High-resolution spatial spectrum estimation method

Abstract

The high-resolution spatial spectrum estimation method solves the problem of low spatial spectrum resolution for closely spaced signals under Gaussian white noise and non-Gaussian noise conditions, and belongs to the field of spatial spectrum estimation. The present invention includes: establishing a spatial spectrum estimation network, including a detection network 1, a detection network 2 and a judgment network, wherein the detection network 1 includes a preprocessing network, a residual network, an LSTM network, a fusion network, a fully connected layer and an output layer; the present invention utilizes the detection network 1 to fully mine the characteristics of the signal to estimate the spatial spectrum of the distantly spaced signal; the detection network 2 is trained to perform fine resolution on closely spaced signals, and during testing, the judgment network integrates the results of the detection network 1 and the detection network 2, thereby effectively improving the resolution ability and estimation efficiency of the signal spatial spectrum.

Description

Technical Field

[0001] The invention relates to a high-resolution spatial spectrum estimation method, and belongs to the field of spatial spectrum estimation. Background Art

[0002] Spatial spectrum estimation technology has a wide range of applications in radar, sonar, navigation, radio monitoring and biomedicine. It receives spatial signals by placing sensor array elements in a certain way, and then uses a certain algorithm to obtain the parameters such as the signal arrival angle we need. In traditional array signal processing systems, it is generally assumed that the background noise obeys the Gaussian white noise distribution. However, in actual environments, the Gaussian noise assumption is not always valid. For example, car engine startup, electric drill noise, and lightning noise all obey non-Gaussian noise distribution. The performance of traditional methods will be greatly affected, especially for scenarios such as mobile communications and electronic warfare where the signal intervals are close. Therefore, the study of spatial spectrum estimation of closely spaced signals under Gaussian white noise and non-Gaussian noise backgrounds has strong theoretical research value and practical significance.

[0003] Spatial spectrum estimation algorithms can be divided into three categories, namely, classic spectrum estimation algorithms, compressed sensing algorithms, and machine learning algorithms. The first category is the classic subspace estimation algorithm, which breaks the limitation of Rayleigh limit and is therefore called super-resolution direction finding. The most famous subspace decomposition algorithms are the Multiple Signal Classification (MUSIC) algorithm and the rotation-invariant subspace technology. Some scholars have proposed that the MUSIC algorithm mainly utilizes the orthogonal characteristics of the subspace and searches on the spatial spectrum function. The signal angle corresponding to the sharp spectrum peak is the angle estimate of the signal. Based on this algorithm, some scholars have made some improvements to the MUSIC algorithm, such as the weighted MUSIC algorithm and the root-finding MUSIC algorithm. Since these MUSIC-related algorithms require complex spectrum peak search operations, the direction finding speed is slow. To address this problem, some scholars have proposed the rotation-invariant subspace technology based on the rotation invariance between subarrays, which utilizes the rotation invariance of the two subarrays. This algorithm does not require spectral peak search, so the direction finding speed is fast, but the disadvantage is that the direction finding accuracy is not high; the second category is the compressed sensing algorithm. Many scholars have found that the estimation performance can be further improved by using the sparsity of spatial signals in the spatial domain and compressed sensing technology, and proposed a spectral estimation method based on compressed sensing. Among them, the Matching Pursuit (MP) algorithm proposed by some scholars uses a large number of iterations to obtain the optimal solution. Because the over-complete dictionary has a great influence on the reconstruction of sparse signals, it is necessary to maintain the completeness of the over-complete dictionary during the iteration process. Due to the poor anti-interference performance of MP, some scholars have proposed an orthogonal matching pursuit algorithm to improve the stability of the MP algorithm. Some scholars have proposed l 1-SVD (Singular Value Decomposition, SVD) algorithm uses the angle grid to sparsely represent the signal source, and reduces the computational complexity through the singular value decomposition method, and finally solves the optimization problem to obtain the spatial spectrum estimation of the signal. 1 -Sparse representation of array covariance vector (l 1 -Sparese Representation of ArrayCovariance Vectors,l 1 -SRACV) reconstructs the covariance matrix and solves the second-order cone problem based on the sparsity of the spatial signal itself and the sample covariance matrix, thereby obtaining the direction of the signal source. Other scholars have applied sparse Bayesian learning to spectral estimation and introduced an alternating optimization algorithm based on the variational Bayesian inference method to iteratively obtain a stable solution to the real number sparse representation problem, thereby improving the estimation performance.

[0004] The third category is the spatial spectrum estimation algorithm of machine learning, which has been popular in recent years. For example, applying support vector regression and deep neural network (DNN) in supervised learning to it can greatly improve the adaptability of traditional algorithms. When establishing mathematical models or building neural networks, machine learning algorithms do not need to search for spectral peaks, and the direction finding speed is fast. Some scholars have proposed applying support vector regression to spectrum estimation. Simulation experiments show that when simultaneously finding the direction of multiple signals, this method has high direction finding accuracy and good adaptability. Some scholars have used DNN to estimate the spatial spectrum of two signals at the same time. Although this method is feasible, the accuracy is not high. Some scholars have introduced codecs based on deep neural networks, which can estimate multiple signals and have high direction finding accuracy. Since deep neural networks have complex network topology structures, applying them to spectrum estimation will increase the computational complexity while improving the estimation accuracy, thereby slowing down the estimation speed. To address this problem, some scholars applied convolutional neural networks to the spectrum estimation of broadband signals. Compared with DNN, the estimation time was reduced, but the estimation performance was poor under low signal-to-noise ratio (SNR). Some scholars proposed a DOA estimation based on back propagation neural network (BPNN), and used particle swarm algorithm to optimize network parameters, which reduced the computational complexity and achieved high direction finding accuracy. Some scholars applied deep convolutional networks to the arrival angle estimation of signals to restore the spatial spectrum. Some scholars proposed a frequency-related processing algorithm based on Markov chain under the sparse Bayesian learning framework, and adopted a new frequency domain structure-related prior model, which can be adaptively changed to adapt to multi-broadband source scenarios with different frequency characteristics, improving the estimation performance of broadband signals. Some scholars proposed a gridless spectrum estimation algorithm with unsupervised deep learning to eliminate the influence of spatial angle discretization on the estimation results and the dependence of deep neural networks on labels in the training data set, solving the grid mismatch problem and being more robust to the training data set.

[0005] Generally speaking, the larger the interval between signals, the easier it is to distinguish, and vice versa. However, the above traditional estimation methods are only applicable to Gaussian white noise backgrounds, and there is a certain interval between signals. They have low spatial spectral resolution for closely spaced signals under non-Gaussian noise conditions. Summary of the invention

[0006] To solve the problem of low spatial spectrum resolution for closely spaced signals under Gaussian white noise and non-Gaussian noise conditions, the present invention provides a high-resolution spatial spectrum estimation method.

