A shortwave communication behavior recognition method based on autocorrelation high-order spectrum features

Abstract

The present invention discloses a method for identifying shortwave communication behavior based on autocorrelation high-order spectrum features. The method comprises the following steps: calculating the autocorrelation function of a time domain signal to obtain an autocorrelation sequence; performing a bispectral transformation on the autocorrelation sequence to calculate a third-order cumulant; sampling the obtained third-order cumulant matrix and converting it into a three-channel format similar to an image to construct a data set; designing a convolutional neural network model with two inputs, and further improving it by increasing the model depth, introducing a batch normalization layer, and improving the activation function to obtain a final network model; inputting the data set into the final network model to complete the training and classification tasks. The present invention can avoid a series of operations such as demodulation, deinterleaving, and decoding of the signal, and can directly determine the communication behavior by identifying the physical layer signal. It also has a good recognition effect in a low signal-to-noise ratio environment.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent communication countermeasures, and in particular to a shortwave communication behavior recognition method based on autocorrelation high-order spectrum features. Background Art

[0002] With the advent and development of cognitive electronic warfare, the application of "cognition" in electronic warfare is increasingly demanded. Communication and radar countermeasures are evolving towards intelligence. Communication emitters, such as shortwave and ultra-shortwave radios, satellite links, and tactical data links, play a crucial role on the informationized battlefield. Because they have operators, communication emitters carry their behavioral intentions and, to a certain extent, reflect the actions, situation, and status of non-cooperative actors. By performing behavioral-level analysis on intercepted communication emitter signals, it is possible to reverse engineer the behavioral information of the emitter operator, thereby gaining an advantage in communication countermeasures.

[0003] Research on behavioral-level cognition based on intercepted physical-layer electromagnetic signals has just begun, and few studies have been carried out so far. In complex electromagnetic environments, especially low signal-to-noise ratio environments, how to infer behavior through intercepted physical-layer signals is an urgent problem to be solved. Summary of the Invention

[0004] The purpose of the present invention is to provide a shortwave communication behavior identification method based on autocorrelation high-order spectrum characteristics, so as to achieve the goal of reverse reasoning behavior from the physical layer.

[0005] The technical solution to achieve the purpose of the present invention is: a shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics, the steps are as follows:

[0006] S1. Calculate the autocorrelation function of the time domain signal and obtain the autocorrelation sequence;

[0007] S2. Perform bispectral transformation on the autocorrelation sequence and calculate the third-order cumulant;

[0008] S3. Sampling the obtained third-order cumulant matrix and converting it into a three-channel format similar to an image to construct a data set;

[0009] S4. Design a two-input convolutional neural network model and further improve it by increasing the model depth, introducing the BatchNormalization layer, and improving the activation function to obtain the final network model;

[0010] S5. Input the data set into the final network model to complete the training and classification tasks.

[0011] Compared with the prior art, the present invention has the following significant advantages:

[0012] (1) Combining signal processing and deep learning, the fingerprint features of physical layer signals with different behaviors are extracted through signal processing, and then convolutional neural networks are used to train and classify the features, achieving the purpose of reverse reasoning behavior from physical layer signals, providing ideas for the behavioral research of communication radiation sources;

[0013] (2) It is suitable for environments with high noise levels and has good recognition effects under low signal-to-noise ratio conditions. In addition, the model is trained quickly and has good real-time performance, allowing for real-time analysis.

[0014] (3) The physical layer shortwave signal received can be directly analyzed without the need for tedious operations such as demodulation, deinterleaving, and decoding of the signal, thereby achieving the purpose of shortwave communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 The figure is a flow chart of the shortwave communication behavior identification method based on the autocorrelation high-order spectrum characteristics of the present invention.

[0016] Figure 2 This is the network model structure diagram.

[0017] Figure 3 Figure 2 is a diagram showing the relationship between five burst waveforms and communication behaviors.

[0018] Figure 4a This is the shortwave burst waveform BW0 signal forming flow chart.

[0019] Figure 4b This is the shortwave burst waveform BW1 signal forming flow chart.

[0020] Figure 4c This is the shortwave burst waveform BW2 signal shaping flow chart.

[0021] Figure 4d This is the shortwave burst waveform BW3 signal shaping flow chart.

