Least Squares OTFS System Channel Estimation Method Based on Deep Neural Network

Abstract

Least Squares OTFS System Channel Estimation Method Based on Deep Neural Network, belonging to the field of wireless communication technology. In view of the requirements of accurate channel estimation and reliable information interaction in the vehicle-to-everything (V2X) network, the present invention designs an efficient and low-latency channel estimation method based on DNN. The method includes three steps: First, in the transmitter of the V2X network OTFS system, block pilots are inserted from the time-frequency domain, and at the receiver, they are extracted from the time-frequency domain. The traditional LS channel estimation method is used to perform time-frequency domain channel estimation to obtain a roughly estimated channel matrix H LS ; Second, use DNN to optimize the estimation of H LS , complete the offline training of each parameter of DNN and obtain the channel matrix H LS‑DNN ; Finally, use H LS‑DNN to realize the online recovery of transmitted information data. Based on LS channel estimation, the present invention can not only achieve low-complexity channel estimation and relatively accurate channel estimation results, but also meet good timeliness and low latency, making the information transmission efficiency higher.

Description

Technical Field

[0001] The present invention relates to a least squares OTFS system channel estimation method based on a deep neural network, belonging to the technical field of channel estimation in wireless communication transmission. Background Art

[0002] Currently, intelligent transportation systems based on the Internet of Vehicles (IoV) have received extensive attention. In the IoV scenario, the communication transceiver has characteristics such as fast moving speed, complex channel, and low transmission delay. The present invention is based on the framework of the IoV OTFS system. The OTFS technology can achieve a higher data transmission rate and solve problems such as interference between symbols and carriers and Doppler interference in high-speed mobile communication. Selecting an appropriate channel model and using a suitable channel estimation method can better meet the requirements of IoV communication for accurate and reliable channel estimation and ensure the communication quality of the IoV. Channel estimation is an important functional module of a wireless mobile communication system, mainly used to estimate the impulse response of the channel experienced by the signal and for subsequent channel equalization processing, aiming to eliminate intersymbol interference (ISI) caused by multipath signal aliasing, etc. Typical channel estimation methods include the least squares (LS) channel estimation method and the minimum mean square error (MMSE) channel estimation method, etc. These methods are all non-blind estimations based on pilots for channel estimation, with low spectral efficiency but good estimation effects. The MMSE channel estimation method can effectively suppress noise interference, and its performance is superior to the LS channel estimation method. However, due to the high complexity of inverse matrix solution, the hardware implementation cost is high. The least squares LS channel estimation method ignores the influence of noise, has low complexity and is easy to implement, and is a channel estimation method widely used in many wireless communication systems. However, it is difficult to effectively solve the influence of noise at low signal-to-noise ratios, resulting in a significant decrease in channel estimation accuracy. Therefore, it can be considered to combine it with a deep neural network (DNN) to improve its channel estimation performance. DNN is also called a deep feedforward network because the data flow in the DNN network is unidirectional and more specific, with a flexible model structure and high degrees of freedom. In recent years, DNN has been widely used in various aspects of the wireless communication field, such as channel estimation, signal detection, etc.

[0003] Li Jiaojun et al. (see Li Jiaojun, Zhang Tingting, Huang Mingmin, "An Improved LS Channel Estimation Algorithm", Journal of Chongqing University of Technology (Natural Science), 2018(12): 170 - 174, 192.) proposed an adaptive noise cancellation technology to improve the LS algorithm based on the recursive least squares (RLS) adaptive filtering algorithm. The simulation results show that the RLS adaptive filtering algorithm has improved performance compared to the LS algorithm, but the algorithm complexity is relatively high, the channel estimation accuracy is somewhat lacking, and the hardware of this invention is difficult to implement. Summary of the Invention

[0004] In view of the defects and deficiencies existing in the typical channel estimation methods in the existing vehicle networking, the present invention proposes a least squares channel estimation method based on a deep neural network, which combines the LS channel estimation method with the deep neural network and further optimizes the rough estimation result of the LS algorithm by using the deep neural network to significantly improve the accuracy of channel estimation.

