Weak scattered wave detection method based on complex valued neural network

Abstract

The invention discloses a weak scattered wave detection method based on a complex valued neural network, which relates to the technical field of signal processing, and comprises the following steps: constructing a receiving signal model of a far-field multi-target signal source; constructing a complex value neural network model; performing data segmentation based on a receiving array antenna and known direct wave signals and scattered wave signals to obtain multiple corresponding direct wave signal segments and scattered wave signal segments; calculating a multi-section two-dimensional fuzzy function according to the multi-section direct wave signal and the scattered wave signal; performing maximum value search in the multi-section two-dimensional fuzzy function, and taking out a maximum unit to construct a virtual snapshot; constructing a virtual covariance matrix according to the virtual snapshot; and inputting the virtual covariance matrix into a complex valued neural network to obtain a weak scattered wave direction finding result. The direction finding precision of weak scattered waves can be improved, coherent signals can be detected, multi-target detection is achieved, and the estimation effect of the scattered waves is enhanced.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method for detecting weak scattered waves based on complex-valued neural networks. Background Technology

[0002] Direction of Arrival (DOA) estimation, a core technology in space signal processing, plays an irreplaceable role in radar target detection, seismic wavefield inversion, underwater sonar positioning, 5G / 6G massive MIMO systems, and passive reconnaissance. Its core technology involves jointly analyzing the phase difference and amplitude variations of the received signal from the array to invert the spatial propagation characteristics of the scattered wave. The classical DOA theory is built upon the orthogonality principle of the signal and noise subspaces, represented by algorithms such as Multiple Signal Classification (MUSIC) and Rotation Invariant Subspace (ESPRIT), achieving sub-degree-level direction-finding accuracy in single-target, incoherent signal scenarios.

[0003] However, with the exponential increase in the complexity of electromagnetic environments, such as dense multi-target scenarios like drone swarms and naval formations, existing methods face the following severe technical bottlenecks: 1. Coherent signal degradation problem: When multiple scattered wave signals exhibit strong coherence, the rank of the received signal covariance matrix will collapse, leading to a mismatch between the signal subspace dimension and the number of targets. For example, in drone swarm scenarios, the motion correlation of formation targets can reduce the spectral peak resolution of the MUSIC algorithm, or even cause it to fail completely.

[0004] 2. Insufficient sensitivity to weak signals: Traditional methods rely on accurate estimation of the covariance matrix, which limits their performance. For weak scattered waves with low signal-to-noise ratio, it is difficult to achieve effective estimation.

[0005] 3. The curse of computational dimensionality: Existing algorithms construct spatial spectra through exhaustive search, and their computational complexity increases explosively with the number of array elements, making it difficult to meet real-time requirements.

[0006] Therefore, a method for detecting weak scattered waves based on complex-valued neural networks is provided to solve the above problems. Summary of the Invention

[0007] To address the aforementioned challenges, this invention provides a weak scattered wave detection method based on a complex-valued neural network. This method effectively enhances weak signal detection capabilities, improves multi-target resolution, enhances environmental adaptability, optimizes computational efficiency, and reduces physical hardware costs.

[0008] 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: S1: Obtain the number of sensor elements and array structure of the receiving array antenna; 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; S3: Construct a complex valued neural network model based on the array structure of sensor array elements in the receiving array antenna; S4: Obtaining direct wave and scattered wave signals based on the received signal model of a far-field multi-target signal source; 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. 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; S7: Based on multiple distance-Doppler spectra, perform spectral peak search to obtain spectral peak units and construct virtual snapshots; S8: Obtain the virtual covariance matrix based on virtual snapshots; S9: Input the virtual covariance matrix into the complex-valued neural network model to obtain the weak scattered wave direction finding results.

[0009] Preferably, S2 specifically includes the following steps: 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: 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: ; 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.

