Deep learning-based compressed sensing impulse noise suppression method for NOMA (Non-Orthogonal Multiple Access) system

Abstract

The invention discloses a deep learning-based compressed sensing impulse noise suppression method for an NOMA (Non-Orthogonal Multiple Access) system, which uses a compressed sensing reconstruction network to replace a traditional compressed sensing algorithm, and can more effectively learn the characteristics of impulse noise by using a huge receptive field of the compressed sensing reconstruction network, so that the impulse noise is more accurately reconstructed, and the noise suppression efficiency is improved. The pulse noise suppression effect is improved; in order to further optimize the training efficiency of the network, the compressed sensing reconstruction network uses a residual connection structure, so that the convergence speed of the network in the training process is accelerated; a simulation result proves that compared with the prior art, the method disclosed by the invention has the advantages that the convergence speed during training is obviously accelerated while the performance of lower bit error rate is obtained.

Description

Technical Field

[0001] The present invention relates to a NOMA (Non-Orthogonal Multiple Access) system technology, and in particular to a compressed sensing impulse noise suppression method based on deep learning in a NOMA system. Background Art

[0002] With the increasing application of IoT technology, NOMA has been widely introduced as an effective access technology to meet the connectivity, reliability and low latency requirements for massive device access. NOMA allows multiple users to share the same spectrum resources through power domain reuse, thereby achieving large-scale connectivity and significantly improving spectrum efficiency. Therefore, NOMA has become an important candidate solution in IoT and future radio network systems (such as 5G and Beyond 5G / 6G).

[0003] However, multiple studies have shown that impulse noise is a common source of interference in various indoor environments, manufacturing plants, industrial equipment, and high-voltage environments. The presence of this non-Gaussian impulse noise will cause the performance of communication systems designed based on the Additive White Gaussian Noise (AWGN) assumption to drop sharply. Especially in NOMA systems, power domain multiplexing and successive interference cancellation (Successive Interference Cancellation, SIC) technology make the system particularly sensitive to impulse noise interference. The SIC process relies on accurate signal estimation, and impulse noise can interfere with this process, resulting in decoding errors or failures, which in turn affects the overall performance of the system.

[0004] Traditional impulse noise suppression methods usually detect the high peak amplitude in the signal at the receiving end, and perform limiting, blanking, or a combination of the two (combined limiting and blanking) on ​​the detected high peak amplitude. Although this processing can reduce the impact of high peak amplitude interference on the received signal, when the channel conditions change, the preset detection threshold may no longer adapt to the new channel characteristics, resulting in the setting parameters not matching the actual situation (i.e., model mismatch). Specifically, traditional impulse noise suppression methods rely on fixed detection thresholds to identify and process impulse noise. When channel conditions (such as multipath effects, fading, changes in interference intensity, etc.) change, these fixed detection thresholds may no longer be accurate, resulting in the system being unable to correctly distinguish between noise and useful signals. This will not only cause false detection (misidentifying normal signals as noise) and missed detection (failure to correctly identify actual noise), but will also ultimately affect the performance of the communication system, such as increased bit error rate and reduced reliability.

[0005] In order to cope with the limitations of traditional methods, impulse noise suppression methods based on compressed sensing have emerged. Such methods use the sparse characteristics of impulse noise in the time domain to convert the impulse noise estimation problem into a sparse signal estimation problem. Although such methods have potential in suppressing impulse noise, they have poor bit error rate performance in some applications, especially in the case of high noise intensity or poor signal quality, the bit error rate may increase significantly, thus affecting the overall reliability and performance of the communication system. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a compressed sensing pulse noise suppression method for a NOMA system based on deep learning, which has good bit error rate performance when applied.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a compressed sensing impulse noise suppression method based on deep learning in a NOMA system, wherein the method assumes that there are multiple users in the NOMA system, and the entire frequency band in the NOMA system is divided into multiple subcarriers, including null subcarriers and data subcarriers; the method is characterized in that the method comprises the following steps:

[0008] Step 1: At the transmitting end of the NOMA system, the NOMA time-domain transmission signal with a cyclic prefix is ​​continuously transmitted to all users through a multipath channel;

[0009] Step 2: At the receiving end of the NOMA system, the cyclic prefix is ​​removed from the received time domain signal; then, based on the time domain signal obtained after removing the cyclic prefix, the NOMA time domain received signal for any user is obtained; then, a discrete Fourier transform is performed on the NOMA time domain received signal to convert it from the time domain to the frequency domain to obtain the NOMA frequency domain received signal; then, the NOMA frequency domain received signal is divided into two parts: a data subcarrier-related signal and a null subcarrier-related signal;

[0010] Step 3: The true value of the time domain impulse noise in the NOMA system transmission process is used as the impulse noise label, the empty subcarrier related signal and the impulse noise label are combined into a training sample, and several training samples are combined into a training set;

[0011] Step 4: Construct a compressed sensing reconstruction network, which includes a fully connected layer, a first one-dimensional convolutional layer, four residual gated convolutional modules, and a second one-dimensional convolutional layer; then train the compressed sensing reconstruction network based on the training set, as follows:

[0012] Step 4.1: Randomly initialize all weights and biases in the compressed sensing reconstruction network;

