An OTFS system signal detection method based on an adaptive wavelet scattering convolutional neural network

Abstract

This invention discloses a signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network, comprising: converting the data symbols to be transmitted to the DD domain, and then obtaining an OTFS signal through an OTFS modulator; the OTFS signal reaching the receiver through a wireless channel; at the receiver, transforming the received signal back to the DD domain using an OTFS demodulator; extracting the real and imaginary signal matrices from the received OTFS signal, performing a three-layer wavelet scattering network transformation on these two matrices to obtain scattering feature coefficients for each layer, concatenating the scattering feature coefficients along the feature channel direction to reconstruct a high-dimensional feature matrix of the signal, and using it as the input to an adaptive wavelet convolutional neural network 2D-AWCNN to obtain the possible values ​​corresponding to each QAM symbol; and performing 16-QAM demodulation on the output of the adaptive wavelet convolutional neural network 2D-AWCNN using a demodulator to obtain the output bits used for signal detection.

Description

Technical Field

[0001] This invention relates to the field of signal detection technology, and in particular to a signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network. Background Technology

[0002] With the rapid development of wireless communication technology, Orthogonal Time-Frequency Space (OTFS) has become an effective solution for data transmission in high-mobility environments, addressing the high-mobility dual-dispersion channel problem. OTFS modulates information symbols in the two-dimensional delayed Doppler domain rather than the time-frequency domain, utilizing full channel diversity in both time and frequency.

[0003] However, in existing OTFS systems, signal detection methods based on algorithms such as message passing (MP) and maximum ratio combining (MRC) have achieved good performance, but in actual wireless communication systems, it is often difficult to obtain accurate channel models and CSI, which inevitably leads to errors in channel estimation.

[0004] In summary, existing OTFS system signal detection methods have the following drawbacks:

[0005] (1) Wireless channels have characteristics such as time delay and Doppler, making it difficult to accurately obtain CSI and establish an analytical channel model;

[0006] (2) For certain special communication scenarios (such as underwater wireless communication), there is currently no unified and analytical channel model for research. Underwater communication is affected by effects such as scattering and absorption, making traditional signal detection methods difficult to apply.

[0007] Therefore, when CSI cannot be accurately obtained, there is an urgent need for a new algorithm to solve the signal detection problem in the above scenario, thereby improving the robustness of the OTFS system in complex communication environments. Summary of the Invention

[0008] Purpose of the invention: To solve the signal detection problem caused by inaccurate channel models, this invention proposes a signal detection method for OTFS systems based on adaptive wavelet scattering convolutional neural networks, which greatly reduces the bit error rate of the system.

[0009] Technical solution: A signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network, comprising the following steps:

[0010] At the transmitting end, the information to be transmitted is modulated using 16-QAM to obtain the data symbol to be transmitted; the data symbol is mapped to the DD domain, and the data symbol mapped to the DD domain is passed through the OTFS modulator to obtain the OTFS signal;

[0011] The OTFS signal reaches the receiving end via a wireless channel;

[0012] At the receiving end, the received signal is converted back to the received signal in the DD domain by the OTFS demodulator;

[0013] At the receiving end, the real part signal matrix and the imaginary part signal matrix are extracted from the received OTFS signal, and these two matrices are transformed by a three-layer wavelet scattering network. First, a low-pass filter is used to extract the low-frequency features of the signal matrix, and then the high-frequency information in the signal is extracted by Morlet wavelet mode transform. The high-frequency information is then processed nonlinearly to obtain the scattering feature coefficients of each layer.

[0014] At the receiving end, the scattering feature coefficients of each layer are concatenated along the feature channel direction to reconstruct the high-dimensional feature matrix of the signal, which is then used as the input to the adaptive wavelet convolutional neural network 2D-AWCNN. The adaptive wavelet convolutional module AWCM with self-learning characteristics is used as the first convolutional layer of 2D-AWCNN. The scaling factor and translation factor parameters in the adaptive wavelet convolutional module AWCM with self-learning characteristics are iteratively updated by subtracting the product of the learning rate γ and the gradient δ. The second and third convolutional layers use traditional convolutional kernels, and the parameters are further detected by the backpropagation algorithm. Finally, the possible values ​​corresponding to each QAM symbol are obtained.

