A method for detecting weak scattered waves based on complex-valued neural networks

Abstract

This invention discloses a method for detecting weak scattered waves based on a complex-valued neural network, relating to the field of signal processing technology. The method includes: constructing a received signal model of a far-field multi-target signal source; constructing a complex-valued neural network model; segmenting data based on a receiving array antenna and known direct wave and scattered wave signals to obtain multiple corresponding direct wave and scattered wave signal segments; calculating multiple two-dimensional ambiguity functions based on the multiple direct wave and scattered wave signal segments; performing a maximum value search within the multiple two-dimensional ambiguity functions and extracting the maximum unit to construct a virtual snapshot; constructing a virtual covariance matrix based on the virtual snapshot; and inputting the virtual covariance matrix into the complex-valued neural network to obtain the direction-finding result of the weak scattered waves. This method not only improves the direction-finding accuracy of weak scattered waves but also enables the detection of coherent signals, achieving multi-target detection and enhancing the estimation effect of scattered waves.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of signal processing, in particular to a weak scattering wave detection method based on a complex-valued neural network. BACKGROUND

[0002] The Direction of Arrival Estimation (DOA) of weak scattering waves, as a core technology of spatial signal processing, plays an irreplaceable role in radar target detection, seismic wave field inversion, underwater sonar positioning, 5G / 6G large-scale MIMO systems, and passive reconnaissance. The technical essence is to analyze the phase difference and amplitude change of the array received signal to invert the spatial propagation characteristics of the scattering wave. The classical DOA theory system is based on the orthogonality principle of signal subspace and noise subspace, and is represented by the multiple signal classification (MUSIC) algorithm and the rotation invariant subspace (ESPRIT) algorithm. In the single target and non-coherent signal scene, sub-degree direction finding accuracy has been achieved.

[0003] However, with the exponential growth of the electromagnetic environment complexity, such as dense multi-target scenes like UAV swarms and ship formations, the existing methods face the following severe technical bottlenecks:

[0004] 1. Coherent signal degradation problem. When multiple scattering wave signals have strong coherence, the rank of the received signal covariance matrix will collapse, causing the signal subspace dimension and the target number to be mismatched. For example, in the UAV swarm scene, the motion correlation of the formation targets will cause the spectral peak resolution of the MUSIC algorithm to decrease, and even completely fail.

[0005] 2. Weak signal sensitivity is insufficient. Traditional methods rely on accurate estimation of the covariance matrix, and its performance boundary is limited. For weak scattering waves with low signal-to-noise ratio, it is difficult to achieve effective estimation.

[0006] 3. Computational dimension disaster. The existing algorithm constructs a spatial spectrum by exhaustive search, and its computational complexity increases exponentially with the number of array elements, making it difficult to meet real-time requirements.

[0007] Therefore, a weak scattering wave detection method based on a complex-valued neural network is provided to solve the above problems. SUMMARY

[0008] To solve the above problems, the present application provides a weak scattering wave detection method based on a complex-valued neural network. Through the designed weak scattering wave detection method based on a complex-valued neural network, the detection ability of weak signals can be effectively enhanced, the multi-target resolution ability can be improved, the environmental adaptability can be enhanced, the computational efficiency can be optimized, and the physical hardware expenditure can be reduced.

[0009] To achieve the above objectives, this invention provides a method for detecting weak scattered waves based on a complex-valued neural network, comprising the following steps:

[0010] S1: Obtain the number of sensor elements and array structure of the receiving array antenna;

[0011] S2: Construct a received signal model for a far-field multi-target signal source based on the number of sensor elements in the receiving array antenna;

[0012] S3: Construct a complex valued neural network model based on the array structure of sensor array elements in the receiving array antenna;

[0013] S4: Obtaining direct wave and scattered wave signals based on the received signal model of a far-field multi-target signal source;

[0014] S5: Adopt a sliding segmentation strategy to segment the direct wave signal and the scattered wave signal based on the number of sensor elements of the receiving array antenna, and obtain multiple segments of direct wave signal and scattered wave signal.