[0022] Figure 4e This is the shortwave burst waveform BW4 signal shaping flow chart.

[0023] Figure 5 This is a graph showing the recognition accuracy results of different network models. DETAILED DESCRIPTION

[0024] The present invention provides a shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics, comprising the following steps:

[0025] S1. Calculate the autocorrelation function of the time domain signal and obtain the autocorrelation sequence;

[0026] S2. Perform bispectral transformation on the autocorrelation sequence and calculate the third-order cumulant;

[0027] S3. Sampling the obtained third-order cumulant matrix and converting it into a three-channel format similar to an image to construct a data set;

[0028] S4. Design a two-input convolutional neural network model and further improve it by increasing the model depth, introducing the BatchNormalization layer, and improving the activation function to obtain the final network model;

[0029] S5. Input the data set into the final network model to complete the training and classification tasks.

[0030] As a specific example, the specific steps of S1 are:

[0031] Step S11: According to the five burst waveforms BW0, BW1, BW2, BW3, and BW4 specified in the US military shortwave radio standard MIL-STD-188-141B, MATLAB is used to simulate and generate 1000 signal samples of each of the five burst waveforms. The signals are I and Q signals, and the time series x is generated. k ;

[0032] Step S12: Calculate x k The autocorrelation function is defined as:

[0033]

[0034] For the receiving end signal s k , consider the additive white Gaussian noise n k , then s k =x k +n k ;

[0035] Define the receiving end signal s k The autocorrelation function r is:

[0036]

[0037] in is the variance of Gaussian white noise, r xx (m) is x k The autocorrelation function of .

[0038] As a specific example, the specific steps of S2 are:

[0039] Step S21: using a non-parametric method to estimate the third-order spectrum of the generated autocorrelation sequence;

[0040] Signal high-order spectrum kx (ω1,···,ω k-1 ) is defined as follows:

[0041]

[0042] where c kx (τ1,···,τ k-1 ) is x k The k-order cumulant of ;

[0043] Define the k-1 spectrum of the signal as the k-order spectrum of the signal, so the bispectrum s of the signal 3x (ω1,ω2) is defined as follows:

[0044]

[0045] c 3x (τ1,τ2) is x k The third-order cumulant of

[0046] Step S22: Calculate the autocorrelation sequence r according to the definition of the bispectrum ss The bispectral transformation matrix s;

[0047] The length of the FFT is set to 256, the length of the Rao optimal window function is set to 5, the length of each segment is 250, and the overlap length of each segment is 30, resulting in a 256×256 matrix s:

[0048]

[0049] Among them, c 3r (τ1,τ2) is the third-order cumulative amount of the autocorrelation function r, and s(ω1,ω2) is the cumulative amount of the autocorrelation function r according to c 3r (τ1,τ2) calculated bispectrum.

[0050] As a specific example, the specific steps of S3 are:

[0051] Step S31: Sampling the matrix s obtained by bispectral transformation. The original matrix is 256×256 in dimension. Odd rows are sampled with 1, 3, 5…255 points, and even rows are sampled with 2, 4, 6…256 points. Two 128×128 matrices s are obtained. I 、s Q ;

[0052] Step S32: Use the maximum and minimum normalization to normalize s I 、s Q Preprocess each row to make the value within the range of [0,1]. The specific update process is as follows:

[0053]

[0054]

[0055] in, For sI The i-th row of For s Q The jth row of , i, j∈[1,128]; get the updated matrix s after preprocessing I and s Q ;

[0056] Step S33: I and s Q Splicing is performed in the third dimension to obtain a three-dimensional matrix S of 128×128×2;

[0057] Step S34: Perform the above operations on 5000 samples one by one to construct a four-dimensional matrix Y of 5000×128×128×2 to make a data set.