[0013] Step 4.2: Input the training samples into the compressed sensing reconstruction network. The input end of the fully connected layer is the input end of the compressed sensing reconstruction network, and the output end of the second one-dimensional convolutional layer is the output end of the compressed sensing reconstruction network. The input end of the fully connected layer receives the empty subcarrier related signal in the training sample, and the vector output by the output end of the fully connected layer is input into the input end of the first one-dimensional convolutional layer after the relu activation function. The vector output by the output end of the first one-dimensional convolutional layer is input into the input end of the first residual gated convolution module, and the first The vector output from the output end of the residual gated convolution module is input to the input end of the second residual gated convolution module, the vector output from the output end of the second residual gated convolution module is input to the input end of the third residual gated convolution module, the vector output from the output end of the third residual gated convolution module is input to the input end of the fourth residual gated convolution module, the vectors output from the output ends of the four residual gated convolution modules are connected through a skip layer and then input to the second one-dimensional convolution layer after passing through a relu activation function, and the vector output from the output end of the second one-dimensional convolution layer is used as an estimated value of the time domain impulse noise;

[0014] Step 4.3: According to the back-propagation algorithm, the adaptive moment estimation optimizer is used to minimize the loss function and update all weights and biases in the compressed sensing reconstruction network; after the training is completed, the trained compressed sensing reconstruction network is obtained;

[0015] Step 5: For any NOMA time-domain received signal, follow the process of step 2 to obtain the empty subcarrier related signal in the same way; then input the empty subcarrier related signal into the trained compressed sensing reconstruction network, and the vector output by the trained compressed sensing reconstruction network is the reconstructed time-domain impulse noise; then subtract the reconstructed time-domain impulse noise from the NOMA time-domain received signal to obtain the signal after suppressing the impulse noise.

[0016] In step 2, the NOMA time domain received signal is recorded as Among them, H represents the channel circular convolution matrix, x t represents the time domain signal obtained after removing the cyclic prefix, n represents the total noise, n follows the Bernoulli-Gaussian process, n = n w +n I , n w represents the time domain background noise, n I represents the time domain impulse noise; the NOMA frequency domain received signal is recorded as Y, Where F represents the normalized discrete Fourier transform matrix, the superscript “*” represents the conjugate transpose operation, and x t After discrete Fourier transform, we get x, that is, x = Fx t , Λ=FHF *, Λ is a diagonal matrix, W represents the frequency domain background noise, W = Fn w ; The data subcarrier related signal and the empty subcarrier related signal are correspondingly recorded as Y D and Y P , Y D =(Λx) D +F D n I +W D , Y P =(Λx) P +F P n I +W P =F P n I +W P , where (Λx) D Indicates that N in Λx is related to the data subcarrier D A vector consisting of elements, (Λx) P Indicates that N associated with the empty subcarrier in Λx P A vector consisting of elements, F D Indicates that N associated with the data subcarrier in F D The matrix composed of row vectors, F P Indicates that N associated with the empty subcarrier in F P The matrix composed of row vectors, W D Represents the N associated with the data subcarrier in W D A vector consisting of elements, W P Represents the N associated with the empty subcarrier in W P A vector consisting of N elements, D Indicates the number of data subcarriers, N P Indicates the number of empty subcarriers, N D +N P =N, where N represents the number of subcarriers.

[0017] In step 4.2, the vector output from the output end of the fully connected layer is obtained after the relu activation function, and h=relu(ω h Y P +b h ), where ω h Y P +b h represents the vector output from the output of the fully connected layer, relu(·) represents the relu activation function, ω h represents the weight matrix of the fully connected layer, Y P represents the null subcarrier related signal in the training sample, b h Represents the bias vector of the fully connected layer.

[0018] In step 4.2, the vector output from the output end of the first one-dimensional convolutional layer is a vector y obtained after the relu activation function. in, represents the vector output from the output of the first one-dimensional convolutional layer, relu(·) represents the relu activation function, and w y represents the convolution kernel of the first one-dimensional convolutional layer, h represents the vector obtained by the relu activation function after the output vector of the fully connected layer is activated, and b y represents the bias vector of the first one-dimensional convolutional layer, is the convolution operator symbol.

[0019] In the step 4.2, the four residual gated convolution modules have the same structure, including a gated convolution module and a one-dimensional convolution layer, the gated convolution module is composed of an activation layer and a gated layer arranged in parallel, the input end of the activation layer is connected to the input end of the gated layer and serves as the input end of the gated convolution module, the input end of the gated convolution module is the input end of the residual gated convolution module, the input end of the one-dimensional convolution layer receives the vector output by the output end of the gated convolution module, the vector received by the input end of the gated convolution module is added to the vector output by the output end of the one-dimensional convolution layer through a skip layer, and the vector obtained by the addition is output by the output end of the residual gated convolution module;

[0020] The output vector of the gated convolution module in the first residual gated convolution module is z 1 , z 1 =tanh(w 1,1 *y)⊙S(w 1,2 *y), where tanh(w 1,1 *y) represents the vector output from the output end of the activation layer in the gated convolution module in the first residual gated convolution module. The activation layer includes a dilated convolution layer and a tanh activation function layer. The vector output from the dilated convolution layer passes through the tanh activation function layer as the output vector of the activation layer. S(w 1,2 *y) represents the vector output from the output end of the gated layer in the gated convolution module in the first residual gated convolution module. The gated layer includes a dilated convolution layer and a sigmoid activation function layer. The vector output from the dilated convolution layer is used as the vector output from the gated layer after passing through the sigmoid activation function layer. tanh(·) represents the tanh activation function, S(·) represents the sigmoid activation function, “⊙” is the Hadamard product operator, “*” is the dilated convolution operator, y represents the vector obtained after the vector output from the output end of the first one-dimensional convolution layer passes through the relu activation function, and w 1,1 represents the dilated convolution kernel of the dilated convolution layer in the activation layer of the gated convolution module in the first residual gated convolution module, w 1,2represents the dilated convolution kernel of the dilated convolution layer in the gated layer in the gated convolution module in the first residual gated convolution module; the vector output at the output end of the first residual gated convolution module is f 1 , Among them, w f,1 represents the convolution kernel of the one-dimensional convolution layer in the first residual gated convolution module, is the convolution operator symbol, b f,1 Represents the bias vector of the one-dimensional convolution layer in the first residual gated convolution module;