[0015] At the receiving end, the output of the adaptive wavelet convolutional neural network 2D-AWCNN is demodulated using a demodulator in 16-QAM mode to obtain the output bits used for signal detection.

[0016] Furthermore, the process of mapping the data symbol to the DD domain and then using the DD domain-mapped data symbol to obtain an OTFS signal via an OTFS modulator includes the following specific operations:

[0017] Mapping M×N data symbols onto the DD domain signal grid, where N and M represent the time delay and Doppler dimensions respectively, yields the signal in the time-delay Doppler domain, represented as: x[k,l], k=0,1,2,...,N-2,N-1, l=0,1,2,...,M-2,M-1; k and l represent the indices of the time delay domain and the Doppler domain respectively;

[0018] The time-delay Doppler domain signal x[k,l] is converted to the TF domain by ISFFT to obtain the TF domain signal, which is represented as:

[0019]

[0020] In the formula, X[n,m] represents the TF domain signal, n and m represent the time-frequency domain index, n=0,1,2,…,N-2,N-1,m=0,1,2,…,M-2,M-1,j is the imaginary unit, e represents the exponential function, and π is a constant;

[0021] The TF domain signal X[n,m] is converted into a continuous time-domain transmitted signal s(t), i.e., an OTFS signal, using the Heisenberg transform, as follows:

[0022]

[0023] In the formula, T represents the duration of the symbol, and g tx (·) represents the shaping filter function for the transmitted pulse, and Δf represents the frequency interval.

[0024] Furthermore, the OTFS signal reaches the receiving end via a wireless channel, where the following signal r(t) is received:

[0025] r(t)=∫ v ∫ τ h(τ,v)s(tv)e j2πv(t-v) dτdv+n(t)

[0026] in,

[0027] In the formula, n(t) represents noise, h(τ,v) is the DD domain channel response, reflecting the signal propagation in the time-delay-Doppler domain. There are a total of P paths in the DD domain channel, where the channel amplitude response of the Pth path is β. P In the time delay domain and the Doppler domain, the impulse function δ(τ-τ) is used respectively. i ) and δ(vv i The focal point of the signal is represented by τ, where τ and v represent the time delay and Doppler shift, respectively.

[0028] Delay τ i and Doppler frequency shift v i The characteristics corresponding to the i-th path are expressed as:

[0029]

[0030] Where, τ i v represents the delay of the i-th path. i This indicates an integer multiple of Doppler offset.

[0031] Furthermore, at the receiving end, the received signal is converted back to the received signal in the DD domain using an OTFS demodulator. Specific operations include:

[0032] The signal r(t) is compared with the pulse-shaped waveform g. rx (t) Perform matched filtering and calculate the received signal in the time-frequency domain according to the following formula:

[0033]

[0034] In the formula, Represents the cross-fuzzy function. Let t' represent the matched filter function, and t' represent the integration variable;

[0035] The time-frequency received signal Y(t,f) is sampled at intervals of t = nT and f = mΔf to obtain a discrete time-frequency received signal, which is expressed as:

[0036]

[0037] By processing the discrete time-frequency domain received signal Y[n,m] using SFFT, the received signal y[k,l] in the D domain is obtained, expressed as:

[0038]

[0039] Furthermore, at the receiving end, the real and imaginary signal matrices of the received OTFS signal are extracted respectively, and these two matrices are subjected to a three-layer wavelet scattering network transform. First, low-pass filters are used to extract the low-frequency features of the signal matrix, and then Morlet wavelet mode transform is used to extract the high-frequency information in the signal. The high-frequency information is then subjected to nonlinear processing to obtain the scattering feature coefficients of each layer. The specific operations include:

[0040] Y represents the matrix form of the received signal y[k,l], denoted as The real and imaginary parts of the signal are extracted separately to obtain two matrices. and The real and imaginary signal matrices are respectively filtered by a low-pass filter φ. J To extract the low-frequency features of the signal matrix, it is represented as:

