 2.3: Based on the reference frequency point f0 obtained in Step 2.2 and the bilateral correlation transformation algorithm, calculate the focusing matrix T(f j ):

[0033] T(f j )=Q(f0)Q H (f j )

[0034] Among them, Q(f0) and Q(f j ) are P(f0) and P(f j ) eigenvectors, The covariance matrix after denoising at the reference frequency f0 is... For frequency point f j The denoised covariance matrix and They are R0 and R j The average of small eigenvalues;

[0035] Step 2.4: Use the focusing matrix T(f) obtained in Step 2.3 j The frequency f obtained in step 1.3 is used to capture multiple shots. j A point-to-point broadband signal array receives data X(f) j Focusing on the reference frequency point f0, we obtain the array received data matrix X of the reference frequency point after focusing. T (f j ):

[0036] X T (f j )=A(f0,θ)S(f j )+N T (f j )

[0037] Among them, X T (f j )=T(f j )X(f j ), N T (f j )=T(f j )N(f j ) are the focused array received data matrix and noise matrix, respectively, A(f0,θ)=T(f j )A(f j ,θ) is the array manifold matrix at the reference frequency point f0.

[0038] Step 3 is implemented in the following steps:

[0039] Step 3.1: Perform N-point sampling across the entire airspace from -60° to 60° to obtain the set of sampling grid angle information. And satisfy N >> M and N >> K;

[0040] Step 3.2: Based on the data matrix X at the reference frequency point obtained in Step 2.4 after focusing... T (f j The set of angle information obtained in step 3.1 is as follows: Construct a sparse representation model for broadband signals;

[0041] Step 3.3: Based on the sparse representation model of the broadband signal obtained in Step 3.2, construct a sparse representation model of the broadband signal covariance matrix.

[0042] The sparse representation model for broadband signals in step 3.2 is as follows:

[0043]

[0044] in, It is the complete array manifold matrix at the reference frequency point f0. For frequency f j The sparse signal matrix at that location, Represents frequency f j The sparse signal vector of the l-th snapshot of a point, if and only if When the value is zero, the corresponding position has a value, and the other positions are zero.

[0045] The sparse representation model of the broadband signal covariance matrix in step 3.3 is as follows:

[0046]

[0047] in, The covariance matrix of the focused signal, and They have the same row sparse structure.

[0048] Step 4 is implemented in the following steps:

[0049] Step 4.1: Vectorize the broadband signal covariance matrix R0 obtained in Step 3.3 to obtain:

[0050]

[0051] Where vec(·) represents the operation of straightening the matrix by columns, i.e., h = [h1; h2; ...; h M ], h m Let R0 be the m-th column vector.

[0052] B = [B1; B2; ...; B M ] represents the observation matrix,

[0053]

[0054] e m Let e ​​represent a column vector where the m-th element is 1 and the rest are 0, and let e = [e1; e2; ...; e...]. M ], η=[η1,η2,…,η N ] T It represents the true spatial spectrum of a broadband signal, and has values ​​only within the angle range of the incident signal;

[0055] Step 4.2: Based on the covariance vectorized vector h obtained in Step 4.1, calculate the spatial pseudospectrum η of the broadband signal:

[0056]

[0057] Step 5 is implemented in the following steps:

[0058] Step 5.1: Based on the spatial pseudospectrum obtained in Step 4.2 and

[0059] Deep learning theory, the structure of a deep convolutional neural network is as follows:

[0060] The input is the spatial pseudospectral of a broadband signal.

[0061] Convolutional Layer-1: Kernel size 25, output channels 12, activation function: ReLU, padding method: input and output sizes are the same;

[0062] Convolutional Layer-2: Kernel size 15, output channels 6, activation function: ReLU, padding method: input and output sizes are the same;

[0063] Convolutional layer-3: kernel size 5, output channels 3, activation function: ReLU, padding method: input and output sizes are the same;

[0064] Convolutional layer-4: kernel size 3, output channel 1, activation function: ReLU, padding method: input and output sizes are the same;

[0065] Fully connected layer-1: Number of neurons: 128, Activation function: ReLU;

[0066] Random deactivation layer: probability p = 0.3;

[0067] Fully connected layer-2: Number of neurons: 100, Activation function: ReLU;

[0068] Fully connected layer-3: Number of neurons: 80, Activation function: ReLU;

[0069] Output: 121 neurons, activation function: Sigmoid;

[0070] Step 5.2: Combining steps 1, 2, 3, and 4, generate D sets of training samples and labels for K targets, resulting in the network input sample dataset:

[0071]

[0072] in, Let η represent the pseudospectral of the training sample space of the d-th group. d The true spatial spectral label corresponding to the d-th training sample is represented by... Together, they constitute the d-th group of network input data. The sample dataset D is divided into training set D in an 8:2 ratio. train and verification set D test Let z be the iteration number, and z = 1, and the maximum number of iterations be epochs;

[0073] Step 5.3, the training set D obtained from step 5.2 train A sample is extracted and input into the deep convolutional neural network structure built in step 5.1 to obtain the convolutional layer output data c. i :

[0074] c i =P(ReLU(κ) i *c i-1 +b i ), i = 1, 2, 3, 4

[0075] Among them, c i This is the input to the i-th convolutional layer, where i = 1, 2, 3, 4. κ i Let b represent the weight matrix of the i-th layer. i Represents the bias term of the i-th layer, ReLU(·) represents the ReLU activation function, and P(·) is the zero-padding operation, which expands the ReLU(·) output to the original input size;

[0076] Step 5.4: Take the output data c from the fourth convolutional layer obtained in step 5.3. 4 The input is fed into a fully connected layer, and the output of the j-th fully connected layer is...

[0077]

[0078] Where, d j Let d be the output of the j-th fully connected layer. 0 =c 4 σ(·) represents the activation function, ω j Let J be the weight matrix of the j-th layer. For the bias term of the j-th layer, when j = 1, 2, 3, the activation function σ(·) is ReLU; when j = 4, which is the output layer, the activation function σ(·) is Sigmoid. The resulting network output spatial spectrum...

