阅读说明：本技术 一种基于深度展开网络的近场源定位方法及系统 (Near-field source positioning method and system based on deep expansion network ) 是由 刘振 苏晓龙 户盼鹤 刘天鹏 彭勃 刘永祥 黎湘 于 2021-07-21 设计创作，主要内容包括：本发明公开了一种基于深度展开网络的近场源定位方法及系统,方法包括：S1、利用嵌套对称阵列得到近场源波达方向的四阶累积量矩阵；S2、将四阶累积量矩阵的信息输入波达方向深度展开网络,计算近场源的波达方向；S3、利用波达方向深度展开网络的输出信息,得到近场源距离相位向量；S4、将距离相位向量的信息输入距离深度展开网络,计算近场源的距离。本发明本发明相较于传统神经网络,深度展开网络的参数具有可解释性,具有泛化能力,而相较于ISTA算法,本发明能够提高近场源波达方向的分辨力,加快收敛速度,提高参数估计精度。(The invention discloses a near field source positioning method and a system based on a deep expansion network, wherein the method comprises the following steps: s1, obtaining a fourth-order cumulant matrix of the near-field source direction of arrival by using the nested symmetric array; s2, inputting the information of the fourth-order cumulant matrix into a wave arrival direction depth expansion network, and calculating the wave arrival direction of the near-field source; s3, utilizing the output information of the depth expansion network in the direction of arrival to obtain a near-field source distance phase vector; and S4, inputting the information of the distance phase vector into a distance depth expansion network, and calculating the distance of the near field source. Compared with the traditional neural network, the method has the advantages that the parameters of the deep expansion network are interpretable and have generalization capability, and compared with the ISTA algorithm, the method can improve the resolution of the near-field source direction of arrival, accelerate the convergence speed and improve the parameter estimation precision.)

1. A near-field source positioning method based on a deep expansion network is characterized by comprising the following steps:

s1, obtaining a fourth-order cumulant matrix of the near-field source direction of arrival by using the nested symmetric array;

s2, inputting the information of the fourth-order cumulant matrix into a wave arrival direction depth expansion network, and calculating the wave arrival direction of the near-field source;

s3, utilizing the output information of the depth expansion network in the direction of arrival to obtain a near-field source distance phase vector;

and S4, inputting the information of the distance phase vector into a distance depth expansion network, and calculating the distance of the near field source.

2. The near-field source positioning method based on the deep unfolding network of claim 1, wherein the step S1 specifically includes:

the nested symmetrical array comprises 2M +1 array elements and x_m(N) represents a numerical value of an nth sampling point of an mth array element, M ═ M., -2, -1,0,1,2,.., M, N ═ 1,2,. and N, N is a fast beat number, and the mth array element is calculated by using the following equation₁Array element, m₁Array element, m₂Array element and m₂Fourth order cumulant c of individual array element₄(m₁，m₂)：

Wherein (·)^*Represents the operation of taking conjugate complex number, m₁，m₂-2, -1,0,1,2,. M, a fourth order cumulant matrix C of M × M dimensions of near-field source directions of arrival is formed by the fourth order cumulants, wherein (M) th order₁，m₂) An element is c₄(m₁，m₂)。

3. The near-field source positioning method based on the deep unfolding network as claimed in claim 2, wherein said step S2 specifically includes:

firstly, vectorizing the real part and the imaginary part of a fourth-order cumulant matrix C to obtain a vector

Wherein(·)^TRepresenting the vector transposition, real (-) representing the real part operation, imag (-) representing the imaginary part operation,m3 th column, m, representing the fourth order cumulant matrix C₃＝-M，…，-2，-1，0，1，2，...，M；

Then, willThe input direction of arrival deeply expands the network to obtain the output of the networkI.e. the near-field source direction-of-arrival spatial spectrum, L_θRepresenting the number of layers of the network, spatial spectrum of direction of arrival for a near-field sourcePerforming spectral peak search, and determining the estimated value of the direction of arrival of the near-field source according to the position corresponding to the spectral peakK represents the number of near field sources.