[0021] The vector output at the output of the gated convolution module in the kth residual gated convolution module is z k , z k =tanh(w k,1 *f k-1 )⊙S(w k,2 *f k-1 ), where k = 2, 3, 4, tanh(w k,1 *f k-1 ) represents the vector output from the output of the activation layer in the gated convolution module in the kth residual gated convolution module, S(w k,2 *f k-1 ) represents the vector output from the output of the gated layer in the gated convolution module in the kth residual gated convolution module, f k-1 represents the vector output from the output of the k-1th residual gated convolution module, w k,1 represents the dilated convolution kernel of the dilated convolution layer in the activation layer of the gated convolution module in the kth residual gated convolution module, w k,2 represents the dilated convolution kernel of the dilated convolution layer in the gated layer in the gated convolution module in the kth residual gated convolution module; the vector output at the output end of the kth residual gated convolution module is f k , Among them, w f,k represents the convolution kernel of the one-dimensional convolution layer in the kth residual gated convolution module, b f,k Represents the bias vector of the one-dimensional convolutional layer in the k-th residual gated convolution module.

[0022] In step 4.2, the vector outputted by the output terminal of the second one-dimensional convolutional layer is f, Among them, w f represents the convolution kernel of the second one-dimensional convolutional layer, f 1 、f 2 、f 3 、f 4 Corresponding to the vectors of the output of the first, second, third, and fourth residual gated convolution modules, f 1 +f 2 +f3 +f 4 The vectors representing the outputs of the four residual gated convolutional modules are connected via skip layers, b f Represents the bias vector of the second one-dimensional convolutional layer.

[0023] In step 4.3, the loss function is calculated using the mean square error, and the calculation formula of the loss function is: Where MSE represents the loss function value, Num represents the number of training samples contained in the training set, i = 1, 2, ..., Num, Y P,i represents the null subcarrier related signal in the i-th training sample in the training set, G WaveNet (·) represents the compressed sensing reconstruction network, G WaveNet (Y P,i ) represents the vector output from the output of the compressed sensing reconstruction network, that is, the estimated value of the time-domain impulse noise, Represents Y P,i The corresponding impulse noise label.

[0024] In step 4.1, the initial learning rate is set to 0.0001, batch_size=128, and epoch=300.

[0025] In step 1, the acquisition process of the NOMA time domain transmission signal with a cyclic prefix is ​​as follows: channel coding is performed on the binary signal sequence sent to each user; then the bit stream obtained after channel coding is interleaved; then the signal obtained after the interleaving process is modulated; then the modulated signals corresponding to all users are superposition coded; then the composite signal obtained after superposition coding is inversely discrete Fourier transformed to convert it from the frequency domain to the time domain to obtain a time domain baseband signal; finally, a cyclic prefix is ​​inserted before each OFDM symbol of the time domain baseband signal to obtain a NOMA time domain transmission signal with a cyclic prefix.

[0026] Compared with the prior art, the advantages of the present invention are:

[0027] (1) The method of the present invention can estimate the impulse noise in the NOMA system more accurately. By dilating the convolution, the compressed sensing reconstruction network can cover a wider input range and more effectively capture the long-term time dependence of the impulse noise, thereby estimating the impulse noise more accurately. Compared with the existing method, a bit error rate gain of about 5db can be obtained.

[0028] (2) The method of the present invention has a significant advantage in convergence speed in neural network training. It uses a residual connection mechanism, which not only helps to avoid the gradient vanishing problem that may occur during deep network training, but also accelerates the learning process and promotes the effective learning of deeper features. Compared with existing deep learning methods, it can achieve lower loss function values ​​with fewer training rounds, and has faster convergence speed and higher training efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A flowchart for implementing impulse noise suppression of the entire NOMA system using the method of the present invention;

[0030] Figure 2 A schematic diagram of the structure of a compressed sensing reconstruction network constructed in the method of the present invention;

[0031] Figure 3 Schematic diagram of the change of loss function values ​​of CSR-WaveNet method and DCNN method with training rounds (epoch);

[0032] Figure 4 Schematic diagram of the change of the bit error rate (BER) of the first user with the signal-to-noise ratio (SNR) when using the BP method, SL0 method, DCNN method, and CSR-WaveNet method respectively;

[0033] Figure 5 Schematic diagram of the change of the bit error rate (BER) of the first user with the number of empty subcarriers when using the BP method, SL0 method, DCNN method, and CSR-WaveNet method respectively;

[0034] Figure 6 Schematic diagram of the change of the bit error rate (BER) of the first user with the impulse noise sparsity when using the BP method, SL0 method, DCNN method, and CSR-WaveNet method respectively;

[0035] Figure 7 Schematic diagram of the change of bit error rate (BER) of two users with signal-to-noise ratio (SNR) when using DCNN method and CSR-WaveNet method respectively. DETAILED DESCRIPTION

[0036] The present invention is further described in detail below with reference to the accompanying drawings.