[0079] Step 5.5: Based on the network output of step 5.4 and the corresponding label η established in step 5.2 d Construct the optimization objective function:

[0080]

[0081] in These are the parameters of a deep convolutional neural network;

[0082] Step 5.6: Optimize the deep convolutional neural network built in Step 5.1 based on the loss function constructed in Step 5.5, and update the network parameters using the Adam optimization algorithm. The calculation process is as follows:

[0083] Ω z =Ω z-1 +ΔΩ z

[0084] Among them, Ω z Here are the parameters of the deep convolutional neural network in the z-th iteration, and Ω0 is the network initialization parameter. This represents the parameter increment in the z-th iteration. They represent g respectively z First-order and second-order momentum correction values, Represents the loss function Regarding the parameter Ω in Ω z-1 gradient on, For gradient operators, m z n z They represent the gradients g and g respectively. z The first and second momentum are given, and β1 and β2 are the first and second momentum decay coefficients, respectively, set to 0.9 and 0.999. ε is a small constant, l r The learning rate;

[0085] Step 5.7: Repeat steps 5.3, 5.4, 5.5, and 5.6 until the training set D has been completely traversed. train All samples in the middle;

[0086] Step 5.8: Determine the iteration number z:

[0087] 1) If z > epochs, then the deep convolutional neural network used for DOA estimation is trained.

[0088] 2) If z≤epochs, proceed to step 5.9.

[0089] Step 5.9: Let z = z + 1, and repeat steps 5.3 to 5.8.

[0090] Step 6 is implemented in the following steps:

[0091] Step 6.1: Randomly generate target angle information θ, and obtain test samples according to steps 1, 2, 3, and 4.

[0092] Step 6.2: Take the test sample obtained in Step 6.1. The input is fed into the deep convolutional neural network trained in step 5 to obtain the network output reconstructed spatial spectrum.

[0093] Step 6.3: Use the spectral peak search algorithm to find the spatial spectrum. There are K corresponding main peaks, where the amplitude of the kth main peak is denoted as α. k,1 The corresponding angle value is denoted as

[0094] Step 6.4: Use the spectral peak search algorithm to find secondary peaks within a 1° range to the left and right of the K main peaks.

[0095] Step 6.4 is implemented in accordance with the following steps:

[0096] 1) If there are no secondary peaks within 1° to the left and right of the k-th primary peak, then the estimated angle of DOA for the k-th target is...

[0097] 2) If there is a secondary peak within 1° to the left and right of the k-th primary peak, and the amplitude of the secondary peak is denoted as α. k,2 The corresponding angle value is denoted as The estimated angle of the DOA for the k-th target is then...

[0098]

[0099] The beneficial effects of this invention are as follows: Compared with existing broadband signal DOA estimation methods, the broadband signal DOA estimation method based on deep convolutional neural networks benefits from the following: 1) This invention achieves joint estimation of multiple frequency bands of broadband signals, effectively reducing the estimation time and improving the real-time performance of the algorithm. 2) This invention is data-driven and does not depend on model structure, thus exhibiting better robustness. 3) Compared with existing methods, this invention uses deep convolutional neural networks, resulting in higher estimation accuracy and resolution performance. Attached Figure Description

[0100] Figure 1This is a flowchart illustrating the implementation of the present invention;

[0101] Figure 2(a) shows the simulation results of spatial spectrum estimation of the first set of test data using existing methods;

[0102] Figure 2(b) is a simulation result of spatial spectrum estimation of the first set of test data using the method of the present invention;

[0103] Figure 2(c) shows the simulation results of spatial spectrum estimation of the second set of test data using existing methods;

[0104] Figure 2(d) is a simulation result of spatial spectrum estimation of the second set of test data using the method of the present invention;

[0105] Figure 3(a) shows the simulation results of estimating the information source at three different angle intervals using existing methods;

[0106] Figure 3(b) shows the simulation results of the estimation error of the information source at three different angle intervals using the existing method;

[0107] Figure 3(c) is a simulation result of the estimation of the information source at three different angles using the method of the present invention;

[0108] Figure 3(d) shows the simulation results of the estimation error of three different angle intervals of the information source using the method of the present invention;

[0109] Figure 4(a) is a simulation result of reconstructing the spatial spectrum of a source using the method of the present invention;

[0110] Figure 4(b) shows the simulation results of reconstructing the spatial spectrum of three information sources using the method of the present invention;

[0111] Figure 5(a) shows the simulation results of reconstructing the spatial spectrum of the BPSK signal using the method of this invention;

[0112] Figure 5(b) shows the simulation results of the spatial spectrum of LFM signal type using the method of the present invention;

[0113] Figure 6(a) is a simulation result of the variation curve of the root mean square error of multiple signals with the source spacing using existing methods and the method of the present invention;

[0114] Figure 6(b) is a simulation result of the root mean square error of multiple signals versus signal-to-noise ratio using existing methods and the method of the present invention;

[0115] Figure 7(a) is a simulation result of the curves showing the change of the probability of successful resolution of multiple signals with the source spacing using existing methods and the method of the present invention;

[0116] Figure 7(b) is a simulation result of the curves showing the change of the probability of successful resolution of multiple signals with the signal-to-noise ratio using existing methods and the method of the present invention. Detailed Implementation

[0117] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0118] This invention presents a broadband signal DOA estimation method based on deep convolutional neural networks, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0119] Step 1: Based on the array structure of the uniform linear array and the spatial target information, calculate the array mathematical model under multiple snapshots of the broadband signal;

[0120] Step 1 is implemented in the following steps:

[0121] Step 1.1: Based on the array structure of the uniform linear array and the spatial target information, calculate the echo signal x received by the m-th array element at time t. m (t):

[0122]

[0123] Among them, s k (t) represents the k-th wideband signal, k = 1, 2, ..., K, where K represents the number of signal sources, τ m,k = (m-1)dsinθ k / c indicates source s k (t) represents the time delay difference relative to the reference element when reaching the m-th element, where M represents the number of elements, and θ k Let n be the direction of arrival of the k-th broadband signal, c be the electromagnetic wave propagation speed, d be the element spacing, and n be the direction of arrival. m (t) represents the Gaussian white noise on the m-th element, with a mean of 0 and a variance of .

