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

Abstract

The invention discloses an OTFS system signal detection method based on an adaptive wavelet scattering convolutional neural network, and the method comprises the steps: converting a to-be-transmitted data symbol to a DD domain, and obtaining an OTFS signal through an OTFS modulator; the OTFS signal reaches a receiving end through a wireless channel; at a receiving end, converting the received signal back to a receiving signal of a DD domain through an OTFS demodulator; the method comprises the following steps: respectively extracting a real part signal matrix and an imaginary part signal matrix from a received OTFS signal, respectively carrying out three-layer wavelet scattering network transformation on the two matrixes to obtain a scattering characteristic coefficient of each layer, splicing the scattering characteristic coefficients of each layer along a characteristic channel direction to reconstruct a signal high-dimensional characteristic matrix, and carrying out three-layer wavelet scattering network transformation on the reconstructed signal high-dimensional characteristic matrix; taking the data as the input of a self-adaptive wavelet convolutional neural network 2D-AWCNN to obtain a possible value corresponding to each QAM symbol; and 16-QAM demodulation is carried out on the output of the adaptive wavelet convolutional neural network 2D-AWCNN through a demodulator to obtain an output bit for signal detection.

Description

Technical Field

[0001] The present invention relates to the technical field of signal detection, and particularly relates to a signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network. Background Art

[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, used to solve the problem of high-mobility double-dispersion channels. OTFS modulates information symbols in the two-dimensional delay-Doppler domain rather than the time-frequency domain, and can utilize the full channel diversity of time and frequency.

[0003] However, in existing OTFS systems, signal detection methods based on algorithms such as Message Passing (MP) and Maximal Ratio Combining (MRC), although achieving good performance, often have difficulty obtaining an accurate channel model and CSI in an actual wireless communication system, resulting in inevitable errors in channel estimation.

[0004] Generally speaking, the existing signal detection methods for OTFS systems have the following defects:

[0005] (1) The wireless channel has characteristics such as time delay and Doppler, making it difficult to accurately obtain CSI and establish an analytic channel model;

[0006] (2) For some special communication scenarios (such as underwater wireless communication), there is currently no unified and analytic 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, in the case where CSI cannot be accurately obtained, there is an urgent need for a new algorithm to solve the signal detection problem in the above scenarios, thereby improving the robustness of the OTFS system in complex communication environments. Summary of the Invention

[0008] Object of the Invention: To solve the signal detection problem caused by an inaccurate channel model, the present invention proposes a signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network, 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 includes the following steps:

[0010] At the transmitting end, the information to be transmitted is modulated by 16-QAM to obtain the data symbols to be sent; the data symbols are mapped to the DD domain, and the data symbols mapped to the DD domain are used by an OTFS modulator to obtain an OTFS signal;

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

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

[0013] At the receiving end, the real part signal matrix and the imaginary part signal matrix are respectively extracted from the received OTFS signal, and three-layer wavelet scattering network transforms are respectively performed on these two matrices; first, low-pass filters are respectively used to extract the low-frequency features of the signal matrix, and then the high-frequency information in the signal is extracted through Morlet wavelet modulus transformation, and the high-frequency information is non-linearly processed to obtain the scattering feature coefficients of each layer;

[0014] At the receiving end, the scattering feature coefficients of each layer are spliced along the feature channel direction to reconstruct the high-dimensional feature matrix of the signal, which is used as the input of 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 dilation 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 from the convolutional kernel. The second and third convolutional layers use traditional convolutional kernels, and the parameters are used for further signal detection by the backpropagation algorithm. Finally, the possible values corresponding to each QAM symbol are obtained;

[0015] At the receiving end, 16-QAM demodulation is performed on the output of the adaptive wavelet convolutional neural network 2D-AWCNN by a demodulator to obtain the output bits for signal detection.

