CN115987734A - Low-complexity OTFS system symbol detection method based on deep neural network - Google Patents

Abstract

The invention discloses a deep neural network-based OTFS (optical transmission system) system symbol detection method, which mainly solves the problems of high symbol detection complexity and low symbol receiving detection speed in the prior art. The method comprises the following implementation steps: 1. obtaining a training set; 2. constructing a neural network; 3. training the deep neural network by using a training set; 4. receiving a time domain signal sent by a transmitting terminal, and carrying out Virger transformation on the time domain signal to obtain a time-frequency domain signal; 5. carrying out Fourier transform on the time-frequency domain signal to obtain a receiving symbol of a delay-Doppler domain; 6. and detecting the received symbols by adopting the trained deep neural network to obtain the estimated value of the transmitted symbols. The invention reduces the complexity of the whole symbol detection of the OTFS system, improves the speed of detecting the received symbol, and can be used for recovering the transmitted signal from the received signal of the OTFS system.

Description

Low-complexity OTFS system symbol detection method based on deep neural network

Technical Field

The present invention belongs to the field of communication technology, and further relates to a low-complexity OTFS system symbol detection method, which can be used to recover a transmission signal from an OTFS system reception signal.

Background Art

At present, the Orthogonal Frequency Division Multiplexing (OFDM) modulation technology widely used in 4G, 5G and WIFI wireless networks is susceptible to the Doppler effect. Orthogonal Time-Frequency Space Modulation (OTFS) has better performance than OFDM in high-mobility wireless communication scenarios. OTFS is a two-dimensional modulation scheme that modulates in the delay-Doppler domain. Through a series of two-dimensional transformations, the dual-dispersion channel is converted into an approximately non-fading channel in the delay-Doppler domain. The two challenges faced by the OTFS system are: how to accurately estimate the delay-Doppler channel state information (CSI); and after obtaining the CSI, a low-complexity and efficient algorithm is required for received signal detection. Received signal detection is to detect the corresponding symbol from the received signal that matches the transmitted symbol. If the detection algorithm complexity of the OTFS system is high, it will cause the entire system to detect the received symbol slowly and cause a high delay, which is not conducive to the practicality of the actual system.

In recent years, with the development of big data, supercomputing, neuroscience, etc., artificial intelligence has developed rapidly, solving some bottleneck problems in the development of neural networks, making it possible to realize high-efficiency, high-accuracy, high-integration, low-power, and low-cost neural networks, and playing an important role in many fields. Deep neural network DNN has achieved great success in image processing, natural language processing, and language recognition. DNN is a multi-layer neural network structure composed of complex connections. The multi-layer structure is more expressive than a few neural network layer structures and has strong fitting ability. DNN networks have a wide range of applications in various fields and have been successfully applied in the field of communications. Their application in the physical layer design of wireless communications is receiving more and more research attention. Constellation design, transceiver design, coding design using autoencoders, channel estimation, signal detection and demodulation are some of the fields. Especially in the re-detection problem, the detection problem can also be regarded as a classification problem, and the DNN network has a strong classification ability, so it is very suitable for the detection of communication signals. In addition, with the continuous maturity of neural network technology, it has created conditions for its application in high-mobility devices such as high-speed rail and automobiles, and can also effectively solve the detection difficulties of OTFS systems.

Therefore, the use of deep neural networks for OTFS signal detection can rely on its powerful learning ability to perform effective detection. This method can not only achieve lower complexity and higher performance than traditional detection methods, but also does not require channel estimation, thereby sending more data.

Existing OTFS detectors include traditional detection methods such as minimum mean square error detector MMSE, maximum likelihood detector ML, various iterative detectors based on message passing MP and its variants. These solutions either have high detection algorithm complexity or poor detection performance. Therefore, there is an urgent need for a low-complexity and efficient detection algorithm. In addition, traditional methods require accurate channel estimation, which not only makes the algorithm complex, but also causes additional overhead for pilot and guard intervals.