[0037] The present invention proposes a NOMA system compressed sensing impulse noise suppression method based on deep learning. Figure 1The implementation process of the impulse noise suppression of the entire NOMA system using the method of the present invention is shown. The method assumes that there are multiple users in the NOMA system, and the entire frequency band in the NOMA system is divided into multiple subcarriers, including null subcarriers and data subcarriers; the method includes the following steps:

[0038] Step 1: At the transmitting end of the NOMA system, the NOMA time domain transmission signal with a cyclic prefix is ​​continuously transmitted to all users through a multipath channel. In this embodiment, a first-order multipath channel is selected as the multipath channel.

[0039] It is further defined that the acquisition process of the NOMA time-domain transmission signal with a cyclic prefix is ​​as follows: channel coding is performed on the binary signal sequence sent to each user; then the bit stream obtained after the channel coding is interleaved; then the signal obtained after the interleaving process is modulated, that is, the signal obtained after the interleaving process is mapped to the points of the constellation diagram; then, superposition coding, that is, power domain multiplexing, is performed on the modulated signals corresponding to all users; then, an inverse discrete Fourier transform (IDFT) is performed on the composite signal obtained after the superposition coding, and it is converted from the frequency domain to the time domain to obtain a time domain baseband signal; finally, a cyclic prefix (CP) is inserted before each OFDM symbol of the time domain baseband signal to obtain the NOMA time-domain transmission signal with a cyclic prefix.

[0040] Step 2: At the receiving end of the NOMA system, the cyclic prefix is ​​removed from the received time domain signal; then, based on the time domain signal obtained after removing the cyclic prefix, the NOMA time domain received signal for any user is obtained; then, a discrete Fourier transform is performed on the NOMA time domain received signal to convert it from the time domain to the frequency domain to obtain the NOMA frequency domain received signal; then, the NOMA frequency domain received signal is divided into two parts: data subcarrier-related signals and empty subcarrier-related signals.

[0041] Further definition, the NOMA time domain received signal is recorded as Among them, H represents the channel circular convolution matrix, x t represents the time domain signal obtained after removing the cyclic prefix, n represents the total noise, n follows the widely used Bernoulli-Gaussian process, n = n w +n I , n w represents the time domain background noise, n I represents the time domain impulse noise; the NOMA frequency domain received signal is recorded as Y, Where F represents the normalized discrete Fourier transform matrix, the superscript “*” represents the conjugate transpose operation, and x tAfter discrete Fourier transform, we get x, that is, x = Fx t , Λ=FHF * , Λ is a diagonal matrix, the elements on its diagonal are the frequency domain response of the channel, W represents the frequency domain background noise, W = Fn w ; The data subcarrier related signal and the empty subcarrier related signal are correspondingly recorded as Y D and Y P , Y D =(Λx) D +F D n I +W D , Y P =(Λx) P +F P n I +W P =F P n I +W P , because there is no data in the empty subcarrier, so (Λx) P =0, where (Λx) D Indicates that N in Λx is related to the data subcarrier D A vector consisting of elements, (Λx) P Indicates that N associated with the empty subcarrier in Λx P A vector consisting of elements, F D Indicates that N associated with the data subcarrier in F D The matrix composed of row vectors, F P Indicates that N associated with the empty subcarrier in F P The matrix composed of row vectors, W D Represents the N associated with the data subcarrier in W D A vector consisting of elements, W P Represents the N associated with the empty subcarrier in W P A vector consisting of N elements, D Indicates the number of data subcarriers, N P Indicates the number of empty subcarriers, N D +N P =N, N represents the number of subcarriers, x t 、n、n w 、n I The dimensions of Y, x, and W are all N×1, the dimensions of H, F, and Λ are all N×N, and Y D , (Λx) D , W D The dimension is N D ×1, F D The dimension is N D ×N,Y P, (Λx) P , W P The dimension is N P ×1, F D The dimension is N P ×N.

[0042] Step 3: The true value of the time domain impulse noise in the NOMA system transmission process is used as the impulse noise label, the empty subcarrier related signal and the impulse noise label are combined into a training sample, and several training samples constitute a training set.

[0043] Here, Num NOMA time-domain transmission signals with cyclic prefixes are transmitted at the transmitting end of the NOMA system, and then Num training samples can be obtained.

[0044] Step 4: Construct a compressed sensing reconstruction network (Compressed Sensing Reconstruction WaveNet, CSR-WaveNet), such as Figure 2 As shown in the figure, it includes a fully connected layer, a first one-dimensional convolutional layer, four residual gated convolutional modules, and a second one-dimensional convolutional layer; then, based on the training set, the compressed sensing reconstruction network is trained as follows:

[0045] Step 4.1: Randomly initialize all weights and biases in the compressed sensing reconstruction network, and set the initial learning rate to 0.0001, batch_size = 128, and training round epoch = 300.

[0046] Step 4.2: Input the training samples into the compressed sensing reconstruction network. The input end of the fully connected layer is the input end of the compressed sensing reconstruction network, and the output end of the second one-dimensional convolutional layer is the output end of the compressed sensing reconstruction network. The input end of the fully connected layer receives the empty subcarrier related signal in the training sample, and the vector output by the output end of the fully connected layer is input into the input end of the first one-dimensional convolutional layer after the relu activation function. The vector output by the output end of the first one-dimensional convolutional layer is input into the input end of the first residual gated convolution module, and the first The vector output from the output end of the residual gated convolution module is input to the input end of the second residual gated convolution module, the vector output from the output end of the second residual gated convolution module is input to the input end of the third residual gated convolution module, the vector output from the output end of the third residual gated convolution module is input to the input end of the fourth residual gated convolution module, the vectors output from the output ends of the four residual gated convolution modules are connected through skip layers and then input to the second one-dimensional convolution layer after passing through the relu activation function, and the vector output from the output end of the second one-dimensional convolution layer is used as the estimated value of the time domain impulse noise.