[0015] S6: Based on the segmentation of the direct wave signal and the scattered wave signal, calculate the multi-segment two-dimensional ambiguity function to obtain multiple range-Doppler spectra;

[0016] S7: Based on multiple distance-Doppler spectra, perform spectral peak search to obtain spectral peak units and construct virtual snapshots;

[0017] S8: Obtain the virtual covariance matrix based on virtual snapshots;

[0018] S9: Input the virtual covariance matrix into the complex-valued neural network model to obtain the weak scattered wave direction finding results.

[0019] Preferably, S2 specifically includes the following steps:

[0020] Taking a one-dimensional uniform linear array as an example, the received signal model of the target signal source is obtained based on the number of sensor elements in the receiving array antenna, specifically including:

[0021] One-dimensional linear arrays have The array element, the first The position of each element is represented as follows: ,in When there is A far-field, narrowband, independent, and wavelength-... The signal from the angle When incident on the array, the received signal model of the target signal source is represented as:

[0022] ;

[0023] in, For array manifold matrix, , The incident angle of the signal. The incident angle of the signal is Array guidance amount at time, ; j The imaginary unit, For signal vectors, , This is the Kth semaphore; For noise vectors, , For the first Noise level.

[0024] Preferably, the complex-valued neural network model in S3 includes a complex signal input module, a four-level complex convolution processing module, a complex batch normalization module, an activation function module, a feature flattening module, a three-level complex fully connected module, a complex random deactivation module, a complex feature fusion module, and a real number classification module;

[0025] Complex signal input module, used to receive virtual covariance matrix in complex form;

[0026] The four-level complex convolution processing module contains four complex convolutional layers, each employing a different kernel size and stride strategy.

[0027] The complex batch normalization module is placed after each complex convolutional layer;

[0028] The activation function module is set after the complex batch normalization module;

[0029] The feature flattening module is used to convert a four-dimensional tensor into a two-dimensional feature vector;

[0030] The three-level fully connected module for complex numbers contains three fully connected layers and is used to map the input complex feature vector to the feature space of the target.

[0031] Complex random deactivation modules are configured between fully connected layers;

[0032] The complex feature fusion module is used to concatenate the real and imaginary parts along the feature dimension;

[0033] The real number classification module includes a linear transformation layer and a sigmoid activation function, which outputs the direction finding results of weak scattered waves.

[0034] Preferably, the four-level complex convolution processing module includes a first complex convolutional layer, a second complex convolutional layer, a third complex convolutional layer, and a fourth complex convolutional layer;

[0035] The first complex convolutional layer uses a 3×3 convolutional kernel, a stride of 2×2, and 1×1 edge padding;

[0036] The second complex convolutional layer uses a 3×3 convolutional kernel, a stride of 1×1, and 1×1 edge padding.

[0037] The third complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1;

[0038] The fourth complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1.

[0039] Preferably, the three-level complex fully connected module includes a first fully connected layer, a second fully connected layer, and a third fully connected layer;

[0040] The first fully connected layer maps 4608-dimensional features to 2048 dimensions;

[0041] The second fully connected layer maps 2048-dimensional features to 1024 dimensions;

[0042] The third fully connected layer maps 1024-dimensional features to 121 dimensions.

[0043] Preferably, S5 specifically includes the following steps:

[0044] S51: Using a direct wave and scattered wave beamforming method, based on the direct wave signal and the scattered wave signal, the separated direct wave and scattered wave data are obtained;

[0045] S52: Adopt a sliding segmentation strategy to segment the separated direct wave and scattered wave data based on the number of sensor elements of the receiving array antenna, and obtain multiple segments of direct wave signal and scattered wave signal.

[0046] Preferably, S6 specifically includes the following steps:

[0047] The direct wave signal is segmented as follows The scattered wave signal is segmented as follows The two-dimensional ambiguity functions for segmented direct wave signal and segmented scattered wave signal are calculated, and the range-Doppler spectrum is obtained as follows:

[0048] ;

[0049] For time delay, The scattered wave signal is time-delayed and its conjugate is taken;

[0050] The direct wave signal is represented in segments as follows:

[0051] ;

[0052] in, For the complex fundamental band envelope of the direct wave, The carrier frequency of the direct wave. The amplitude attenuation coefficient of the scattered wave relative to the direct wave. For time delay, For the Doppler frequency shift, the target scattered wave is represented as:

[0053] ;

[0054] in, The carrier frequency of the scattered wave;

[0055] Will and Substitution have to:

[0056] ;

[0057] in, For carrier frequency.