4. The method of claim 3, wherein the layer 1 output of the DOA deep unfolding network is

First_θThe output of the layer is

l_θ＝2，3，...，L_θ，h_st(. epsilon.) represents a non-linear transformation function, i.e.

h_st(β，ε)＝sgn(β)⊙max(|β|-ε，0)

sgn (·) denotes a sign function, which indicates a Hadamard product, and the initialization parameters of the deep-expansion network in the direction of arrival are:

ε(θ)＝0.05

wherein α (θ) is 0.9/δ (θ), and δ (θ) representsI (theta) represents an identity matrix,representing redundant dictionary matrices of directions of arrival, i.e.

Wherein the content of the first and second substances,which represents the product of the Kronecker reaction,p represents the number of sampling points in the direction of arrival, and λ representsThe wavelength of the near-field source,indicating the position of the m3 th array element.

5. The near-field source positioning method based on the deep unfolding network as claimed in claim 4, wherein the near-field source positioning method based on the deep unfolding network is characterized in that the near-field source positioning method is trained before the deep unfolding network in the direction of arrival is used, random gradient descent is used in the training to update network parameters Ψ (θ), Φ (θ) and ε (θ), and an optimized objective function is as follows:

wherein the content of the first and second substances,represents the square of 2-norm, | ·| non-woven phosphor₁Represents the 1-norm and μ represents the regularization parameter.

6. The near-field source positioning method based on the deep unfolding network of claim 5, wherein the step S3 specifically comprises:

calculating the distance phase vector g of the kth near-field source by using a formula_k：

Wherein arg (·) represents taking phase operation (·)^-1It is shown that the inversion operation is performed, u represents the noise subspace of the signal,can be calculated by

7. The near-field source positioning method based on the deep unfolding network of claim 6, wherein the step S4 specifically comprises:

first, from a distance phase vector g_kReal and imaginary parts of the vector to obtain a vector

Then, the vector is addedThe input distance deeply expands the network to obtain the output of the networkI.e. the kth near-field source range spatial spectrum, L_rIndicating the number of layers of the network;

finally, for near field source distance spatial spectrumPerforming spectral peak search, and determining the distance estimation value of the near-field source according to the position corresponding to the spectral peakK represents the number of near field sources.

8. The method according to claim 7, wherein the layer 1 output of the distance-depth expansion network is

First_rThe output of the layer is

Wherein l_r＝2，3，...，L_r；

The initialization parameters of the network are as follows:

ε(r)＝0.05

wherein α (r) is 0.9/δ (r), and δ (r) representsI (r) represents an identity matrix,representing a distance redundant dictionary matrix:

B(r)＝[b(r₁) b(r₂) … b(r_Q)]

wherein the content of the first and second substances, r_qrepresents distance samples in space, Q is 1,2, …, Q represents the number of distance sample points.

9. The near-field source positioning method based on the deep unfolding network as claimed in claim 8, wherein the distance deep unfolding network is trained before being used, network parameters Ψ (r), Φ (r), and ε (r) are updated by using SGD in the training, and the optimized objective function is:

10. the system of the near-field source localization method based on the deep-developed network according to any one of claims 1 to 9, comprising:

the fourth-order cumulant matrix module is used for obtaining a fourth-order cumulant matrix of the near-field source direction of arrival by utilizing the nested symmetric array;

the first calculation module is used for inputting the information of the fourth-order cumulant matrix into a wave arrival direction depth expansion network and calculating the wave arrival direction of the near-field source;

the near-field source distance phase vector module is used for obtaining a near-field source distance phase vector by utilizing output information of the depth expansion network in the direction of arrival;

the second calculation module is used for inputting the information of the distance phase vector into a distance depth expansion network and calculating the distance of the near field source;

the fourth-order cumulant matrix module, the first calculation module, the near-field source distance phase vector module and the second calculation module are sequentially connected.

Technical Field

The invention relates to the technical field of array signal processing and deep learning, in particular to a near-field source positioning method and system based on a deep expansion network.

