Nonlinear equalization method for photonic terahertz communication signals based on complex-valued convolutional neural network

Abstract

The present invention discloses a nonlinear equalization method for photon terahertz communication signals based on a complex-valued convolutional neural network, which is used in the field of terahertz communication. The method of the present invention includes: intercepting the signals of the transmitting end and the receiving end of the terahertz communication system, separating the real part and the imaginary part of the signal, generating input samples and label data, and dividing the training set and the test set; constructing a signal equalization model of a 1D-CNN complex-valued neural network structure, wherein the model includes multiple 1D complex-valued convolutional layers and a complex-valued fully connected layer; using the training set to train the signal equalization model until the accuracy of the model meets the requirements, deploying the trained signal equalization model at the receiving end of the terahertz communication system, and compensating the signal before demapping at the receiving end in real time. The present invention can directly and effectively compensate for the damage and nonlinear effects of complex-valued signals, meet the needs of signal equalization processing, realize nonlinear equalization of terahertz communication system signals, and improve the transmission performance of high-frequency band communication systems.

Description

Technical Field

[0001] The invention belongs to the field of terahertz communication, and relates to signal processing of a light-borne terahertz communication system, and specifically is a nonlinear equalization method for photon terahertz communication signals based on a complex-valued convolutional neural network. Background Art

[0002] The terahertz frequency band (0.1-10 THz) is located between microwaves and infrared light waves and has rich spectrum resources. As an extension of microwaves and millimeter waves, the communication bandwidth it provides is much greater than that of millimeter waves. Under the current condition of relatively tight spectrum resources in the low-frequency band, terahertz has gradually come into people's sight and is considered to be the next breakthrough point in the revolution of communication technology.

[0003] The photon-assisted method is the mainstream form of generating terahertz signals at home and abroad. It can overcome the bandwidth limitation of electronic devices, provide a wider modulation bandwidth, and meet the needs of wide bandwidth and high mobility in future 6G communication applications. In optical fiber communication systems, there are many factors that limit the quality of signal transmission, such as dispersion, noise, and nonlinear effects of devices. Therefore, using reasonable digital signal processing algorithms at the receiving end of the system to reduce damage and nonlinear effects, etc., is a key scientific issue in realizing terahertz frequency band communication systems.

[0004] At present, the traditional digital signal processing DSP compensation algorithm for the above-mentioned damage and nonlinear effects is difficult to apply to the actual optical fiber transmission channel due to its complexity and huge amount of calculation. However, due to its unique nonlinear mapping ability, neural networks have been regarded as a powerful equalization tool for compensating linear and nonlinear damage in the field of optical communications. At present, many neural networks, including convolutional neural networks (CNN), recurrent neural networks (RNN), and long short-term memory networks (LSTM), have been used to improve nonlinear equalizers in some millimeter-wave communication systems. In 2019, Chang et al. from the University of Electronic Science and Technology of China applied an end-to-end training method based on real-valued CNN with a hybrid connection structure to signal equalization, aiming to directly recover communication signals from noise signals affected by wireless channels. Experiments have found that the effect of this method on GMSK signals is particularly satisfactory, and 100% accuracy can be achieved when the signal-to-noise ratio is greater than 0dB. In 2020, Aldaya et al. proposed a new nonlinear equalizer based on multiple-input multiple-output (MIMO) and deep neural network (DNN), and experimentally verified it in a 40Gb / s coherent optical orthogonal frequency division multiplexing system. In 2022, Nakamura et al. from Meiji University in Japan compared the equalization effects of two effective neural networks. The experiment confirmed the equalization effect by performing nonlinear compensation on 16QAM signals transmitted at a transmission rate of 40G bit / s on a 100km standard single-mode fiber (SSMF). Terahertz communication has many advantages such as high speed, wide bandwidth, good directivity, and good confidentiality, but it is also a field that has not been fully developed. At present, research on the terahertz frequency band is mostly focused on devices such as terahertz sources, power amplifiers, and terahertz antennas. Signal equalization mostly uses traditional equalization methods such as blind equalization and equalization algorithms based on training sequences. Although the equalization technology using neural networks has a lot of work foundation in many systems in the field of optical communications, it has not yet been widely used in optical terahertz communication systems.