[0010] 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; Complex signal input module, used to receive virtual covariance matrix in complex form; The four-level complex convolution processing module contains four complex convolutional layers, each employing a different kernel size and stride strategy. The complex batch normalization module is placed after each complex convolutional layer; The activation function module is set after the complex batch normalization module; The feature flattening module is used to convert a four-dimensional tensor into a two-dimensional feature vector; 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. Complex random deactivation modules are configured between fully connected layers; The complex feature fusion module is used to concatenate the real and imaginary parts along the feature dimension; 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.

[0011] 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; The first complex convolutional layer uses a 3×3 convolutional kernel, a stride of 2×2, and 1×1 edge padding; The second complex convolutional layer uses a 3×3 convolutional kernel, a stride of 1×1, and 1×1 edge padding. The third complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1; The fourth complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1.

[0012] 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; The first fully connected layer maps 4608-dimensional features to 2048 dimensions; The second fully connected layer maps 2048-dimensional features to 1024 dimensions; The third fully connected layer maps 1024-dimensional features to 121 dimensions.

[0013] Preferably, S5 specifically includes the following steps: S51: Using a direct wave and scattered wave beamforming method, the separated direct wave and scattered wave data are obtained based on the direct wave signal and the scattered wave signal; 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. Preferably, S6 specifically includes the following steps: 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: ; For time delay, The scattered wave signal is time-delayed and its conjugate is taken; The direct wave signal is represented in segments as follows: ; 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: ; in, The carrier frequency of the scattered wave; Will and Substitution have to: ; in, For carrier frequency.

[0014] Preferably, in S7, spectral peak search is performed based on multiple distance-Doppler spectra to obtain spectral peak units, specifically including: 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.

[0015] Preferably, S8 specifically includes: 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 .

[0016] Preferably, S9 specifically includes: 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 .

[0017] 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.

[0018] 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

[0019] 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. 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; Figure 3 This is a diagram of the complex-valued neural network structure in an embodiment of the present invention; Figure 4The 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. Figure 5 This is a graph showing the change in 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. 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

[0020] 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.

[0021] Example A method for detecting weak scattered waves based on complex-valued neural networks, such as Figure 1 As shown, it includes the following steps: S1: Obtain the number of sensor elements and array structure of the receiving array antenna; 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; 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: 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: ; 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. .

[0022] The number of sensor elements in the receiving antenna of a preset far-field multi-target signal source The received signal model is obtained. .

[0023] S3: Construct a complex valued neural network model based on the array structure of sensor array elements in the receiving array antenna; 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; Complex signal input module, used to receive complex signals of shape. The virtual covariance matrix; The four-level complex convolution processing module includes, in sequence: The first complex convolutional layer uses a 3×3 convolutional kernel, a stride of 2×2, and 1×1 edge padding; The second complex convolutional layer uses a 3×3 convolutional kernel, a stride of 1×1, and 1×1 edge padding. The third complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1; The fourth complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1; 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.

[0024] The ComplexBatchNorm2d module is placed after each complex convolutional layer; The activation function module is connected after each batch of normalization layers; The feature flattening module converts a four-dimensional tensor into a two-dimensional feature vector. A three-level fully connected module for complex numbers, including: The first fully connected layer maps 4608-dimensional features to 2048 dimensions; The second fully connected layer maps 2048-dimensional features to 1024 dimensions; The third fully connected layer maps 1024-dimensional features to 121 dimensions; Complex random deactivation modules are configured between fully connected layers; The complex feature fusion module concatenates the real and imaginary parts of the network output along the feature dimension; 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.

[0025] S4: Obtaining direct wave and scattered wave signals based on the received signal model of a far-field multi-target signal source; 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: S51: Using a direct wave and scattered wave beamforming method, the separated direct wave and scattered wave data are obtained based on the direct wave signal and the scattered wave signal; 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. 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 : ; After execution, obtain Segmentation of direct wave signal and segmentation of scattered wave signal.

[0026] 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; 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: ; For time delay, To delay and conjugate the scattered wave signal; Assume the direct wave is represented as: ; 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: ; in, The carrier frequency of the scattered wave; Will and Substitution have to: ; in, For carrier frequency; Therefore, it can be seen that the distance-Doppler spectrum is in , It reached its peak at that point.