Background

Near-field source positioning plays an important role in proximity fuses and passive radar. The radiation source in the space can be divided into a far-field source and a near-field source according to the distance between the radiation source and the receiving array, the far-field source can be regarded as plane wave incidence, and the arrival direction parameters need to be estimated; the near-field source needs to be described by spherical waves, and the direction of arrival and distance parameters need to be estimated.

In the prior art, a convolution neural network is adopted to position a Near-Field source (27th European Signal Processing Conference (EUSIPCO),2019: page 1 to page 5) by 'Deep Learning Based Localization of Near-Field source with Exact statistical Model [ J ]' (the method has high convergence speed, but has poor generalization capability, namely, a large error occurs when a Near-Field source parameter which is not trained is estimated.

In the prior art, a Nested Symmetric Array is adopted in 'constraint Neural Networks for Localization of Near-Field Sources Double-Nested Array [ J ]' (Wireless Communications and Mobile Computing, 2021, DOI:10.1155/2021/9996780), the aperture of the Array can be increased under the condition of the same number of Array elements, so that the Near-Field source parameter estimation accuracy is improved, but the method is a 'black box model', and the parameters of the network do not have interpretability.

In the prior art, "Direction-of-arrival estimation with circular array using compressed sensing in 20GHz band [ J ]" (ieee antennas and wireless processing Letters,2021, 20(5): pages 703 to 707) expands an Iterative Shrinkage Threshold Algorithm (ISTA) into a network cascade form, and realizes estimation of far-field source wave arrival Direction. Compared with the traditional data-driven method based on deep learning, the method integrates the model-driven method into the network structure design, so that the parameters of the network have interpretability and the generalization capability is improved. However, the method cannot realize near-field source positioning, and only can process real signals, but cannot process complex signals.

Therefore, it is necessary to design a near-field source positioning method and system based on a deep unfolding network to overcome the above technical problems.

Disclosure of Invention

The invention aims to provide a near-field source positioning method and a near-field source positioning system based on a deep expansion network, which are used for overcoming the defects in the prior art.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a near-field source positioning method based on a deep expansion network comprises the following steps:

s1, obtaining a fourth-order cumulant matrix of the near-field source direction of arrival by using the nested symmetric array;

s2, inputting the information of the fourth-order cumulant matrix into a wave arrival direction depth expansion network, and calculating the wave arrival direction of the near-field source;

s3, utilizing the output information of the depth expansion network in the direction of arrival to obtain a near-field source distance phase vector;

and S4, inputting the information of the distance phase vector into a distance depth expansion network, and calculating the distance of the near field source.

Further, the step S1 specifically includes:

the nested symmetrical array comprises 2M +1 array elements and x_m(N) represents a numerical value of an nth sampling point of an mth array element, M ═ M., -2, -1,0,1,2,.., M, N ═ 1,2,. and N, N is a fast beat number, and the mth array element is calculated by using the following equation₁Array element, m₁Array element, m₂Array element and m₂Fourth order cumulant c of individual array element₄(m₁,m₂)：

Wherein (·)^*Represents the operation of taking conjugate complex number, m₁,m₂-2, -1,0,1,2, …, M, a fourth order cumulant matrix C of M × M dimensions of near field source directions of arrival formed by fourth order cumulants, wherein the fourth order cumulant matrix C is the second order cumulant matrix C(m₁,m₂) An element is c₄(m₁,m₂)。

Further, the step S2 specifically includes:

firstly, vectorizing the real part and the imaginary part of a fourth-order cumulant matrix C to obtain a vector

Wherein(·)^TRepresenting the vector transposition, real (-) representing the real part operation, imag (-) representing the imaginary part operation,m3 th column, m, representing the fourth order cumulant matrix C₃＝-M,...,-2，-1,0,1,2,...,M；

Then, willThe input direction of arrival deeply expands the network to obtain the output of the networkI.e. the near-field source direction-of-arrival spatial spectrum, L_θRepresenting the number of layers of the network, spatial spectrum of direction of arrival for a near-field sourcePerforming spectral peak search, and determining the estimated value of the direction of arrival of the near-field source according to the position corresponding to the spectral peakK is 1,2, …, K denotes the number of near field sources.