[0016] Further, the operation of mapping the data symbols to the DD domain and using the OTFS modulator to obtain an OTFS signal from the data symbols mapped to the DD domain specifically includes:

[0017] M×N data symbols are mapped to the DD domain signal grid, where N and M respectively represent the sizes of the time delay and Doppler dimensions, to obtain the signal in the time delay-Doppler domain, denoted as: x[k, l], k = 0, 1, 2,..., N - 2, N - 1, l = 0, 1, 2,..., M - 2, M - 1; k and l respectively represent the indices in the time delay domain and the Doppler domain;

[0018] The signal x[k, l] in the time delay-Doppler domain is transformed to the TF domain through ISFFT to obtain the TF domain signal, denoted as:

[0019]

[0020] Wherein, X[n, m] represents the TF-domain signal, n and m represent the time-frequency domain indices, 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) by using the Heisenberg transform, that is, the OTFS signal, which is expressed as:

[0022]

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

[0024] Furthermore, the OTFS signal reaches the receiving end through the wireless channel, and the following signal r(t) is received at the receiving end:

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

[0026] Wherein,

[0027] Wherein, n(t) represents the noise, h(τ, v) is the DD-domain channel response, which reflects the propagation of the signal in the delay-Doppler domain. There are a total of P paths in the DD-domain channel, and the channel amplitude response of the Pth path is β P , in the delay domain and the Doppler domain, the impulse functions δ(τ - τ i ) and δ(v - v i ) are used to represent the concentrated positions of the signal, and τ and v represent the delay and the Doppler frequency shift respectively;

[0028] The delay τ i and the Doppler frequency shift v i correspond to the characteristics of the ith path, which are expressed as:

[0029]

[0030] Wherein, τ i represents the delay of the ith path, and v i represents the integer multiple Doppler shift.

[0031] Furthermore, at the receiving end, the received signal is transformed back into the received signal in the DD domain through the OTFS demodulator. The specific operations include:

[0032] Match filter the signal r(t) with the pulse shaping waveform g rx (t), and calculate the received signal in the time-frequency domain according to the following formula:

[0033]

[0034] wherein, represents the cross ambiguity function, represents the matched filter function, and t′ represents the integration variable;

[0035] Sample the received signal Y(t,f) in the time-frequency domain at intervals of t = nT, f = mΔf to obtain the discrete received signal in the time-frequency domain, denoted as:

[0036]

[0037] Process the discrete received signal Y[n,m] in the time-frequency domain using SFFT to obtain the received signal y[k,l] in the DD domain, denoted as:

[0038]

[0039] Furthermore, at the receiving end, the received OTFS signal is respectively extracted into a real part signal matrix and an imaginary part signal matrix, and these two matrices are respectively subjected to a three-layer wavelet scattering network transformation; first, a low-pass filter is respectively used to extract the low-frequency characteristics of the signal matrix, and then the high-frequency information in the signal is extracted through the Morlet wavelet modulus transformation, and the high-frequency information is non-linearly processed to obtain the scattering characteristic coefficients of each layer. The specific operations include:

[0040] Y represents the matrix form of the received signal y[k,l], denoted as and the real and imaginary parts of its signal are respectively extracted to obtain two matrices and The real part signal matrix and the imaginary part signal matrix are respectively used with the low-pass filter φ J to extract the low-frequency characteristics of the signal matrix, denoted as:

[0041] S 0 Y real = Y real * τ J

[0042] S 0 Y imag = Y imag * φ J

[0043] wherein, * represents the convolution operation;

[0044] Extract the high-frequency information in the signal through the Morlet wavelet modulus transformation. For each convolution result, apply the modulus operation |·|, and take the local mean of the low-pass filter with a downsampling factor of 2 J to obtain the first-order scattering coefficient, which is expressed as:

[0045]

[0046] where represents the Morlet wavelet basis function, λ 1 represents the parameter for controlling the scale and position, i represents the index for identifying the wavelet functions at different scales, and J represents the current decomposition level;

[0047] Perform non-linear processing on the high-frequency information to extract the second-order scattering coefficient S 2 Y, which is expressed as:

[0048]

[0049] where represents the Morlet wavelet basis function used in the wavelet transform, λ 2 represents the parameter for controlling the scale and position, and j represents the index for identifying the wavelet functions at different scales.