[0007] A high-resolution spatial spectrum estimation method of the present invention comprises:

[0008] Establishing a spatial spectrum estimation network, wherein the spatial spectrum estimation network includes a detection network 1, a detection network 2 and a judgment network, wherein both the detection network 1 and the detection network 2 are neural networks;

[0009] During training, a training set 1 including antenna array receiving signals with the same change step size and different arrival angle intervals is established, wherein the input data is the antenna array receiving signal, and the format is two in-phase orthogonal components, Z columns, and M channels, and the output data is the arrival angle corresponding to the antenna array receiving signal; Z represents the number of snapshots, and M represents the number of array elements in the array;

[0010] The input data in the training set 1 is passed through the detection network 1 to obtain the arrival angles of multiple groups of antenna array received signals. The screening network divides the arrival angles of multiple groups of antenna array received signals into antenna array received signals with longer intervals in the arrival angles and antenna array received signals with shorter intervals. The antenna array received signals with shorter intervals in the arrival angles and the arrival angles form the training set 2. and The antenna array receives the signals with the arrival angle as the signals with a longer distance, otherwise it receives the signals with a shorter distance. and is the estimated value of the arrival angle of the received signal of the adjacent antenna array obtained by using the detection network 1 in the same batch; θ i For The corresponding true value, θ j For The corresponding truth value;

[0011] Detection network 1 includes preprocessing network, residual network, LSTM network, fusion network, fully connected layer and output layer;

[0012] The antenna array receives the signal and inputs it into the preprocessing network. The preprocessing network extracts high-order cumulative features and instantaneous features. The high-order cumulative features are input into the residual network, and the instantaneous features are input into the LSTM network. The output of the residual network and the output of the LSTM network are fused by the fusion network, and then enter the fully connected layer and the output layer in turn. The output of the output layer is the output of the detection network 1.

[0013] Extract the features of the antenna array receiving signal in training set 2 as input, and use the corresponding arrival angle as output to train detection network 2;

[0014] During estimation, the antenna array receives signals that are simultaneously input into the detection network 1 and the detection network 2, and the outputs of the detection network 1 and the detection network 2 are simultaneously input into the judgment network;

[0015] The judgment network obtains the final prediction result based on the output of detection network 1 and the output of detection network 2:

[0016] If both detection network 1 and detection network 2 have outputs, the result of detection network 2 is used as the final output result. If only detection network 1 has outputs, the result of detection network 1 is used as the final output result.

[0017] Preferably, in the training set, the input data is divided into 8 batches, and the arrival angle intervals Δθ of the 8 batches are 8°, 7°, …, 1°, respectively. The intervals of adjacent signal angles in the same batch are the same, and the signal angles of each batch are sampled between [-60°, 60°], with a step size of 0.5° each time, covering the entire [-60°, 60°] interval.

[0018] Preferably, the residual network includes a plurality of cascaded residual modules and a global pooling layer;

[0019] The residual module includes 2×3 convolution layer No. 1, matrix transformation layer No. 1, batch normalization layer No. 1, ReLU activation layer No. 1, 2×3 convolution layer No. 2, matrix transformation layer No. 2, batch normalization layer No. 2, ReLU activation layer No. 2, compression layer, fully connected layer No. 1, ReLU activation layer No. 3, fully connected layer No. 2, and Sigmoid activation layer;

[0020] The input signal passes through the first 2×3 convolution layer, the first matrix transformation layer, the first batch normalization layer, the first ReLU activation layer, the second 2×3 convolution layer, the second matrix transformation layer, the second batch normalization layer, and the second ReLU activation layer to obtain the feature X;

[0021] Feature X passes through the compression layer to obtain a one-dimensional real number matrix, which is fully connected through the No. 1 fully connected layer, and then activated by the No. 3 ReLU activation function layer. After activation, it passes through the No. 2 fully connected layer and is normalized to the range of [0,1] by the Sigmoid function layer to obtain the weight;

[0022] The weights are added to the feature X channel by channel, and the weighted features are directly connected to the antenna array received signal matrix B to obtain the output data of the residual module;

[0023] The input of the first residual module in the cascade is the high-order cumulative feature of the antenna array received signal, and the output of the last residual module is the output of the residual network after passing through the global pooling layer.

[0024] Preferably, the compression method of the compression layer is:

[0025] F=F 1 +F 2

[0026] Among them, F is the compressed feature, F 1 =MLP(a(Avgpool(X))),F 2 =MLP((1-a)(Maxpool(X))), MLP is a multi-layer perceptron, Avgpool is average pooling, Maxpool is maximum pooling, a is determined using training set 1, obtain the feature X corresponding to training set 1, input feature X into the compression layer, and calculate F 1 With F 2 The overlap rate d(F 1 ,F 2 ), d is the Euclidean distance, and d(F 1 ,F 2 ) is mapped to [0,1], and d n , when d n In the interval [0,0.5], a increases; otherwise, a decreases until the training is completed, and the mean of the a values ​​corresponding to all samples is taken as the final value of a.

[0027] Preferably, the preprocessing network obtains the high-order cumulant candidate features of the antenna array received signal in the training set 1, selects the high-order cumulant features from the high-order cumulant candidate features and inputs them into the residual network, and the high-order cumulant candidate features include:

[0028] P 1 =M 20

[0029] P 2 =M 21

[0030]

[0031] P 4 =M 41 -3M 20 M 21

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Among them, the k-order mixing matrix M of the antenna array receiving signal x km =E[x k-m (x * ) m ], E represents the mathematical expectation, k represents the order at the current moment, m represents the position of the conjugate, and the symbol * is the conjugate operator;

[0041] The k-th order cumulant of x is Cum[] represents the cumulant operator;

[0042] The redundant decision conditions are used to remove redundant features from the candidate features of the high-order cumulant. The remaining features are the selected high-order cumulant features. The redundant decision conditions are:

[0043]

[0044] SU(f i ,f j ) represents the feature f i With feature f j The symmetric uncertainty between IR(f i ,f j ,D) are two features f i 、f j and the interaction coefficient between label D.

[0045] Preferably, the instantaneous characteristics include:

[0046] The maximum value of the normalized instantaneous amplitude power spectral density of the signal γ max :

[0047]

[0048] Among them, K is the number of signal sample points, a cn (i) is the normalized instantaneous amplitude value of the i-th signal, a(i) is the instantaneous amplitude value of the i-th signal, i is the signal index value, max means taking the maximum value, || means taking the absolute value, and FFT[] means using fast Fourier transform to obtain the spectrum;

[0049] The standard deviation σ of the normalized instantaneous amplitude of the signal aa :

[0050]

[0051] The standard deviation of the absolute value of the nonlinear component of the instantaneous phase center is σ dp :

[0052]

[0053] φ NL (i) is the absolute value of the nonlinear component at the instantaneous phase center, a t is the decision threshold for weak signals, and C represents the number of non-weak signals;

[0054] The standard deviation of the absolute value of the normalized central instantaneous frequency σ af :

[0055]

[0056] Among them, f N (i) is the absolute value of the normalized center instantaneous frequency, R b is the sample signal rate.