Further, the output of layer 1 of the DOA deep unfolding network is

First_θThe output of the layer is

l_θ＝2,3,...,L_θ，h_st(. epsilon.) represents a non-linear transformation function, i.e.

h_st(β,ε)＝sgn(β)⊙max(|β|-ε,0)

sgn (·) denotes a sign function, which indicates a Hadamard product, and the initialization parameters of the deep-expansion network in the direction of arrival are:

ε(θ)＝0.05

wherein α (θ) is 0.9/δ (θ), and δ (θ) representsI (theta) represents an identity matrix,representing redundant dictionary matrices of directions of arrival, i.e.

Wherein the content of the first and second substances,which represents the product of the Kronecker reaction,p is 1,2, …, P represents the number of sampling points in the direction of arrival, λ represents the wavelength of the near-field source,indicating the position of the m3 th array element.

Further, before the network is deeply expanded by using the direction of arrival, the network needs to be trained, random gradient descent is used in the training to update network parameters psi (theta), phi (theta) and epsilon (theta), and the optimized objective function is as follows:

wherein the content of the first and second substances,represents the square of 2-norm, | ·| non-woven phosphor₁Represents the 1-norm and μ represents the regularization parameter.

Further, the step S3 specifically includes:

calculating the distance phase vector g of the kth near-field source by using a formula_k：

Wherein arg (·) represents taking phase operation (·)^-1It is shown that the inversion operation is performed, u represents the noise subspace of the signal,can be calculated by

Further, the step S4 specifically includes:

first, from a distance phase vector g_kReal and imaginary parts of the vector to obtain a vector

Then, the vector is addedThe input distance deeply expands the network to obtain the output of the networkI.e. the kth near-field source range spatial spectrum, L_rIndicating the number of layers of the network;

finally, for near field source distance spatial spectrumPerforming spectral peak search, and determining the distance estimation value of the near-field source according to the position corresponding to the spectral peakK is 1,2, …, K denotes the number of near field sources.

Further, the output of layer 1 of the distance-depth expansion network is

First_rThe output of the layer is

Wherein l_r＝2,3,...,L_r；

The initialization parameters of the network are as follows:

ε(r)＝0.05

wherein α (r) is 0.9/δ (r), and δ (r) representsI (r) represents an identity matrix,representing a distance redundant dictionary matrix:

B(r)＝[b(r₁) b(r₂) ... b(r_Q)]

wherein the content of the first and second substances, m₄＝0，1，...,M，r_qrepresents distance samples in space, Q is 1,2, …, Q represents the number of distance sample points.

Further, before the distance deep expansion network is used, training needs to be performed on the distance deep expansion network, network parameters Ψ (r), Φ (r), and epsilon (r) are updated by using the SGD in the training, and an optimized objective function is as follows:

the invention also provides a system of the near-field source positioning method based on the deep unfolding network, which comprises the following steps:

the fourth-order cumulant matrix module is used for obtaining a fourth-order cumulant matrix of the near-field source direction of arrival by utilizing the nested symmetric array;

the first calculation module is used for inputting the information of the fourth-order cumulant matrix into a wave arrival direction depth expansion network and calculating the wave arrival direction of the near-field source;

the near-field source distance phase vector module is used for obtaining a near-field source distance phase vector by utilizing output information of the depth expansion network in the direction of arrival;

the second calculation module is used for inputting the information of the distance phase vector into a distance depth expansion network and calculating the distance of the near field source;

the fourth-order cumulant matrix module, the first calculation module, the near-field source distance phase vector module and the second calculation module are sequentially connected.

Compared with the prior art, the invention has the advantages that: compared with the traditional neural network, the method has the advantages that the parameters of the deep expansion network are interpretable and have generalization capability, and compared with the ISTA algorithm, the method can improve the resolution of the near-field source wave arrival direction, accelerate the convergence speed and improve the parameter estimation precision.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a flowchart of a near-field source positioning method based on a deep unfolding network according to the present invention.