In order to solve the shortcomings of traditional detection methods, Ashwitha Naikoti and A.Chockalingam mentioned in their published paper "Low-complexity Delay-Doppler Symbol DNN for OTFS Signal Detection" (IEEE93rd Vehicular Technology Conference 2021) that two low-complexity OTFS detection methods based on DNN were proposed, one is the FULL-DNN network, and the other is the symbol DNN detector that detects symbol by symbol. The symbol-based DNN detector uses MN DNN networks to detect symbols one by one. The number of neurons at the output end of each neural network is determined by the points mapped by the constellation diagram. Therefore, the number of output neurons increases linearly with the increase of MN, while the number of output neurons of the FULL-DNN network increases exponentially with the size of the transmitted symbol vector. Therefore, its complexity is significantly lower than that of FULL-DNN, and its performance is comparable to that of FULL-DNN, and its performance is similar to that of maximum likelihood detection ML. In comparison, the detection performance of the two networks is close, but the complexity of the symbol DNN is significantly lower. Although the second method reduces a large number of neurons, since this method uses data from the entire delay-Doppler domain for detection, a large number of neurons are still required at the input end of the deep neural network. A large number of neurons need to be increased proportionally in the hidden layer, which requires training more parameters, resulting in a slower detection speed of received symbols in the OTFS communication system.

Beijing University of Posts and Telecommunications proposed "a signal detection method and device for an OTFS system" in its patent document with application number CN202010158335.1. It first establishes a corresponding factor graph, and constructs a neural network based on the factor graph. The number of layers of the hidden layer of the neural network is the same as the number of iterations of message transmission, and the hidden layer includes message calculation neurons and probability calculation neurons. The message calculation neurons correspond to the nodes and/or edges of the factor graph; the probability calculation neurons are used to calculate the probability of each modulation symbol in the transmitted signal obtained after the transmitted signal passes through the channel based on the signal detection performance parameters and the data output by the message calculation neurons. This method uses a neural network for training to obtain optimized signal detection performance parameters, thereby improving signal detection performance. However, its shortcomings are: the complexity of the detection method is related to the neural network and the iterative AMP algorithm used. When the number of symbols transmitted per frame is large, the number of iterations is large, and the corresponding detection complexity will also increase significantly. Therefore, it is not suitable for scenarios with a large number of transmission frame symbols. In addition, the number of network layers is large, making the entire neural network system complex and requiring training of a large number of parameters.

Summary of the invention

The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a low-complexity OTFS system symbol detection method based on a deep neural network to improve the speed of the OTFS communication system in detecting received symbols, simplify the complexity of detection, and improve transmission efficiency.

To achieve the above object, the implementation scheme of the present invention includes the following:

(1) Obtain a training set;

1a) The transmitter of the OTFS system sends a modulated signal, one-hot encodes the points on the constellation diagram of the transmitted signal, and stores the encoded data as a label;

1b) The receiving end of the OTFS system receives the data through the channel, transforms it into the delay-Doppler domain, and stores MN received symbols in the domain;

1c) looping steps 1a) and 1b) for C times to obtain a training set, where C is determined based on the performance of the OTFS system;

(2) Build MN deep neural networks with exactly the same structure. Each network contains an input layer, a hidden layer, and an output layer. Each layer is fully connected. Label the MN networks so that they correspond to the MN received symbols in the OTFS system, where M and N represent the total number of subcarriers and the total number of symbols in the OTFS system, respectively.

(3) Use the training set to train each deep neural network:

3a) According to the correspondence between the time delay and Doppler of the OTFS system, the maximum time delay of the detection symbol corresponding to the network and all data within the maximum Doppler range are used as input signals and input into the input layer of the neural network;

3b) using a gradient descent algorithm to train the deep neural network to obtain output layer data;

3c) Use the minimum mean square error function as the loss function of the deep neural network, compare the output layer data obtained in 3b) with the label in 1a) to determine whether the loss function converges:

If so, the training is completed and the trained deep neural network is obtained:

Otherwise, return to step (3b);

(4) The receiving end of the OTFS system receives the time domain signal sent by its transmitting end and performs Wigner transform on the time domain signal to obtain the time-frequency domain signal Y[n,m];

(5) performing a sigmoid Fourier transform (SFFT) on the signal in the time-frequency domain to obtain MN received symbols in the delay-Doppler domain;

(6) Use the trained MN deep neural networks to detect the received symbols one by one:

6a) Match the MN symbols received in (5) with the MN deep neural networks trained in (3) to find the deep neural network corresponding to each received symbol;

6b) taking all data within the maximum delay and maximum Doppler range of each received symbol as the corresponding trained deep neural network input layer data, and obtaining the output layer data of each neural network;

(6c) Based on the output layer data of each neural network, the estimated value of its transmitted symbol is obtained to complete the detection of the OTFS system symbol.