[0058] As a specific example, the specific steps of S4 are:

[0059] Step S41: Based on the structures of the classic convolutional neural networks LeNet-5 and AlexNet, two branches are constructed for the network model, which are respectively denoted as path I and path II;

[0060] In the two branches, the activation functions used include relu and leakyrelu. The expression of the relu activation function is:

[0061] f(x)=max(0,x)

[0062] The expression of the Leakyrelu activation function is:

[0063] f(x)=max(0,x)+leak*min(0,x)

[0064] Where x is the input of the activation function, and f(x) is the output of the activation function; leak is a very small constant to retain the value of the negative half axis of x, usually around 0.01;

[0065] Step S42: Increase the model depth of path II by adding a fully connected layer; the output dimension of the last fully connected layer of the two branches is 256;

[0066] Step S43: The 256-dimensional vectors output by the two fully connected layers are superimposed, and then passed through the leaky relu activation function, batch normalization layer, dropout layer, and finally through the softmax classifier to output the classification result.

[0067] As a specific example, the specific steps of S5 are:

[0068] Step S51: Create 5000 labels based on the dataset and perform labeled learning through the network; the preprocessed dataset Y is divided into a training set, a validation set, and a test set in a ratio of 3:1:1;

[0069] The pre-training set is input into the network model, and the momentum gradient descent algorithm (Momentum algorithm) is used to update the weights. The parameter update process of the Momentum algorithm is as follows:

[0070]

[0071]

[0072] W←W-αν dw

[0073] b←b-αν db

[0074] where x (i) Collect m samples for the training set {x (1) ,x (2) ,···,x (m)} the i-th data, g is the gradient, v k is the kth update speed, θ k is the kth iteration weight; ε is the learning rate, α is the momentum parameter, the initial learning rate ε is set to 0.001, and the momentum parameter α is set to 0.9; W, b are the weight value and offset of the neural network, ν dw 、ν db The gradient connection between two adjacent steps is established. is the gradient of the loss function with respect to the weights and offsets, α and β are momentum parameters in the algorithm, β is usually set to 0.9, but can also be set to other values;

[0075] The cross entropy loss function is used, which is expressed as follows:

[0076]

[0077] Where M is the number of categories, y i is the true label of the sample, P i is the probability that the sample belongs to the i-th category;

[0078] The batch size of samples selected for one training is set to 64, and the number of sample training epochs is set to 500;

[0079] Step S52: After completing the model training, save the model weights, input the preprocessed test set into the trained model for testing, and output the classification results and recognition accuracy for real-time classification and recognition of communication behaviors.

[0080] As a specific example, step S52 further includes:

[0081] Step S53: Set different signal-to-noise ratio conditions, namely 0dB, 5dB, 8dB, 10dB and 15dB; add corresponding noise to the 5000 samples generated by S1 and create a data set according to the steps of S2 and S3, repeat the experiment, and verify the reliability of the algorithm under noisy conditions.

[0082] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0083] Example

[0084] Combine Figure 1 The present invention proposes a shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics, which achieves the purpose of physical layer signal classification to behavior recognition. The steps are as follows:

[0085] S1. Calculate the autocorrelation function of the time domain signal and obtain the autocorrelation sequence;

[0086] Step S11: According to the five burst waveforms BW0, BW1, BW2, BW3, and BW4 specified in the US military shortwave radio standard MIL-STD-188-141B, MATLAB is used to simulate and generate 1000 signal samples of each of the five burst waveforms. The signals are I and Q signals, and the time series x is generated. k .

[0087] Step S1.2: Find x k The autocorrelation function is defined as:

[0088]

[0089] For the receiving end signal s k , consider the additive white Gaussian noise n k , then s k =x k +n k .

[0090] Define the receiving end signal s k The autocorrelation function r is

[0091]

[0092] in is the variance of Gaussian white noise, r xx (m) is x k The autocorrelation function of . It can be seen that the autocorrelation function can effectively eliminate noise. r is x k The autocorrelation function sequence.

[0093] S2. Perform bispectral transformation on the autocorrelation sequence and calculate the third-order cumulant;

[0094] Step S21: For the generated autocorrelation sequence, estimate its third-order spectrum using a non-parametric method.

[0095] Signal high-order spectrum kx (ω1,···,ω k-1 ) is defined as follows:

[0096]

[0097] where c kx (τ1,···,τ k-1 ) is x k The k-order cumulant of ;

[0098] Define the k-1 spectrum of the signal as the k-order spectrum of the signal, so the bispectrum s of the signal 3x (ω1,ω2) is defined as follows:

[0099]

[0100] Step S22: According to the definition of bispectrum, find the autocorrelation sequence r ss The bispectral transformation matrix s of .