[0047] Further, in step 4.2, the vector output from the output end of the fully connected layer after the relu activation function is obtained as h, h = relu (ω h Y P +b h ), where ω h Y P +b h represents the vector output from the output of the fully connected layer, relu(·) represents the relu activation function, ω h represents the weight matrix of the fully connected layer, Y P represents the null subcarrier related signal in the training sample, b h Represents the bias vector of the fully connected layer.

[0048] Further defined, in step 4.2, the vector output from the output end of the first one-dimensional convolutional layer after the relu activation function is the vector y, in, represents the vector output from the output of the first one-dimensional convolutional layer, relu(·) represents the relu activation function, and w y represents the convolution kernel of the first one-dimensional convolutional layer, h represents the vector obtained by the relu activation function after the output vector of the fully connected layer is activated, and b y represents the bias vector of the first one-dimensional convolutional layer, is the convolution operator symbol.

[0049] It is further defined that in step 4.2, the structures of the four residual gated convolution modules are the same, including a gated convolution module and a one-dimensional convolution layer. The gated convolution module is composed of an activation layer and a gated layer arranged in parallel. The input end of the activation layer is connected to the input end of the gated layer and serves as the input end of the gated convolution module. The input end of the gated convolution module is the input end of the residual gated convolution module in which it is located. The input end of the one-dimensional convolution layer receives the vector output by the output end of the gated convolution module. The vector received by the input end of the gated convolution module is added to the vector output by the output end of the one-dimensional convolution layer through the skip layer, and the added vector is output by the output end of the residual gated convolution module in which it is located. The vector output by the output end of the gated convolution module in the first residual gated convolution module is z 1 , z 1 =tanh(w 1,1 *y)⊙S(w 1,2 *y), where tanh(w 1,1 *y) represents the vector output from the output end of the activation layer in the gated convolution module in the first residual gated convolution module. The activation layer includes a dilated convolution layer and a tanh activation function layer. The vector output from the dilated convolution layer passes through the tanh activation function layer as the output vector of the activation layer. S(w 1,2*y) represents the vector output from the output end of the gated layer in the gated convolution module in the first residual gated convolution module. The gated layer includes a dilated convolution layer and a sigmoid activation function layer. The vector output from the dilated convolution layer is used as the vector output from the gated layer after passing through the sigmoid activation function layer. tanh(·) represents the tanh activation function, S(·) represents the sigmoid activation function, “⊙” is the Hadamard product operator, “*” is the dilated convolution operator, y represents the vector obtained after the vector output from the output end of the first one-dimensional convolution layer passes through the relu activation function, and w 1,1 represents the dilated convolution kernel of the dilated convolution layer in the activation layer of the gated convolution module in the first residual gated convolution module, w 1,2 represents the dilated convolution kernel of the dilated convolution layer in the gated layer in the gated convolution module in the first residual gated convolution module; the vector output at the output end of the first residual gated convolution module is f 1 , Among them, w f,1 represents the convolution kernel of the one-dimensional convolution layer in the first residual gated convolution module, is the convolution operator symbol, b f,1 represents the bias vector of the one-dimensional convolution layer in the first residual gated convolution module. The vector output at the output of the gated convolution module in the kth residual gated convolution module is z k , z k =tanh(w k,1 *f k-1 )⊙S(w k,2 *f k-1 ), where k = 2, 3, 4, tanh(w k,1 *f k-1 ) represents the vector output from the output of the activation layer in the gated convolution module in the kth residual gated convolution module, S(w k,2 *f k-1 ) represents the vector output from the output of the gated layer in the gated convolution module in the kth residual gated convolution module, f k-1 represents the vector output from the output of the k-1th residual gated convolution module, w k,1 represents the dilated convolution kernel of the dilated convolution layer in the activation layer of the gated convolution module in the kth residual gated convolution module, w k,2 represents the dilated convolution kernel of the dilated convolution layer in the gated layer in the gated convolution module in the kth residual gated convolution module; the vector output at the output end of the kth residual gated convolution module is f k , Among them, w f,k represents the convolution kernel of the one-dimensional convolution layer in the kth residual gated convolution module, b f,kRepresents the bias vector of the one-dimensional convolutional layer in the k-th residual gated convolution module.

[0050] Further defining, in step 4.2, the vector outputted by the output terminal of the second one-dimensional convolutional layer is f, Among them, w f represents the convolution kernel of the second one-dimensional convolutional layer, f 1 、f 2 、f 3 、f 4 Corresponding to the vectors of the output of the first, second, third, and fourth residual gated convolution modules, f 1 +f 2 +f 3 +f 4 The vectors representing the outputs of the four residual gated convolutional modules are connected via skip layers, b f Represents the bias vector of the second one-dimensional convolutional layer.

[0051] Step 4.3: According to the back-propagation algorithm, the Adaptive Moment Estimation (Adam) optimizer is used to minimize the loss function and update all weights and biases in the compressed sensing reconstruction network; after the training is completed, the trained compressed sensing reconstruction network is obtained. Here, the weight matrix, convolution kernel, and dilated convolution kernel in the compressed sensing reconstruction network are all weights, and the bias vector is a bias.