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

[0051] SY real =[S 0 Y real ,S 1 Y real ,S 2 Y real

[0052] SY imag =[S 0 Y imag ,S 1 Y imag ,S 2 Y imag

[0053]

[0054] where [] represents the 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] Take the signal high-dimensional feature matrix as the input;

[0057] For the first-layer adaptive wavelet convolutional layer, set the dilation factor and translation factor of the adaptive wavelet convolutional module AWCM with self-learning characteristics as learnable parameters, reduce its corresponding wavelet convolution kernel from 64 to 32, use 32 3×3 convolution kernels, and update the parameters iteratively by subtracting the product of the learning rate γ and the gradient δ;

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

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

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

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

[0062] In the flattening layer, convert the multi-dimensional convolutional feature map into a one-dimensional vector;

[0063] The fully connected layer sets the number of output node neurons;

[0064] Finally, the network output layer has the number of neurons corresponding to the 16-QAM modulation symbol number, and the output layer outputs the possible values corresponding to 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 ability of the wavelet scattering network and replacing the first-layer traditional convolutional layer with an adaptive wavelet convolutional module, while ensuring efficient feature extraction, reducing the computational complexity of the system, and still being able to maintain good bit error rate performance in a multipath fading environment;

[0067] (2) The method of the present invention provides lower time complexity and space complexity in a high-speed mobile scenario, improving the signal detection accuracy and robustness of the OTFS system. Brief description of the drawings

[0068] Figure 1 It is a flowchart of a signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network proposed by the present invention;

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

[0070] Figure 3It is the architecture diagram of the adaptive wavelet scattering convolutional neural network;

[0071] Figure 4 It is the diagram of the adaptive wavelet convolution AWCM module;

[0072] Figure 5 It is the diagram of the convolutional layer CONV module. Specific implementation manner

[0073] Now, the technical solution of this embodiment will be further elaborated in conjunction with the accompanying drawings.

[0074] As Figure 1 shown, 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: The information to be transmitted is modulated by 16-QAM to obtain the data symbols to be sent; the data symbols are mapped to the DD domain, and an OTFS signal is obtained through an OTFS modulator, and then reaches the receiving end through a wireless channel. The receiving end transforms the OTFS signal back to the DD domain through an OTFS demodulator.

[0076] In step 1, for mapping the data symbols to the DD domain, obtaining an OTFS signal through an OTFS modulator, and reaching the receiving end through a wireless channel, it includes:

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

[0078] S1_2: The DD domain signal x[k, l] is transformed to the TF domain through an ISFFT to obtain the TF domain signal, denoted as:

[0079]

[0080] In the formula, X[n, m] represents the TF time-frequency domain signal, N and M respectively represent the sizes of the delay and Doppler dimensions, 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 signal in the delay-Doppler domain, k and l respectively represent the indices in the delay domain and the Doppler domain, 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], use the Heisenberg transform to convert X[n, m] into the continuous time-domain transmitted signal s(t), that is, the OTFS signal, denoted as:

[0082]

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

[0084] S1_4: The time-domain transmitted signal s(t) reaches the receiving end after passing through the wireless channel, and the following signal r(t) is received at the receiving end:

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

[0086] wherein,

[0087] in the formula, n(t) represents noise, and h(τ, v) is the DD-domain channel response, reflecting the propagation of the signal in the time-delay - Doppler domain. The channel has a total of P paths, and the channel amplitude response of the Pth path is β P . In the time-delay domain and the Doppler domain, the impulse functions δ(τ - τ i ) and δ(v - v i ) are respectively used to represent the concentrated positions of the signals. τ and v respectively represent the time delay and the Doppler frequency shift.

[0088] The time delay τ i and the Doppler frequency shift v i correspond to the characteristics of the ith path, which are expressed as:

[0089]

[0090] wherein, τ i is used to represent the time delay of the ith path, and the integer part of v i represents the integer multiple Doppler shift, and the fractional part reflects the offset from the nearest Doppler frequency shift.

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

[0092]

[0093] in the formula, represents the cross ambiguity function, represents the matched filtering function, and t' represents the integration variable.

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

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

[0096]

[0097] Finally, process the received signal \(Y[n, m]\) in the TF domain using SFFT to obtain the received signal \(y[k, l]\) in the DD domain, which is expressed as:

[0098]

[0099] By deriving the signal processing flow of the OTFS system's transmitter and receiver, the input-output relationship of the signal in the delay-Doppler domain can be expressed using the following formula:

[0100] y = Hx + n

[0101] where \(y\), H is the equivalent channel, and n is the additive white noise.