[0101] The length of the FFT is set to 256, the length of the Rao optimal window function is set to 5, the length of each segment is 250, and the overlap length of each segment is 30, resulting in a 256×256 matrix s:

[0102]

[0103] Among them, c 3r (τ1,τ2) is the third-order cumulative amount of the autocorrelation function r, and s(ω1,ω2) is the cumulative amount of the autocorrelation function r according to c 3r (τ1,τ2) calculated bispectrum.

[0104] S3. Sampling the obtained third-order cumulant matrix and converting it into a three-channel format similar to an image to construct a data set;

[0105] Step S31: Sampling the matrix s obtained by bispectral transformation. The original matrix is 256×256 in dimension. Odd rows are sampled with 1, 3, 5…255 points, and even rows are sampled with 2, 4, 6…256 points. Two 128×128 matrices s are obtained. I 、s Q .

[0106] Step S32: Use the maximum and minimum normalization to normalize s I 、s QPreprocess each row to make the value within the range of [0,1]. The specific update process is as follows:

[0107]

[0108]

[0109] in, For s I The i-th row of For s Q The jth row of , i, j∈[1,128]; get the updated matrix s after preprocessing I and s Q .

[0110] Step S33: I and s Q Splicing is performed in the third dimension to obtain a three-dimensional matrix S of 128×128×2.

[0111] Step S34: Perform the above operations on 5000 samples one by one to construct a four-dimensional matrix Y of 5000×128×128×2 to make a data set.

[0112] S4. Design a two-input convolutional neural network model and further improve the model by increasing the model depth, introducing the BatchNormalization layer, and improving the activation function, such as Figure 2 shown.

[0113] Step S41: Based on the structure of the classic convolutional neural network LeNet-5 and AlexNet, two branches are constructed for the network model, which are respectively recorded as path I and path II.

[0114] In the two branches, the activation functions used include relu and leakyrelu. The expression of the relu activation function is:

[0115] f(x)=max(0,x)

[0116] The expression of the Leakyrelu activation function is:

[0117] f(x)=max(0,x)+leak*min(0,x)

[0118] Where x is the input of the activation function and f(x) is the output of the activation function; leak is a very small constant to retain the value of the negative half axis of x, usually around 0.01.

[0119] Step S42: Increase the model depth of path II by adding a fully connected layer. The output dimension of the last fully connected layer of the two branches is 256.

[0120] Step S43: The 256-dimensional vectors output by the two fully connected layers are superimposed, and then passed through the leaky relu activation function, batch normalization layer, dropout layer, and finally through the softmax classifier to output the classification result.

[0121] S5. Input the data set into the network model to complete the training and classification tasks.

[0122] Step S51: Create 5,000 labels based on the dataset and perform labeled learning through the network. The preprocessed dataset Y is divided into a training set, a validation set, and a test set in a ratio of 3:1:1. The pre-trained set is input into the network model and the momentum gradient descent algorithm (Momentum) is used to update the weights. The Momentum algorithm is as follows:

[0123]

[0124]

[0125] W←W-αν dw

[0126] b←b-αν db

[0127] where x (i) Collect m samples for the training set {x (1) ,x (2) ,···,x (m)} the i-th data, g is the gradient, v k is the kth update speed, θ k is the kth iteration weight; ε is the learning rate, α is the momentum parameter, the initial learning rate ε is set to 0.001, and the momentum parameter α is set to 0.9; W, b are the weight value and offset of the neural network, ν dw 、ν db The gradient connection between two adjacent steps is established. is the gradient of the loss function with respect to the weights and offsets, α and β are momentum parameters in the algorithm, β is usually set to 0.9, but can also be set to other values;

[0128] The cross entropy loss function is used, which is expressed as follows:

[0129]

[0130] Where M is the number of categories, y i is the true label of the sample, P i is the probability that the sample belongs to the i-th category.

[0131] In this experiment, the batch size is set to 64 and the epoch is set to 500.

[0132] Step S52: After completing the model training, save the model weights, input the preprocessed test set into the trained model for testing, and output the classification results and recognition accuracy for real-time classification and recognition of communication behavior.