[0041] S0Y real =Y real *τ J

[0042] S0Y imag =Y imag *φ J

[0043] In the formula, * denotes the convolution operation;

[0044] High-frequency information in the signal is extracted using Morlet wavelet modulus transform. For each convolution result, modulus operation |·| is applied, followed by a result of size 2. JThe first-order scattering coefficients are obtained by taking the local mean of the downsampled low-pass filter, and are expressed as:

[0045]

[0046] in, Let λ represent the Morlet wavelet basis function, λ1 represent the parameters controlling the scale and position, i represent the index used to identify the wavelet function at different scales, and J represent the current decomposition level.

[0047] The high-frequency information is processed nonlinearly to extract the second-order scattering coefficient S2Y, which is expressed as:

[0048]

[0049] in, λ represents the Morlet wavelet basis function used in the wavelet transform, λ2 represents the parameter controlling the scale and position, and j represents the index used to identify the wavelet function at different scales.

[0050] Furthermore, at the receiving end, the scattering characteristic coefficients of each layer are spliced ​​along the characteristic channel direction to reconstruct the high-dimensional characteristic matrix of the signal, which is expressed as:

[0051] SY real =[S0Y real S1Y real S2Y real ]

[0052] SY imag =[S0Y imag S1Y imag S2Y imag ]

[0053]

[0054] [] indicates a splicing operation.

[0055] Furthermore, the adaptive wavelet convolutional neural network 2D-AWCNN includes an input layer, a first adaptive wavelet convolutional layer, a second convolutional layer, a third convolutional layer, an activation function layer, a batch normalization layer, a pooling layer, a flattening layer, a fully connected layer, and an output layer.

[0056] Use the high-dimensional feature matrix of the signal as input;

[0057] In the first layer of adaptive wavelet convolution, the scaling factor and translation factor of the adaptive wavelet convolution module AWCM with self-learning characteristics are set as learnable parameters, and the corresponding wavelet convolution kernel is reduced from 64 to 32, using 32 3×3 convolution kernels. The parameters are iteratively updated by subtracting the product of the learning rate γ and the gradient δ.

[0058] The second convolutional layer uses 128 traditional 3×3 convolutional kernels;

[0059] The third convolutional layer uses 256 traditional 3×3 convolutional kernels; the weight parameters in the traditional convolutional kernels are trained using the backpropagation algorithm.

[0060] Apply the ReLU activation function after each convolutional layer;

[0061] In the pooling layer, a 2×2 pooling window and a stride of 2 are used to reduce the size of the feature map;

[0062] In the flattening layer, multidimensional convolutional feature maps are converted into one-dimensional vectors;

[0063] The number of neurons in the output node is set in the fully connected layer;

[0064] Finally, the network output layer has a number of neurons corresponding to the number of 16-QAM modulation symbols, and the output layer outputs the possible values ​​for each QAM symbol.

[0065] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0066] (1) The method of the present invention optimizes the convolutional neural network by combining the feature extraction capability of wavelet scattering network and replacing the first traditional convolutional layer with an adaptive wavelet convolution module. While ensuring efficient feature extraction, the system can reduce computational complexity and maintain good bit error rate performance in multipath fading environment.

[0067] (2) The method of the present invention provides lower time and space complexity in high-speed mobile scenarios, and improves the signal detection accuracy and robustness of the OTFS system. Attached Figure Description

[0068] Figure 1 This is a flowchart of an OTFS system signal detection method based on an adaptive wavelet scattering convolutional neural network proposed in this invention;

[0069] Figure 2 This is a block diagram of wavelet scattering transform;

[0070] Figure 3 Diagram of the adaptive wavelet scattering convolutional neural network architecture;

[0071] Figure 4 Diagram of the Adaptive Wavelet Convolutional (AWCM) module;

[0072] Figure 5 This is a diagram of the CONV module for a convolutional layer. Detailed Implementation

[0073] The technical solution of this embodiment will now be further described with reference to the accompanying drawings.