[0124] Step 1.2: Perform a Discrete Fourier Transform on the array echo signal obtained in Step 1.1 to obtain the single-shot frequency f. j The mathematical model for a point broadband signal is:

[0125] x(f j )=A(f j ,θ)s(f j )+n(f j ), j=1,2,…,J

[0126] Where x(f) j )=[x1(f j ),x2(f j ),…,x M (f j )] T ,s(f j )=[s1(f j ),s2(fj ),…,s K (f j )] T and n(f j )=[n1(f j ),n2(f j ),…,n M (f j )] T They are frequencies f j Discrete Fourier transforms of the array echo signal, target signal, and noise signal, assuming that the noise in each sub-band is independent, and J represents the number of sub-bands, (·) T This is a transpose operation;

[0127] θ = [θ1, θ2, ..., θ K ],A(f j ,θ)=[a(f j ,θ1),…,a(f j ,θ K )]∈C M×K For frequency f j The array manifold matrix of points, Represents angle θ k The guide vector;

[0128] Step 1.3: Based on the single-shot frequency f obtained in Step 1.2 j The mathematical model of a broadband signal divides a fixed time interval into L equally spaced segments, and then performs a discrete Fourier transform on each segment to obtain the frequency f of each beat. j The mathematical model for a point-based broadband signal array is:

[0129] X(f j )=A(f j ,θ)S(f j )+N(f j ), j=1,2,…,J

[0130] Where X(f) j )=[x1(f j ),x2(f j ),…,x L (f j )]∈C M×L It is the array receiving data matrix, x l (f j )=[x l (1,f j ),x l (2,f j ),…,x l (M,f j )] represents frequency fj The frequency domain data of the l-th snapshot of the point, l = 1, 2, ..., L, S(f j )=[s1(f j ),s2(f j )...,s L (f j )]∈C K×L It is a signal waveform matrix, s l (f j )=[s1(f j ),…,s K (f j )] T Represents frequency f j The signal vector of the l-th snapshot of the point;

[0131] N(f j )=[n1(f j ),n2(f j ...,n L (f j )]∈C M×L It is a noisy data matrix;

[0132] n l (f j )=[n l (1,f j ),n l (2,f j ),…,n l (M,f j )] represents the frequency point f j The noise vector at the l-th snapshot, where L represents the frequency domain snapshot number.

[0133] Step 2: Based on the array mathematical model obtained in Step 1, calculate the array received data matrix at the reference frequency point after focusing;

[0134] Step 2 is implemented in the following steps:

[0135] Step 2.1: Based on the frequency f obtained in Step 1.3, take multiple shots at the same frequency f. j A mathematical model of a broadband signal at a point assumes that the signal and noise are uncorrelated, and that the noise from different channels is also uncorrelated, thus obtaining the frequency f. j The covariance matrix R corresponding to the point j for:

[0136]

[0137] in, Let I be the signal covariance matrix, and let I denote the identity matrix. H This represents the conjugate transpose operation;

[0138] Step 2.2: Set the lowest frequency point of the broadband signal as the reference frequency point f0;

[0139] Step 2.3: Based on the reference frequency point f0 obtained in Step 2.2 and the bilateral correlation transformation algorithm, calculate the focusing matrix T(f j ):

[0140] T(f j )=Q(f0)Q H (f j )

[0141] Among them, Q(f0) and Q(f j ) are P(f0) and P(f j ) eigenvectors, The covariance matrix after denoising at the reference frequency f0 is... For frequency point f j The denoised covariance matrix and They are R0 and R j The average of small eigenvalues;

[0142] Step 2.4: Use the focusing matrix T(f) obtained in Step 2.3 j The frequency f obtained in step 1.3 is used to capture multiple shots. j A point-to-point broadband signal array receives data X(f) j Focusing on the reference frequency point f0, we obtain the array received data matrix X of the reference frequency point after focusing. T (f j ):

[0143] X T (f j )=A(f0,θ)S(f j )+N T (f j )

[0144] Among them, X T (f j )=T(f j )X(f j ), N T (f j )=T(f j )N(f j ) are the focused array received data matrix and noise matrix, respectively, A(f0,θ)=T(f j )A(f j ,θ) is the array manifold matrix at the reference frequency point f0.

[0145] Step 3: Based on the reference frequency array received data matrix and sparse representation theory obtained in Step 2, establish a sparse representation model of the broadband signal covariance matrix.

[0146] Step 3 is implemented in the following steps:

[0147] Step 3.1: Perform N-point sampling across the entire airspace from -60° to 60° to obtain the set of sampling grid angle information. And satisfy N >> M and N >> K;

[0148] Step 3.2: Based on the data matrix X at the reference frequency point obtained in Step 2.4 after focusing... T (f j The set of angle information obtained in step 3.1 is as follows: Construct a sparse representation model for broadband signals;

[0149] The sparse representation model for broadband signals in step 3.2 is as follows:

[0150]

[0151] in, It is the complete array manifold matrix at the reference frequency point f0. For frequency f j The sparse signal matrix at that location, Represents frequency f j The sparse signal vector of the l-th snapshot of a point, if and only if When the value is zero, the corresponding position has a value, and the other positions are zero.

[0152] Step 3.3: Based on the sparse representation model of the broadband signal obtained in Step 3.2, construct a sparse representation model of the broadband signal covariance matrix.

[0153] The sparse representation model of the broadband signal covariance matrix in step 3.3 is as follows:

[0154]

[0155] in, The covariance matrix of the focused signal, and They have the same row sparse structure.

[0156] Step 4: Preprocess the sparse representation model of the broadband signal covariance matrix obtained in Step 3 to obtain the pseudospectrum of the network input space;

[0157] Step 4 is implemented in the following steps:

[0158] Step 4.1: Vectorize the broadband signal covariance matrix R0 obtained in Step 3.3 to obtain:

[0159]

[0160] Where vec(·) represents the operation of straightening the matrix by columns, i.e., h = [h1; h2; ...; h M ], h m Let R0 be the m-th column vector.

[0161] B = [B1; B2; ...; B M ] represents the observation matrix,

[0162]

[0163] e m Let e ​​represent a column vector where the m-th element is 1 and the rest are 0, and let e = [e1; e2; ...; e...]. M ], η=[η1,η2,…,η N ] T It represents the true spatial spectrum of a broadband signal, and has values ​​only within the angle range of the incident signal;

[0164] Step 4.2: Based on the covariance vectorized vector h obtained in Step 4.1, calculate the spatial pseudospectrum η of the broadband signal:

[0165]

[0166] Step 5: Based on the pseudospectral of the network input space obtained in Step 4 and the deep learning theory, build and train a deep convolutional neural network model for DOA estimation.

[0167] Step 5 is implemented in the following steps:

[0168] Step 5.1: Based on the spatial pseudospectrum obtained in Step 4.2 and

[0169] Deep learning theory, the structure of a deep convolutional neural network is as follows:

[0170] The input is the spatial pseudospectral of a broadband signal.