Compared with the prior art, the present invention has the following advantages:

First, the present invention utilizes the characteristics of the OTFS system in the delay-Doppler domain and selects the data within the maximum delay and maximum Doppler domain of each symbol as the input of the neural network for detection, rather than selecting all the data for detection, thereby reducing the input data, thereby reducing the parameters that the neural network needs to learn, and reducing the detection complexity;

Second, since the present invention utilizes the ability of deep neural networks to extract data features, it avoids the difficulty of channel estimation and saves the overhead of pilot and guard intervals, so more valid data can be sent and transmission efficiency is improved.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is an implementation flow chart of the present invention;

FIG2 is a structural diagram of a deep neural network constructed in the present invention;

FIG3 is a data diagram of the maximum time delay and the maximum Doppler domain range for the neural network input layer in the present invention;

FIG. 4 is a comparison diagram of simulation results of detection of OTFS system symbols by the present invention and the existing detection method.

DETAILED DESCRIPTION

The embodiments and effects of the present invention are further described in detail below with reference to the accompanying drawings:

Referring to FIG. 1 , the implementation steps of this embodiment are as follows:

Step 1: Use MATLAB software to run the OTFS system to obtain the training set.

1.1) The transmitter of the OTFS system sends a modulated signal and arranges the points on the constellation diagram in order from left to right and from top to bottom as 1, 2, ..., q, ..., Q. For the qth point, the qth bit in the corresponding one-hot code is 1, and the rest are 0.

This example uses BPSK modulation. The number of points on the constellation is 2. The position of -1 on the constellation is encoded as binary data 10 using one-hot encoding, and the position of 1 is encoded as binary data 01 using one-hot encoding. The encoded data is then stored as a label.

1.2) The receiving end of the OTFS system receives the data through the channel, transforms it into the delay-Doppler domain, and stores MN received symbols in the domain:

The BPSK signal is placed in the M×N delay-Doppler domain, and then after the two-dimensional inverse sigmoid Fourier transform ISFFT and Heisenberg transform of the time domain signal, the signal-to-noise ratio is selected to be 10dB, the carrier center frequency is 4GHz, the subcarrier spacing is 15KHz, and it is transmitted through a multipath channel;

After receiving the time domain signal, the receiving end obtains MN delay-Doppler domain data after two-dimensional sigmoid Fourier transform and Wigner transform, and stores MN received symbols as training set data;

1.3) Repeat steps 1.1) and 1.2) for a total of C times. The number of training examples is selected through experiments. The principle of starting from small to large is adopted. Start with a small number of examples and then gradually increase the number of examples until the deep neural network becomes stable. The training set is obtained. C is determined according to the bit error rate requirements of the OTFS system.

In this example, M=16 and N=16 represent the total number of subcarriers and the total number of carrier symbols of the OTFS system respectively, the number of cycles C=30000, 8 transmission paths are used, and the position of each path is shown in Table 1.

Table 1 The delay-Doppler position of the path

path 1 2 3 4 5 6 7 8 Delay(us) 0 4.16 8.32 12.48 16.64 20.8 24.96 29.12 Doppler(Hz) 0 0 938.5 938.5 938.5 1875 1875 1875 Delay offset 0 1 2 3 4 5 6 7 Doppler shift 0 0 1 1 1 2 2 2

Step 2: Use the Tensorflow framework to build MN deep neural networks with exactly the same structure.

2.1) A three-layer structure including an input layer, a hidden layer, and an output layer is set up. The layers are connected in a fully connected manner to build a deep neural network, as shown in Figure 2.

The number of neurons in the input layer is determined by:

Since Doppler is divided into positive Doppler and negative Doppler, (2×k _max +1) neurons are required. At the same time, since Doppler data is complex, the input layer of the neural network is divided into the real part and imaginary part of (l _max +1)×(2×k _max +1) data. Therefore, the number of neurons in the input layer is finally determined as follows: K=2×(l _max +1)×(2×k _max +1), where l _max is the index of the maximum delay of the OTFS system, and _kmax is the index of the maximum Doppler of the OTFS system.