[0102] Step 2: Use the wavelet scattering network transform to extract features from the OTFS received signal. Extract the real part signal matrix and the imaginary part signal matrix of the received signal respectively. Take these two matrices as the data of two channels, and perform the wavelet scattering network transform on each channel respectively, that is, as the input of the wavelet scattering transform, which is expressed as:

[0103]

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

[0105] S3_1: Use the low-pass filter \(\varphi\) J to convolve the input signal and extract the low-frequency features, which is expressed as:

[0106] S 0 Y real = Y real * \(\varphi\) J

[0107] S 0 Y imag = Y imag * \(\varphi\) J

[0108] Extract the high-frequency information in the signal through the Morlet wavelet modulus transform, and perform non-linear processing on the high-frequency information to obtain the scattering characteristic coefficients. Therefore, in order to obtain the translation-invariant part of |Y*ψ|, the modulus operation is used to non-linearly activate the convolution result to remove negative values and highlight the frequency characteristics. For each convolution result, apply the modulus operation |·|, which needs to be locally averaged by a low-pass filter with a size of 2 J downsampled to obtain the first-order scattering coefficient by taking the local mean of the low-pass filter. The formula for the convolution operation is:

[0109]

[0110] where φ J is the low-pass filter, and * represents the convolution operation, represents the Morlet wavelet basis function used in the wavelet transform, and λ 1 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 the data dimension.

[0111] S3_2: Perform non-linear operation and downsampling operation on the high-frequency signal in the signal again to further extract the low-frequency characteristics to obtain the second-order scattering coefficient S 2 Y, and obtain higher-order features, which are expressed as:

[0112]

[0113] where, represents the Morlet wavelet basis function used in the wavelet transform. λ 2 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 respectively transformed through a three-layer wavelet scattering network to obtain the output wavelet scattering characteristic coefficients SY real and SY imag . The scattering characteristic coefficients output by each layer are spliced along the feature channel direction to reconstruct the high-dimensional feature matrix SY of the signal, which is expressed as:

[0115] SY real =[S 0 Y real ,S 1 Y real ,S 2 Y real

[0116] SY imag =[S 0 Y imag ,S 1 Y imag ,S 2 Y imag ​

[0117]

[0118] Among them, [] represents the splicing operation.

[0119] The 2D-AWCNN model of this embodiment 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. In the second and third traditional convolutional layers, the padding mode "same" is set and the stride is 1, so the input and output shapes of each layer remain the same. In each CNN layer, the filter (f cn ) extracts relevant features from the input data through element-wise operations. Subsequently, the obtained input data is normalized through batch normalization to improve the stability and training effect of the model.

[0120] Step 4: Concatenate the scattering feature coefficients output by each layer along the feature channel direction to reconstruct the signal high-dimensional feature matrix SY as the input of the adaptive wavelet convolutional neural network 2D-AWCNN. Use the adaptive wavelet convolution module AWCM as the first convolutional layer of 2D-AWCNN, and optimize the convolutional kernel using the adaptively learned dilation factor and translation factor. The dilation factor and translation factor parameters in 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 signal detected by the backpropagation algorithm, and finally the possible values corresponding to each QAM symbol are obtained; in this step, the convolutional network parameters are optimized by the adaptive Morlet wavelet basis to improve the symbol detection accuracy. The specific operations include:

[0121] The 2D-AWCNN network training uses the Adam optimizer for stochastic gradient descent (SGD). The adaptive wavelet convolutional neural network 2D-AWCNN includes: an input layer, a first layer of 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] Use the adaptive wavelet convolution module AWCM with self-learning characteristics as the first convolutional layer, set the dilation factor and translation factor of the Morlet wavelet convolutional kernel as learnable parameters, and keep the rotation angle fixed at four main direction angles: 0°, 90°, 180°, 270°. Initialize the dilation factor and displacement factor at each direction angle, and the training dilation factor d takes values of 1, 1 / 2, 1 / 4, 1 / 8, corresponding to the translation factor s 1 and s 2 ​The values are -1 and 1. During the backpropagation process, these factors will be iteratively updated as learnable parameters by subtracting the product of the learning rate γ and the gradient δ during network training. In 2D-AWCNN, due to the self-learning characteristics of the dilation factor and the translation factor, the corresponding wavelet convolution kernel is reduced from 64 to 32, and 32 3×3 convolution kernels will be used to extract the low-level features of the input data.