[0005] The technical solution of the present invention is as follows:

[0006] A least squares OTFS system channel estimation method based on a deep neural network is implemented by an orthogonal time-frequency-space OTFS modulation communication system for vehicle networking; the system includes a transmitter and a receiver. The transmitter includes a quadrature phase shift keying (QPSK) modulation module, an inverse symplectic Fourier transform (ISFFT) module, an orthogonal frequency division multiplexing (OFDM) modulator, and a transmitting antenna connected in sequence; the receiver includes a receiving antenna, an OFDM demodulator, a channel estimation module, a channel equalization module, a symplectic Fourier transform (SFFT) module, and a QPSK demodulation module connected in sequence. The channel estimation module includes an LS channel estimation and a DNN model. The implementation process of channel estimation is as follows: First, the transmitter groups random bit streams in the delay-Doppler domain in pairs and modulates them in the QPSK modulation module to form a delay-Doppler domain signal. Subsequently, through the ISFFT module, the delay-Doppler domain signal is converted into a time-frequency domain signal. At this time, block pilots are inserted into the time-frequency domain signal for LS channel estimation; then, the OFDM modulator converts the time-frequency domain signal with pilots into a time domain signal through the Heisenberg transform and transmits it through the transmitting antenna in the time domain channel; the receiver receives the signal through the receiving antenna, and then demodulates the received signal through the OFDM demodulator, that is, obtains the time-frequency domain signal through the Wigner transform, separates the pilot and the data signal, and uses the received pilot in the channel estimation module to perform LS channel estimation to obtain a roughly estimated channel matrix H LS , and then uses the DNN to optimize H LS to obtain H LS-DNN ; finally, the receiver performs time-frequency domain channel equalization of the OTFS system at the channel equalization module using H LS-DNN to obtain a time-frequency domain data recovery signal, and passes it through the SFFT module to obtain a delay-Doppler domain signal, and then passes it through the corresponding demodulation and recovery in the QPSK demodulation module to obtain the original bit stream; the specific steps are as follows:

[0007] 1) Generation of the channel matrix data set for the vehicle networking OTFS system:

[0008] (1) Group the random bit stream in the time-delay Doppler domain into pairs, and obtain the time-delay Doppler domain signal x(k, l) through QPSK modulation in the QPSK modulation module, where k ∈ {0, 1,..., N - 1}, l ∈ {0, 1,..., M - 1}, and M and N are the number of time-delay dimensions and the number of Doppler dimensions respectively; at the ISFFT module, the time-delay Doppler domain signal x(k, l) is obtained as the time-frequency domain signal through ISFFT where n and m respectively represent the time-domain index position and the frequency-domain index position of the time-frequency domain signal; place two columns of the same pilot symbols p 1 [q] and p 2 [q] in front of the time-frequency domain signal X p [n, m] for LS channel estimation, where q is the q-th subcarrier in the time-frequency domain signal, and p 1 [q] and p 2 [q] are bit sequences with all elements being "1". Here, the all-ones sequence is used as the pilot symbol to enable the received pilot symbols y 1 [q] and y 2 [q] to more completely record the time-frequency domain channel response; in the OFDM modulator, the time-frequency domain signal X p [n, m] with pilots is transformed into the time-domain signal s(t) through the Heisenberg transform, expressed as where t is the sampling moment of the time-domain signal, g tx (t) is the time-domain transmit pulse, and T and Δf are the minimum sampling interval and the minimum sampling frequency in the time-frequency domain respectively; then add a cyclic prefix at the beginning of each information symbol of the time-domain signal s(t) as a guard interval, and then perform a serial-to-parallel conversion on the signal stream, and transmit the signal after the serial-to-parallel conversion through the transmit antenna in the time-domain channel;

[0009] (2) The receiving antenna receives the signal r(t) transmitted through the time-varying channel, which is expressed as r(t) = ∫∫h(τ, ν)g tx (t - τ)e j2πνt dτdν + v(t), where v(t) represents the time-domain additive white Gaussian noise, h(τ, v) is the channel impulse response with the number of sparse paths being P, and τ and v respectively represent the time-delay of the path in the time-delay Doppler domain and the Doppler frequency shift; then the receiver performs a parallel-to-serial conversion on r(t) and removes the cyclic prefix, and then converts the received time-domain signal into the time-frequency domain signal Y p [n, m] = ∫g rx (t - τ)r(t)e -j2π(t-τ) dt, where g rx (t) represents the time-domain receive pulse; then the two columns of received pilot symbols y 1 [q] and y2 [q]Extract from Y p [n,m] and perform LS channel estimation in the channel estimation module to obtain the channel response at the pilot Here, the LS channel estimation algorithm is based on the estimated channel matrix Take the derivative to minimize the cost function to obtain where X is the transmitter time-frequency domain pilot symbol vector, Y is the receiver time-frequency domain pilot symbol vector, ||·|| 2 represents the square of the modulo operation, and (·) -1 represents matrix inversion; the mean square error of the LS channel estimation algorithm is where represents the noise power, represents the signal power. Therefore, the MSE of the LS algorithm is inversely proportional to the signal-to-noise ratio. Thus, the LS channel estimation matrix obtained by rough estimation can be further optimized by combining DNN ;