Fig. 2 is a schematic structural view of a direction-of-arrival depth-expanded network according to the present invention.

FIG. 3 is a schematic diagram of a distance-deep unfolding network according to the present invention.

FIG. 4 is a schematic diagram of a scenario for near field source localization using nested symmetric arrays.

FIG. 5 shows the estimation results of the near-field source in different directions of arrival using the present invention.

FIG. 6 shows the estimation error of the near-field source obtained by the present invention in different directions of arrival.

FIG. 7 shows the estimation results of the near-field source at different distances using the present invention.

FIG. 8 shows the estimated error of the near-field source at different distances obtained by the present invention.

FIG. 9 shows a near-field source direction-of-arrival spatial spectrum obtained using a different approach.

Fig. 10 shows the near-field source direction of arrival NMSE obtained using a different approach.

Fig. 11 shows the near field source distance NMSE obtained using a different method.

Detailed Description

The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, and the scope of the present invention will be more clearly and clearly defined.

Referring to fig. 1, the embodiment discloses a near-field source positioning method based on a deep deployment network, including:

step S1, obtaining a fourth-order cumulant matrix of the near-field source direction of arrival by using the nested symmetric array, specifically:

since the known antennaThe array is in nested symmetrical arrangement and comprises 2M +1 array elements. Let x_m(N) represents a numerical value of an nth sampling point of an mth array element, M ═ M., -2, -1,0,1,2,.., M, N ═ 1,2,. and N, N is a fast beat number, and the mth array element is calculated by using the following equation₁Array element, m₁Array element, m₂Array element and m₂Fourth order cumulant c of individual array element₄(m₁,m₂)：

Wherein, (.)^*Represents the operation of taking conjugate complex number, m₁,m₂-2, -1,0,1,2,. M, a fourth order cumulant matrix C of M × M dimensions of near-field source directions of arrival is formed by the fourth order cumulants, wherein (M) th order₁,m₂) An element is c₄(m₁,m₂)。

In this embodiment, the antenna array is preferably nested with a symmetric linear array, and this array can obtain a fourth-order cumulant matrix only including the near-field source direction of arrival by using the symmetric characteristic of the array elements, and increase the aperture of the array and improve the parameter estimation accuracy under the condition that the number of the array elements is the same.

Step S2, inputting the information of the fourth-order cumulant matrix into a direction of arrival depth expansion network, and calculating the direction of arrival of the near-field source, specifically:

firstly, vectorizing the real part and the imaginary part of a fourth-order cumulant matrix C to obtain a vector

Wherein the content of the first and second substances,(·)^Trepresents vector transposition, real (-) represents real part operation, imag (-) represents fetchingThe operation of the imaginary part is carried out,m3 th column, m, representing the fourth order cumulant matrix C₃＝-M,...,-2,-1,0,1,2,...,M。

Then, the vector is addedThe input direction of arrival deeply expands the network to obtain the output of the networkI.e. the near-field source direction-of-arrival spatial spectrum, L_θIndicating the number of layers of the network.

Finally, the DOA spatial spectrum of the near-field sourcePerforming spectral peak search, and determining the estimated value of the direction of arrival of the near-field source according to the position corresponding to the spectral peakK is 1,2, …, K denotes the number of near field sources.

The structure of the depth-of-arrival expanded network is shown in fig. 2, where the output of layer 1 is:

first_θThe output of the layer is:

l_θ＝2,3,...,L_θ，h_st(. epsilon.) represents a nonlinear transformation function, namely:

h_st(β,ε)＝sgn(β)⊙max(|β|-ε,0)

sgn (·) denotes a sign function, which indicates a Hadamard product, and the initialization parameters of the deep-evolving network in the direction of arrival are as follows:

ε(θ)＝0.05

wherein α (θ) is 0.9/δ (θ), and δ (θ) representsI (theta) represents an identity matrix,representing a redundant dictionary matrix of directions of arrival, namely:

wherein the content of the first and second substances,which represents the product of the Kronecker reaction,p is 1,2, …, P represents the number of sampling points in the direction of arrival, λ represents the wavelength of the near-field source,represents the m3 th array elementThe position of (a).