[0005] At the same time, unlike image processing, most signals in communication systems exist in complex form, while the input and output of traditional neural networks are real numbers, which makes it difficult to meet the needs of processing complex values. Most of the current signal equalization algorithms based on neural networks use I and Q signals for neural network prediction respectively. Although the effect of compensating signals can be achieved, the relationship between signal amplitude and phase is abandoned. Therefore, the introduction of complex-valued neural networks can better adapt to the function of signal processing, while retaining the correspondence between the real part and the imaginary part of the signal, and giving full play to the great ability of neural networks to handle high-complexity, high-dimensional and nonlinear problems. In the process of constructing complex-valued networks for communication signals, the setting of network dimensions, the setting of the number of convolutional layers, the retention and abandonment of pooling layers, the selection of fully connected layer functions, etc., will have more or less effects on the equalization effect. Therefore, how to improve and reconstruct the input layer, hidden layer and output layer of traditional neural networks, and make CNN no longer limited to classification prediction functions, so that it can realize complex value processing functions and regression prediction, and can be used for signal processing in communication systems, is a current demand, which has very important research significance and application prospects. Summary of the invention

[0006] Since the signals of the communication system exist in complex form, the relationship between the signal amplitude and phase is mostly abandoned when neural networks are currently introduced. It is necessary to build a suitable complex-valued neural network for signal equalization processing. The present invention provides a nonlinear equalization method for photonic terahertz communication signals based on a complex-valued convolutional neural network, modifies and reconstructs the structure of a traditional convolutional neural network, and realizes compensation for complex-valued signal damage and nonlinear effects in a light-borne terahertz communication system, thereby improving the transmission performance of a high-frequency band communication system.

[0007] To achieve the above object, the present invention provides a nonlinear equalization method for photon terahertz communication signals based on a complex-valued convolutional neural network, comprising the following steps:

[0008] Step 1: intercept the signals of the transmitting and receiving ends of the terahertz communication system to generate training sets and test sets;

[0009] The signal is intercepted from the transmitting end after the signal is mapped as the label data, and the signal is intercepted from the receiving end before the signal is demapped as the input data; when intercepting the signal, the input sample is generated by intercepting it according to the preset length, each sample contains multiple signals and the signal to be processed by the sample is the signal located in the middle of the sample; each signal is represented as complex data, and the real part and imaginary part data of each signal are separated and stored in the dimension of a vector respectively; each sample is represented as a matrix containing multiple signals;

[0010] Step 2, construct a signal equalization model of 1D-CNN complex-valued neural network structure;

[0011] The signal equalization model uses a 1D-CNN complex-valued neural network structure, including: an input layer for receiving sample input, a 1D complex-valued convolution layer for extracting features from the signal in the sample, and a complex-valued fully connected layer; wherein the 1D complex-valued convolution layer is provided with h layers, and h is greater than 2; each 1D complex-valued convolution layer first performs a complex-valued convolution operation on the input data and then activates it using a CReLU activation function; in the 1D complex-valued convolution layer, the obtained sample feature map is kept the same size as the matrix of the input sample;

[0012] Step 3: Use the training set to train the signal equalization model until the accuracy of the signal equalization model meets the test requirements, deploy the trained signal equalization model at the receiving end of the terahertz communication system, and compensate the signal before demapping at the receiving end in real time to achieve nonlinear equalization of the terahertz communication system signal.

[0013] In the step 2, four 1D complex-valued convolutional layers are set in the signal equalization model.

[0014] In step 2, the preset length is assumed to be 2k+1, and the signal to be processed by the current sample is the i-th signal x i , then the k signals before and after the signal are intercepted as a sample, expressed as S = [x i-k , ..., x i , ..., x i+k ], the real and imaginary data of each signal are stored separately, then the current sample is represented as a (2k+1)*2 matrix; the size of the output feature map is padded with zeros, so that the sample feature maps after each layer of 1D complex-valued convolution layer processing are the same as the matrix size of the input sample.