[0058] Preferably, in S7, spectral peak search is performed based on multiple distance-Doppler spectra to obtain spectral peak units, specifically including:

[0059] Will The direct wave signal and the scattered wave signal corresponding to the segment are subjected to two-dimensional fuzzy function calculation to obtain the result. The distance-Doppler spectrum, the distance-Doppler spectrum in , Peak value was achieved at [location]; Each distance-Doppler spectrum is used to perform a peak search and obtain... The coordinates of each spectral peak are obtained. Each spectral peak unit.

[0060] Preferably, S8 specifically includes:

[0061] Based on virtual snapshots, using formulas The virtual covariance matrix in the distance-Doppler domain is calculated. ;in, For the expected operation, For the distance-Doppler domain A virtual snapshot data, for The conjugate transpose of .

[0062] Preferably, S9 specifically includes:

[0063] By inputting the virtual covariance matrix into the complex-valued neural network model, the specific direction of the target scattered wave can be obtained. Choose the probability with the highest probability. As a result of weak scattered wave direction finding .

[0064] Therefore, this invention employs a weak scattered wave detection method based on a complex-valued neural network. By deeply integrating the complex-valued neural network with an electromagnetic scattering physical model, a "data-driven + model-guided" intelligent DOA framework is constructed. This develops a weak scattered wave detection method based on a complex-valued neural network in multi-target, coherent signal scenarios, breaking through the dual constraints of traditional methods in terms of theoretical boundaries and engineering limits, and providing a new technical path for high-precision detection in complex electromagnetic environments. Based on the direction-finding requirements of far-field signal sources, the designed weak scattered wave detection method based on a complex-valued neural network not only improves the direction-finding accuracy of weak scattered waves but also detects coherent signals, achieving multi-target detection and enhancing the estimation effect of scattered waves.

[0065] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating a method for detecting weak scattered waves based on a complex-valued neural network according to the present invention.

[0067] Figure 2 This is a schematic diagram of the received signal model of a far-field multi-target signal source in an embodiment of the present invention;

[0068] Figure 3 This is a diagram of the complex-valued neural network structure in an embodiment of the present invention;

[0069] Figure 4 The following are spatial spectrum reconstruction diagrams in embodiments of the present invention: (a) is a spatial spectrum diagram estimated by using the traditional MUSIC algorithm in the range-Doppler domain for coherent signals with different incoming wave directions; (b) is a spatial spectrum diagram estimated by using the weak scattered wave detection method based on complex-valued neural network for coherent signals with different incoming wave directions; (c) is a spatial spectrum diagram estimated by using the traditional MUSIC algorithm in the range-Doppler domain for coherent signals with similar incoming wave directions; and (d) is a spatial spectrum diagram estimated by using the weak scattered wave detection method based on complex-valued neural network for coherent signals with similar incoming wave directions.

[0070] Figure 5 This is a graph showing the change of the root mean square error of the detected scattered wave DOA as the signal-to-noise ratio of the scattered wave changes in an embodiment of the present invention.

[0071] Figure 6 This is a graph showing the change in the root mean square error (ROA) of the detected scattered wave as the number of snapshots varies in an embodiment of the present invention. Detailed Implementation

[0072] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0073] Example

[0074] A method for detecting weak scattered waves based on complex-valued neural networks, such as Figure 1 As shown, it includes the following steps:

[0075] S1: Obtain the number of sensor elements and array structure of the receiving array antenna;

[0076] S2: Construct a received signal model for a far-field multi-target signal source based on the number of sensor elements in the receiving array antenna, such as... Figure 2 As shown;

[0077] Taking a one-dimensional uniform linear array as an example, the received signal model of the target signal source is obtained based on the number of sensor elements in the receiving array antenna, specifically including:

[0078] Assume a one-dimensional linear array has The array element, the first The position of each element is represented as follows: ,in When there is A far-field, narrowband, independent, and wavelength-... The signal from the angle When incident on the array, the array output data can be represented as:

[0079] ;

[0080] in, For array manifold matrix, , The incident angle of the signal. The incident angle of the signal is Array guidance amount at time, ; j The imaginary unit, For signal vectors, , This is the Kth semaphore; For noise vectors, , For the first The noise level is a factor. The array output data is closely related to the array manifold matrix, signal characteristics, and noise type, while the array manifold matrix is ​​determined by the array structure and the signal incident direction. .