[0171] Convolutional Layer-1: Kernel size 25, output channels 12, activation function: ReLU, padding method: input and output sizes are the same;

[0172] Convolutional Layer-2: Kernel size 15, output channels 6, activation function: ReLU, padding method: input and output sizes are the same;

[0173] Convolutional layer-3: kernel size 5, output channels 3, activation function: ReLU, padding method: input and output sizes are the same;

[0174] Convolutional layer-4: kernel size 3, output channel 1, activation function: ReLU, padding method: input and output sizes are the same;

[0175] Fully connected layer-1: Number of neurons: 128, Activation function: ReLU;

[0176] Random deactivation layer: probability p = 0.3;

[0177] Fully connected layer-2: Number of neurons: 100, Activation function: ReLU;

[0178] Fully connected layer-3: Number of neurons: 80, Activation function: ReLU;

[0179] Output: 121 neurons, activation function: Sigmoid;

[0180] Step 5.2: Combining steps 1, 2, 3, and 4, generate D sets of training samples and labels for K targets, resulting in the network input sample dataset:

[0181]

[0182] in, Let η represent the pseudospectral of the training sample space of the d-th group. d The true spatial spectral label corresponding to the d-th training sample is represented by... Together, they constitute the d-th group of network input data. The sample dataset D is divided into training set D in an 8:2 ratio. train and verification set D test Let z be the iteration number, and z = 1, and the maximum number of iterations be epochs;

[0183] Step 5.3, the training set D obtained from step 5.2 train A sample is extracted and input into the deep convolutional neural network structure built in step 5.1 to obtain the convolutional layer output data c. i :

[0184] c i =P(ReLU(κ) i *c i-1 +b i ), i = 1, 2, 3, 4

[0185] Among them, c i This is the input to the i-th convolutional layer, where i = 1, 2, 3, 4. κ i Let b represent the weight matrix of the i-th layer. i Represents the bias term of the i-th layer, ReLU(·) represents the ReLU activation function, and P(·) is the zero-padding operation, which expands the ReLU(·) output to the original input size;

[0186] Step 5.4: Take the output data c from the fourth convolutional layer obtained in step 5.3. 4 The input is fed into a fully connected layer, and the output of the j-th fully connected layer is...

[0187]

[0188] Where, d j Let d be the output of the j-th fully connected layer. 0 =c 4 σ(·) represents the activation function, ω j Let J be the weight matrix of the j-th layer. For the bias term of the j-th layer, when j = 1, 2, 3, the activation function σ(·) is ReLU; when j = 4, which is the output layer, the activation function σ(·) is Sigmoid. The resulting network output spatial spectrum...

[0189] Step 5.5: Based on the network output of step 5.4 and the corresponding label η established in step 5.2 d Construct the optimization objective function:

[0190]

[0191] in These are the parameters of a deep convolutional neural network;

[0192] Step 5.6: Optimize the deep convolutional neural network built in Step 5.1 based on the loss function constructed in Step 5.5, and update the network parameters using the Adam optimization algorithm. The calculation process is as follows:

[0193] Ω z =Ω z-1 +ΔΩ z

[0194] Among them, Ω z Here are the parameters of the deep convolutional neural network in the z-th iteration, and Ω0 is the network initialization parameter. This represents the parameter increment in the z-th iteration. They represent g respectively z First-order and second-order momentum correction values, Represents the loss function Regarding the parameter Ω in Ω z-1 gradient on, For gradient operators, m z n z They represent the gradients g and g respectively. z The first and second momentum, β1 and β2 are the first and second momentum decay coefficients, respectively, set to 0.9 and 0.999, mz =β1*m z-1 +(1-β1)*g z , ε is a small constant, usually set to 10. -8 , l r The learning rate;

[0195] Step 5.7: Repeat steps 5.3, 5.4, 5.5, and 5.6 until the training set D has been completely traversed. train All samples in the middle;

[0196] Step 5.8: Determine the iteration number z:

[0197] 1) If z > epochs, then the deep convolutional neural network used for DOA estimation is trained.

[0198] 2) If z≤epochs, proceed to step 5.9.

[0199] Step 5.9: Let z = z + 1, and repeat steps 5.3 to 5.8.

[0200] Step 6: Input the test samples into the deep convolutional neural network model trained in Step 5 to calculate the estimated DOA value of the broadband signal.

[0201] Step 6 is implemented in the following steps:

[0202] Step 6.1: Randomly generate target angle information θ, and obtain test samples according to steps 1, 2, 3, and 4.

[0203] Step 6.2: Take the test sample obtained in Step 6.1. The input is fed into the deep convolutional neural network trained in step 5 to obtain the network output reconstructed spatial spectrum.

[0204] Step 6.3: Use the spectral peak search algorithm to find the spatial spectrum. There are K corresponding main peaks, where the amplitude of the kth main peak is denoted as α. k,1 The corresponding angle value is denoted as

[0205] Step 6.4: Use the spectral peak search algorithm to find secondary peaks within a 1° range to the left and right of the K main peaks.

[0206] Step 6.4 is implemented in accordance with the following steps:

[0207] 1) If there are no secondary peaks within 1° to the left and right of the k-th primary peak, then the estimated angle of DOA for the k-th target is...

[0208] 2) If there is a secondary peak within 1° to the left and right of the k-th primary peak, and the amplitude of the secondary peak is denoted as α. k,2 The corresponding angle value is denoted as The estimated angle of the DOA for the k-th target is then...

[0209]

[0210] Example 1

[0211] This invention presents a broadband signal DOA estimation method based on deep convolutional neural networks, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0212] Step 1: Based on the array structure of the uniform linear array and the spatial target information, calculate the array mathematical model under multiple snapshots of the broadband signal;

[0213] Step 2: Based on the array mathematical model obtained in Step 1, calculate the array received data matrix at the reference frequency point after focusing;

[0214] Step 3: Based on the reference frequency array received data matrix and sparse representation theory obtained in Step 2, establish a sparse representation model of the broadband signal covariance matrix.

[0215] Step 4: Preprocess the sparse representation model of the broadband signal covariance matrix obtained in Step 3 to obtain the pseudospectrum of the network input space;

[0216] Step 5: Based on the pseudospectral of the network input space obtained in Step 4 and the deep learning theory, build and train a deep convolutional neural network model for DOA estimation.