[0057] In order to further suppress the influence of non-Gaussian noise, as a preferred method, the features of the antenna array receiving signal in the training set 2 are extracted, including features r1, r2, and r, which are respectively:

[0058] r1=[R 4 (1,2),…,R 4 (1,M 2 ),R 4 (2,3),…,R 4 (2,M 2 ),…,R 4 (M 2 -1,M 2 )]

[0059] r2=[R(1,2),…,R(1,M),R(2,3),…,R(2,M),…,R(M-1,M)]

[0060] r=[R 4 (1,2),…,R 4 (1,M 2 ),R 4 (2,3),…,R 4 (2,M 2 ),…,R 4 (M 2 -1,M 2 ),R(1,2),…,R(1,M),

[0061] R(2,3),…,R(2,M),…,R(M-1,M)]

[0062] Among them, the covariance matrix E{} represents solving the mathematical expectation, covariance matrix R 4 For an M 2 ×M 2 The Hermitian matrix, R 4(,) is the covariance matrix R 4 The elements of a row and column of And it is a Hermitian matrix, R(,) is an element of a row and column of the covariance matrix R.

[0063] Preferably, the detection network 2 is a deep neural network, the number of neurons in the input layer of the deep neural network is determined by the number of features, the number of neurons in the hidden layer is set to 500, 400, 300, 200, and 100, respectively, and ReLU is used as the activation function; the drop probability dropout=0.5 is set after the hidden layer; the number of neurons in the output layer is determined by the total number of angles in the interval, and the normalized exponential function Softmax is used to generate the estimated probability of each arrival angle, and then the arrival angles corresponding to the two largest probabilities are selected as the final result.

[0064] The beneficial effects of the present invention are as follows: the present invention utilizes detection network 1 to fully exploit the characteristics of signals to estimate the spatial spectrum of signals with farther intervals; trains detection network 2 to finely distinguish signals with closer intervals; during testing, the judgment network combines the results of detection network 1 and detection network 2, thereby effectively improving the resolution ability and estimation efficiency of the signal spatial spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a schematic diagram of radio monitoring;

[0066] Figure 2 It is a uniform linear array;

[0067] Figure 3 This is the network structure diagram for spatial spectrum estimation;

[0068] Figure 4 It is the structural diagram of the detection network 1;

[0069] Figure 5 It is the structural diagram of the residual module;

[0070] Figure 6 It is a deep neural network (DNN) structure;

[0071] Figure 7 is the estimation result under Gaussian white noise;

[0072] Figure 8 is the estimation result under non-Gaussian noise. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0075] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0076] In array signal processing, the most commonly used and simplest antenna array is the uniform linear array. Figure 2 As shown in the figure, it consists of M array elements, and the array element spacing d is half of the signal wavelength. This array is used to receive K far-field narrowband signals, and its arrival angle is θ = {θ 1 ,…,θ K}, where θ 1 is the arrival angle of the first signal, θ K is the arrival angle of the Kth signal, and these signals have the same wavelength.

[0077] Assuming that the incident signal is a zero-mean stationary random process, its envelope changes slowly, so the envelope of the same signal received by the uniform linear array is the same. Taking the first array element as the reference array element, the kth signal s at time t is k The delay of (t) reaching the adjacent array element is:

[0078]

[0079] In the formula, θ k For signal s k (t), c represents the propagation speed of electromagnetic waves in space, then at time t, the output of the mth array element is:

[0080]

[0081] In the formula, λ represents the wavelength of the signal, n m (t) is the noise on the mth array element at time t, and the number of signal sampling snapshots is Z. Then the output of the entire array is

[0082] Y = A(θ)S+N (3)

[0083] in

[0084]

[0085] is the signal matrix, s 1 (1)s 1 (2) and s 1 (Z) are the 1st, 2nd and Zth samples of the 1st signal respectively; s 2 (1)s 2 (2) and s 2 (Z) are the first, second and Zth samples of the second signal respectively; s K (1)s K (2) and s K (Z) are the 1st, 2nd and Zth samples of the Kth signal, respectively, and

[0086]

[0087] is the noise matrix, n 1 (1) n 1 (2) and n 1 (Z) are the first, second and Zth noise samples on the first array element respectively; n 2 (1) n 2 (2) and n 2 (Z) are the first, second and Zth noise samples on the second array element respectively; n M (1) n M (2) and n M (Z) are the first, second and Zth noise samples on the Mth array element respectively. In formula (3), A(θ) is an M×K-dimensional array flow matrix that stores the angle vector of each signal and is expressed as:

[0088] A(θ)=[a(θ 1 ),a(θ 2 ),…,a(θ K )] (6)

[0089] Where a(θ 1 ), a(θ 2 ) and a(θ K ) are the angle vectors of the 1st, 2nd and Kth signals respectively, and the angle vector of the kth signal is:

[0090]

[0091] also

[0092]

[0093] To receive the data matrix, y 1 (1) y 1 (2) and y 1(Z) are the first, second and Zth snapshot data on the first array element respectively; y 2 (1) y 2 (2) and y 2 (Z) are the first, second and Zth snapshot data on the second array element respectively; y M (1) y M (2) and y M (Z) are the first, second and Zth snapshot data on the Mth array element respectively. The zth snapshot data on the mth array element can be expressed as

[0094] y m (z)=I m (z)+jQ m (z), m =1,2,…, M. z =1,2,…, Z. (9)

[0095] Here I m (z) and Q m (z) are the real and imaginary parts of the zth snapshot data on the mth array element, that is, the in-phase (I) and quadrature (Q) components of the data. Therefore, the array output Y can also be regarded as a three-dimensional matrix B 2×Z×M , which includes two components of in-phase and orthogonal, Z columns, and M channels. The data of each channel is the received data on the corresponding array element, that is, the data of the mth channel is

[0096]

[0097] Among them I m (1) I m (2) and I m (Z) are the real parts of the first, second and Zth snapshot data on the mth array element respectively; Q m (1) Q m (2) and Q m (Z) are the imaginary parts of the first, second and Zth snapshot data on the mth array element respectively. Most of the current spatial spectrum estimation methods, especially the neural network methods based on machine learning, have low resolution for closely spaced signals under non-Gaussian noise conditions. To this end, this embodiment proposes a high-resolution spatial spectrum estimation method, including:

[0098] Establish a spatial spectrum estimation network, such as Figure 3 As shown, the spatial spectrum estimation network includes a detection network 1, a detection network 2 and a judgment network, and both the detection network 1 and the detection network 2 are neural networks;

[0099] During training, a training set 1 including antenna array receiving signals with the same change step size and different arrival angle intervals is established, wherein the input data is the antenna array receiving signal, and the format is two in-phase orthogonal components, Z columns, and M channels, and the output data is the arrival angle corresponding to the antenna array receiving signal; Z represents the number of snapshots, and M represents the number of array elements in the array;

[0100] The input data in the training set 1 is passed through the detection network 1 to obtain the arrival angles of multiple groups of antenna array received signals. The screening network divides the arrival angles of multiple groups of antenna array received signals into antenna array received signals with longer intervals in the arrival angles and antenna array received signals with shorter intervals. The antenna array received signals with shorter intervals in the arrival angles and the arrival angles form the training set 2. and The antenna array receives the signals with the arrival angle as the signals with a longer distance, otherwise it receives the signals with a shorter distance. and is the estimated value of the adjacent antenna array received signal obtained by using the detection network 1 in the same batch; θ i For The corresponding true value, θ j For The corresponding truth value;

[0101] like Figure 4 As shown, the detection network 1 includes a preprocessing network, a residual network, an LSTM network, a fusion network, a fully connected layer and an output layer;

[0102] The antenna array receives the signal and inputs it into the preprocessing network. The preprocessing network extracts high-order cumulative features and instantaneous features. The high-order cumulative features are input into the residual network, and the instantaneous features are input into the LSTM network. The output of the residual network and the output of the LSTM network are fused by the fusion network, and then enter the fully connected layer and the output layer in turn. The output of the output layer is the output of the detection network 1. The fusion network assigns weights to the outputs of the residual network and the LSTM network. The outputs of the residual network and the LSTM network are multiplied by the corresponding weights and then summed to obtain the recognition result.