[0133] Step S53: Set different signal-to-noise ratio conditions, namely 0dB, 5dB, 8dB, 10dB, and 15dB. Add corresponding noise to the 5000 samples generated in S1 and create a data set according to steps S2 and S3. Repeat the experiment to verify the reliability of the algorithm under noisy conditions.

[0134] The superiority of the present invention is demonstrated through Experiments 1 to 3.

[0135] In this experiment, MATLAB simulates the physical layer burst waveform and extracts features to create a dataset. The deep learning environment is: Windows 10 operating system, 11th Gen Intel(R) Core(TM) i5-11260H CPU, NVIDIA GeForce RTX3050 graphics card, Python 3.7, TensorFlow 2.5.0, and Keras 2.8.0.

[0136] Experiment 1: Comparative experiment under different signal-to-noise ratio conditions

[0137] The autocorrelation high-order spectrum feature extraction method designed in the present invention can effectively reduce the mailbox caused by noise. In order to verify the effectiveness of the method, this experiment identified the burst waveforms corresponding to five communication behaviors under different signal-to-noise ratio conditions. The test results are shown in Table 1. Figure 3 The relationship diagram of five burst waveforms and communication behaviors is shown in Figure 2. Figure 4a to Figure 4e Signal shaping flow chart for shortwave burst waveforms BW0, BW1, BW2, BW3, and BW4

[0138] Table 1 Recognition results under different signal-to-noise ratio conditions

[0139]

[0140] Experimental results demonstrate that this method performs well. At a signal-to-noise ratio (SNR) of 0dB, the recognition rate for all communication behaviors, except for traffic management behavior (BW1), is over 80%, and the recognition rates for BW0, BW3, and BW4 are over 90%. The feature extraction method proposed in this paper can effectively reduce noise interference and improve recognition accuracy under low SNR conditions.

[0141] Experiment 2: Comparative experiment of different algorithms

[0142] Table 2 Recognition results of different algorithms

[0143]

[0144] Experimental results demonstrate that the proposed denoising method using autocorrelation effectively overcomes the problem of low recognition accuracy under low signal-to-noise ratio conditions. When the signal-to-noise ratio is 15dB, the proposed algorithm has a lower recognition rate than the dual-spectrum amplitude-phase algorithm. This is because the autocorrelation method removes not only noise but also some useful feature information. Since the noise level is relatively low, relatively more feature information is removed, while relatively fewer features are retained. The improvement brought about by noise removal cannot offset the loss of features. Therefore, the proposed method is more suitable for environments with a certain amount of noise.

[0145] Experiment 3: Comparative experiment of different network models

[0146] The present invention designs a dual-input convolutional neural network model, which extracts features through two branches respectively, and superimposes the output through the fully connected layer and then further processes it. In order to verify the improvement of the recognition rate of this model, this experiment selects four network models for comparison. The results are shown in Table 3. Figure 5 shown.

[0147] Table 3 Recognition results of different network models

[0148]

[0149] Table 3 Figure 5 The experimental results show that the dual-input network model used in the present invention can further extract features and improve the recognition rate.

[0150] In summary, the present invention has made optimizations in both feature extraction method and neural network model, which can further improve the recognition effect under low signal-to-noise ratio conditions and is practical.

Claims

1. A shortwave communication behavior recognition method based on autocorrelation high-order spectrum features, characterized in that: Here are the steps: S1. Calculate the autocorrelation function of the time domain signal and obtain the autocorrelation sequence; S2. Perform bispectral transformation on the autocorrelation sequence and calculate the third-order cumulant; S3. Sampling the obtained third-order cumulant matrix and converting it into a three-channel format similar to an image to construct a data set; S4. Design a two-input convolutional neural network model and further improve it by increasing the model depth, introducing the BatchNormalization layer, and improving the activation function to obtain the final network model; S5. Input the data set into the final network model to complete the training and classification tasks; The specific steps of S1 are: Step S11: According to the five burst waveforms BW0, BW1, BW2, BW3, and BW4 specified in the shortwave radio specification MIL-STD-188-141B, MATLAB is used to simulate and generate 1000 signal samples of each of the five burst waveforms. The signals are I and Q signals, and a time series is generated. ; Step S12: The autocorrelation function is defined as: ； For the receiving signal , considering additive Gaussian white noise ,So ; Define the receiving end signal The autocorrelation function for: ； in is the variance of Gaussian white noise, yes The autocorrelation function of The specific steps of S4 are: Step S41: Based on the structures of the classic convolutional neural networks LeNet-5 and AlexNet, two branches are constructed for the network model, which are respectively denoted as path I and path II; Step S42: Increase the model depth of path II by adding a fully connected layer; the output dimension of the last fully connected layer of the two branches is 256; Step S43: The 256-dimensional vectors output by the two fully connected layers are superimposed, and then passed through the leaky relu activation function, batch normalization layer, dropout layer, and finally through the softmax classifier to output the classification result.