The number of neurons in the hidden layer is half of that in the input layer, that is, the number of neurons in the hidden layer is (l _max +1)×(2×k _max +1);

The number of neurons in the output layer is equal to the number Q=2 on the constellation diagram;

2.2) The sending and receiving relationship of OTFS is expressed in matrix form as follows:

y＝Hx+n

y表示接收信号，H表示矩阵，x表示发射信号，n表示噪声，向量y中的第k+Nl个元素满足关系y_k+Nl＝y[k,l]，同理x，n也满足该关系式，H中的元素则根据x，y的对应关系进行摆放。in,

y represents the received signal, H represents the matrix, x represents the transmitted signal, and n represents the noise. The k+Nlth element in the vector y satisfies the relationship y _k+Nl =y[k,l]. Similarly, x and n also satisfy this relationship. The elements in H are arranged according to the corresponding relationship between x and y.

2.3) Label the MN deep neural networks with the same structure as 2.1) as 1, 2, ..., MN, so that they correspond to the 1st to MN elements of the vector y in the OTFS system respectively.

Step 3: Use the training set to train the MN deep neural network separately.

Each network uses the same training method. This example takes the pth network as an example, and its training steps are as follows:

3.1) For the OTFS transceiver system, let the delay τ _i and Doppler υ _i on the i-th path be expressed as:

Wherein, l _i and k _i represent the indexes of the delay tap and Doppler tap respectively, Δf is the bandwidth of each subcarrier, T = 1/Δf;

3.2) Select the index range of maximum delay and maximum Doppler:

In this example, the maximum delay τ _max =29.12 μs, the maximum Doppler υ _max =1.875 KHz, and the corresponding indexes of the maximum delay tap and the maximum Doppler tap are:

l _max ＝τ _max MΔf,k _max ＝υ _max NT

We can find l _max =7, _kmax =2, then for the pth position y _p [k _p ,l _p ], 0≤k _p ≤N-1, 0≤l _p ≤M-1,

For this position, the index range of its maximum delay is selected as: l _p ≤L≤[l _p +l _max ] _M , the index range of the maximum Doppler is [k _p -k _max ] _N ≤K≤[k _p +k _max ] _N , there are a total of (l _max +1)×(2×k _max +1) data, where [.] _N represents a cyclic shift of N, and [.] _M represents a cyclic shift of M. This range is shown in the dotted box in FIG3 , where the data in the solid box represents the symbol of the p-th position;

3.3) For any training data in the training set, according to the corresponding relationship of the OTFS system in the delay-Doppler domain, separate the real and imaginary parts of the (l _max +1)×(2×k _max +1) data within the index range described in step 3.2) to form a new training data;

3.4) Repeat step 3.3) for a total of C times to form a new C-dimensional training set;

3.5) Use the new training set to train the deep neural network using batch gradient descent:

Although this training method consumes a lot of memory and takes a long time to train, it can ensure that each update is in the right direction and finally converges to the extreme point. Its performance is better than the stochastic gradient descent algorithm and the small batch gradient descent algorithm. The specific implementation steps are as follows:

3.5.1) Using random initialization method, the training parameters ω and b are initially assigned values;

3.5.2) The C-dimensional training set data is fed into the network, Adam is used as the optimizer, and the minimum mean square error function is used as the loss function;

3.5.3) The deep neural network uses the Sigmoid function as the output layer activation function, and the other layers use the Relu function as the activation function to obtain the output layer data of the network. The role of using the activation function here is to introduce nonlinear factors to make the network's learning ability stronger;

3.5.4) According to the current training parameters ω and b, calculate the gradient of the loss function at the current moment, and multiply the learning rate by the gradient of the loss function as the step size for the next update of the training parameters ω and b;

3.5.5) Calculate the loss function based on the output layer data and labels of the neural network and observe whether the loss function converges:

If converged, retain the training parameters ω and b in step 3.5.4) as the final training result;

If the loss function does not converge, re-update the training parameters ω and b according to the step size in step 3.5.4) so that they move in the direction of gradient descent, and then return to step 3.5.2) for retraining until the loss function converges.

Step 4: The receiving end of the OTFS system obtains the signal in the time-frequency domain.