[0027] S7: Based on multiple distance-Doppler spectra, perform spectral peak search to obtain spectral peak units and construct virtual snapshots; 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. (Regarding...) Each distance-Doppler spectrum is used to perform a peak search and obtain... The coordinates of each spectral peak, i.e. indivual , Combined information.

[0028] use indivual , Combined information, spectral peak units are extracted to obtain a virtual snapshot of the distance-Doppler domain. Its shape is .

[0029] S8: Obtain the virtual covariance matrix based on virtual snapshots; 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 .

[0030] S9: Input the virtual covariance matrix into the complex-valued neural network model to obtain the weak scattered wave direction finding results.

[0031] 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 .

[0032] Example 1 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.

[0033] 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.

[0034] Example 2 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).

[0035] Example 3 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.

[0036] 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.

[0037] 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 method for detecting weak scattered waves based on complex-valued neural networks, characterized in that: Includes the following steps: S1: Obtain the number of sensor elements and array structure of the receiving array antenna; 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; S3: Construct a complex valued neural network model based on the array structure of sensor array elements in the receiving array antenna; S4: Obtaining direct wave and scattered wave signals based on the received signal model of a far-field multi-target signal source; 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. 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; S7: Based on multiple distance-Doppler spectra, perform spectral peak search to obtain spectral peak units and construct virtual snapshots; S8: Obtain the virtual covariance matrix based on virtual snapshots; S9: Input the virtual covariance matrix into the complex-valued neural network model to obtain the weak scattered wave direction finding results.

2. The method for detecting weak scattered waves based on a complex-valued neural network as described in claim 1, characterized in that: S2 specifically includes the following steps: 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: 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: ； 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 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; Complex signal input module, used to receive virtual covariance matrix in complex form; The four-level complex convolution processing module contains four complex convolutional layers, each employing a different kernel size and stride strategy. The complex batch normalization module is placed after each complex convolutional layer; The activation function module is set after the complex batch normalization module; The feature flattening module is used to convert a four-dimensional tensor into a two-dimensional feature vector; 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. Complex random deactivation modules are configured between fully connected layers; The complex feature fusion module is used to concatenate the real and imaginary parts along the feature dimension; 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.

4. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 3, characterized in that: The four-level complex convolution processing module includes a first complex convolution layer, a second complex convolution layer, a third complex convolution layer, and a fourth complex convolution layer; The first complex convolutional layer uses a 3×3 convolutional kernel, a stride of 2×2, and 1×1 edge padding; The second complex convolutional layer uses a 3×3 convolutional kernel, a stride of 1×1, and 1×1 edge padding. The third complex convolutional layer uses a 2×2 convolutional kernel and a stride of 1×1; The fourth complex convolutional layer uses a 2×2 convolutional kernel and a stride 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 fully connected complex module includes a first fully connected layer, a second fully connected layer, and a third fully connected layer; The first fully connected layer maps 4608-dimensional features to 2048 dimensions; The second fully connected layer maps 2048-dimensional features to 1024 dimensions; The third fully connected layer maps 1024-dimensional features to 121 dimensions.

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

7. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 6, characterized in that: S6 specifically includes the following steps: 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 signals and segmented scattered wave signals are calculated, and the range-Doppler spectrum is obtained as follows: ； For time delay, To delay and conjugate the scattered wave signal; The direct wave signal is represented in segments as follows: ； 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: ； in, The carrier frequency of the scattered wave; Will and Substitution have to: ； in, For carrier frequency.

8. The method for detecting weak scattered waves based on a complex-valued neural network according to claim 7, characterized in that: S7 performs spectral peak search based on multiple distance-Doppler spectra to obtain spectral peak units, specifically including: 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 includes: 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. A method for detecting weak scattered waves based on a complex-valued neural network according to claim 9, characterized in that: S9 specifically includes: 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 .

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