2. The shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics according to claim 1 is characterized in that: The specific steps of S2 are: Step S21: using a non-parametric method to estimate the third-order spectrum of the generated autocorrelation sequence; Signal high-order spectrum The definition of is as follows: ； in for The k-order cumulant of ; Define the k-1 spectrum of the signal as the k-order spectrum of the signal, so the bispectrum of the signal The definition is as follows: ； for The third-order cumulant of Step S22: Calculate the autocorrelation sequence according to the definition of the bispectrum The bispectral transformation matrix ; The length of FFT is set to 256, the length of Rao optimal window function is set to 5, the length of each segment is 250, and the overlap length of each segment is 30, resulting in a 256×256 matrix : ； in, is the autocorrelation function above The third-order cumulant of Based on Calculated bispectrum.

3. The shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics according to claim 2 is characterized in that: The specific steps of S3 are: Step S31: transform the matrix obtained by bispectral transformation Sampling is performed. The original matrix is 256×256 in dimension. Odd rows are sampled with 1, 3, 5…255 points, and even rows are sampled with 2, 4, 6…256 points, resulting in two 128×128 matrices. 、 ; Step S32: Use the maximum and minimum normalization to 、 Preprocess each row to make the value within the range of [0,1]. The specific update process is as follows: ； ； in, for No. OK, for No. OK, ; Get the updated matrix after preprocessing and ; Step S33: and Splicing is performed in the third dimension to obtain a three-dimensional matrix of 128×128×2 ; Step S34: Perform the above operations on 5000 samples one by one to construct a 5000×128×128×2 four-dimensional matrix. , and make a data set.

4. The shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics according to claim 3 is characterized in that: In the two branches of step S41, the activation functions used include relu and leakyrelu. The expression of the relu activation function is: ； The expression of the Leakyrelu activation function is: ； in, is the input of the activation function, is the output of the activation function; leak is a constant.

5. The shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics according to claim 4 is characterized in that: The specific steps of S5 are: Step S51: Create 5000 labels based on the dataset and perform labeled learning through the network; the preprocessed dataset Y is divided into a training set, a validation set, and a test set in a ratio of 3:1:1; The pre-training set is input into the network model, and the momentum gradient descent algorithm (Momentum algorithm) is used to update the weights. The parameter update process of the Momentum algorithm is as follows: ； in Collect m samples for the training set The i-th data, is the gradient, is the kth update speed, is the kth iteration weight; is the learning rate, is the momentum parameter, initialize the learning rate Set to 0.001, the momentum parameter Set to 0.9; 、 are the weights and offsets of the neural network, 、 The gradient connection between two adjacent steps is established. 、 is the gradient of the loss function with respect to weights and offsets, 、 is the momentum parameter in the algorithm; The cross entropy loss function is used, which is expressed as follows: ； in is the number of categories, is the true label of the sample, This sample belongs to class probability; The batch size of samples selected for one training is set to 64, and the number of sample training epochs is set to 500; Step S52: After completing the model training, save the model weights, input the preprocessed test set into the trained model for testing, and output the classification results and recognition accuracy for real-time classification and recognition of communication behaviors.

6. The shortwave communication behavior recognition method based on autocorrelation high-order spectrum characteristics according to claim 5 is characterized in that: After step S52, the following steps are also included: Step S53: Set different signal-to-noise ratio conditions, namely 0dB, 5dB, 8dB, 10dB and 15dB; add corresponding noise to the 5000 samples generated by S1 and create a data set according to the steps of S2 and S3, repeat the experiment, and verify the reliability of the algorithm under noisy conditions.

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