[0015] In step 3, when training the signal equalization model, the loss function is set to calculate the mean square error between the predicted value after input sample compensation and the label data.

[0016] Compared with the prior art, the advantages and positive effects of the present invention are: the method of the present invention can directly process complex-valued signals by modifying each level of the general convolutional neural network, using only a signal equalization model of a 1D-CNN complex-valued neural network structure, which not only retains the correspondence between the real and imaginary parts of the signal, but also achieves the regression prediction effect of the network, and broadens the application scope of convolutional neural networks in the field of communications. Experimental verification shows that the method of the present invention is suitable for processing data such as photonic terahertz communication signals, meets the needs of signal equalization processing, and can effectively compensate for the damage and nonlinear effects of complex-valued signals. The use of the method of the present invention can improve the transmission performance of high-frequency communication systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a block diagram of a 16-QAM OFDM terahertz communication system;

[0018] Figure 2 This is a flow chart of digital signal processing at the receiving end of the OFDM system;

[0019] Figure 3 It is a flow chart of a signal equalization method based on a complex-valued convolutional neural network of the present invention;

[0020] Figure 4 This is the structural diagram of the 1D-CNN complex-valued neural network model;

[0021] Figure 5 This is a signal spectrum diagram before UTC-PD of the terahertz communication system in an embodiment of the present invention;

[0022] Figure 6 This is a signal electrical spectrum diagram after UTC-PD of the terahertz communication system in an embodiment of the present invention;

[0023] Figure 7 The figure is a comparison diagram of the constellation diagram of the receiving end of the system using the signal equalization method of the present invention and not using the method of the present invention. DETAILED DESCRIPTION

[0024] The nonlinear equalization method for photonic terahertz communication signals based on a complex-valued convolutional neural network of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0025] When constructing a complex-valued convolutional neural network, it is necessary not only to refer to the settings of traditional neural networks in image processing, but also to take into account the differences between the two. The present invention performs analysis and theoretical deduction based on digital signal processing, modifies and adds to the general structure of traditional neural networks, and thus applies this unique neural network structure to photonic terahertz communication signal processing.

[0026] Convolutional neural network (CNN) is essentially a deep neural network with a convolution structure. It uses convolution operation to replace the product operation in deep neural network. Compared with other neural networks, it can extract data features with fewer calculation parameters. Among them, the three basic layers of CNN are convolution layer, pooling layer and fully connected layer. Convolutional neural network is currently widely used in image processing. To apply it to signal processing, it is necessary not only to refer to the settings of image processing, but also to consider the differences between the two, analyze and derive theoretically based on digital signal processing, and modify and add general structures. The setting of dimension, the setting of the number of convolution layers, the retention and abandonment of pooling layers, the selection of fully connected layer functions, etc., will have more or less impact on the equalization effect.

[0027] like Figure 1As shown in the figure, the 16-QAM orthogonal frequency division multiplexing system (16-QAM OFDM) uses the optical heterodyne method to obtain a terahertz signal by beating two signals. At the transmitting end, there are two external cavity laser transmitters (ECL). ECL1 generates a continuous light wave (CW) to carry the 16-QAM signal, and then the CW from ECL1 is converted into an electrical signal by an arbitrary waveform generator (AWN) and loaded onto the optical carrier through an I / Q modulator. ECL2 is a local oscillator light source, and there is a frequency interval of 350GHz between it and ECL1. After modulation by the I / Q modulator, an optical modulated signal carrying vector baseband information is generated, which is coupled to the local oscillator light source through a coupler (OC). The optical signal is transmitted through a standard single-mode fiber (SSMF) link, passes through an amplifier, and then beats through a single-line carrier photodetector (UTC-PD) to obtain a terahertz wave with a frequency of 350GHz. At the receiving end, a down-conversion process is required. The received signal and the RF signal generated by a microwave source are mixed through a mixer to obtain an intermediate frequency signal for sampling by a digital oscilloscope. The sampled signal can be processed by offline digital signal processing (DSP) to restore the original information. The neural network-based equalization module is used here. QAM stands for quadrature amplitude modulation.