[0081] The number of sensor elements in the receiving antenna of a preset far-field multi-target signal source The received signal model is obtained. .

[0082] S3: Construct a complex valued neural network model based on the array structure of sensor array elements in the receiving array antenna;

[0083] Based on the number of sensor elements in the receiving signal antenna We determine the construction of a complex-valued neural network model for weak scattered wave detection, with its input dimension... The virtual covariance matrix. A 16-element uniform linear array is used as the receiving antenna, with a detection range of... For example, Figure 3 As shown, the complex-valued neural network model includes a complex signal input module, a four-level complex convolution processing module, a complex batch normalization module, an activation function module, a feature flattening module, a three-level complex fully connected module, a complex random deactivation module, a complex feature fusion module, and a real number classification module;

[0084] Complex signal input module, used to receive complex signals of shape. The virtual covariance matrix;

[0085] The four-level complex convolution processing module includes, in sequence:

[0086] The first complex convolutional layer uses a 3×3 convolutional kernel, a stride of 2×2, and 1×1 edge padding;

[0087] The second complex convolutional layer uses a 3×3 convolutional kernel, a stride of 1×1, and 1×1 edge padding.

[0088] The third complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1;

[0089] The fourth complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1;

[0090] The four-level complex convolution processing module employs a progressive feature extraction strategy, with the kernel size decreasing sequentially (3×3 → 2×2). The stride strategy uses a 2×2 downsampling stride in the first layer and maintains a 1×1 stride in subsequent layers. The network's forward propagation process includes a transformation strategy from the complex feature space to the real feature space, preserving complete complex feature information by concatenating the real and imaginary parts of the complex output along the feature dimension.

[0091] The ComplexBatchNorm2d module is placed after each complex convolutional layer;

[0092] The activation function module is connected after each batch of normalization layers;

[0093] The feature flattening module converts a four-dimensional tensor into a two-dimensional feature vector.

[0094] A three-level fully connected module for complex numbers, including:

[0095] The first fully connected layer maps 4608-dimensional features to 2048 dimensions;

[0096] The second fully connected layer maps 2048-dimensional features to 1024 dimensions;

[0097] The third fully connected layer maps 1024-dimensional features to 121 dimensions;

[0098] Complex random deactivation modules are configured between fully connected layers;

[0099] The complex feature fusion module concatenates the real and imaginary parts of the network output along the feature dimension;

[0100] The real number classification module includes a linear transformation layer and a sigmoid activation function, which maps 242-dimensional fused features to a 121-dimensional classification output.

[0101] S4: Obtaining direct wave and scattered wave signals based on the received signal model of a far-field multi-target signal source;

[0102] S5: Adopting a sliding segmentation strategy, the direct wave signal and the scattered wave signal are segmented based on the number of sensor elements in the receiving array antenna, resulting in multiple segments of direct wave signal and scattered wave signal; specifically including the following steps:

[0103] S51: Using a direct wave and scattered wave beamforming method, based on the direct wave signal and the scattered wave signal, the separated direct wave and scattered wave data are obtained;

[0104] S52: Adopt a sliding segmentation strategy to segment the separated direct wave and scattered wave data based on the number of sensor elements of the receiving array antenna, and obtain multiple segments of direct wave signal and scattered wave signal.

[0105] Specifically, assume that the number of sensor elements in the receiving signal antenna is... Then at least sliding segments Segment. If the length of the signal data is Then the length of each segment of data after segmentation is The sliding step size is :

[0106] ;

[0107] After execution, obtain Segmentation of direct wave signal and segmentation of scattered wave signal.