It should be noted that, when the deep deployment network in the direction of arrival is used, it must be trained first, and in the training, the network parameters Ψ (θ), Φ (θ), and ∈ (θ) are updated by using Stochastic Gradient Descent (SGD), and the optimized objective function is:

wherein,Represents the square of 2-norm, | ·| non-woven phosphor₁Represents the 1-norm and μ represents the regularization parameter.

Step S3, obtaining a near-field source distance phase vector by using output information of the depth-of-arrival expansion network, specifically: calculating the distance phase vector g of the kth near-field source by using the following formula_k：

Wherein, arg (·) represents taking phase operation (·)^-1It is shown that the inversion operation is performed, u represents the noise subspace of the signal,can be calculated from the following formula:

step S4, inputting the information of the distance phase vector into a distance depth expansion network, and calculating the distance of the near field source, specifically:

first, from a distance phase vector g_kReal and imaginary parts of the vector to obtain a vector

Then, the vector is addedThe input distance deeply expands the network to obtain the output of the networkI.e. the kth near-field source range spatial spectrum, L_rIndicating the number of layers of the network.

Finally, for near field source distance spatial spectrumPerforming spectral peak search, and determining the distance estimation value of the near-field source according to the position corresponding to the spectral peakK is 1,2, …, K denotes the number of near field sources.

The structure of the distance-depth expansion network in this embodiment is shown in fig. 3, where the output of layer 1 is:

first_rThe output of the layer is:

wherein l_r＝2,3,...,L_r。

The initialization parameters of the distance-depth expansion network are as follows:

ε(r)＝0.05

wherein α (r) is 0.9/δ (r), δ (r) representsI (r) represents an identity matrix,representing distance redundant dictionary matrices, i.e.

B(r)＝[b(r₁) b(r₂) … b(r_Q)]

Wherein the content of the first and second substances, m₄＝0，1，...，M，r_qrepresents distance samples in space, Q is 1,2, …, Q represents the number of distance sample points.

In this embodiment, before the distance depth expansion network is used, it must be trained, and in the training, the SGD is used to update the network parameters Ψ (r), Φ (r), and ∈ (r), and the optimized objective function is:

the invention also provides a system of the near-field source positioning method based on the deep unfolding network, which comprises the following steps: the fourth-order cumulant matrix module is used for obtaining a fourth-order cumulant matrix of the near-field source direction of arrival by utilizing the nested symmetric array; the first calculation module is used for inputting the information of the fourth-order cumulant matrix into a wave arrival direction depth expansion network and calculating the wave arrival direction of the near-field source; the near-field source distance phase vector module is used for obtaining a near-field source distance phase vector by utilizing output information of the depth expansion network in the direction of arrival; the second calculation module is used for inputting the information of the distance phase vector into a distance depth expansion network and calculating the distance of the near field source; the four-order cumulant matrix module, the first calculation module, the near-field source distance phase vector module and the second calculation module are sequentially connected.

In order to verify the positioning performance of the invention on the near-field source, four simulation experiments are used for explanation.

Simulation experiment I

In the simulation experiment, the two-stage nested symmetrical linear array is shown in fig. 4, the number of array elements is 17, M is 8, the solid circles represent the first-stage sub-array, the spacing is λ/8, the hollow circles represent the second-stage sub-array, and the spacing is 5 λ/8. At intervals of 1 deg. and 1 lambda for wave reaching directions of-60 deg. and 60 deg. respectively]And a distance [5 λ,30 λ ]]And carrying out uniform sampling to generate a training sample of a near-field source, wherein the number N of snapshots is 10000. Number of layers L of DOA deep-developed network_θAnd number of layers L of the distance-depth expanded network_rBoth 50, the epoch is set to 300 and the mini-batch is set to 32 during training of both deep deployment nets.