[0103] Extract the features of the antenna array receiving signal in training set 2 as input, and use the corresponding arrival angle as output to train detection network 2;

[0104] During estimation, the antenna array receives signals that are simultaneously input into the detection network 1 and the detection network 2, and the outputs of the detection network 1 and the detection network 2 are simultaneously input into the judgment network;

[0105] The judgment network obtains the final prediction result based on the output of detection network 1 and the output of detection network 2:

[0106] If both detection network 1 and detection network 2 have outputs, the result of detection network 2 is used as the final output result. If only detection network 1 has outputs, the result of detection network 1 is used as the final output result. Figure 3 As shown. Detection network 1 is used to classify the arrival angles of antenna array received signals, find out the antenna array received signals with close intervals in the arrival angles, and form training set 2. During testing, the two networks are tested at the same time, and then the final prediction result of network fusion is determined.

[0107] Taking two signals as an example, in the training stage, the two signals can be divided into 8 batches according to the interval of arrival angles Δθ = 8°, 7°, ..., 1°, that is, the intervals of adjacent signal angles in the same batch are the same. In addition, the angle signal angle is sampled between [-60°, 60°], and the step size of each change is 0.5°. There are a total of (60+60) / 0.5+1=241 angles, covering the entire [-60°, 60°] interval, that is:

[0108] (1) The interval between the two signals in the first batch is 8°, where the arrival angle of the first signal in the first group of the first batch is θ 1 =-60°, then the arrival angle θ of the second signal in the first group of the first batch 2 =-60°+8°=-52°. The arrival angle θ of the first signal in the second group of the first batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the first batch 2 = -59.5° + 8° = -51.5°. …. The arrival angle θ of the first signal in the last group of the first batch 1 =52°, then the arrival angle of the second signal in the last group of the first batch is θ 2 =60°, we can know that there are 225 groups in this batch;

[0109] (2) The interval between the two signals in the second batch is 7°, where the arrival angle θ of the first signal in the first group of the second batch is 1 =-60°, then the arrival angle θ of the second signal in the first group of the second batch 2 =-60°+7°=-53°. The arrival angle θ of the first signal in the second group of the second batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the second batch 2 = -59.5° + 7° = -52.5°. …. The arrival angle θ of the first signal in the last group of the second batch 1 =53°, then the arrival angle θ of the second signal in the last group of the second batch 2 =60°, we can know that there are 227 groups in this batch;

[0110] (3) The interval between the two signals in the third batch is 6°, where the arrival angle θ of the first signal in the first group of the third batch is 1 =-60°, then the arrival angle θ of the second signal in the first group of the third batch 2 =-60°+6°=-54°. The arrival angle θ of the first signal in the second group of the third batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the third batch 2 = -59.5° + 6° = -53.5°. …. The arrival angle θ of the first signal in the last group of the third batch 1 =54°, then the arrival angle θ of the second signal in the last group of the third batch 2 =60°, we can know that there are 229 groups in this batch;

[0111] (4) The interval between the two signals in the fourth batch is 5°, where the arrival angle θ of the first signal in the first group of the fourth batch is 1 =-60°, then the arrival angle θ of the second signal in the first group of the fourth batch 2 =-60°+5°=-55°. The arrival angle θ of the first signal in the second group of the fourth batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the fourth batch 2 = -59.5° + 5° = -54.5°. …. The arrival angle θ of the first signal in the last group of the fourth batch 1 =55°, then the arrival angle θ of the second signal in the last group of the fourth batch 2 =60°, we can know that there are 231 groups in this batch;

[0112] (5) The interval between the two signals in the fifth batch is 4°, where the arrival angle of the first signal in the first group of the fifth batch is θ 1 =-60°, then the arrival angle θ of the second signal in the first group of the fifth batch 2 = -60° + 4° = -56°. The arrival angle θ of the first signal in the second group of the fifth batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the fifth batch 2 = -59.5° + 4° = -55.5°. …. The arrival angle θ of the first signal in the last group of the fifth batch 1 =56°, then the arrival angle θ of the second signal in the last group of the fifth batch 2 =60°, we can know that there are 233 groups in this batch;

[0113] (6) The interval between the two signals in the sixth batch is 3°, where the arrival angle θ of the first signal in the first group of the sixth batch is 1 =-60°, then the arrival angle θ of the second signal in the first group of the sixth batch 2 =-60°+3°=-57°. The arrival angle θ of the first signal in the second group of the sixth batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the sixth batch 2 = -59.5° + 3° = -56.5°. …. The arrival angle θ of the first signal in the last group of the sixth batch 1 =57°, then the arrival angle of the second signal in the last group of the sixth batch is θ 2 =60°, we can know that there are 235 groups in this batch;

[0114] (7) The interval between the two signals in the 7th batch is 2°, where the arrival angle of the first signal in the first group of the 7th batch is θ 1 =-60°, then the arrival angle θ of the second signal in the first group of the seventh batch 2 = -60° + 2° = -58°. The arrival angle θ of the first signal in the second group of the seventh batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the seventh batch 2 = -59.5° + 2° = -57.5°. …. The arrival angle θ of the first signal in the last group of the 7th batch 1 =58°, then the arrival angle θ of the second signal in the last group of the 7th batch 2 =60°, we can know that there are 237 groups in this batch;

[0115] (8) The interval between the two signals in the 8th batch is 1°, where the arrival angle θ of the first signal in the first group of the 8th batch is 1 =-60°, then the arrival angle θ of the second signal in the first group of the eighth batch 2 =-60°+1°=-59°. The arrival angle θ of the first signal in the second group of the eighth batch 1 =-59.5°, then the arrival angle θ of the second signal in the second group of the eighth batch 2 = -59.5° + 1° = -58.5°. …. The arrival angle θ of the first signal in the last group of the 8th batch 1 =59°, then the arrival angle of the second signal in the last group of the 8th batch is θ 2 =60°, we can know that there are 239 groups in this batch.