[0217] Step 6: Input the test samples into the deep convolutional neural network model trained in Step 5 to calculate the estimated DOA value of the broadband signal.

[0218] Example 2

[0219] This invention presents a broadband signal DOA estimation method based on deep convolutional neural networks, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0220] Step 1: Based on the array structure of the uniform linear array and the spatial target information, calculate the array mathematical model under multiple snapshots of the broadband signal;

[0221] Step 1 is implemented in the following steps:

[0222] Step 1.1: Based on the array structure of the uniform linear array and the spatial target information, calculate the echo signal x received by the m-th array element at time t. m (t):

[0223]

[0224] Among them, s k (t) represents the k-th wideband signal, k = 1, 2, ..., K, where K represents the number of signal sources, τ m,k = (m-1)dsinθ k / c indicates source s k (t) represents the time delay difference relative to the reference element when reaching the m-th element, where M represents the number of elements, and θ k Let n be the direction of arrival of the k-th broadband signal, c be the electromagnetic wave propagation speed, d be the element spacing, and n be the direction of arrival. m (t) represents the Gaussian white noise on the m-th element, with a mean of 0 and a variance of .

[0225] Step 1.2: Perform a Discrete Fourier Transform on the array echo signal obtained in Step 1.1 to obtain the single-shot frequency f. j The mathematical model for a point broadband signal is:

[0226] x(f j )=A(f j ,θ)s(f j )+n(f j ), j=1,2,…,J

[0227] Where x(f) j )=[x1(f j ),x2(f j ),…,x M (f j )] T ,s(f j )=[s1(f j ),s2(f j ),…,s K (f j )] T and n(f j )=[n1(f j ),n2(f j ),…,n M (f j )] T They are frequencies f j Discrete Fourier transforms of the array echo signal, target signal, and noise signal, assuming that the noise in each sub-band is independent, and J represents the number of sub-bands, (·) T This is a transpose operation;

[0228] θ = [θ1, θ2, ..., θ K ],A(f j ,θ)=[a(fj ,θ1),…,a(f j ,θ K )]∈C M×K For frequency f j The array manifold matrix of points, Represents angle θ k The guide vector;

[0229] Step 1.3: Based on the single-shot frequency f obtained in Step 1.2 j The mathematical model of a broadband signal divides a fixed time interval into L equally spaced segments, and then performs a discrete Fourier transform on each segment to obtain the frequency f of each beat. j The mathematical model for a point-based broadband signal array is:

[0230] X(f j )=A(f j ,θ)S(f j )+N(f j ), j=1,2,…,J

[0231] Where X(f) j )=[x1(f j ),x2(f j ),…,x L (f j )]∈C M×L It is the array receiving data matrix, x l (f j )=[x l (1,f j ),x l (2,f j ),...,x l (M,f j )] represents frequency f j The frequency domain data of the l-th snapshot of the point, l = 1, 2, ... L, S(f j )=[s1(f j ),s2(f j )...,s L (f j )]∈C K×L It is a signal waveform matrix, s l (f j )=[s1(f j ),…,s K (f j )] T Represents frequency f j The signal vector of the l-th snapshot of the point;

[0232] N(f j )=[n1(f j),n2(f j ...,n L (f j )]∈C M×L It is a noisy data matrix;

[0233] n l (f j )=[n l (1,f j ),n l (2,f j ),…,n l (M,f j )] represents the frequency point f j The noise vector at the l-th snapshot, where L represents the frequency domain snapshot number.

[0234] Step 2: Based on the array mathematical model obtained in Step 1, calculate the array received data matrix at the reference frequency point after focusing;

[0235] Step 3: Based on the reference frequency array received data matrix and sparse representation theory obtained in Step 2, establish a sparse representation model of the broadband signal covariance matrix.

[0236] Step 4: Preprocess the sparse representation model of the broadband signal covariance matrix obtained in Step 3 to obtain the pseudospectrum of the network input space;

[0237] Step 5: Based on the pseudospectral of the network input space obtained in Step 4 and the deep learning theory, build and train a deep convolutional neural network model for DOA estimation.

[0238] Step 6: Input the test samples into the deep convolutional neural network model trained in Step 5 to calculate the estimated DOA value of the broadband signal.

[0239] Example 3

[0240] This invention presents a broadband signal DOA estimation method based on deep convolutional neural networks, the flowchart of which is shown below. Figure 1 As shown, please follow these steps:

[0241] Step 1: Based on the array structure of the uniform linear array and the spatial target information, calculate the array mathematical model under multiple snapshots of the broadband signal;

[0242] Step 2: Based on the array mathematical model obtained in Step 1, calculate the array received data matrix at the reference frequency point after focusing;

[0243] Step 2 is implemented in the following steps:

[0244] Step 2.1: Based on the frequency f obtained in Step 1.3, take multiple shots at the same frequency f. jA mathematical model of a broadband signal at a point assumes that the signal and noise are uncorrelated, and that the noise from different channels is also uncorrelated, thus obtaining the frequency f. j The covariance matrix R corresponding to the point j for:

[0245]

[0246] in, Let I be the signal covariance matrix, and let I denote the identity matrix. H This represents the conjugate transpose operation;

[0247] Step 2.2: Set the lowest frequency point of the broadband signal as the reference frequency point f0;

[0248] Step 2.3: Based on the reference frequency point f0 obtained in Step 2.2 and the bilateral correlation transformation algorithm, calculate the focusing matrix T(f j ):

[0249] T(f j )=Q(f0)Q H (f j )

[0250] Among them, Q(f0) and Q(f j ) are P(f0) and P(f j ) eigenvectors, The covariance matrix after denoising at the reference frequency f0 is... For frequency point f j The denoised covariance matrix and They are R0 and R j The average of small eigenvalues;

[0251] Step 2.4: Use the focusing matrix T(f) obtained in Step 2.3 j The frequency f obtained in step 1.3 is used to capture multiple shots. j A point-to-point broadband signal array receives data X(f) j Focusing on the reference frequency point f0, we obtain the array received data matrix X of the reference frequency point after focusing. T (f j ):

[0252] X T (f j )=A(f0,θ)S(f j )+N T (f j )

[0253] Among them, X T (f j )=T(f j )X(fj ), N T (f j )=T(f j )N(f j ) are the focused array received data matrix and noise matrix, respectively, A(f0,θ)=T(f j )A(f j ,θ) is the array manifold matrix at the reference frequency point f0.