[0074] like Figure 1 As shown in the figure, this embodiment proposes a signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network, which mainly includes the following steps:

[0075] Step 1: Modulate the information to be transmitted using 16-QAM to obtain the data symbols to be transmitted; map the data symbols to the DD domain, obtain the OTFS signal through the OTFS modulator, and reach the receiving end through the wireless channel. The receiving end converts the OTFS signal back to the DD domain through the OTFS demodulator.

[0076] In step 1, the data symbols are mapped to the DD domain, the OTFS signal is obtained through the OTFS modulator, and then reaches the receiver via the wireless channel, including:

[0077] S1_1: Map M×N data symbols to the DD domain signal grid to obtain the DD domain signal, represented as: x[k,l], k=0,1,2,...,N-2,N-1, l=0,1,2,...,M-2,M-1;

[0078] S1_2: The DD domain signal x[k,l] is transformed to the TF domain by ISFFT to obtain the TF domain signal, which is represented as:

[0079]

[0080] In the formula, X[n,m] represents the TF time-frequency domain signal, N and M represent the size of the time delay and Doppler dimension, respectively, n and m are the time-frequency domain indices, n = 0, 1, 2, ..., N-2, N-1, m = 0, 1, 2, ..., M-2, M-1, x[k,l] represents the time-delay Doppler domain signal, k and l represent the indices of the time delay domain and Doppler domain, respectively, j is the imaginary unit, e represents the exponential function, and π is a constant.

[0081] S1_3: After obtaining the TF time-frequency domain signal X[n,m], the Heisenberg transform is used to convert X[n,m] into a continuous time-domain transmitted signal s(t), i.e., the OTFS signal, expressed as:

[0082]

[0083] In the formula, T represents the duration of the symbol, and g tx (·) represents the shaping filter function for the transmitted pulse, and Δf represents the frequency interval.

[0084] S1_4: The time-domain transmitted signal s(t) arrives at the receiver after passing through the wireless channel, and the receiver receives the following signal r(t):

[0085] r(t)=∫ v ∫ τ h(τ,v)s(tv)e j2πv(t-v) dτdv+n(t)

[0086] in,

[0087] In the formula, n(t) represents noise, and h(τ,v) is the channel response in the DD domain, reflecting the signal propagation in the time-delay-Doppler domain. The channel has a total of P paths, where the channel amplitude response of the Pth path is β. P In the time delay domain and the Doppler domain, the impulse function δ(τ-τ) is used respectively. i ) and δ(vv i The focal point of the signal is represented by τ, where τ and v represent the time delay and Doppler shift, respectively.

[0088] Delay τ i and Doppler frequency shift v i The characteristics corresponding to the i-th path are expressed as:

[0089]

[0090] Where, τ i v is used to represent the delay of the i-th path. i The integer part represents an integer multiple of the Doppler shift, while the fractional part reflects the shift relative to the most recent Doppler shift.

[0091] S1_5: Combine the received signal r(t) with the pulse shaping waveform g at the receiving end. rx (t) is subjected to matched filtering to obtain the received data. The time-frequency domain received signal is calculated using the following formula:

[0092]

[0093] In the formula, Represents the cross-fuzzy function. Let t' represent the matched filter function, and t' represent the integration variable.

[0094] S1_6: After the OTFS signal passes through the wireless channel, it is demodulated by the OTFS demodulator to obtain the OTFS symbol frame in the DD domain;

[0095] Then, Y(t,f) is sampled at intervals of t = nT and f = mΔf to obtain the discrete time-frequency domain received signal. This step is called the Wegener transform, and is expressed as:

[0096]

[0097] Finally, SFFT is used to process the received signal Y[n,m] in the TF domain to obtain the received signal y[k,l] in the DD domain, which is represented as:

[0098]

[0099] Based on the derivation of the signal processing flow at the transmitting and receiving ends of the OTFS system, the input-output relationship of the signal in the time delay-Doppler domain can be expressed by the following formula:

[0100] y = Hx + n

[0101] In the formula, y, H represents the equivalent channel, and n represents additive white noise.