[0010] 2) Preprocessing of the channel matrix dataset and offline training of DNN parameters:

[0011] (1) Before offline training of DNN parameters, preprocessing of the channel matrix dataset is required. Duplicate and expand the estimated channel response h LS [q] to the channel matrix H p corresponding to the size of the time-frequency domain signal X LS , and separate the real and imaginary parts of the obtained H LS and the true channel matrix H Perfect to form a new matrix as the dataset. The upper part of this new matrix is the real part of the elements of H LS and H Perfect , and the lower part is the imaginary part of the elements of the two; after loading the channel matrix H LS and H Perfect datasets, it is necessary to normalize the datasets for scaling or transforming the data; then shuffle the order of the datasets, that is, perform the Shuffle operation;

[0012] (2) Use the preprocessed H LS and H Perfect as the input and output of the DNN respectively. This DNN consists of an input layer, three hidden layers, and an output layer. The number of neural nodes in each hidden layer is 100, 200, and 300 respectively. The activation function of each hidden layer is the rectified linear unit ReLU, the loss function is the mean square error function MSE, which represents the mean of the sum of the squares of the differences between the predicted value and the target value, the optimizer uses the stochastic gradient descent method SGD, the set learning rate is 0.0001, and the number of training times is 500 times;

[0013] 3) Online recovery of information data:

[0014] After the DNN parameter training at the receiving end is completed, channel equalization is performed on the time-frequency domain channel of the OTFS system at the channel equalization module, that is, the H obtained after optimized estimation using the network model completed by offline training is used. LS-DNN The received signal in the time-frequency domain is recovered to obtain X eq [n,m], and then through the SFFT module, the time-delay Doppler domain signal y(k,l) is obtained, expressed as Finally, the original signal is recovered through the QPSK demodulation module.

[0015] The so-called LS is the abbreviation of the English Least Square, and its Chinese meaning is least squares.

[0016] The so-called OTFS is the abbreviation of the English Orthogonal time frequency space, and its Chinese meaning is orthogonal time-frequency space.

[0017] The so-called OFDM is the abbreviation of the English Orthogonal Frequency Division Multiplexing, representing the orthogonal frequency division multiplexing technology.

[0018] The so-called QPSK is the abbreviation of the English Quadrature Phase Shift Keying, and its Chinese meaning is quadrature phase shift keying, which is a digital modulation method.

[0019] The so-called SGD is the abbreviation of the English Stochastic Gradient Descent, and its Chinese meaning is stochastic gradient descent, which is an implementation of the gradient descent algorithm.

[0020] The present invention combines the LS channel estimation algorithm with a deep neural network, enabling the deep neural network to optimize the rough estimation result of the LS algorithm. Based on the LS channel estimation, both low-complexity channel estimation and relatively accurate channel estimation results can be achieved. Facing the requirements of information interaction and collaboration in the vehicle-to-everything network, it can meet better timeliness and low latency, making the information transmission efficiency higher. Brief Description of the Drawings

[0021] Figure 1 It is a schematic diagram of the system framework of the method of the present invention.

[0022] Figure 2 It is a schematic diagram of pilot insertion into the time-frequency domain signal under the condition that the number of subcarriers Q = 64 and the number of symbols S = 5 in the time-frequency domain signal.

[0023] Figure 3 It is a schematic diagram of the deep neural network structure of the method of the present invention.

[0024] Figure 4 、 Figure 5 Under the conditions of the number of subcarriers Q = 64 and the number of symbols S = 5, the performance of the method of the present invention is compared with the traditional LS channel estimation algorithm in terms of bit error rate and normalized mean square error. As can be seen from Figure 3 、 Figure 4 the method has significantly improved performance in terms of bit error rate and normalized mean square error compared with the traditional LS channel estimation algorithm. Specific implementation manners

[0025] The present invention will be further described below in conjunction with the drawings and embodiments, but is not limited thereto.