[0254] Step 3: Based on the reference frequency array received data matrix and sparse representation theory obtained in Step 2, establish a sparse representation model of the broadband signal covariance matrix.

[0255] Step 4: Preprocess the sparse representation model of the broadband signal covariance matrix obtained in Step 3 to obtain the pseudospectrum of the network input space;

[0256] Step 5: Based on the pseudospectral of the network input space obtained in Step 4 and the deep learning theory, build and train a deep convolutional neural network model for DOA estimation.

[0257] Step 6: Input the test samples into the deep convolutional neural network model trained in Step 5 to calculate the estimated DOA value of the broadband signal.

[0258] Example 4

[0259] The estimation performance of the present invention for target angle information can be further verified through the following simulation experiments.

[0260] 1. Experimental setup

[0261] A uniform linear array with M=10 elements is used. It is assumed that all far-field broadband signal sources have the same bandwidth B=4MHz, a center frequency of 10MHz, an element spacing d equal to half the wavelength of the center frequency, and J=64 sub-bands. The spatial range of -60° to 60° is defined with a resolution of... The region is divided into N = 121 equally spaced regions, resulting in a discrete angle set Θ = [-60°:1°:60°]. The training epochs are 300, and the learning rate is l. r =0.0001.

[0262] 2. Experimental Content and Analysis

[0263] Experiment 1: Assuming two far-field broadband signals exist in space, this experiment investigates the spatial spectrum reconstruction performance. During the training phase, the angle range of the two signals is [-60°, 60°], with a step of 1° and an angle interval of [2°:2°:40°]. Ten different signal-to-noise ratios are randomly selected from [-10, 0] dB, and the frequency domain snapshot count is 1024, generating a total of 20,000 training samples. During the testing phase, two sets of data are used, both with a signal-to-noise ratio of 0 dB and a frequency domain snapshot count of 1024. The broadband signal incident angles of the first set of data are {-1.02°, 2.26°}, and the broadband signal incident angles of the second set of data are {-6.32°, 9.06°}. The spatial spectrum estimation results of the first set of data using existing methods and the method of this invention are as follows: Figure 2(a) and 2(b) As shown, the spatial spectrum estimation results for the second set of data are as follows: Figure 2(c) and 2(d) As shown, the black lines represent the spatial spectrum, and the black squares represent the actual positions of the two incident signals.

[0264] from Figures 2(a) to 2(d) It can be seen that when two broadband incident signals are incident at angles {-1.02°, 2.26°}, existing methods have low spatial resolution due to beamwidth limitations and cannot effectively distinguish the two signals, while the method of this invention can successfully distinguish the two signals. When incident at {-6.32°, 9.06°}, both existing methods and the method of this invention can successfully distinguish the two signals, but the method of this invention has lower sidelobes and a smoother output spatial spectrum. This indicates that the method of this invention has better resolution performance.

[0265] Example 5

[0266] Experiment 2: Assume two independent far-field broadband signals exist in the spatial domain with a signal-to-noise ratio of 0dB, a frequency domain snapshot number of 1024, and an angular range of [-60°, 60°] with a step of 1°. Three signal intervals {5.4°, 15.2°, 25.8°} not within the training set's angular interval range are selected, generating a total of 300 test samples. The direction-finding results and errors for the two signals using existing methods are as follows: Figure 3(a) and 3(b) As shown, the direction finding results and errors of the two signals using the method of this invention are as follows: Figure 3(c) and 3(d) As shown.

[0267] As shown in Figure 3, existing methods cannot distinguish signals when the angular interval is smaller than the beamwidth, resulting in significant deviations between the direction-finding results and the actual signal values. In contrast, the direction-finding results of the method of this invention at different angular intervals are very close to the actual signal values, with significantly lower errors than existing methods, demonstrating better estimation performance and higher estimation accuracy.

[0268] Example 6

[0269] Experiment 3: This experiment verifies the generalization performance of the method of this invention. Assuming a single or three broadband signals are incident in the far field, which differs from the two signal sources in the training sample dataset, the method of this invention is used to perform direction finding on a single signal with an incident angle of 15.84°, resulting in the spatial spectrum shown in Figure 4(a). The method of this invention is also used to perform direction finding on three signals with incident angles of -19.1°, 0.2°, and 18.3°, resulting in the spatial spectrum shown in Figure 4(b). Changing the experimental conditions, assuming two broadband signals exist in the far field with incident directions of 16.72° and 22.53°, and their signal types are BPSK and LFM signals, respectively, neither of which have been trained by the network. The method of this invention is used to perform direction finding on these signals, resulting in the reconstructed spatial spectrum of the BPSK signal shown in Figure 5(a) and the reconstructed spatial spectrum of the LFM signal shown in Figure 5(b).

[0270] As shown in Figures 4(a) and 4(b), the method of the present invention is still applicable to spatial spectrum estimation of a single signal or three signals, verifying the generalization performance of the method for the number of signal sources. This ensures that the method can provide reliable direction finding results in varying signal environments, especially when the number of signals fluctuates. As shown in Figures 5(a) and 5(b), the method of the present invention can correctly reconstruct the spatial spectrum of both BPSK and LFM signal types, verifying the generalization performance of the method for signal types.

[0271] Example 7

[0272] Experiment 4: Verify the estimation performance of the method of the present invention, using the root mean square error (RMSE) as the evaluation index. Assume there are two broadband far-field signals, the first broadband signal has an incident angle of θ1 = 5° + ξ, and the second broadband signal has an incident angle of θ2 = 5° + ξ + Δθ, where ξ is randomly selected within the range of [-0.5°, 0.5°], and Δθ is the interval difference between the two signal angles, Δθ∈(2°, 4°…, 20°). The signal-to-noise ratio is fixed at 0dB, and the number of frequency domain snapshots is 1024. 1000 Monte Carlo experiments are performed at each angle interval. The curves of the root mean square error of the existing method and the method of the present invention as a function of the angle interval are shown in Figure 6(a). The experimental conditions were changed, and two broadband signals were incident at θ1 = -6.84° + ξ and θ2 = 9.32° + ξ, respectively, with ξ randomly selected within the range of [-0.5°, 0.5°]. The number of snapshots in the frequency domain was 1024, and the signal-to-noise ratio (SNR) increased in 2dB increments between -10dB and 10dB. 1000 Monte Carlo experiments were conducted at each SNR. The root mean square error (RMSE) of the existing method and the method of this invention as a function of SNR was statistically analyzed, as shown in Figure 6(b).