[0108] S6: Based on the segmentation of the direct wave signal and the scattered wave signal, calculate the multi-segment two-dimensional ambiguity function to obtain multiple range-Doppler spectra;

[0109] Specifically, assuming the direct wave signal is segmented as follows: The scattered wave signal is segmented as follows The two-dimensional ambiguity function of the two, namely the distance-Doppler spectrum, is defined as:

[0110] ;

[0111] For time delay, To delay and conjugate the scattered wave signal;

[0112] Assume the direct wave is represented as:

[0113] ;

[0114] in, For the complex fundamental band envelope of the direct wave, The carrier frequency of the direct wave. The amplitude attenuation coefficient of the scattered wave relative to the direct wave. For time delay, For the Doppler frequency shift, the target scattered wave is represented as:

[0115] ;

[0116] in, The carrier frequency of the scattered wave;

[0117] Will and Substitution have to:

[0118] ;

[0119] in, For carrier frequency;

[0120] Therefore, the distance-Doppler spectrum is... , It reached its peak at that point.

[0121] S7: Based on multiple distance-Doppler spectra, perform spectral peak search to obtain spectral peak units and construct virtual snapshots;

[0122] Specifically, will The direct wave signal and the scattered wave signal corresponding to the segment are subjected to two-dimensional fuzzy function calculation, and finally obtained The distance-Doppler spectrum, and the distance-Doppler spectrum in , It reached its peak at that point. Each distance-Doppler spectrum is used to perform a peak search and obtain... The coordinates of each spectral peak, i.e. indivual , Combined information.

[0123] use indivual , Combined information, spectral peak units are extracted to obtain a virtual snapshot of the distance-Doppler domain. Its shape is .

[0124] S8: Obtain the virtual covariance matrix based on virtual snapshots;

[0125] Specifically, through virtual snapshots in the distance-Doppler domain ,calculate The virtual covariance matrix in the distance-Doppler domain is obtained. , as input data for the complex-valued neural network, where, For the expected operation, For the distance-Doppler domain A virtual snapshot data, for The conjugate transpose of .

[0126] S9: Input the virtual covariance matrix into the complex-valued neural network model to obtain the weak scattered wave direction finding results.

[0127] Specifically, the virtual covariance matrix is ​​input into the complex-valued neural network model to obtain the specific direction of the target scattered wave. Choose the probability with the highest probability. As a result of weak scattered wave direction finding .

[0128] Example 1

[0129] Consider a set of three coherent signals with identical or nearly identical Doppler frequency shifts and time delays, a signal-to-noise ratio of -25 dB, a snapshot number of 200, and different directions of arrival. Estimation is performed using both the traditional range-Doppler domain MUSIC algorithm and a weak scattered wave detection method based on complex-valued neural networks. The spatial spectra (MUSIC spectra) estimated by both methods are shown below. Figure 4 (a) and Figure 4 As shown in (b), the traditional MUSIC algorithm using the range-Doppler domain cannot form an effective spectral peak and cannot estimate the number of waves and azimuth angle. However, the weak scattered wave detection method based on complex-valued neural networks can form an effective spectral peak and accurately estimate the number of incoming waves and azimuth angle.

[0130] Consider a set of coherent signals containing two signals with identical or nearly identical Doppler frequency shifts and time delays, both having a signal-to-noise ratio of -10 dB, a snapshot number of 200, and very similar directions of arrival. Estimation is performed using both the traditional MUSIC algorithm in the range-Doppler domain and a weak scattered wave detection method based on complex-valued neural networks. The spatial spectra (MUSIC spectra) estimated by both methods are as follows: Figure 4 (c) and Figure 4 As shown in (d), the traditional MUSIC algorithm using the range-Doppler domain only forms one spectral peak, which cannot estimate the number of waves and the azimuth angle. However, the weak scattered wave detection method based on complex-valued neural networks can form two effective spectral peaks and accurately estimate the number of incoming waves and the azimuth angle.

[0131] Example 2

[0132] like Figure 5 As shown, consider a set of coherent signals containing two signals with identical or nearly identical Doppler frequency shifts and time delays, a signal-to-noise ratio (SNR) ranging from -30dB to 10dB, and 200 snapshots each, but with different directions of arrival. Estimation is performed using the traditional range-Doppler domain MUSIC algorithm (RD-MUSIC), the root-finding MUSIC algorithm (R-MUSIC), the ESPRIT algorithm, and the weak scattering wave detection method based on complex-valued neural networks (RD-CVNN). The root mean square error (RMSE) between the estimated direction of arrival and the true direction is calculated for each algorithm. Comparison reveals that the ESPRIT algorithm fails to provide an effective estimate. While the results from the traditional range-Doppler domain MUSIC algorithm (RD-MUSIC) and the root-finding MUSIC algorithm (R-MUSIC) improve with increasing SNR, they are still not as accurate as those from the weak scattering wave detection method based on complex-valued neural networks (RD-CVNN).