[0028] Figure 2 The common digital signal processing flow at the receiving end of the OFDM (Orthogonal Frequency Division Multiplexing) system is given. At the receiving end Rx, after the fast Fourier transform (FFT), an equalization algorithm based on a neural network is added. Through the multi-layer network structure of the neural network and repeated iterative training, the best model can be obtained to output the predicted value closest to the original signal.

[0029] The nonlinear equalization method of photon terahertz communication signal based on complex-valued convolutional neural network of the present invention uses 1D-CNN complex-valued neural network to compensate the signal in the optical terahertz communication system. Figure 3 As shown, it includes the following 4 steps.

[0030] Step 1: intercept the signals of the transmitting end and the receiving end of the terahertz communication system to generate a training set and a test set.

[0031] The signals are intercepted after the signal mapping at the transmitting end and before the signal demapping at the receiving end. The former is used as the label data of the input neural network, and the latter is used as the input layer data of the neural network. The intercepted signals can be represented as complex data. Since the complex-valued convolution operation is actually converted into four real-valued convolution operations, the real and imaginary parts of the signal need to be separated for the convenience of later input into the neural network.

[0032] The preset sample length is 2k+1. The signal is intercepted according to the preset length to obtain samples. For the i-th signal x i, intercept the k signals before and after the signal as a sample, expressed as S = [x i-k , ..., x i , ..., x i+k ]. For each signal, separate the real and imaginary parts of the complex representation and put them into the 0 and 1 dimensions of the vector respectively. Each sample is represented as a matrix containing multiple signals. The label data is obtained by cutting the signal according to the corresponding preset length.

[0033] Step 2: Construct a signal equalization model of 1D-CNN complex-valued neural network structure.

[0034] Convolutional neural networks generally include three basic layers: convolution layer, pooling layer, and fully connected layer. In the convolution layer, it usually contains multiple learnable convolution kernels. The feature map output by the previous layer is convolved with the convolution kernel, and then the result is sent to the activation function to extract the output feature map. The main purpose of the pooling layer is to compress the image and reduce parameters by downsampling without affecting the image quality. The present invention is aimed at signal processing scenarios, and the constructed 1D-CNN complex-valued neural network structure mainly includes an input layer, four 1D complex-valued convolution layers and a complex-valued fully connected layer. Taking into account that the feature map of the signal itself is small in size, does not need to be compressed, and will change the statistical characteristics of the modulated signal, etc., the pooling layer is abandoned. For example Figure 4 As shown, each 1D complex-valued convolution layer of the 1D-CNN complex-valued neural network contains a complex-valued convolution layer and a complex-valued activation layer.

[0035] The computational operation of the complex-valued convolution layer can be regarded as four real-valued convolution operations. For each complex-valued signal x in the sample, let its complex number representation be x = M r +jM i , complex-valued convolution kernel W = K r +jK i , then the complex-valued convolution can be expressed as:

[0036] W*x=(M r +jM i )*(K r +jK i )=(M r *K r -M i *K i )+j(M r *K i +M i *K r )

[0037] After each complex-valued convolutional layer operation, a complex-valued rectified linear unit (CReLU) is used for activation. Complex-valued activation actually uses the ReLU function to activate the real part and the imaginary part respectively. The formula is as follows:

[0038] CReLU(W*x)=ReLU(Re{W*x}+jReLU(Im{W*x})

[0039] Re represents the real part, and Im represents the imaginary part.

[0040] The embodiment of the present invention extracts the features of the input signal through four layers of 1D complex-valued convolutional layer operations, and then sets a complex-valued fully connected layer at the end of the neural network to achieve the regression prediction function, integrates the features extracted by the previous 1D complex-valued convolutional layer, and outputs the regression prediction value. The core operation of the fully connected layer is the matrix-vector product. The implementation ideas of the complex-valued fully connected layer and the complex-valued convolution are basically the same, both of which convert the complex number calculation process into several real number operations. The formula is as follows:

[0041] Y=X*W fc + b = (X r +jX i )*(W r +jW i )+b

[0042] =(X r *W r -X i *W i )+j(X r *W i +X i *W r )+b

[0043] Among them, Y represents the output of the complex-valued fully connected layer, that is, the compensated signal, X represents the feature of the output of the previous 1D complex-valued convolutional layer, X = X r +jX i , W fc is the weight matrix of the fully connected layer, W fc =W r +jW i , b is the vector bias of the fully connected layer.