4.1) At the transmitting end, the transmitted signal in the delay-Doppler domain is x[k,l]. After the two-dimensional symplectic inverse Fourier transform ISFFT, the time-frequency domain signal X[n,m] is obtained, and X[n,m] is transformed by Heisenberg to obtain the time domain signal x(t), which are expressed as follows:

Where g _tx (t) is the transmitted waveform pulse, and the time domain signal is transmitted through the wireless channel;

4.2) The receiver of the OTFS system receives the time domain signal y(t) sent by its transmitter:

Where h(τ,υ) represents the channel information, τ represents the delay index, and υ represents the Doppler index;

4.3) Perform Wigner transform on the time domain signal y(t) to obtain the signal Y[n,m] in the time-frequency domain;

Y[n,m]＝A _grx,y (t,f)| _{t＝nT,f＝mΔf}

Among them, A _grx,y (t,f) represents the mutual ambiguity function obtained by the matched filter at the receiving end, t represents the time index, f represents the frequency index, Δf is the bandwidth of each subcarrier, T = 1/Δf, represents the time interval, g _rx (t) is the received waveform pulse at the receiving end, g _r ^* _x (t) represents the conjugate transpose, and j represents the imaginary part.

Step 5: The receiving end obtains MN received symbols in the delay-Doppler domain.

Perform a two-dimensional sigmoid Fourier transform SFFT on the signal Y[n,m] in the time-frequency domain to obtain MN received symbols in the delay-Doppler domain:

h_i表示第i条路径上的信道系数，υ_i，τ_i分别表示该条路径上的时延和多普勒，l_i和k_i分别表示第i条路径的时延抽头和多普勒抽头的索引，v[k,l]表示在时延-多普勒域中时延索引为k、多普勒索引为l位置的噪声。Where y[k,l] represents a received symbol with delay index k and Doppler index l in the delay-Doppler domain, k = 0, 1...N-1, l = 0, 1...M-1, P represents the number of channel paths,

_hi represents the channel coefficient on the i-th path, _υi , _τi represent the delay and Doppler on the path respectively, _li and _ki represent the indexes of the delay tap and Doppler tap of the i-th path respectively, and v[k,l] represents the noise at the position with delay index k and Doppler index l in the delay-Doppler domain.

Step 6: Use the trained MN deep neural networks to detect the received symbols one by one.

6.1) The MN received symbols in the delay-Doppler domain are respectively corresponded to the MN trained deep neural networks, and the same method is used to detect any of the received signals;

6.2) For the pth received symbol _yp [ _kp , _lp ], select the data of ( _lmax +1)×(2× _kmax +1) positions within the dotted line range in Figure 3, and the index range of the delay is _lp≤L≤ [ _lp + _lmax ] _M , and the index range of the Doppler is

[k _p -k _max ] _N ≤K≤[k _p +k _max ] _N ;

6.3) Separate the real and imaginary parts of the data within the delay index range and the Doppler index range, and obtain

2×(l _max +1)×(2×k _max +1) data are used as the input layer signal of the pth deep neural network. After passing through (l _max +1)×(2×k _max +1) hidden layer neurons and Q output layer neurons in the network, the output of the neuron is obtained.

6.4) The output layer uses the Sigmoid function as the activation function. The output range of each neuron is in the interval [0,1]. The data of all output neurons are traversed to obtain the maximum data.

6.5) The position of the maximum data is recorded as a, a = 1, 2, ..., Q, and the points on the constellation diagram are sorted from left to right and from top to bottom as 1, 2, ..., a, ..., Q, where the data corresponding to the point on the a-th constellation diagram is the estimated value of the transmitted symbol.

For this example, Q=2, when a=1, it indicates a point with a value of -1 on the constellation diagram, and when a=2, it indicates a point with a value of 1 on the constellation diagram.

The effect of the present invention can be further illustrated by the following simulation experiment:

1. Simulation conditions

The hardware platform of the simulation experiment is: the processor is Intel i3 8100CPU, the main frequency is 3.6GHz, and the memory is 8GB.

The software platform for the simulation experiment is: Windows 10 operating system, MATLAB R2020b and Python3.6.

The channel type of the simulation experiment is a complex Gaussian channel, the number of channel paths is selected as 8, the subcarrier spacing is 15KHz, the maximum Doppler is 1.875KHz, the maximum delay is 29.12μs, and the number of cycles for statistical bit error rate is 1000000 times.