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

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

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

[0127] The batch normalization layer is used to accelerate the training process, stabilize the training of the network, and reduce the problem of gradient vanishing.

[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, retaining the most important features and reducing the computational amount.

[0129] The flattening layer converts the multi-dimensional convolutional feature map into a one-dimensional vector, preparing to enter the fully connected layer for further processing.

[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 the number of neurons corresponding to the number of 16-QAM modulation symbols. Usually, there are 16 output nodes, corresponding to the possible values of each QAM symbol.

[0132] During the training process, the dilation factor and translation factor parameters in the adaptive wavelet convolution module AWCM are iteratively updated by subtracting the product of the learning rate γ and the gradient δ. The second and third convolutional layers update the training parameters using the backpropagation algorithm. The Adam optimizer is used to perform stochastic gradient descent (SGD) and self-adjust the learning rate according to the gradient information of each parameter, usually showing good training effects and stability.

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

[0134]

[0135] where X i represents the actually transmitted symbol, Let \(S_Y\) denote the symbol obtained through network training, \(m\) denote the number of samples in the training dataset, \(\theta\) denote the parameters (weights and biases) of the neural network, and \(f(S_Y;\theta)\) denote the function that depends on the input and network parameters and generates the predicted value.

[0136] The network parameters are optimized through backpropagation and gradient descent. In each round of training, the Adam optimizer updates all network parameters according to the backpropagation algorithm. As the first layer of the model structure, during the backpropagation of the 2D-AMCNN network model, the scaling factor and translation factor parameters in the AWCM are iteratively updated by subtracting the product of the learning rate \(\gamma\) and the gradient \(\delta\), enabling the network to gradually improve the accuracy of symbol detection. The Adam optimizer combines momentum and adaptive learning rate, 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. Symbol demodulation is performed through a 16-QAM demodulator, mapping the output result of the network to the output bits for signal detection.

[0138] Through the above method, it is used to solve the problems of channel modeling and incomplete channel information in future communication scenarios. Using a deep learning network based on wavelet scattering feature extraction and transferred to adaptive wavelet convolution, the signal detection algorithm in the present invention does not rely on CSI. Instead, it directly performs wavelet scattering network transformation on the received signal passing through the OTFS system for feature extraction and uses adaptive wavelet bases to optimize the training of the convolutional neural network to recover the input signal. Compared with the signal detection schemes in other existing technologies, the present invention aims to achieve better signal detection performance with lower time complexity and space complexity in high-mobility communication scenarios and achieve better bit error rate performance.

Claims

1. A signal detection method for an OTFS system based on an adaptive wavelet scattering convolutional neural network, characterized in that: The following steps are involved: At the transmitting end, the information to be transmitted is modulated by 16-QAM to obtain data symbols to be sent; 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 through the wireless channel; At the receiving end, the received signal is converted back to the received signal in the DD domain through the OTFS demodulator; At the receiving end, the real signal matrix and the imaginary signal matrix of the received OTFS signal are extracted respectively, and the two matrices are transformed by three-layer wavelet scattering network respectively; firstly, low-pass filters are used to extract the low-frequency characteristics of the signal matrix, and then the high-frequency information in the signal is extracted by Morlet wavelet mode transformation, and the high-frequency information is processed nonlinearly to obtain the scattering characteristic coefficients of each layer; 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 and use it as the input of the adaptive wavelet convolution neural network 2D-AWCNN. The adaptive wavelet convolution module AWCM with self-learning characteristics is used as the first convolution layer of 2D-AWCNN. The scaling factor and translation factor parameters in the adaptive wavelet convolution 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 convolution layers use traditional convolution kernels, and the parameters are further detected by the back propagation 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 by a demodulator to obtain the output bits for signal detection.