[0102] Step 2: Feature extraction of the OTFS received signal using wavelet scattering network transform. The real part signal matrix is ​​extracted from the received signal. and imaginary part signal matrix These two matrices are used as data for two channels, and each channel undergoes a wavelet scattering network transform, which serves as the input to the wavelet scattering transform, as follows:

[0103]

[0104] Step 3: Perform wavelet scattering network transform on both channels respectively. The general process is as follows:

[0105] S3_1: Use a low-pass filter φ J Convolution is performed on the input signal to extract low-frequency features, which is represented as:

[0106] S0Y real =Y real *φ J

[0107] S0Y imag =Y imag *φ J

[0108] High-frequency information is extracted from the signal using Morlet wavelet modulus transform. This high-frequency information is then nonlinearly processed to obtain scattering characteristic coefficients. Therefore, to obtain the translation-invariant portion of |Y*ψ|, modulus operation is used to nonlinearly activate the convolution result, removing negative values ​​and highlighting frequency features. For each convolution result, the modulus operation |·| is applied, requiring a step size of 2... J The first-order scattering coefficients are obtained by taking the local mean of the downsampled low-pass filter. The formula for the convolution operation is:

[0109]

[0110] Where, φ JFor low-pass filters, * indicates convolution operation. This represents the Morlet wavelet basis function used in the wavelet transform. λ1 mainly controls the scale and position, i is used to identify the index of the wavelet function at different scales, and J is the current decomposition level to reduce data dimensionality.

[0111] S3_2: Further nonlinear operations and downsampling are performed on the high-frequency signals in the signal to extract low-frequency features, obtaining the second-order scattering coefficient S2Y, thus obtaining higher-order features, expressed as:

[0112]

[0113] in, This represents the Morlet wavelet basis functions used in the wavelet transform. λ2 mainly controls the scale and position, and j is used to identify the index of the wavelet function at different scales.

[0114] S3_3: The two channel signals are transformed by a three-layer wavelet scattering network to obtain the output wavelet scattering characteristic coefficients SY of each layer. real and SY imag The scattering characteristic coefficients of each layer's output are spliced ​​along the characteristic channel direction to reconstruct the high-dimensional characteristic matrix SY of the signal, which is represented as:

[0115] SY real =[S0Y real S1Y real S2Y real ]

[0116] SY imag =[S0Y imag S1Y imag S2Y imag ]

[0117]

[0118] [] indicates a splicing operation.

[0119] In this embodiment, the 2D-AWCNN model is trained using a frame size of N×M, and the adaptive wavelet convolution module is used as the first convolutional layer of the convolutional neural network. The second and third traditional convolutional layers use a "same" padding mode and a stride of 1, thus ensuring consistent input and output shapes for each layer. In each CNN layer, the filter (f... cn Relevant features are extracted from the input data through element-wise operations. Subsequently, batch normalization is used to standardize the obtained input data to improve the stability of the model and the training effect.

[0120] Step 4: Concatenate the scattering feature coefficients of each layer's output along the feature channel direction to reconstruct the high-dimensional feature matrix SY of the signal. Use this as the input to the 2D-AWCNN (Adaptive Wavelet Convolutional Neural Network). The Adaptive Wavelet Convolutional Module (AWCM) is used as the first convolutional layer of the 2D-AWCNN. The convolutional kernel is optimized using adaptive learning scaling and translation factors. The scaling and translation factors in the AWCM are iteratively updated by subtracting the product of the learning rate γ and the gradient δ. The second and third convolutional layers use traditional convolutional kernels, and the parameters are further processed by backpropagation to detect the signal, ultimately obtaining the possible values ​​for each QAM symbol. In this step, the accuracy of symbol detection is improved by optimizing the convolutional network parameters using an adaptive Morlet wavelet basis. Specific operations include:

[0121] The 2D-AWCNN network is trained using the Adam optimizer for stochastic gradient descent (SGD). This adaptive wavelet convolutional neural network 2D-AWCNN consists of: an input layer, a first adaptive wavelet convolutional layer, a second convolutional layer, a third convolutional layer, an activation function layer, a batch normalization layer, a pooling layer, a flattening layer, a fully connected layer, and an output layer.