The simulation and network parameters are shown in Table 2.

Table 2 Simulation and network parameters

parameter Symbolic DNN Low Complexity DNN Channel Path 8 8 Number of subcarriers (M) 16 16 Total number of symbols (N) 16 16 Carrier center frequency 4GHz 4GHz Modulation BPSK BPSK Number of input neurons 512 80 Number of output neurons 2 2 Output layer activation function Softmax Sigmoid The activation functions of the remaining layers Relu Relu Optimizer Adam Adam Loss Function Binary-crossentropy MMSE Training SNR 10dB 10dB Training set size 30000 30000 Number of training sessions 100 100

2. Analysis of simulation results:

Simulation experiment 1, under the above simulation conditions, the present invention and the existing MMSE technology and symbol-DNN technology are used to perform symbol detection on 1,000,000 received symbols of the OTFS system, and the corresponding detection bit error rate is obtained. The results are shown in Figure 4. The horizontal axis represents the signal-to-noise ratio of the transmitted symbol, in dB; the vertical axis represents the bit error rate of symbol detection.

In the simulation experiment of the present invention, two prior arts refer to:

MMSE technology: Ahmad Nimr et al. in “Extended GFDM Framework: OTFS and GFDM

Comparison, 2018IEEE Global Communications Conference (GLOBECOM), 2018, pp.1-6.”

Detection method of the MMSE detector proposed in the OTFS system.

Symbol-DNN technology: Ashwitha Naikoti et al. proposed a symbol-DNN detection method in the OTFS system in their paper "Low-complexity Delay-Doppler Symbol DNN for OTFS Signal Detection" (IEEE 93rd Vehicular Technology Conference 2021).

As can be seen from FIG4 , the performance of the present invention is significantly better than the traditional MMSE detection scheme and the complexity is lower than the MMSE detector. Compared with the existing symbol-DNN network, the performance is similar but the complexity is reduced.

In simulation experiment 2, the number of parameters required to be trained for the present invention and the existing symbol-DNN technology when MN=256 is calculated respectively. The results are shown in Table 3:

Table 3: Number of training parameters M=N=16

As can be seen from Table 3, the amount of training data of the present invention is reduced by 40 times compared with the prior art. This is because the present invention uses the data of maximum delay and maximum Doppler for detection. For each received symbol to be detected, the input end of the detector is all the data within the maximum delay index and maximum Doppler index range of the symbol. According to the characteristic that any symbol of the OTFS system will not exceed its maximum delay and maximum Doppler, the signal within this range is used for feature extraction. Although this scheme contains a lot of useless information, it can still be ignored due to the powerful learning ability of neural networks. Compared with the existing symbol-DNN technology, which uses all signals in the entire delay-Doppler domain for detection, the useless information in the present invention is much less than the symbol-DNN technology, and the parameters to be trained and the number of neurons required are also significantly less than the symbol-DNN network, thereby reducing the complexity of the entire detection system.

Claims (6)

1. The OTFS system symbol detection method based on the deep neural network is characterized by comprising the following steps

(1) Obtaining a training set;

1a) The OTFS system transmitting terminal sends the modulated signal, one-hot coding is carried out on the point on the constellation diagram of the transmitted signal, and the coded data is stored as a label;

1b) Receiving end of OTFS system receives data passing through channel, converting it to time delay-Doppler domain, and storing MN receiving symbols of the domain;

1c) Circulating the steps 1 a) and 1 b) for C times to obtain a training set, wherein C is determined according to the performance of the OTFS system;

(2) MN deep neural networks with completely identical structures are built, each network comprises an input layer, a hidden layer and an output layer, and all the layers are connected in a full-connection mode; marking MN networks to respectively correspond to MN receiving symbols in the OTFS system, wherein M and N respectively represent the total number of subcarriers and the total number of symbols of the OTFS system;

(3) Training each deep neural network using a training set:

3a) According to the corresponding relation between the time delay and the Doppler of the OTFS system, all data in the maximum time delay and the maximum Doppler range of the detection symbol corresponding to the network are used as input signals and input into an input layer of a neural network;

3b) Training the deep neural network by adopting a gradient descent algorithm to obtain data of an output layer;