2. The OTFS system signal detection method based on an adaptive wavelet scattering convolutional neural network according to claim 1 is characterized in that: The data symbols are mapped to the DD domain, and the data symbols mapped to the DD domain are obtained through the OTFS modulator to obtain the OTFS signal, and the specific operations include: Map M×N data symbols to the DD domain signal grid, where N and M represent the size of the delay and Doppler dimensions respectively, and obtain the signal in the delay-Doppler domain, which is expressed as: x[k, l], k = 0, 1, 2, ..., N-2, N-1, l = 0, 1, 2, ..., M-2, M-1; k and represent the indexes of the delay domain and Doppler domain respectively; The delay-Doppler domain signal x[k,l] is converted to the TF domain through ISFFT to obtain the TF domain signal, which is expressed as: Wherein, X[n,m] represents the TF domain signal, n and m represent the time-frequency domain index, nn=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 transmission signal s(t) by using the Heisenberg transform, namely the OTFS signal, which is expressed as: Where T represents the symbol duration, g tx (·) represents the shaping filter function of 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 is characterized in that: The OTFS signal reaches the receiving end through the wireless channel, and the receiving end receives the following signal r(t): r(t)=∫ v ∫ τ h(τ,v)s(t-v)e j2πv(t-v) dτdv+n(t) in, Where n(t) represents noise, h(τ, v) is the DD domain channel response, which reflects the propagation of the signal in the delay-Doppler domain. There are a total of P paths in the DD domain channel, and the channel amplitude response of the Pth path is β P , in the delay domain and Doppler domain, the impulse function δ(τ-τ i ) and δ(vv i ) is used to represent the concentrated position of the signal, τ, v represent the time delay and Doppler frequency shift respectively; Delay τ i and Doppler shift v i The characteristics corresponding to the i-th path are expressed as: Among them, τ i represents the delay of the ith path, v i Indicates integer Doppler shift.

4. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 3 is characterized in that: At the receiving end, the received signal is converted back to a received signal in the DD domain by an OTFS demodulator. The specific operations include: The signal r(t) is combined with the pulse shaping waveform g rx (t) performs matched filtering and calculates the received signal in the time-frequency domain according to the following formula: In the formula, represents the cross fuzzy function, represents the matched filter function, t′ represents the integral variable; The time-frequency domain received signal Y(t, f) is sampled at intervals of t=nT, f=mΔf to obtain a discrete time-frequency domain received signal, which is expressed as: The discrete time-frequency domain received signal Y[n, m] is processed by SFFT to obtain the DD domain received signal y[k, l], which is expressed as:

5. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 4 is characterized in that: At the receiving end, the real signal matrix and the imaginary signal matrix of the received OTFS signal are respectively extracted, and the two matrices are respectively transformed by three-layer wavelet scattering network; firstly, low-pass filters are used to extract the low-frequency characteristics of the signal matrix, and then the high-frequency information in the signal is extracted by Morlet wavelet mode transformation, and the high-frequency information is nonlinearly processed to obtain the scattering characteristic coefficient of each layer. The specific operations include: Y represents the matrix form of the received signal y[k, l], denoted as And extract the real and imaginary parts of the signal respectively, and get two matrices and The real signal matrix and the imaginary signal matrix are respectively filtered by a low-pass filter φ J To extract the low-frequency features of the signal matrix, expressed as: I AM real =And real *φ J I AM imag =And imag *φ J In the formula, * represents the convolution operation; The high-frequency information in the signal is extracted by Morlet wavelet modulus transform. For each convolution result, the modulus operation |·| is applied to the convolution result with a size of 2. J The downsampled low-pass filter is locally averaged to obtain the first-order scattering coefficient, expressed as: in, represents the Morlet wavelet basis function, λ1 represents the parameter controlling the scale and position, i represents the index used to identify the wavelet function at different scales, and J represents the current decomposition level; The high-frequency information is processed nonlinearly to extract the second-order scattering coefficient S2Y, which is expressed as: in, represents the Morlet wavelet basis function used in 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 is characterized in that: 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: AND real =|S0Y real ,S1Y real ,S2Y real ] AND imag =[S0Y imag ,S1Y imag ,S2Y imag ] Among them, [] represents the concatenation operation.

7. The OTFS system signal detection method based on adaptive wavelet scattering convolutional neural network according to claim 6 is 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; Take the signal high-dimensional feature matrix as input; For the first adaptive wavelet convolution layer, 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. 32 3×3 convolution kernels are used, and the parameters are iteratively updated by subtracting the product of the learning rate γ and the gradient δ; The second convolution layer uses 128 3×3 traditional convolution kernels; The third convolution layer uses 256 3×3 traditional convolution kernels; the weight parameters in the traditional convolution kernels are trained by the back propagation algorithm; Apply 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, the multi-dimensional convolutional feature map is converted into a one-dimensional vector; The fully connected layer sets the number of output node neurons; 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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