[0116] Therefore, there are D = 225 + 227 + 229 + 231 + 233 + 235 + 237 + 239 = 1856 groups of signals, that is, 1856 situations. The following is divided into two stages: training and testing:

[0117] In the training phase, the detection network 1 first converts the array output matrix Y to obtain the array output matrix B in the format of 2×Z×M dimensions for processing. Then, the network in the detection network 1 is used to estimate the arrival angles of the two signals. If

[0118]

[0119] If the estimation is successful, it is considered as estimation failure, otherwise, the i is the arrival angle of the first signal, is its corresponding estimated value; θ j is the arrival angle of the second signal, The corresponding estimated value is given by . The angles with successful estimation are regarded as the angles with longer intervals, otherwise they are regarded as the angles with shorter intervals. The signals with shorter intervals in the training set are retained so that they are sent to the training set 2, and the detection network 2 is trained in a targeted manner to further extract the features of the training set 2, and then sent to the detection network 2 for estimation.

[0120] During the test phase, the array output matrix Y will be sent to detection network 1 and detection network 2 at the same time. The judgment network will receive the recognition results of the two detection networks at the same time, and merge the prediction results of detection network 1 with the prediction results in detection network 2 to obtain the final prediction results (the specific analysis is as follows: if the input is a signal with a large interval, detection network 1 will give a result, and detection network 2 will not give a result; if the input is a signal with a small interval, both detection network 1 and detection network 2 will give results, indicating that the input is a signal with a small interval, and the result of detection network 2 shall prevail).

[0121] The training effect of the detection network 1 is related to the structure and data of the detection network 1. In order to solve the problem of difficulty in feature extraction caused by too much interference information in the input data, this implementation method can automatically learn features of different importance and select the key information that has the greatest impact on the training of the detection network 1, so as to achieve the purpose of improving the performance of the model; select features with high discrimination for easily confused signals from the original feature set, and this implementation extracts multiple types of features with strong representation and high discrimination for training and testing, among which high-order cumulative feature and residual network combination, instantaneous feature and LSTM network combination;

[0122] High-order cumulants (HOCs) can represent the high-order statistical characteristics of antenna signals. To extract the high-order cumulants, we must first calculate the high-order moments (HOMs) of the signal. The k-order mixing moment of the signal x is defined as:

[0123] M km (x) = E[x k-m (x * ) m ] (12)

[0124] Where E represents the mathematical expectation, k represents the order at the current moment, m represents the position of the conjugate, and the symbol * is the conjugate operator. The k-order cumulant of the zero-mean signal x can be calculated by the following formula:

[0125]

[0126] here

[0127]

[0128] Where Cum[] represents the cumulant operator, Φ = {1, 2, ..., n} is a symbol set, n and i are the sample numbers of the signal x, v is a member in Φ, and c is the number of subsets in Φ. In the preferred embodiment, the present implementation first considers the following 8 alternative features:

[0129] P 1 =C 20 =Cum(x, x)=M 20 (15)

[0130] P 2 =C 21 =Cum(x, x*)=M 21 (16)

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] This embodiment selects the following high-order cumulant-based deformations as candidate features:

[0138]

[0139]

[0140]

[0141]

[0142] In order to better distinguish multiple confusing signals and speed up the network operation, it is necessary to use feature selection methods to select features that are more discriminative of confusing signals. The feature selection algorithm can use the causal relationship between features and categories to select the most relevant feature subset from the original feature set. This implementation method redesigns the feature selection algorithm:

[0143] In order to evaluate the quality of the extracted features, the present invention first uses the concepts of entropy and mutual information in information theory. Entropy is used to measure the uncertainty of random variables, while mutual information is used to characterize the amount of information transmission between random variables. The relationship between the two can be expressed as:

[0144] I(X;Y)=H(X)-H(X / Y)=H(Y)-H(Y / X)=H(X)+H(Y)-H(XY) (27)

[0145] Where H(X) and H(Y) represent the entropies of variables X and Y respectively, H(XY) represents the joint entropy of X and Y, H(X|Y) represents the conditional entropy, and I(X;Y) is the mutual information of X and Y.

[0146] The greater the mutual information between the feature and the label, the more information the current feature can provide for the label, and the more important the feature is. The present invention normalizes the mutual information and measures the feature f with symmetric uncertainty (SU). i The correlation between the signal label D (i.e., the angle of arrival). The larger the SU value, the more information the feature can provide for the label, and the more relevant the feature is to the angle of arrival. The formula is as follows:

[0147]

[0148] After calculating the symmetric uncertainty between each feature and the arrival angle in the original feature set A, the features are arranged in descending order according to their SU values ​​to achieve the sorting of the correlation between the features and the labels in the original feature set A.

[0149] Redundancy is usually used to measure the degree of information overlap between features. The greater the redundancy, the higher the degree of overlap between the two feature information; the smaller the redundancy, the greater the independent contribution of the two feature information to the analysis event. Considering only the correlation between features and labels is not enough to eliminate redundancy in the feature set. Therefore, after completing the descending order of correlation, it is necessary to find a standard for measuring redundant features. The present invention calculates the features f from front to back in sequence. i With feature f j The symmetric uncertainty between SU(f i ,f j ) is used to measure the redundancy between different features. i ,f j ) is larger, indicating that the characteristic f i With feature f j The greater the redundancy between them, the specific calculation formula is:

[0150]

[0151] In the process of feature selection, in addition to fully analyzing and considering the correlation between features and labels and the redundancy between features, the joint effect between multiple features and labels should also be considered. In order to more accurately measure the importance of features, the present invention selects feature f i 、f j The three-dimensional interaction information (II) of the label D is normalized, and the interaction ratio (IR) between the two features is used to measure the joint effect between the features. The calculation formula is:

[0152]

[0153] It can take positive, negative or zero values. When it is a positive value, it means f i and f j The information provided by the combination of two features is greater than the sum of the information provided by each of them, which indicates that the information provided by the two features for label D is complementary; when it is a negative value, it means that the information provided by the combination of the two features is less than the sum of the information provided by each of them, indicating that there may be information redundancy between the two features; when it is a zero value, it indicates that the information provided by the two features for label D is independent.

[0154] In summary, the redundant decision condition of the feature selection algorithm in this embodiment is as follows:

[0155]

[0156] The first inequality shows that the characteristic f i and fj There is an intersection between them, and combined with the second inequality, it shows that there is indeed information redundancy between the two features. This algorithm first retains the feature with the highest correlation with the arrival angle in the original feature set F, and then calculates the symmetric uncertainty SU(f i ,f j ) and the combined effect of the two features on the arrival angle (interaction coefficient IR). In the calculation process, if the feature f j If both redundant decision conditions (31) are satisfied at the same time, then f j The redundant features will be deleted. After traversing all the elements in the feature set, the remaining elements in the feature set constitute the optimal feature subset selected by this algorithm. Since this feature selection algorithm combines Fast Correlation Sorting and Redundancy Analysis, it is referred to as FCSRA algorithm.

[0157] In the preferred embodiment, this implementation adopts 4 transient features:

[0158] The first key feature max is the maximum value of the normalized instantaneous amplitude power spectral density of the signal, which is defined as:

[0159]

[0160] in

[0161]

[0162] Here K is the number of signal sample points, a cn (i) is the normalized instantaneous amplitude value of the ith signal, a(i) is the instantaneous amplitude value of the ith signal, i is the signal index value, max means taking the maximum value, || means taking the absolute value, and FFT[] means using fast Fourier transform to obtain the spectrum.