[0052] Further, in step 4.3, the loss function is calculated using mean-square error (MSE), and the calculation formula of the loss function is: Where MSE represents the loss function value, Num represents the number of training samples contained in the training set, i = 1, 2, ..., Num, Y P,i represents the null subcarrier related signal in the i-th training sample in the training set, G WaveNet (·) represents the compressed sensing reconstruction network, G WaveNet (Y P,i ) represents the vector output from the output of the compressed sensing reconstruction network, that is, the estimated value of the time-domain impulse noise, Represents Y P,i The corresponding impulse noise label.

[0053] Step 5: For any NOMA time-domain received signal, follow the process of step 2 to obtain the empty subcarrier related signal in the same way; then input the empty subcarrier related signal into the trained compressed sensing reconstruction network, and the vector output by the trained compressed sensing reconstruction network is the reconstructed time-domain impulse noise; then subtract the reconstructed time-domain impulse noise from the NOMA time-domain received signal to obtain the signal after suppressing the impulse noise.

[0054] In order to verify the feasibility and effectiveness of the method of the present invention, computer simulation was performed on the method of the present invention.

[0055] The computer simulation is performed on a two-user NOMA system, that is, the number of users is 2. In the computer simulation, the simulation parameters of the NOMA system are set as follows: the number of subcarriers N = 256, the number of empty subcarriers N P =100, the power allocation coefficient of the first user is 0.9 during frequency domain superposition coding, the power allocation coefficient of the second user is 0.1, the modulation method is 4-QAM, the time domain impulse noise adopts Bernoulli Gaussian impulse noise, and the real value of the time domain impulse noise is 30db.

[0056] In the simulation result diagram, “CSR-WaveNet” represents the method of the present invention, “BP” represents the basis pursuit method, and “SL0” represents the smooth 0 Norm method, "DCNN" stands for deep convolutional neural network method. The above comparison methods are all known in the art.

[0057] Figure 3 The loss function values ​​of the CSR-WaveNet method and the DCNN method change with the training epoch. Figure 3 It can be seen that the loss function values ​​of the two methods decrease significantly with the increase of training rounds, and the loss function value of the CSR-WaveNet method decreases significantly faster than that of the DCNN method. Specifically, the CSR-WaveNet method can achieve a lower loss function value within 50 training rounds, while the DCNN method requires more than 300 training rounds to reach a similar level. This result further proves the significant advantage of the CSR-WaveNet method in convergence speed, indicating that it can achieve a lower loss function value in fewer training rounds, with faster convergence speed and higher training efficiency.

[0058] Figure 4 The variation of the bit error rate (BER) of the first user with the signal-to-noise ratio (SNR) is shown when using the BP method, SL0 method, DCNN method, and CSR-WaveNet method respectively. Figure 4 It can be seen that the bit error rate of all methods decreases with the increase of signal-to-noise ratio, while the CSR-WaveNet method shows a significant advantage over the comparison method in the entire signal-to-noise ratio range, thus verifying that the CSR-WaveNet method is better than the comparison method in terms of impulse noise suppression performance. Especially when BER=10 -2 When , the signal-to-noise ratio gain of the CSR-WaveNet method is about 5dB compared with the DCNN method.

[0059] Figure 5 The variation of the bit error rate (BER) of the first user with the number of empty subcarriers is shown when using the BP method, SL0 method, DCNN method, and CSR-WaveNet method respectively. Figure 5 It can be seen that the BER of all methods decreases with the increase of the number of empty subcarriers, and the impulse noise suppression performance of the CSR-WaveNet method under different numbers of empty subcarriers is better than that of the comparison method. Because when the number of empty subcarriers is small, there are fewer observations available in the observation matrix, and the CSR-WaveNet method also has better performance when there are fewer observations.

[0060] Figure 6 The variation of the bit error rate (BER) of the first user with the impulse noise sparsity is shown when using the BP method, SL0 method, DCNN method, and CSR-WaveNet method respectively. Figure 6 It can be seen that when the sparsity of impulse noise increases, the corresponding BER will increase, because the more impulse noise interference in a short time, the greater the impact on the performance of the NOMA system. Although the corresponding BER performance is affected as the sparsity of impulse noise increases, the impulse noise estimation performance of the CSR-WaveNet method is better than the comparison method.

[0061] Figure 7 The results show how the bit error rate (BER) of two users changes with the signal-to-noise ratio (SNR) when using the DCNN method and the CSR-WaveNet method respectively. Figure 7 It can be seen from the figure that the BER of the two users decreases as the SNR increases, but the BER of the high-order user (the user with a higher power allocation coefficient, i.e. the first user) is lower than that of the low-order user (the user with a lower power allocation coefficient, i.e. the second user) because the high-order user gets more power allocation and there is no error accumulation in the SIC. -2 When , the CSR-WaveNet method can achieve a 4dB signal-to-noise ratio gain compared with the DCNN method in both low-price and high-order users.