[0133] Example 3

[0134] like Figure 6As shown, consider a set of coherent signals containing two signals, whose Doppler frequency shift and time delay are the same or almost the same, the number of snapshots varies from 200 to 1000, the signal-to-noise ratio is -25dB, and the directions of arrival are different. Estimation is performed using the traditional range-Doppler domain MUSIC algorithm (RD-MUSIC), the root-finding MUSIC algorithm (R-MUSIC), the ESPRIT algorithm, and the weak scattered wave detection method based on complex-valued neural networks (RD-CVNN). The root mean square error between the estimated direction of arrival and the true direction is calculated for each algorithm. Comparison reveals that the ESPRIT algorithm and the root-finding MUSIC algorithm (R-MUSIC) cannot achieve effective estimation. While the result estimated by the traditional range-Doppler domain MUSIC algorithm (RD-MUSIC) can improve with the increase of the number of snapshots, it is still not as accurate as the estimation result provided by the weak scattered wave detection method based on complex-valued neural networks (RD-CVNN) in this embodiment.

[0135] Therefore, the present invention adopts the above-mentioned weak scattered wave detection method based on complex-valued neural network. By constructing a received signal model and a complex-valued neural network model, and combining data segmentation, two-dimensional fuzzy function calculation, maximum value search to construct virtual snapshots and virtual covariance matrices, specific input data is provided to the complex-valued neural network to achieve direction finding of weak scattered waves. This can effectively enhance the weak signal detection capability, improve the multi-target resolution capability, enhance environmental adaptability, optimize computational efficiency, and reduce physical hardware expenses.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A weak scattered wave detection method based on a complex-valued neural network, characterized in that: The method comprises the following steps: S1: obtaining the number and array structure of sensor elements of a receiving array antenna; S2: constructing a receiving signal model of a far-field multi-target signal source based on the number of sensor elements in the receiving array antenna; S3: constructing a complex-valued neural network model based on the array structure of the sensor elements in the receiving array antenna; S4: obtaining direct wave signals and scattered wave signals based on the receiving signal model of the far-field multi-target signal source; S5: adopting a sliding segmentation strategy, segmenting the direct wave signals and the scattered wave signals based on the number of sensor elements of the receiving array antenna to obtain multiple segments of direct wave signal segments and scattered wave signal segments; S6: calculating multiple two-dimensional ambiguity functions according to the multiple segments of direct wave signal segments and scattered wave signal segments to obtain multiple range-Doppler spectra; S7: performing spectrum peak searching based on the multiple range-Doppler spectra to obtain spectrum peak units and construct virtual snapshots; S8: obtaining a virtual covariance matrix based on the virtual snapshots; S9: inputting the virtual covariance matrix into the complex-valued neural network model to obtain a weak scattered wave direction finding result.

2. The method of claim 1, wherein the method is based on a complex-valued neural network. S2 specifically comprises the following steps: Taking a one-dimensional uniform linear array as an example, a receiving signal model of a target signal source is obtained according to the number of sensor elements of the receiving array antenna, specifically comprising: A one-dimensional linear array has elements, the position of the th element is denoted as , where , when there are far-field, narrow-band, independent and wavelength signals incident on the array from angle , the received signal model of the target signal source is represented as: ； in, For array manifold matrix, , The incident angle of the signal. The incident angle of the signal is Array guidance amount at time, ; j The imaginary unit, For signal vectors, , This is the Kth semaphore; For noise vectors, , For the first Noise level.

3. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 2, characterized in that: The complex-valued neural network model in S3 comprises a complex signal input module, a four-level complex convolution processing module, a complex batch normalization module, an activation function module, a feature flattening module, a three-level complex full connection module, a complex random inactivation module, a complex feature fusion module and a real number classification module; The complex signal input module is used for receiving a virtual covariance matrix in complex form; The four-level complex convolution processing module comprises four complex convolution layers, each layer adopts a convolution kernel of different size and a step strategy; The complex batch normalization module is arranged after each complex convolution layer; The activation function module is arranged after the complex batch normalization module; The feature flattening module is used for converting a four-dimensional tensor into a two-dimensional feature vector; The three-level complex full connection module comprises three full connection layers and is used for mapping an input complex feature vector to a target feature space; The complex random inactivation module is arranged between the full connection layers; The complex feature fusion module is used for splicing a real part and an imaginary part along a feature dimension; The real number classification module comprises a linear transformation layer and a Sigmoid activation function and outputs a direction finding result of the weak scattered wave.

4. The method of claim 3, wherein the complex-valued neural network is trained using a training dataset comprising a plurality of training samples, each training sample comprising a set of training data and a corresponding set of training labels. The four-level complex convolution processing module comprises a first complex convolution layer, a second complex convolution layer, a third complex convolution layer and a fourth complex convolution layer; The first complex convolution layer adopts a 3×3 convolution kernel, a step of 2×2 and 1×1 edge padding; The second complex convolution layer adopts a 3×3 convolution kernel, a step of 1×1 and 1×1 edge padding; The third complex convolution layer adopts a 2×2 convolution kernel and a step of 1×1; The fourth complex convolution layer adopts a 2×2 convolution kernel and a step of 1×1.

5. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 4, characterized in that: The three-level complex full connection module comprises a first full connection layer, a second full connection layer and a third full connection layer; The first full connection layer maps 4608-dimensional features to 2048-dimensional features; The second full connection layer maps 2048-dimensional features to 1024-dimensional features; The third full connection layer maps 1024-dimensional features to 121-dimensional features.

6. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 5, characterized in that: S5 specifically comprises the following steps: S51: using a direct wave and scattered wave beam forming method, based on the direct wave signal and the scattered wave signal, obtaining separated direct wave and scattered wave data; S52: adopting a sliding segmentation segmentation strategy, based on the number of sensor elements of the receiving array antenna, segmenting the separated direct wave and scattered wave data to obtain multiple direct wave signal segments and scattered wave signal segments.

7. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 6, characterized in that: S6 specifically comprises the following steps: The direct wave signal segment is , the scattered wave signal segment is , and a two-dimensional ambiguity function of the direct wave signal segment and the scattered wave signal segment is calculated to obtain a range-Doppler spectrum represented as: ； delaying, delaying and conjugating the scattered wave signal; The direct wave signal segment is expressed as: ； wherein, is the complex baseband envelope of the direct wave, is the carrier frequency of the direct wave, is the amplitude attenuation coefficient of the scattered wave with respect to the direct wave, is the time delay, is the Doppler shift, the target scattered wave being represented as: ； wherein is the carrier frequency of the scattered wave; Substituting and into gives: ； wherein is the carrier frequency.

8. The method of claim 7, wherein the complex-valued neural network is trained using a training dataset comprising a plurality of training samples, each training sample comprising a set of training data and a corresponding set of training labels. In S7, a spectrum peak search is performed based on multiple range-Doppler spectra to obtain a spectrum peak unit, specifically comprising: Will The direct wave signal and the scattered wave signal corresponding to the segment are subjected to two-dimensional fuzzy function calculation to obtain the result. The distance-Doppler spectrum, the distance-Doppler spectrum in , The peak value was achieved at that location; Each distance-Doppler spectrum is used to perform a peak search and obtain... The coordinates of each spectral peak are obtained. Each spectral peak unit.

9. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 8, characterized in that: S8 specifically comprises: Based on virtual snapshots, using formulas The virtual covariance matrix in the distance-Doppler domain is calculated. ;in, For the expected operation, For the distance-Doppler domain A virtual snapshot data, for The conjugate transpose of .

10. The method of claim 9, wherein the complex-valued neural network is trained using a training dataset comprising a plurality of training samples, each training sample comprising a set of training data and a corresponding set of training labels. S9 specifically comprises: The virtual covariance matrix is input into a complex-valued neural network model to obtain a probability of a specific direction to which the target scattered wave belongs , and the highest probability is taken as a weak scattered wave direction finding result . .

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