[0026] A least squares OTFS system channel estimation method based on a deep neural network is implemented by a vehicle-to-everything (V2X) orthogonal time-frequency-space (OTFS) modulation communication system. The system includes a transmitter and a receiver. The transmitter includes a quadrature phase shift keying (QPSK) modulation module, an inverse symplectic Fourier transform (ISFFT) module, an orthogonal frequency division multiplexing (OFDM) modulator, and a transmitting antenna connected in sequence. The receiver includes a receiving antenna, an OFDM demodulator, a channel estimation module, a channel equalization module, a symplectic Fourier transform (SFFT) module, and a QPSK demodulation module connected in sequence. The channel estimation module includes an LS channel estimation and a DNN model. The implementation process of channel estimation is as follows: First, the transmitter groups random bit streams in the delay-Doppler domain in pairs and modulates them in the QPSK modulation module to form a delay-Doppler domain signal. Subsequently, through the ISFFT module, the delay-Doppler domain signal is converted into a time-frequency domain signal. At this time, block pilots are inserted into the time-frequency domain signal for LS channel estimation. Then, the OFDM modulator converts the time-frequency domain signal with pilots into a time domain signal through the Heisenberg transform and transmits it through the transmitting antenna in the time domain channel. The receiver receives the signal through the receiving antenna, and then demodulates the received signal through the OFDM demodulator, that is, obtains the time-frequency domain signal through the Wigner transform, separates the pilot and data signals, and uses the received pilot in the channel estimation module to perform LS channel estimation to obtain a roughly estimated channel matrix H LS , and then uses the DNN to optimize H LS to obtain H LS-DNN ; Finally, the receiver uses H LS-DNN in the channel equalization module to perform time-frequency domain channel equalization of the OTFS system, obtain a time-frequency domain data recovery signal, and pass it through the SFFT module to obtain a delay-Doppler domain signal, and then perform corresponding demodulation and recovery in the QPSK demodulation module to obtain the original bit stream. The specific steps are as follows:

[0027] 1) Generation of the channel matrix dataset for the vehicle networking OTFS system:

[0028] (1) Group the random bit streams in the delay-Doppler domain pairwise, and obtain the delay-Doppler domain signal x(k, l) through QPSK modulation in the QPSK modulation module, where k ∈ {0, 1,..., N - 1}, l ∈ {0, 1,..., M - 1}, and M and N are the numbers of delay dimensions and Doppler dimensions respectively; at the ISFFT module, the delay-Doppler domain signal x(k, l) is obtained as the time-frequency domain signal where n and m represent the time-domain index position and frequency-domain index position of the time-frequency domain signal respectively; place two columns of the same pilot symbols p 1 [q] and p 2 [q] in front of the time-frequency domain signal X p [n, m] for LS channel estimation, where q is the q-th subcarrier in the time-frequency domain signal, and p 1 [q] and p 2 [q] are bit sequences with all elements being "1". Here, the all-ones sequence is used as the pilot symbol to enable the pilot symbols y 1 [q] and y 2 [q] at the receiving end to more completely record the time-frequency domain channel response; in the OFDM modulator, the time-frequency domain signal X p [n, m] with pilots is transformed into the time-domain signal s(t) through the Heisenberg transform, expressed as where t is the sampling moment of the time-domain signal, g tx (t) is the time-domain transmit pulse, and T and Δf are the minimum sampling interval and minimum sampling frequency in the time-frequency domain respectively; subsequently, a cyclic prefix is added at the beginning of each information symbol of the time-domain signal s(t) as a guard interval, and then the signal stream is serially-parallel converted, and the serially-parallel converted signal is transmitted in the time-domain channel through the transmit antenna;

[0029] (2) The receiving antenna receives the signal r(t) transmitted through the time-varying channel, which is expressed as r(t) = ∫∫h(τ, ν)g tx (t - τ)e j2πνt dτdν + v(t), where v(t) represents the time-domain additive white Gaussian noise, h(τ, v) is the channel impulse response with the number of sparse paths being P, and τ and v represent the path delay and Doppler frequency shift in the delay-Doppler domain respectively; subsequently, the receiver performs serial-parallel conversion on r(t), removes the cyclic prefix, and then converts the received time-domain signal into the time-frequency domain signal Y p [n, m] = ∫g rx (t - τ)r(t)e -j2π(t-τ) dt, where g rx(t) represents the time-domain received pulse; then, two received pilot symbols y 1 [q] and y 2 [q] are extracted from Y p [n,m] and LS channel estimation is performed in the channel estimation module to obtain the channel response at the pilots Here, the LS channel estimation algorithm minimizes the cost function by taking the derivative of the estimated channel matrix to obtain where X is the transmit-time-frequency-domain pilot symbol vector, Y is the receive-time-frequency-domain pilot symbol vector, ||·|| represents the square of the modulo operation, and (·) 2 represents matrix inversion; the mean square error of the LS channel estimation algorithm is -1 where represents the noise power, represents the signal power, so the MSE of the LS algorithm is inversely proportional to the signal-to-noise ratio. Therefore, the LS channel estimation matrix obtained from the rough estimation can be further optimized by combining with DNN; 2) Preprocessing of the channel matrix dataset and offline training of DNN parameters:

[0030]

[0031]

[0032] (1) Before offline training of DNN parameters, preprocessing of the channel matrix dataset is required. The channel response h LS [q] at the pilots obtained from the estimation is copied and extended to the channel matrix H p corresponding to the size of the time-frequency-domain signal X LS [n,m]. Then, the real and imaginary parts of the obtained H LS and the true channel matrix H Perfect are separated, and a new matrix is formed as the dataset. The upper part of this new matrix is the real part of the elements of H LS and H Perfect , and the lower part is the imaginary part of their elements; after loading the channel matrix H LS and H Perfect datasets, the datasets need to be normalized to scale or transform the data; then, the order of the datasets is shuffled, i.e., the Shuffle operation is performed;

[0032] (2) The preprocessed H LS and H PerfectRespectively serve as the input and output of the DNN, and the DNN consists of an input layer, three hidden layers, and an output layer. The number of neural nodes in each hidden layer is 100, 200, and 300 respectively. The activation function of each hidden layer is the rectified linear unit ReLU, the loss function is the mean squared error function MSE, which represents the mean of the sum of squares of the differences between the predicted value and the target value. The optimizer uses the stochastic gradient descent method SGD, the set learning rate is 0.0001, and the number of training times is 500 times;

[0033] 3) Online recovery of information data:

[0034] After the DNN parameter training at the receiving end is completed, the time-frequency domain channel of the OTFS system is equalized at the channel equalization module, that is, the H obtained after optimized estimation using the network model completed by offline training LS-DNN The time-frequency domain received signal is recovered to obtain X eq [n,m], and then through the SFFT module, the time-delay Doppler domain signal y(k,l) is obtained, expressed as Finally, the original signal is recovered through the QPSK demodulation module.