Claims

1. A compressed sensing impulse noise suppression method based on deep learning for a NOMA system, wherein the method assumes that there are multiple users in the NOMA system, and the entire frequency band in the NOMA system is divided into multiple subcarriers, including null subcarriers and data subcarriers; characterized in that The method comprises the following steps: Step 1: At the transmitting end of the NOMA system, the NOMA time-domain transmission signal with a cyclic prefix is ​​continuously transmitted to all users through a multipath channel; Step 2: At the receiving end of the NOMA system, the cyclic prefix is ​​removed from the received time domain signal; then, based on the time domain signal obtained after removing the cyclic prefix, the NOMA time domain received signal for any user is obtained; then, a discrete Fourier transform is performed on the NOMA time domain received signal to convert it from the time domain to the frequency domain to obtain the NOMA frequency domain received signal; then, the NOMA frequency domain received signal is divided into two parts: a data subcarrier-related signal and a null subcarrier-related signal; Step 3: The true value of the time domain impulse noise in the NOMA system transmission process is used as the impulse noise label, the empty subcarrier related signal and the impulse noise label are combined into a training sample, and several training samples are combined into a training set; Step 4: Construct a compressed sensing reconstruction network, which includes a fully connected layer, a first one-dimensional convolutional layer, four residual gated convolutional modules, and a second one-dimensional convolutional layer; then train the compressed sensing reconstruction network based on the training set, as follows: Step 4.1: Randomly initialize all weights and biases in the compressed sensing reconstruction network; Step 4.2: Input the training samples into the compressed sensing reconstruction network. The input end of the fully connected layer is the input end of the compressed sensing reconstruction network, and the output end of the second one-dimensional convolutional layer is the output end of the compressed sensing reconstruction network. The input end of the fully connected layer receives the empty subcarrier related signal in the training sample, and the vector output by the output end of the fully connected layer is input into the input end of the first one-dimensional convolutional layer after the relu activation function. The vector output by the output end of the first one-dimensional convolutional layer is input into the input end of the first residual gated convolution module, and the first The vector output from the output end of the residual gated convolution module is input to the input end of the second residual gated convolution module, the vector output from the output end of the second residual gated convolution module is input to the input end of the third residual gated convolution module, the vector output from the output end of the third residual gated convolution module is input to the input end of the fourth residual gated convolution module, the vectors output from the output ends of the four residual gated convolution modules are connected through a skip layer and then input to the second one-dimensional convolution layer after passing through a relu activation function, and the vector output from the output end of the second one-dimensional convolution layer is used as an estimated value of the time domain impulse noise; Step 4.3: According to the back-propagation algorithm, the adaptive moment estimation optimizer is used to minimize the loss function and update all weights and biases in the compressed sensing reconstruction network; after the training is completed, the trained compressed sensing reconstruction network is obtained; Step 5: For any NOMA time-domain received signal, follow the process of step 2 to obtain the empty subcarrier related signal in the same way; then input the empty subcarrier related signal into the trained compressed sensing reconstruction network, and the vector output by the trained compressed sensing reconstruction network is the reconstructed time-domain impulse noise; then subtract the reconstructed time-domain impulse noise from the NOMA time-domain received signal to obtain the signal after suppressing the impulse noise.

2. According to claim 1, the compressed sensing impulse noise suppression method based on deep learning of the NOMA system is characterized in that In step 2, the NOMA time domain received signal is recorded as Among them, H represents the channel circular convolution matrix, x t represents the time domain signal obtained after removing the cyclic prefix, n represents the total noise, n follows the Bernoulli-Gaussian process, n = n w +n I , n w represents the time domain background noise, n I represents the time domain impulse noise; the NOMA frequency domain received signal is recorded as Y, Where F represents the normalized discrete Fourier transform matrix, the superscript "*" represents the conjugate transpose operation, and x t After discrete Fourier transform, we get x, that is, x = Fx t , Λ=FHF * , Λ is a diagonal matrix, W represents the frequency domain background noise, W = Fn w ; The data subcarrier related signal and the empty subcarrier related signal are correspondingly recorded as Y D and Y P , Y D =(Λx) D +F D n I +W D , Y P =(Λx) P +F P n I +W P =F P n I +W P , where (Λx) D Indicates that N in Λx is related to the data subcarrier D A vector consisting of elements, (Λx) P Indicates that N associated with the empty subcarrier in Λx P A vector consisting of elements, F D Indicates that N associated with the data subcarrier in F D The matrix composed of row vectors, F P Indicates that N associated with the empty subcarrier in F P The matrix composed of row vectors, W D Represents the N associated with the data subcarrier in W D A vector consisting of elements, W P Represents the N associated with the empty subcarrier in W P A vector consisting of N elements, D Indicates the number of data subcarriers, N P Indicates the number of empty subcarriers, N D +N P =N, where N represents the number of subcarriers.

3. The NOMA system according to claim 1 or 2, characterized in that the compressed sensing impulse noise suppression method based on deep learning In step 4.2, the vector output from the output end of the fully connected layer is obtained after the relu activation function, and h=relu(ω h Y P +b h ), where ω h Y P +b h represents the vector output from the output of the fully connected layer, relu(·) represents the relu activation function, ω h represents the weight matrix of the fully connected layer, Y P represents the null subcarrier related signal in the training sample, b h Represents the bias vector of the fully connected layer.

4. The NOMA system according to claim 3 is characterized in that the compressed sensing impulse noise suppression method based on deep learning In step 4.2, the vector output from the output end of the first one-dimensional convolutional layer is a vector y obtained after the relu activation function. in, represents the vector output from the output of the first one-dimensional convolutional layer, relu(·) represents the relu activation function, and w y represents the convolution kernel of the first one-dimensional convolutional layer, h represents the vector obtained by the relu activation function after the output vector of the output end of the fully connected layer, and b y represents the bias vector of the first one-dimensional convolutional layer, is the convolution operator symbol.