[0044] The weights of the complex-valued convolutional layer and the weights and biases of the complex-valued fully connected layer are continuously updated by training the network with the training set.

[0045] Step 3: Use the training set to input the 1D-CNN complex-valued neural network for model training.

[0046] Input the processed training set into the 1D-CNN complex-valued neural network, set the learning rate, batch size and other parameters, and adjust the relevant parameters of the 1D-CNN complex-valued neural network according to the loss value between the output prediction result and the label data. Among them, the loss function uses the most commonly used error in the regression loss function - mean square error (MSE). It is the mean of the sum of squares of the difference between the predicted value f(x) and the target value y, and its formula is as follows:

[0047]

[0048] Wherein, n represents the number of samples, f(x) represents the signal obtained after compensating the signal x, y represents the target value corresponding to the signal x, x is the signal intercepted from the receiving end before demapping the signal, and y is the signal intercepted from the transmitting end after mapping the signal.

[0049] After the network parameters are determined, the accuracy of the trained 1D-CNN complex-valued neural network model is tested using the test set, and finally a 1D-CNN neural network model with the best prediction effect can be obtained.

[0050] Step 4: Compensate the signal data at the receiving end of the system through the trained 1D-CNN complex-valued neural network model.

[0051] The trained signal equalization model is deployed at the receiving end of the optical terahertz communication system. The signal before demapping is compensated in real time through the trained 1D-CNN complex-valued neural network model, and then subsequent demapping operations are performed to achieve nonlinear equalization of the terahertz communication system signal.

[0052] Example

[0053] This example demonstrates the process of equalizing 16QAM OFDM signals using 1D-CNN complex-valued neural network in a light-borne terahertz communication system, thereby verifying the compensation effect of the method of the present invention. The system in the present invention is simulated by the simulation software VPI and Matlab, and the neural network algorithm is implemented by Python code. The 16QAM OFDM system used is as follows: Figure 1 As shown, to generate a 350 GHz signal, two external cavity lasers (ECLs) with a frequency interval of 350 GHz are required. Figure 5 This is the signal spectrum entering the single-line charge-carrier photodetector (UTC-PD). After passing through the UTC-PD, a corresponding signal can be generated at a frequency of 350 GHz. Figure 6 This is the signal electrical spectrum generated after UTC-PD.

[0054] First, in MATLAB, the complex valued signal after 16QAM mapping at the transmitter and the complex valued signal without 16QAM demapping at the receiver are extracted to construct the training set and the test set. In this example, the size k of the input feature map is set to 7, and the moving window function is used to obtain the input samples and the corresponding label data.

[0055] Then, the Pytorch framework is used to build the signal equalization model of the 1D-CNN complex-valued neural network. Figure 4 As shown in the figure, the signal equalization model includes an input layer, four 1D complex-valued convolution + complex-valued activation layers, a complex-valued fully connected layer, and an output layer. The size k of each input feature map is set to 7, and each signal contains two components, the real part and the imaginary part. The batchsize is set to 64, that is, the input end of the neural network will input a matrix with a dimension of (64, 7, 2). In the complex-valued convolution layer, two Conv1d functions are used as the real and imaginary parts of the complex-valued convolution kernel, and the following convolution operation is performed with the input data:

[0056] W*x=(M r +jM i )*(K r +jK i )=(M r *K r -M i *K i )+j(M r *K i +M i *K r )

[0057] Zero padding is used during the convolution process to ensure that the feature map maintains its original size and is not compressed after convolution.

[0058] There is a complex-valued activation layer after each complex-valued convolution layer, which uses ReLU to activate the real and imaginary parts of the convolution layer output respectively. The formula is as follows:

[0059] CReLU(W*x)=ReLU(Re{W*x}+jReLU(Im{W*x})

[0060] After four complex-valued convolutional layers and four complex-valued activation layers, the tail of the neural network is a complex-valued fully connected layer, which performs complex-valued operations similar to complex-valued convolution and directly outputs the prediction results as the output layer.