[0163] The second key feature σ aa is the standard deviation of the normalized instantaneous amplitude of the signal, which is defined as:

[0164]

[0165] The third key feature σ dp is the standard deviation of the absolute value of the nonlinear component of the instantaneous phase center, evaluated for non-weak segments of the intercepted signal, and is defined as:

[0166]

[0167]

[0168] in is the absolute value of the nonlinear component at the instantaneous phase center, a t is the decision threshold for weak signals, and C represents the number of non-weak signals.

[0169] The fourth key feature σ af is the standard deviation of the absolute value of the normalized central instantaneous frequency, evaluated for the non-weak segment of the intercepted signal, and is defined as:

[0170]

[0171]

[0172] where f N (i) is the absolute value of the normalized center instantaneous frequency, R b is the sample signal rate.

[0173] In a preferred embodiment, the residual network of this embodiment includes a plurality of cascaded residual modules and a global pooling layer;

[0174] The residual module includes 2×3 convolution layer No. 1, matrix transformation layer No. 1, batch normalization layer No. 1, ReLU activation layer No. 1, 2×3 convolution layer No. 2, matrix transformation layer No. 2, batch normalization layer No. 2, ReLU activation layer No. 2, compression layer, fully connected layer No. 1, ReLU activation layer No. 3, fully connected layer No. 2, and Sigmoid activation layer;

[0175] The input signal passes through the first 2×3 convolution layer, the first matrix transformation layer, the first batch normalization layer, the first ReLU activation layer, the second 2×3 convolution layer, the second matrix transformation layer, the second batch normalization layer, and the second ReLU activation layer to obtain the feature feature X;

[0176] The feature feature X passes through the compression layer to obtain a one-dimensional real number matrix, which is fully connected through the No. 1 fully connected layer, and then activated by the No. 3 ReLU activation function layer. After activation, it passes through the No. 2 fully connected layer and is normalized to the range of [0,1] by the Sigmoid function layer to obtain the weight;

[0177] The weights are added to the feature features X channel by channel, and the weighted feature features are directly connected to the antenna array received signal matrix B to obtain the output data of the residual module;

[0178] The input of the first residual module in the cascade is the high-order cumulative feature of the antenna array received signal, and the output of the last residual module is the output of the residual network after passing through the global pooling layer.

[0179] The residual network of this embodiment mainly includes convolution, compression and excitation. Compression is to pool the input feature features and compress each feature feature into a real number with a global receptive field; and the excitation is mainly composed of a fully connected layer and an activation function, which can capture channel correlation and generate the weight of the corresponding channel. Assume that the input is an array B of H'×W'×C' dimensions, H', W' and C' are the number of rows, columns and channels of the array respectively, and then after the convolution operation, a feature feature X of size H×W×C is obtained, and H, W, C are the number of rows, columns and channels of the data after convolution respectively. To adjust the weight relationship between channels, it is necessary to compress the information in all channels, that is, to perform global average pooling (Global Average Pooling, GAP) on all channels to obtain a one-dimensional real number matrix of size 1×1×C, and finally multiply this value as a weight to the C channels of X as the input data of the next level. Because each channel contains different features, the model can screen each channel after processing, focusing on channels that help improve the classification effect, and ignoring those channels with more interference information. The structure of the residual module in this embodiment is as follows Figure 5 As shown in Figure 1. In spatial spectrum estimation, the input signal matrix B consists of two components, in-phase and orthogonal, Z samplings, and M array element data, so the dimension of B is 2×Z×M. In the middle branch, the data of each channel in B is first filled with 0 appropriately, and then convolved with the convolution kernel w of dimension 2×3. m (m=1,2,…,M) for convolution, matrix transformation, batch normalization and ReLU activation to improve convergence speed, and then go down through a set of the same structure, and then divided into two paths: one is downward, and the other is through pooling, full connection, ReLU activation, full connection, Sigmoid activation to achieve compression excitation, generate the weights of the corresponding channels, and weight them channel by channel to the feature features before compression. In order to avoid the gradient disappearance of the network, the left branch introduces a direct connection (shortcut) branch structure, so that the residual unit is implemented in the form of a skip layer connection. This can not only mine the deeper features of the signal, but also solve the problem that the gradient cannot be updated during the back propagation process. Finally, this part of the feature features is sent to the subsequent network for propagation.

[0180] The compression method of the compression layer in this embodiment is:

[0181] F=F 1 +F 2 (39)

[0182] Among them, F is the compressed feature, F 1 =MLP(a(Avgpool(X))),F 2=MLP((1-a)(Maxpool(X))), MLP is a multi-layer perceptron, Avgpool is average pooling, and Maxpool is maximum pooling; maximum pooling selects the maximum value in the local area as the output value to retain the most significant features, while average pooling takes the average value in the local area as the output value to obtain the average representation of the overall features. a is determined using training set 1, and the feature feature X corresponding to training set 1 is obtained. Feature feature X is input into the compression layer to calculate F 1 With F 2 The overlap rate d(F 1 ,F 2 ), d is the Euclidean distance, and d(F 1 ,F 2 ) is mapped to [0,1], and d n , when d n In the interval [0,0.5], it means that the center receives too much attention, then the weight of the maximum pooling should be reduced, so a increases; otherwise, a decreases until the training is completed, and the average of the a values ​​corresponding to all samples is taken as the final a value, thereby balancing the weights of average pooling and maximum pooling.

[0183] The residual network of this embodiment uses the residual block as the basic framework and proposes a structure of the residual network for spatial spectrum estimation. According to experience, the residual module can be set to 6 to 12 levels to achieve good results.

[0184] The idea of ​​LSTM network is to add a layer C to store long-term state in the hidden layer of RNN structure, which is called unit state. It can be simply understood as a "conveyor belt" for transmitting memory information. It enables LSTM network to save relatively long-term information and avoid the loss of long-term memory. LSTM network combines the instantaneous characteristics of the received signal of antenna array. It links the previous information with the current information, so that it can better identify the corresponding features when processing time series rich in a large amount of information and with complex time correlation.