3c) Adopting a minimum mean square error function as a loss function of the deep neural network, comparing the output layer data obtained in the step 3 b) with the label of the step 1 a), and judging whether the loss function is converged:

if so, finishing the training to obtain a trained deep neural network:

otherwise, returning to the step (3 b);

(4) A receiving end of the OTFS system receives a time domain signal sent by a transmitting end of the OTFS system, and carries out Wigner transformation on the time domain signal to obtain a signal Y [ n, m ] of a time-frequency domain;

(5) Performing octave Fourier transform (SFFT) on the signals in the time-frequency domain to obtain MN receiving symbols in the delay-Doppler domain;

(6) Adopting MN deep neural networks after training, carrying out symbol-by-symbol detection on received symbols:

6a) The MN symbols received in the step (5) correspond to the MN deep neural networks trained in the step (3), and the deep neural network corresponding to each received symbol is found;

6b) Taking all data in the maximum time delay and the maximum Doppler range of each received symbol as corresponding trained deep neural network input layer data to obtain output layer data of each neural network;

(6c) And obtaining an estimated value of the sending symbol according to the output layer data of each neural network, and completing the detection of the OTFS system symbol.

2. The method according to claim 1, wherein the one-hot encoding is performed on the points on the constellation diagram of the transmitted signal in step 1 a) as follows:

1a1) Determining the number Q of points on a constellation diagram, and taking the number Q as the bit number of one-hot coding;

1a2) The points on the constellation diagram are sorted into 1,2, …, Q, … and Q according to the sequence from left to right and from top to bottom, and for the Q-th point, the Q-th bit in the corresponding one-hot code is 1, and the rest are 0.

3. The method of claim 1, wherein the deep neural network is trained in step 3 b) using a gradient descent algorithm to obtain output layer data as follows:

3b1) Calculating the gradient of a loss function at the current moment according to the training parameters at the current moment;

3b2) Multiplying the step length by the gradient of the loss function to obtain the descending distance of the current position;

3b3) Setting a threshold value epsilon according to the bit error rate requirement of the OTFS system, and judging whether the gradient descending distance of all training parameters is smaller than epsilon:

if the training parameters are smaller than epsilon, all the current training parameters are the final output layer data;

otherwise, updating all training parameters and returning to the step (3 b 1).

4. The method according to claim 1, wherein the time-frequency domain signal Y [ n, m ] obtained in step (4) is represented as follows:

Y[n,m]＝A _grx,y (t,f)| _{t＝nT,f＝mΔf}

wherein A is _grx,y (T, f) represents the cross-ambiguity function obtained by the matched filter at the receiving end, T represents the time index, f represents the frequency index, Δ f is the bandwidth of each subcarrier, T =1/Δ f represents the time interval, g _rx (t) is a received waveform pulse at the receiving end,

denotes the conjugate transpose, j denotes the imaginary part, y (t) denotes the received time domain signal as:

y(t)＝∫ _υ ∫ _τ h(τ,υ)x(t-τ)e ^j2πυ(t-τ) dτdυ

h (tau, upsilon) represents channel information, tau represents a time delay index, upsilon represents a Doppler index, and x (t) represents a time domain transmitting signal of a transmitting terminal.

5. The method of claim 1, wherein the step (5) obtains MN received symbols in the delay-doppler domain as follows:

wherein, y [ k, l]Denotes one received symbol with delay index k and doppler index l in the delay-doppler domain, k =0,1.. N-1, l =0,1.. M-1,P denotes the number of channel paths,

h _i representing the channel coefficients on the ith path, where v _i ，τ _i Respectively representing the delay and the Doppler on the path,/ _i And k _i Indices representing the delay tap and the doppler tap of the ith path, respectively, [.] _N Represents a cyclic shift of N.] _M Denotes cyclic shift of M, v [ k, l]Representing the noise at the location of delay index k and doppler index l in the delay-doppler domain.

6. The method of claim 1 wherein the step (6 c) of obtaining an estimate of the transmitted symbols from the output layer data of each neural network is

6c1) Traversing Q output layer data of the deep neural network to obtain the position of the maximum value, and marking as a;

6c2) The points on the constellation diagram are sorted into 1,2, … … and Q according to the sequence from left to right and from top to bottom, wherein the data corresponding to the point on the a-th constellation diagram is the estimated value of the transmitted symbol.

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