5. According to claim 4, the compressed sensing impulse noise suppression method based on deep learning of the NOMA system is characterized in that In the step 4.2, the four residual gated convolution modules have the same structure, including a gated convolution module and a one-dimensional convolution layer, the gated convolution module is composed of an activation layer and a gated layer arranged in parallel, the input end of the activation layer is connected to the input end of the gated layer and serves as the input end of the gated convolution module, the input end of the gated convolution module is the input end of the residual gated convolution module, the input end of the one-dimensional convolution layer receives the vector output by the output end of the gated convolution module, the vector received by the input end of the gated convolution module is added to the vector output by the output end of the one-dimensional convolution layer through a skip layer, and the vector obtained by the addition is output by the output end of the residual gated convolution module; The output vector of the gated convolution module in the first residual gated convolution module is z1, z1 = tanh (w 1,1 *y)⊙S(w 1,2 *y), where tanh(w 1,1 *y) represents the vector output from the output end of the activation layer in the gated convolution module in the first residual gated convolution module. The activation layer includes a dilated convolution layer and a tanh activation function layer. The vector output from the dilated convolution layer passes through the tanh activation function layer as the output vector of the activation layer. S(w 1,2 *y) represents the vector output from the output end of the gated layer in the gated convolution module in the first residual gated convolution module. The gated layer includes a dilated convolution layer and a sigmoid activation function layer. The vector output from the dilated convolution layer is used as the vector output from the gated layer after passing through the sigmoid activation function layer. tanh(·) represents the tanh activation function, S(·) represents the sigmoid activation function, "⊙" is the Hadamard product operator, "*" is the dilated convolution operator, y represents the vector obtained by passing the vector output from the output end of the first one-dimensional convolution layer through the relu activation function, w 1,1 represents the dilated convolution kernel of the dilated convolution layer in the activation layer of the gated convolution module in the first residual gated convolution module, w 1,2 represents the dilated convolution kernel of the dilated convolution layer in the gated layer in the gated convolution module in the first residual gated convolution module; the vector output at the output end of the first residual gated convolution module is f1, Among them, w f,1 represents the convolution kernel of the one-dimensional convolution layer in the first residual gated convolution module, is the convolution operator symbol, b f,1 Represents the bias vector of the one-dimensional convolution layer in the first residual gated convolution module; The vector output at the output of the gated convolution module in the kth residual gated convolution module is z k , z k =tanh(w k,1 *f k-1 )⊙S(w k,2 *f k-1 ), where k = 2, 3, 4, tanh(w k,1 *f k-1 ) represents the vector output from the output of the activation layer in the gated convolution module in the kth residual gated convolution module, S(w k,2 *f k-1 ) represents the vector output from the output of the gated layer in the gated convolution module in the kth residual gated convolution module, f k-1 represents the vector output from the output of the k-1th residual gated convolution module, w k,1 represents the dilated convolution kernel of the dilated convolution layer in the activation layer of the gated convolution module in the kth residual gated convolution module, w k,2 represents the dilated convolution kernel of the dilated convolution layer in the gated layer in the gated convolution module in the kth residual gated convolution module; the vector output at the output end of the kth residual gated convolution module is f k , Among them, w f,k represents the convolution kernel of the one-dimensional convolution layer in the kth residual gated convolution module, b f,k Represents the bias vector of the one-dimensional convolutional layer in the k-th residual gated convolution module.

6. The NOMA system according to claim 5 is characterized in that the compressed sensing impulse noise suppression method based on deep learning In step 4.2, the vector outputted by the output terminal of the second one-dimensional convolutional layer is f, Among them, w f represents the convolution kernel of the second one-dimensional convolution layer, f1, f2, f3, and f4 represent the vectors output from the output of the first, second, third, and fourth residual gated convolution modules, respectively, and f1+f2+f3+f4 represents the vectors output from the output of the four residual gated convolution modules connected via a skip layer. f Represents the bias vector of the second one-dimensional convolutional layer.

7. The NOMA system according to claim 6, characterized in that the compressed sensing impulse noise suppression method based on deep learning In step 4.3, the loss function is calculated using the mean square error, and the calculation formula of the loss function is: Where MSE represents the loss function value, Num represents the number of training samples contained in the training set, i = 1, 2, ..., Num, Y P,i represents the null subcarrier related signal in the i-th training sample in the training set, G W ave N et(·) represents the compressed sensing reconstruction network, G WaveNet (Y P,i ) represents the vector output from the output of the compressed sensing reconstruction network, that is, the estimated value of the time-domain impulse noise, Represents Y P,i The corresponding impulse noise label.

8. The NOMA system according to claim 1 is characterized in that the compressed sensing impulse noise suppression method based on deep learning In step 4.1, the initial learning rate is set to 0.0001, batch_size=128, and epoch=300.

9. The NOMA system according to claim 1 is characterized in that the compressed sensing impulse noise suppression method based on deep learning In step 1, the acquisition process of the NOMA time domain transmission signal with a cyclic prefix is ​​as follows: channel coding is performed on the binary signal sequence sent to each user; then the bit stream obtained after channel coding is interleaved; then the signal obtained after the interleaving process is modulated; then the modulated signals corresponding to all users are superposition coded; then the composite signal obtained after superposition coding is inversely discrete Fourier transformed to convert it from the frequency domain to the time domain to obtain a time domain baseband signal; finally, a cyclic prefix is ​​inserted before each OFDM symbol of the time domain baseband signal to obtain a NOMA time domain transmission signal with a cyclic prefix.

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