[0185] The detection network 2 needs to extract high-order statistical features with high signal discrimination of closely spaced intervals from the training set 2 and combine them with the deep neural network (DNN) to estimate the spatial spectrum. The emergence of high-order statistics has opened up a new space for the development of array signal processing. The fourth-order cumulants contain very rich information. There are many ways to define the fourth-order cumulants. These different definitions correspond to different problems and different application objects. They can be used to effectively suppress Gaussian white noise and non-Gaussian noise in spatial spectrum estimation, thereby improving the estimation accuracy. In spatial spectrum estimation, the fourth-order cumulants of zero-mean stationary random processes can be defined in the form of the following Kronecker product:

[0186]

[0187] Among them C 4x (k 1 ,k 2 ,k 3 * ,k 4 * ) represents the fourth-order cumulant, y, k 1 , k 2 , k 3 and k 4 are all intermediate variables, and E{} represents the mathematical expectation of the solution. A careful observation shows that the matrix R 4 For an M 2 ×M 2 The Hermitian matrix carries a large amount of data information. If the background noise is non-Gaussian noise, this embodiment selects the upper triangular elements of the covariance matrix to form a vector, and uses the elements as the input features of the detection network 2 under the non-Gaussian noise background, that is:

[0188] r1=[R 4 (1,2),…, R 4 (1,M 2 ), R 4 (2,3),…, R 4 (2,M 2 ),…, R 4 (M 2 -1, M 2 )] (41)

[0189] Where R 4 (1,2) is the covariance matrix R 4 The element in the first row and second column of 4 (1,M 2 ) is the covariance matrix R 4 The first row of M 2 Elements of the column, R 4 (2,3) is the covariance matrix R 4 The element in the 2nd row and 3rd column of 4 (2,M 2 ) is the covariance matrix R 4 The 2nd row of M 2 Elements of the column, R 4 (M 2 -1,M 2 ) is the covariance matrix R 4 The Mth 2 -1 row M 2 Elements of a column.

[0190] In addition, the covariance matrix of the signal can also be obtained using the input signal matrix Y:

[0191]

[0192] It also carries a lot of data information and is also a Hermitian matrix. Its upper triangular elements can also form a vector:

[0193] r2=[R(1,2),…, R(1,M), R(2,3),…, R(2,M),…, R(M -1, M)] ​​(43)

[0194] Where R(1,2) is the element of the 1st row and 2nd column of the covariance matrix R, R(1,M) is the element of the 1st row and Mth column of the covariance matrix R, R(2,3) is the element of the 2nd row and 3rd column of the covariance matrix R, R(2,M) is the element of the 2nd row and Mth column of the covariance matrix R, and R(M-1,M) is the element of the M-1th row and Mth column of the covariance matrix R. Since the calculation of the fourth-order cumulant itself also has some errors, if the spatial spectrum is estimated under Gaussian white noise, the vector r2 can be used as a supplement to the fourth-order cumulant information. Therefore, this embodiment combines r1 and r2 into a vector r, and uses the elements therein as input features of the detection network 2 under the background of Gaussian white noise.

[0195] r=[R 4 (1,2),…,R 4 (1,M 2 ),R 4 (2,3),…,R 4 (2,M 2 ),…,R 4 (M 2 -1,M 2 ),R(1,2),…,R(1,M),

[0196] R(2,3),…,R(2,M),…,R(M-1,M)](44)

[0197] The deep neural network model has a fully connected feedforward network structure with multiple hidden layers, which enables the deep neural network to extract complex features in high-dimensional space. Therefore, this embodiment uses a deep neural network in the detection network 2 and estimates the spatial spectrum based on the characteristics of the signal. Since the values ​​of different types of features vary greatly, the value of each feature must first be normalized using the zero mean normalization method, and then they are input into the following Figure 6In the deep neural network shown in Figure 1, the number of neurons in the input layer of the deep neural network is determined by the number of features, the number of neurons in the hidden layer is set to 500, 400, 300, 200, and 100, respectively, and ReLU is used as the activation function. In addition, the dropout probability is set after the hidden layer to 0.5; the number of neurons in the output layer is determined by the total number of angles in the interval, and the normalized exponential function Softmax is used to generate the estimated probability of each angle, and then the angles corresponding to the two largest probabilities are selected as the final result.

[0198] Experiments and Discussion:

[0199] Experimental conditions: the number of array elements M = 8, the distance between the array elements is 1 / 2 of the signal wavelength, the background noise is taken as Gaussian white noise and non-Gaussian noise background respectively, the non-Gaussian noise is obtained by nonlinear transformation of Gaussian white noise, the residual module in the detection network 1 is set to 8 levels, the software development platform is MATLAB R2016a, and the hardware conditions of the experiment are I5 ​​3.3GhzCPU, 4G memory.

[0200] In the simulation experiment, the arrival angles of the two signals are located at [-60°, 60°]. The two angles are sampled respectively, and the sampling interval changes from 8° to 1°. The number of samples is 5000. 4 / 5 of the samples are randomly selected as training samples, and the rest are used as test samples. The angle estimation error when the interval between the two signals is Δθ is defined as

[0201]

[0202] where θ 1 is the arrival angle of the first signal, is the lth estimated value of the arrival angle of the first signal; θ 2 =θ 1 +Δθ is the arrival angle of the second signal, is the lth estimated value of the arrival angle of the second signal, L = 200 is the total number of experiments, l is the index of the number of experiments, and the average of the estimation errors of all cases under the same angle interval is taken as the average estimation error. Figure 7 and Figure 8 The curves of the average estimation errors of the two networks changing with the angular interval under the Gaussian white noise background and non-Gaussian noise background when the signal-to-noise ratio is 5dB are given respectively.

[0203] from Figure 7It can be seen that under the background of Gaussian white noise, detection network 1 has a certain estimation error for signals with smaller intervals of 1° to 4°. In contrast, the estimation accuracy of the judgment network has been greatly improved. This is because detection network 2 plays a better role. When the signal interval is 5° to 8°, the estimation error of detection network 1 is less than 0.5°. At this time, detection network 2 no longer gives a result, so the results of the two curves are the same.

[0204] from Figure 8 It can be seen that under the background of non-Gaussian noise, the residual network in the detection network 1 also learns some high-order statistical characteristics of the signal, but the estimation error is large; in contrast, the estimation accuracy of the judgment network has been greatly improved. This is because the detection network 2 simply extracts the fourth-order cumulant of the signal, thus better suppressing the non-Gaussian noise. The estimation result at this time is almost the same as that under Gaussian white noise.

[0205] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A high-resolution spatial spectrum estimation method, characterized in that: The method comprises: Establishing a spatial spectrum estimation network, wherein the spatial spectrum estimation network includes a detection network 1, a detection network 2 and a judgment network, wherein both the detection network 1 and the detection network 2 are neural networks; During training, a training set 1 including antenna array receiving signals with the same change step size and different arrival angle intervals is established, wherein the input data is the antenna array receiving signal, and the format is two in-phase orthogonal components, Z columns, and M channels, and the output data is the arrival angle corresponding to the antenna array receiving signal; Z represents the number of snapshots, and M represents the number of array elements in the array; The input data in the training set 1 is passed through the detection network 1 to obtain the arrival angles of multiple groups of antenna array received signals. The screening network divides the arrival angles of multiple groups of antenna array received signals into antenna array received signals with longer intervals in the arrival angles and antenna array received signals with shorter intervals. The antenna array received signals with shorter intervals in the arrival angles and the arrival angles form the training set 2. and The antenna array receives the signals with the arrival angle as the signals with a longer distance, otherwise it receives the signals with a shorter distance. and is the estimated value of the arrival angle of the received signal of the adjacent antenna array obtained by using the detection network 1 in the same batch; θ i For The corresponding true value, θ j For The corresponding truth value; Detection network 1 includes preprocessing network, residual network, LSTM network, fusion network, fully connected layer and output layer; The antenna array receives the signal and inputs it into the preprocessing network. The preprocessing network extracts high-order cumulative features and instantaneous features. The high-order cumulative features are input into the residual network, and the instantaneous features are input into the LSTM network. The output of the residual network and the output of the LSTM network are fused by the fusion network, and then enter the fully connected layer and the output layer in turn. The output of the output layer is the output of the detection network 1. Extract the features of the antenna array receiving signal in training set 2 as input, and use the corresponding arrival angle as output to train detection network 2; During estimation, the antenna array receives signals that are simultaneously input into the detection network 1 and the detection network 2, and the outputs of the detection network 1 and the detection network 2 are simultaneously input into the judgment network; The judgment network obtains the final prediction result based on the output of detection network 1 and the output of detection network 2: If both detection network 1 and detection network 2 have outputs, the result of detection network 2 is used as the final output result. If only detection network 1 has outputs, the result of detection network 1 is used as the final output result.