[0273] As can be seen from Figures 6(a) and 6(b), under the same angular interval or signal-to-noise ratio, the method of the present invention has a smaller root mean square error value, indicating that the estimation accuracy of the method of the present invention is higher.

[0274] Example 8

[0275] Experiment 5: Verify the resolving performance of the method of this invention. The evaluation index is the probability of successful resolving, defined as the angle estimate satisfying the following in each experiment. and If the experiment is successful, then it is successful; otherwise, it is a failure. Let θ represent the estimate, and the probability of successful resolution is the ratio of the number of successful experiments to the total number of experiments. Assume there are two broadband far-field signals. The first broadband signal has an incident angle of θ1 = 2° + ξ that remains constant, and the second broadband signal has an incident angle of θ2 = 2° + ξ + Δθ, where ξ randomly takes values ​​within the range [-0.5°, 0.5°], and Δθ ∈ (2°, 4°…, 20°). The signal-to-noise ratio is fixed at 0 dB, and the number of snapshots in the frequency domain is 1024. 1000 Monte Carlo experiments are performed at each angular interval. The curves showing the change in the success rate of resolution of the existing method and the method of this invention with the angular interval are shown in Figure 7(a). The experimental conditions were changed. The incident angle of the first signal was fixed at θ1 = -3.84° + ξ, and the incident angle of the second signal was θ2 = 3.62° + ξ, with ξ randomly selected within the range of [-0.5°, 0.5°]. The number of snapshots in the frequency domain was 1024, and the signal-to-noise ratio (SNR) increased in 2dB increments between -10dB and 10dB. 1000 Monte Carlo experiments were conducted at each SNR. The curves showing the change in the success resolution probability of the existing method and the method of this invention with the SNR are shown in Figure 7(b).

[0276] As can be seen from Figures 7(a) and 7(b), the success rate of the method of the present invention increases with the increase of angular spacing and signal-to-noise ratio, reaching 100% first. Under the same angular spacing or signal-to-noise ratio, the success rate of the method of the present invention is significantly higher than that of existing methods, especially under small angular spacing and low signal-to-noise ratio, indicating that the resolution performance of the method of the present invention is higher than that of existing methods.

[0277] Example 9

[0278] Experiment 6: Verifying the real-time performance of the method of this invention. Assuming there are two far-field broadband signals and the number of frequency domain snapshots is 1024, the running time of the training samples of the method of this invention and the running time of 1000 Monte Carlo experiments of the existing method and the method of this invention were statistically analyzed. The results are shown in Table 1.

[0279] Table 1

[0280] Existing methods Method of the present invention Training time (s) \ 1376.54 Estimated time (s) 119.97 0.02

[0281] As shown in Table 1, although the method of this invention requires a relatively long training time, the time for angle estimation is significantly reduced after offline training. Under the same experimental conditions, the method of this invention can quickly predict the signal DOA value, proving that the method of this invention has better real-time performance.

[0282] In summary, the method of the present invention can effectively estimate the DOA of broadband signal sources, improve the accuracy and resolution of target angle estimation, and has good generalization ability and real-time performance, which can better meet the needs of practical engineering applications.

Claims

1. A broadband signal DOA estimation method based on deep convolutional neural networks, characterized in that, The specific steps are as follows: Step 1: Based on the array structure of the uniform linear array and the spatial target information, calculate the array mathematical model under multiple snapshots of the broadband signal; Step 2: Calculate the array received data matrix at the reference frequency after focusing; Step 3: Establish a sparse representation model of the broadband signal covariance matrix; Step 4: Preprocess the sparse representation model of the broadband signal covariance matrix to obtain the pseudospectral of the network input space; Step 5: Build and train a deep convolutional neural network model for DOA estimation; Step 5 is implemented in the following steps: Step 5.1: Based on the spatial pseudospectrum obtained in Step 4.2 Based on deep learning theory, the deep convolutional neural network structure is constructed as follows: The input is the spatial pseudospectral of a broadband signal. ; Convolutional Layer-1: Kernel size 25, output channels 12, activation function: ReLU, padding method: input and output sizes are the same; Convolutional Layer-2: Kernel size 15, output channels 6, activation function: ReLU, padding method: input and output sizes are the same; Convolutional layer-3: kernel size 5, output channels 3, activation function: ReLU, padding method: input and output sizes are the same; Convolutional layer-4: kernel size 3, output channel 1, activation function: ReLU, padding method: input and output sizes are the same; Fully connected layer-1: Number of neurons: 128, Activation function: ReLU; Random deactivation layer: probability p=0.3; Fully connected layer-2: Number of neurons: 100, Activation function: ReLU; Fully connected layer-3: Number of neurons: 80, Activation function: ReLU; Output: 121 neurons, activation function: Sigmoid; Step 5.2: Combine steps 1, 2, 3, and 4 to generate... One goal The training samples and label sets are combined to obtain the network input sample dataset as follows: in, Indicates the first Pseudospectral of training sample space Indicates the first The real spatial spectral labels corresponding to the training samples are derived from... Together constitute the first Group network input data, sample dataset Divide into training sets at an 8:2 ratio. and verification set ,set up Let be the number of iterations, and The maximum number of iterations is ; Step 5.3: The training set obtained from Step 5.2 A sample is extracted and input into the deep convolutional neural network structure built in step 5.1 to obtain the output data of the convolutional layer. : in, For the first The input of each convolutional layer, , , Indicates the first The weight matrix of the layer, Indicates the first Layer bias terms, Represents the ReLU activation function. To perform zero-padding operation, The output is expanded to the original input size; Step 5.4: Output the data from the fourth convolutional layer obtained in Step 5.

3. Input to the fully connected layer, the first The fully connected layer output is in, For the first The output of the fully connected layer, , This represents the activation function. For the first The weight matrix of the layer, For the first The layer's bias term, when Time activation function Choose ReLU. When the output layer is reached, the activation function is... Choosing Sigmoid yields the network output spatial spectrum. ; Step 5.5: Based on the network output of Step 5.4 and the corresponding tags established in step 5.2 Construct the optimization objective function: in These are the parameters of a deep convolutional neural network; Step 5.6: Optimize the deep convolutional neural network built in Step 5.1 based on the loss function constructed in Step 5.5, and update the network parameters using the Adam optimization algorithm. The calculation process is as follows: in, For the first Parameters of the deep convolutional neural network in the next iteration. Initialize network parameters. , indicating the first Parameter increment in the next iteration , They represent First-order and second-order momentum correction values, , , Represents the loss function Regarding parameters exist gradient on, For gradient operators, , They represent gradients respectively. First and second momentum , These are the first-order and second-order momentum decay coefficients, respectively, set to 0.9 and 0.