Simulation experiment one was used to verify the generalization ability of the present invention to near-field source direction of arrival estimation, where the distance of the near-field source was set to 10 λ,3 sets of test samples were generated in airspace, the direction of arrival of the test sample set 1 was set to-59.99 °, -58.99 °, …, -0.99 °, 0.01 °, 1.01 °, …, 59.01 °, the direction of arrival of the test sample set 2 was set to-59.90 °, -58.90 °, …, -0.90 °, 0.10 °, 1.10 °, …, 59.10 °, the direction of arrival of the test sample set 3 was set to-59.70 °, -58.70 °, …, -0.70 °, 0.30 °, 1.30 °, …, 59.30 °, and a total of 360 test samples. Fig. 5 is a view showing the estimation result of the direction of arrival obtained by the present invention, with the abscissa being the test sample number and the ordinate being the estimation result of the direction of arrival, and fig. 6 is a view showing the estimation error of the direction of arrival obtained by the present invention, with the abscissa being the test sample number and the ordinate being the estimation error of the direction of arrival. It can be seen that the estimation errors of the directions of arrival of the first group of test samples and the second group of test samples are 0.01 degrees and 0.1 degrees respectively, and the estimation error of the direction of arrival of the third group of test samples is within 1 degree, which shows that the method has generalization capability on near-field source direction of arrival estimation.

Simulation experiment two

The simulation experiment is used for verifying the generalization ability of the invention to near-field source distance estimation, in the experiment, the direction of arrival of a near-field source is set to be 30 degrees, 3 groups of test samples are generated in a space domain, the distance of the 1 st group of test samples is set to be 5.01 lambda, 6.01 lambda, … and 29.01 lambda, the distance of the 2 nd group of test samples is set to be 5.10 lambda, 6.10 lambda, … and 29.10 lambda, the distance of the 3 rd group of test samples is set to be 5.30 lambda, 6.30 lambda, … and 29.30 lambda, and the total number of the test samples is 75. Fig. 7 is a distance estimation result obtained by the present invention, the abscissa is a test sample number, the ordinate is a distance estimation result, fig. 8 is a distance estimation error obtained by the present invention, the abscissa is a test sample number, and the ordinate is a distance estimation error. It can be seen that the distance estimation errors of the first and second sets of test samples are 0.01 λ and 0.1 λ, and the distance estimation error of the third set of test samples is within 1 λ, indicating that the present invention has generalization capability for near-field source distance estimation.

Simulation experiment III

The simulation experiment is used for verifying the resolution of the invention on the direction of arrival of the near-field source, and the positions of the two near-field sources are respectively set to be (15 degrees, 25 lambada), (20 degrees and 10 lambada) in the experiment. Fig. 9 shows a near-field source spatial spectrum, where a horizontal axis shows an arrival direction, a vertical axis shows spatial spectrum intensity, diamond points show a real arrival direction, a solid line shows the near-field source spatial spectrum obtained by the present invention, and a dotted line shows the near-field source spatial spectrum obtained by 50 iterations using the ISTA algorithm.

Simulation experiment four

The simulation experiment is used to verify the convergence rate of the present invention. Fig. 10 and 11 are normalized root mean square error (NMSE) of the direction of arrival and distance parameters of the near-field source, respectively, where the abscissa indicates the number of depth-spread network layers or iterations of the ISTA algorithm, the ordinate indicates the NMSE of the training sample, the solid line plus "o" indicates the NMSE of the present invention, and the dashed line plus "indicates the NMSE of the ISTA algorithm. It can be seen that the invention and the ISTA algorithm NMSE gradually decrease with the increase of the number of network layers/iteration times, and the invention has faster convergence speed and higher parameter estimation accuracy under the same number of network layers or iteration times.

Although the embodiments of the present invention have been described with reference to the accompanying drawings, various changes or modifications may be made by the patentees within the scope of the appended claims, and within the scope of the invention, as long as they do not exceed the scope of the invention described in the claims.