[0122] In the input layer, the input is the reconstructed high-dimensional signal feature matrix SY, with a shape of N'×M'×C'.

[0123] The first convolutional layer uses an adaptive wavelet convolutional module (AWCM) with self-learning properties. The scaling and translation factors of the Morlet wavelet convolution kernel are set as learnable parameters, while the rotation angles are kept fixed at four main orientation angles: 0°, 90°, 180°, and 270°. The scaling and translation factors are initialized at each orientation angle, with the training scaling factor d taking values ​​of 1, 1 / 2, 1 / 4, and 1 / 8, and the corresponding translation factors s1 and s2 taking values ​​of -1 and 1, respectively. During backpropagation, these factors are iteratively updated as learnable parameters by subtracting the product of the learning rate γ and the gradient δ during network training. Due to the self-learning properties of the scaling and translation factors in 2D-AWCNN, the corresponding wavelet convolution kernels are reduced from 64 to 32, using 32 3×3 convolution kernels to extract low-level features from the input data.

[0124] The second convolutional layer uses 128 3×3 convolutional kernels to further extract deeper features.

[0125] The third convolutional layer uses 256 3×3 convolutional kernels to further extract deeper features.

[0126] A ReLU activation function is applied after each convolutional layer to introduce non-linear features.

[0127] Batch normalization layers are used to accelerate the training process, stabilize network training, and reduce the vanishing gradient problem.

[0128] In the pooling layer, the size of the feature map is reduced by using a 2×2 pooling window and a stride of 2, which preserves the most important features and reduces the amount of computation.

[0129] The flattening layer converts the multidimensional convolutional feature map into a one-dimensional vector, ready for further processing in the fully connected layer.

[0130] The fully connected layer has 256 neurons and is responsible for processing the high-level features obtained after convolution and pooling.

[0131] The output layer has a number of neurons corresponding to the number of 16-QAM modulation symbols. Typically, there are 16 output nodes, each corresponding to a possible value for a QAM symbol.

[0132] During training, the scaling and translation factors in the Adaptive Wavelet Convolutional Module (AWCM) are iteratively updated by subtracting the product of the learning rate γ and the gradient δ. The second and third convolutional layers use backpropagation to update the training parameters. Using the Adam optimizer for stochastic gradient descent (SGD) to self-adjust the learning rate based on the gradient information of each parameter typically demonstrates good training performance and stability.

[0133] Mean squared error (MSE) is used during network training to measure the error between the network output and the actual symbols:

[0134]

[0135] In the formula, X i Symbols representing actual transmission, Let f(SY;θ) represent the symbols obtained through network training, m represent the number of samples in the training dataset, θ represent the parameters of the neural network (weights and biases), and f(SY;θ) represent a function that depends on the input and network parameters and generates the predicted values.

[0136] The Adam optimizer optimizes network parameters through backpropagation and gradient descent. In each training round, the Adam optimizer updates all network parameters according to the backpropagation algorithm. As the first layer of the model structure, the AWCM (Advanced Layout Computation Model) iteratively updates the scaling and translation factors during the backpropagation of the 2D-AMCNN network model by subtracting the product of the learning rate γ and the gradient δ, thus enabling the network to gradually improve the accuracy of symbol detection. The Adam optimizer combines momentum and adaptive learning rates, applying different learning rates to each parameter, making the optimization process more stable.

[0137] The network output is the symbol detection result used to generate the target signal. The symbol is demodulated by a 16-QAM demodulator, and the network output is mapped to the output bits used for signal detection.

[0138] The above method addresses the issues of incomplete channel information and channel modeling in future communication scenarios. Using a deep learning network based on wavelet scattering feature extraction and its application to adaptive wavelet convolution, the signal detection algorithm in this invention does not rely on CSI. Instead, it directly extracts features from the received signal after passing through the OTFS system by first performing wavelet scattering network transformation, and then uses adaptive wavelet basis optimization to train the convolutional neural network to recover the input signal. Compared with other existing signal detection schemes, this invention aims to achieve superior signal detection performance and better bit error rate performance in high-mobility communication scenarios with lower time and space complexity.