999. , , It is a small constant. The learning rate; Step 5.7: Repeat steps 5.3, 5.4, 5.5, and 5.6 until the training set has been completely traversed. All samples in the middle; Step 5.8: Calculate the number of iterations. Make a judgment: 1) If Then the training of the deep convolutional neural network used for DOA estimation is complete; 2) If Proceed to step 5.9; Step 5.9, let Repeat steps 5.3 to 5.

8. Step 6: Input the test samples into the trained deep convolutional neural network model to calculate the estimated DOA value of the broadband signal.

2. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 1, characterized in that, Step 1 is implemented in the following steps: Step 1.1: Based on the array structure of the uniform linear array and the spatial target information, calculate the... Time of the first The echo signal received by each array element : in, Indicates the first A broadband signal , Indicates the number of signal sources. Indicates the source of information To the The time delay difference between each array element and the reference array element. Indicates the number of array elements. For the first The direction of arrival of a broadband signal The speed of electromagnetic wave propagation. Indicates the spacing between array elements. Indicates the first Gaussian white noise on each element, with a mean of 0 and a variance of . ; Step 1.2: Perform a Discrete Fourier Transform on the array echo signal obtained in Step 1.1 to obtain the single-shot frequency. The mathematical model for a point broadband signal is: in, , and Frequency Discrete Fourier transforms of the array echo signal, target signal, and noise signal, assuming that the noise in each sub-band is independent. Indicates the number of sub-bands. This is a transpose operation; , For frequency The array manifold matrix of points, Indicates angle The guide vector; Step 1.3: Based on the single-shot frequency obtained in Step 1.2 A point-based broadband signal mathematical model divides a given time period into equal intervals. Take small segments, then perform a discrete Fourier transform on each segment to obtain the frequency of each beat. The mathematical model for a point-based broadband signal array is: in, It is an array receiving data matrix. Represents frequency The first point Frequency domain data of a snapshot, , It is a signal waveform matrix. Represents frequency The first point A quick snapshot of the signal vector; It is a noisy data matrix; Frequency point First A snapshot of noise vectors, This represents the number of snapshots in the frequency domain.

3. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 2, characterized in that, Step 2 is implemented in the following steps: Step 2.1: Based on the shooting frequency obtained in Step 1.3 A point-based broadband signal mathematical model assumes that the signal and noise are uncorrelated, and that the noise from different channels is also uncorrelated, thus obtaining the frequency... The covariance matrix corresponding to the point for: in, The signal covariance matrix, Represents the identity matrix. This represents the conjugate transpose operation; Step 2.2: Set the lowest frequency point of the broadband signal as the reference frequency point. ; Step 2.3: Based on the reference frequency point obtained in Step 2.2 And a bilateral correlation transformation algorithm to calculate the focusing matrix. : in, They are , eigenvectors, Reference frequency The denoised covariance matrix For frequency point The denoised covariance matrix and They are and The average of small eigenvalues; Step 2.4: Use the focusing matrix obtained in Step 2.3 The frequency of multiple shots obtained in step 1.3 Point-to-point broadband signal array receives data Focus on reference frequency At this point, the array received data matrix of the reference frequency point after focusing is obtained. : in, , These are the focused array received data matrix and noise matrix, respectively. Reference frequency The array manifold matrix at that location.

4. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 3, characterized in that, Step 3 is implemented in the following steps: Step 3.1: Survey the entire airspace conduct Point sampling yields a set of sampling grid angle information. And satisfy and ; Step 3.2: Based on the data matrix at the reference frequency point obtained in Step 2.4 after focusing. And the set of angle information obtained in step 3.1 is Construct a sparse representation model for broadband signals; Step 3.3: Based on the sparse representation model of the broadband signal obtained in Step 3.2, construct a sparse representation model of the broadband signal covariance matrix.

5. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 4, characterized in that, The sparse representation model for broadband signals in step 3.2 is as follows: in, Reference frequency A complete array manifold matrix at the location, For frequency The sparse signal matrix at that location, Represents frequency The first point A sparse signal vector of snapshots, if and only if When the value is zero, the corresponding position has a value, and the other positions are zero.

6. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 5, characterized in that, The sparse representation model of the broadband signal covariance matrix in step 3.3 is as follows: in, The covariance matrix of the focused signal, and They have the same row sparse structure.

7. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 6, characterized in that, Step 4 is implemented in the following steps: Step 4.1: Calculate the broadband signal covariance matrix obtained in Step 3.

3. Vectorization yields: in, This means performing the operation by straightening the matrix by columns. , for The column vectors, Represents the observation matrix. ， Indicates the first A column vector with 1 element and the rest being 0. , It represents the true spatial spectrum of a broadband signal, and has values ​​only within the angle range of the incident signal; Step 4.2: Vectorize the covariance vector obtained in Step 4.

1. Calculate the spatial pseudospectrum of broadband signals : 。 8. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 7, characterized in that, Step 6 is implemented in the following steps: Step 6.1: Randomly generate target angle information And obtain test samples according to steps 1, 2, 3, and 4. ; Step 6.2: Take the test sample obtained in Step 6.

1. The input is fed into the deep convolutional neural network trained in step 5 to obtain the network output reconstructed spatial spectrum. ; Step 6.3: Use the spectral peak search algorithm to find the spatial spectrum. corresponding The main peak, of which the first The amplitude corresponding to each main peak is denoted as The corresponding angle value is denoted as ; Step 6.4, in Each main peak has two sides on the left and right. The secondary peak is found within the range using a spectral peak search algorithm.

9. The broadband signal DOA estimation method based on deep convolutional neural networks according to claim 8, characterized in that, Step 6.4 is implemented in the following steps: 1) If the first Each main peak has two sides on the left and right. If there is no secondary peak within the range, then the first... The estimated angle of DOA for each target is [value missing]. ; 2) If the first Each main peak has two sides on the left and right. There exists a secondary peak within the range, and the amplitude corresponding to the secondary peak is denoted as... The corresponding angle value is denoted as Then the first The estimated angle of DOA for each target is [value missing]. 。

Images