Claims

1. A least squares OTFS system channel estimation method based on a deep neural network, implemented by a vehicle-to-everything (V2X) orthogonal time-frequency-space (OTFS) modulation communication system; the system includes a transmitter and a receiver, the transmitter includes a quadrature phase shift keying (QPSK) modulation module, an inverse symplectic Fourier transform (ISFFT) module, an orthogonal frequency division multiplexing (OFDM) modulator, and a transmitting antenna connected in sequence; the receiver includes a receiving antenna, an OFDM demodulator, a channel estimation module, a channel equalization module, a symplectic Fourier transform (SFFT) module, and a QPSK demodulation module connected in sequence. The channel estimation module includes an LS channel estimation and a DNN model. The implementation process of channel estimation is as follows: First, the transmitter groups random bit streams in the delay-Doppler domain pairwise and modulates them in the QPSK modulation module to form a delay-Doppler domain signal. Subsequently, through the ISFFT module, the delay-Doppler domain signal is converted into a time-frequency domain signal. At this time, block pilots are inserted into the time-frequency domain signal for LS channel estimation. Then, the OFDM modulator converts the time-frequency domain signal with pilots into a time domain signal through the Heisenberg transform and transmits it through the transmitting antenna in the time domain channel. The receiver receives the signal through the receiving antenna, and then demodulates the received signal through the OFDM demodulator, that is, obtains the time-frequency domain signal through the Wigner transform, separates the pilot and data signals, and uses the received pilot in the channel estimation module to perform LS channel estimation to obtain a roughly estimated channel matrix H LS , and then uses the DNN to optimize H LS to obtain H LS-DNN ; Finally, the receiver uses H LS-DNN to perform time-frequency domain channel equalization of the OTFS system in the channel equalization module to obtain a time-frequency domain data recovery signal, and passes it through the SFFT module to obtain a delay-Doppler domain signal, and then passes through the corresponding demodulation in the QPSK demodulation module to recover the original bit stream; the specific steps are as follows: 1) Generation of the channel matrix dataset for the vehicle Internet of Things OTFS system: (1) Group the random bit streams in the delay-Doppler domain in pairs, and obtain the delay-Doppler domain signal x(k, l) through QPSK modulation in the QPSK modulation module, where k ∈ {0, 1,..., N - 1}, l ∈ {0, 1,..., M - 1}, and M and N are the number of delay dimensions and the number of Doppler dimensions, respectively; at the ISFFT module, the delay-Doppler domain signal x(k, l) is obtained through ISFFT to get the time-frequency domain signal where n and m represent the time-domain index position and the frequency-domain index position of the time-frequency domain signal, respectively; place two columns of the same pilot symbols p 1 [q] and p 2 [q] in front of the time-frequency domain signal X p [n, m] for LS channel estimation, where q is the q-th subcarrier in the time-frequency domain signal, and p 1 [q] and p 2 [q] are bit sequences with all elements being "1". Here, the all-ones sequence is used as the pilot symbol to enable the received pilot symbols y 1 [q] and y 2 [q] to more completely record the time-frequency domain channel response; in the OFDM modulator, the time-frequency domain signal X p [n, m] with pilots is obtained through the Heisenberg transform to get the time-domain signal s(t), expressed as where t is the sampling moment of the time-domain signal, and g tx (t) is the time-domain transmit pulse, and T and Δf are the minimum sampling interval and the minimum sampling frequency in the time-frequency domain, respectively; then, a cyclic prefix is added at the beginning of each information symbol of the time-domain signal s(t) as a guard interval, and then the signal stream is converted from parallel to serial and transmitted through the transmit antenna in the time-domain channel; (2) The received antenna receives the signal r(t) transmitted through the time-varying channel, which is expressed as r(t) = ∫∫h(τ,ν)g tx (t - τ)e j2πνt dτdν + v(t), where v(t) represents the time-domain additive white Gaussian noise, h(τ,v) is the channel impulse response with P sparse paths, and τ and v represent the path delay and Doppler frequency shift in the time-delay Doppler domain respectively; Subsequently, the receiver performs serial-to-parallel conversion on r(t) and removes the cyclic prefix, and then converts the received time-domain signal into a time-frequency domain signal Y p [n,m] = ∫g rx (t - τ)r(t)e -j2π(t-τ) dt, where g rx (t) represents the time-domain received pulse; Then the two received pilot symbol columns y 1 [q] and y 2 [q] are extracted from Y p [n,m] and LS channel estimation is performed in the channel estimation module to obtain the channel response at the pilot Here, the LS channel estimation algorithm minimizes the cost function by taking the derivative of the estimated channel matrix , so as to obtain where X is the time-frequency domain pilot symbol vector at the transmitter, Y is the time-frequency domain pilot symbol vector at the receiver, ||·|| represents the square of the modulo operation, and (·) 2 represents matrix inversion; The mean square error of the LS channel estimation algorithm is -1 where represents the noise power, represents the signal power. Therefore, the MSE of the LS algorithm is inversely proportional to the signal-to-noise ratio. Thus, the LS channel estimation matrix estimated roughly can be further optimized by combining with DNN ; ​ 2) Preprocessing of the channel matrix dataset and offline training of DNN parameters: (1) Before offline training of DNN parameters, preprocessing of the channel matrix dataset is required. The channel response h LS [q] at the pilot is replicated and extended to the channel matrix H p corresponding to the time-frequency domain signal X LS [n,m]. Then, the real and imaginary parts of the obtained H LS and the true channel matrix H Perfect are separated, and a new matrix is formed as the dataset. The upper part of this new matrix is the real part of the elements of H LS and H Perfect , and the lower part is the imaginary part of their elements. After loading the channel matrix H LS and H Perfect datasets, the datasets need to be normalized to scale or transform the data. Then, shuffle the dataset order, that is, perform the Shuffle operation; (2) Use the preprocessed H LS and H Perfect as the input and output of the DNN respectively. The DNN consists of an input layer, three hidden layers, and an output layer. The number of neural nodes in each hidden layer is 100, 200, and 300 respectively. The activation function of each hidden layer is the rectified linear unit ReLU, the loss function is the mean squared error function MSE, which represents the mean of the sum of the squares of the differences between the predicted value and the target value. The optimizer uses the stochastic gradient descent method SGD, the set learning rate is 0.0001, and the number of training times is 500 times; 3) Online recovery of information data: After the DNN parameter training is completed, the receiver performs channel equalization on the time-frequency domain channel of the OTFS system at the channel equalization module, that is, the H obtained after optimized estimation using the network model completed by offline training is used. LS-DNN The time-frequency domain received signal is recovered to obtain X eq [n,m], and then through the SFFT module, the time-delay Doppler domain signal y(k,l) is obtained, expressed as Finally, the original signal is recovered through the QPSK demodulation module.

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