2. The high-resolution spatial spectrum estimation method according to claim 1, characterized in that: In the training set, the input data is divided into 8 batches. The arrival angle intervals Δθ of the 8 batches are 8°, 7°, …, 1° respectively. The intervals of adjacent signal angles in the same batch are the same. The signal angles of each batch are sampled between [-60°, 60°], and the step size of each change is 0.5°, covering the entire [-60°, 60°] interval.

3. The high-resolution spatial spectrum estimation method according to claim 1, characterized in that: The residual network consists of multiple cascaded residual modules and a global pooling layer; The residual module includes 2×3 convolution layer No. 1, matrix transformation layer No. 1, batch normalization layer No. 1, ReLU activation layer No. 1, 2×3 convolution layer No. 2, matrix transformation layer No. 2, batch normalization layer No. 2, ReLU activation layer No. 2, compression layer, fully connected layer No. 1, ReLU activation layer No. 3, fully connected layer No. 2, and Sigmoid activation layer; The input signal passes through the first 2×3 convolution layer, the first matrix transformation layer, the first batch normalization layer, the first ReLU activation layer, the second 2×3 convolution layer, the second matrix transformation layer, the second batch normalization layer, and the second ReLU activation layer to obtain the feature X; Feature X passes through the compression layer to obtain a one-dimensional real number matrix, which is fully connected through the No. 1 fully connected layer, and then activated by the No. 3 ReLU activation function layer. After activation, it passes through the No. 2 fully connected layer and is normalized to the range of [0,1] by the Sigmoid function layer to obtain the weight; The weights are added to the feature X channel by channel, and the weighted features are directly connected to the antenna array received signal matrix B to obtain the output data of the residual module; The input of the first residual module in the cascade is the high-order cumulative feature of the antenna array received signal, and the output of the last residual module is the output of the residual network after passing through the global pooling layer.

4. The high-resolution spatial spectrum estimation method according to claim 3, characterized in that: The compression method of the compression layer is: F=F1+F2 Where F is the compressed feature, F1 = MLP(a(Avgpool(X))), F2 = MLP((1-a)(Maxpool(X))), MLP is a multi-layer perceptron, Avgpool is average pooling, Maxpool is maximum pooling, a is determined using training set 1, obtain the feature X corresponding to training set 1, input feature X into the compression layer, calculate the overlap rate d(F1, F2) between F1 and F2, d is the Euclidean distance, map d(F1, F2) to [0, 1], and get d n , when d n In the interval [0,0.5], a increases; otherwise, a decreases until the training is completed, and the mean of the a values ​​corresponding to all samples is taken as the final value of a.

5. The high-resolution spatial spectrum estimation method according to claim 1, characterized in that: The preprocessing network obtains the high-order cumulant candidate features of the antenna array receiving signal in the training set 1, selects the high-order cumulant features from the high-order cumulant candidate features and inputs them into the residual network. The high-order cumulant candidate features include: P1=M 20 P2=M 21 P4=M 41 -3M 20 M 21 Among them, the k-order mixing matrix M of the antenna array receiving signal x km =E[x k-m (x * ) m ], E represents the mathematical expectation, k represents the order at the current moment, m represents the position of the conjugate, and the symbol * is the conjugate operator; The k-th order cumulant of x is Cum[] represents the cumulant operator; The redundant decision conditions are used to remove redundant features from the candidate features of the high-order cumulant. The remaining features are the selected high-order cumulant features. The redundant decision conditions are: SU(f i ,f j ) represents the feature f i With feature f j The symmetric uncertainty between IR(f i ,f j ,D) are two features f i 、f j and the interaction coefficient between label D.

6. The high-resolution spatial spectrum estimation method according to claim 1, characterized in that: The instantaneous characteristics include: The maximum value of the normalized instantaneous amplitude power spectral density of the signal γ max : Among them, K is the number of signal sample points, a cn (i) is the normalized instantaneous amplitude value of the i-th signal, i is the signal index value, max means taking the maximum value, || means taking the absolute value, and FFT[] means using fast Fourier transform to obtain the spectrum; The standard deviation σ of the normalized instantaneous amplitude of the signal aa : The standard deviation of the absolute value of the nonlinear component of the instantaneous phase center is σ dp : φ NL (i) is the absolute value of the nonlinear component at the instantaneous phase center, a t is the decision threshold for weak signals, and C represents the number of non-weak signals; The standard deviation of the absolute value of the normalized central instantaneous frequency σ af : Among them, f N (i) is the absolute value of the normalized central instantaneous frequency.

7. The high-resolution spatial spectrum estimation method according to claim 1, characterized in that: The features of the antenna array receiving signal in training set 2 are extracted, including features r1, r2, and r, which are: r1=[R4(1,2),…,R4(1,M 2 ),R4(2,3),…,R4(2,M 2 ),…,R4(M 2 -1,M 2 )] r2=[R(1,2),…,R(1,M),R(2,3),…,R(2,M),…,R(M-1,M)] r=[R4(1,2),…,R4(1,M 2 ),R4(2,3),…,R4(2,M 2 ),…,R4(M 2 -1,M 2 ),R(1,2),…,R(1,M), R(2,3),…,R(2,M),…,R(M-1,M)] Among them, the covariance matrix E{} represents the mathematical expectation, and the covariance matrix R4 is an M 2 ×M 2 The Hermitian matrix of R4(,) is the element of a row and column of the covariance matrix R4; the covariance matrix And it is a Hermitian matrix, R(,) is an element of a row and column of the covariance matrix R.

8. The high-resolution spatial spectrum estimation method according to claim 1, characterized in that: The detection network 2 is a deep neural network, the number of neurons in the input layer of the deep neural network is determined by the number of features, the number of neurons in the hidden layer is set to 500, 400, 300, 200, and 100 respectively, and ReLU is used as the activation function; the drop probability dropout=0.5 is set after the hidden layer; the number of neurons in the output layer is determined by the total number of angles in the interval, and the normalized exponential function Softmax is used to generate the estimated probability of each arrival angle, and then the arrival angles corresponding to the two largest probabilities are selected as the final result.

Images