Claims

1. A signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network, characterized in that: Includes the following steps: At the transmitting end, the information to be transmitted is modulated using 16-QAM to obtain the data symbols to be transmitted; The data symbol is mapped to the DD domain, and the data symbol mapped to the DD domain is passed through an OTFS modulator to obtain an OTFS signal; The OTFS signal reaches the receiving end via a wireless channel; At the receiving end, the received signal is converted back to the received signal in the DD domain by the OTFS demodulator; At the receiving end, the real part signal matrix and the imaginary part signal matrix are extracted from the received OTFS signal, and these two matrices are transformed by a three-layer wavelet scattering network. First, low-pass filters are used to extract the low-frequency features of the signal matrix, and then Morlet wavelet mode transform is used to extract the high-frequency information in the signal. The high-frequency information is then processed nonlinearly to obtain the scattering feature coefficients of each layer. At the receiving end, the scattering feature coefficients of each layer are concatenated along the feature channel direction to reconstruct the high-dimensional feature matrix of the signal, which is then used as the input to the adaptive wavelet convolutional neural network 2D-AWCNN. The adaptive wavelet convolutional module AWCM with self-learning characteristics is used as the first convolutional layer of 2D-AWCNN. The scaling factor and translation factor parameters in the adaptive wavelet convolutional module AWCM with self-learning characteristics are iteratively updated by subtracting the product of the learning rate γ and the gradient δ. The second and third convolutional layers use traditional convolutional kernels, and the parameters are further detected by the backpropagation algorithm. Finally, the possible values ​​corresponding to each QAM symbol are obtained. At the receiving end, the output of the adaptive wavelet convolutional neural network 2D-AWCNN is demodulated using a demodulator in 16-QAM mode to obtain the output bits used for signal detection.

2. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 1, characterized in that: The process of mapping the data symbols to the DD domain and then using the DD domain-mapped data symbols to obtain the OTFS signal via an OTFS modulator includes the following specific operations: Mapping M×N data symbols onto the DD domain signal grid, where N and M represent the time delay and Doppler dimensions respectively, yields the signal in the time-delay Doppler domain, represented as: x[k, l], k = 0, 1, 2, ..., N-2, N-1, l = 0, 1, 2, ..., M-2, M-1; k and l represent the indices of the time delay domain and the Doppler domain respectively; The time-delay Doppler domain signal x[k,l] is converted to the TF domain by ISFFT to obtain the TF domain signal, which is represented as: In the formula, X[n, m] represents the TF domain signal, n and m represent the time-frequency domain index, n = 0, 1, 2, ..., N-2, N-1, m = 0, 1, 2, ..., M-2, M-1, j is the imaginary unit, e represents the exponential function, and π is a constant; The TF domain signal X[n, m] is converted into a continuous time-domain transmitted signal s(t), i.e., an OTFS signal, using the Heisenberg transform, as follows: In the formula, T represents the duration of the symbol, and g tx (·) represents the shaping filter function for the transmitted pulse, and Δf represents the frequency interval.

3. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 2, characterized in that: The OTFS signal reaches the receiving end via a wireless channel, where the following signal r(t) is received: r(t)=∫ v ∫ τ h(τ,v)s(t-v)e j2πv(t-v) dτdv+n(t) in, In the formula, n(t) represents noise, h(τ, v) is the DD domain channel response, reflecting the signal propagation in the time-delay-Doppler domain. There are a total of P paths in the DD domain channel, where the channel amplitude response of the Pth path is β. P In the time delay domain and the Doppler domain, the impulse function δ(τ-τ) is used respectively. i ) and δ(vv i The focal point of the signal is represented by τ, and the time delay and Doppler shift are represented by v, respectively. Delay τ i and Doppler frequency shift v i The characteristics corresponding to the i-th path are expressed as: Where, τ i v represents the delay of the i-th path. i This indicates an integer multiple of Doppler offset.

4. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 3, characterized in that: At the receiving end, the received signal is converted back to the received signal in the DD domain using an OTFS demodulator. The specific operations include: The signal r(t) is compared with the pulse-shaped waveform g. rx (t) Perform matched filtering and calculate the received signal in the time-frequency domain according to the following formula: In the formula, Represents the cross-fuzzy function. Let t' represent the matched filter function, and t' represent the integration variable; The time-frequency received signal Y(t, f) is sampled at intervals of t = nT and f = mΔf to obtain a discrete time-frequency received signal, which is expressed as: By processing the discrete time-frequency domain received signal Y[n, m] using SFFT, the received signal y[k, l] in the D domain is obtained, expressed as:

5. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 4, characterized in that: At the receiving end, the real and imaginary signal matrices of the received OTFS signal are extracted, and these two matrices are subjected to a three-layer wavelet scattering network transform. First, low-pass filters are used to extract the low-frequency features of the signal matrix, and then Morlet wavelet mode transform is used to extract the high-frequency information in the signal. The high-frequency information is then subjected to nonlinear processing to obtain the scattering feature coefficients for each layer. Specific operations include: Y represents the matrix form of the received signal y[k, l], denoted as The real and imaginary parts of the signal are extracted separately to obtain two matrices. and The real and imaginary signal matrices are respectively filtered by a low-pass filter φ. J To extract the low-frequency features of the signal matrix, it is represented as: I AM real And real *φ J I AM imag And imag *φ J In the formula, * represents the convolution operation; High-frequency information in the signal is extracted using Morlet wavelet modulus transform. For each convolution result, modulus operation |·| is applied, followed by a result of size 2. J The first-order scattering coefficients are obtained by taking the local mean of the downsampled low-pass filter, and are expressed as: in, Let λ represent the Morlet wavelet basis function, λ1 represent the parameters controlling the scale and position, i represent the index used to identify the wavelet function at different scales, and J represent the current decomposition level. The high-frequency information is processed nonlinearly to extract the second-order scattering coefficient S2Y, which is expressed as: in, λ represents the Morlet wavelet basis function used in the wavelet transform, λ2 represents the parameter controlling the scale and position, and j represents the index used to identify the wavelet function at different scales.

6. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 5, characterized in that: At the receiving end, the high-dimensional feature matrix of the signal is reconstructed by stitching together the scattering feature coefficients of each layer along the feature channel direction, as shown below: AND real =[S0Y real ,S1Y real ,S2Y real ] AND imag =[S0Y imag ,S1Y imag ,S2Y imag ] [] indicates a splicing operation.

7. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 6, characterized in that: The adaptive wavelet convolutional neural network 2D-AWCNN includes an input layer, a first adaptive wavelet convolutional layer, a second convolutional layer, a third convolutional layer, an activation function layer, a batch normalization layer, a pooling layer, a flattening layer, a fully connected layer, and an output layer. Use the high-dimensional feature matrix of the signal as input; In the first layer of adaptive wavelet convolution, the scaling factor and translation factor of the adaptive wavelet convolution module AWCM with self-learning characteristics are set as learnable parameters, and the corresponding wavelet convolution kernel is reduced from 64 to 32, using 32 3×3 convolution kernels. The parameters are iteratively updated by subtracting the product of the learning rate γ and the gradient δ. The second convolutional layer uses 128 traditional 3×3 convolutional kernels; The third convolutional layer uses 256 traditional 3×3 convolutional kernels; the weight parameters in the traditional convolutional kernels are trained using the backpropagation algorithm. Apply the ReLU activation function after each convolutional layer; In the pooling layer, a 2×2 pooling window and a stride of 2 are used to reduce the size of the feature map; In the flattening layer, multidimensional convolutional feature maps are converted into one-dimensional vectors; The number of neurons in the output node is set in the fully connected layer; Finally, the network output layer has a number of neurons corresponding to the number of 16-QAM modulation symbols, and the output layer outputs the possible values ​​corresponding to each QAM symbol.

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