[0061] After a large number of iterations of the training set input neural network, the loss function value MSE converges to the minimum value, thus completing the model training process.

[0062] Input the test set data into the trained model. By comparing the true value and the model output value, the accuracy of the model prediction results can be verified and whether the effect of the model training meets the standard can be determined.

[0063] The results show that:

[0064] In order to intuitively reflect the advantages of the present invention, Figure 7 Comparison of the signal constellation diagram before demapping at the receiving end of the system. Figure 7 The left figure does not use the method of the present invention, while the right figure uses the method of the present invention. It can be clearly seen from the figure that the signal constellation diagram with the neural network equalization algorithm of the present invention is closer to the ideal 16QAM signal constellation diagram and has a lower bit error rate. Therefore, the method of the present invention shows an effective and good signal equalization effect.

Claims

1. A nonlinear equalization method for photonic terahertz communication signals based on complex-valued convolutional neural networks, characterized in that: The steps include: Step 1: intercept the signals of the transmitting and receiving ends of the terahertz communication system to generate training sets and test sets; The signal is intercepted from the transmitting end after the signal is mapped as the label data, and the signal is intercepted from the receiving end before the signal is demapped as the input data; when intercepting the signal, the input sample is generated by intercepting it according to the preset length, each sample contains multiple signals and the signal to be processed by the sample is the signal located in the middle of the sample; each signal is represented as complex data, and the real part and imaginary part data of each signal are separated and stored in the dimension of a vector respectively; each sample is represented as a matrix containing multiple signals; The terahertz communication system is a 16-QAM orthogonal frequency division multiplexing system, which uses optical heterodyne method to obtain a terahertz wave with a frequency of 350 GHz by beating two signals. Step 2, constructing a signal equalization model of a 1D-CNN complex-valued neural network structure; the signal equalization model is applied in the receiving end offline digital signal processing DSP, and is set after the fast Fourier transform in the DSP processing and before the signal demapping; The signal equalization model uses a 1D-CNN complex-valued neural network structure, including: an input layer for receiving sample input, a 1D complex-valued convolution layer for extracting features from the signal in the sample, and a complex-valued fully connected layer; wherein the 1D complex-valued convolution layer is provided with h layers, and h is greater than 2; each 1D complex-valued convolution layer first performs a complex-valued convolution operation on the input data and then activates it using a CReLU activation function; in the 1D complex-valued convolution layer, the obtained sample feature map is kept the same size as the matrix of the input sample; Assume that the preset length is 2k+1, and the signal to be processed by the current sample is the i-th signal x i , then the k signals before and after the signal are intercepted as a sample, expressed as S = [x i-k , ..., x i , ..., x i+k ], the real and imaginary data of each signal are stored separately, and the current sample is represented as a (2k+1)*2 matrix; the size of the output feature map is supplemented by zero padding, so that the sample feature map processed by each 1D complex-valued convolution layer has the same matrix size as the input sample; The computation of the complex-valued convolution of each 1D complex-valued convolution layer is regarded as the operation of four real-valued convolutions: for each complex-valued signal x=M in the sample r +jM i , complex-valued convolution kernel W = K r +jK i , the complex-valued convolution is expressed as: W*x=(M r +jM i )*(K r +jK i )=(M r *K r -M i *K i )+j(M r *K i +M i *K r ); In the complex-valued fully connected layer, let the weight matrix W fc =W r +jW i , the vector bias is b, then the output Y of the complex-valued fully connected layer is expressed as follows: Y=X*W fc +b=(X r +jX i )*(W r +jW i )+b =(X r *W r -X i *W i )+j(X r *W i +X i *W r )+b; Where X is the feature of the input complex-valued fully connected layer, expressed as X = X r +jX i ; Step 3: Use the training set to train the signal equalization model until the accuracy of the signal equalization model tested by the test set meets the requirements, and deploy the trained signal equalization model at the receiving end of the terahertz communication system to compensate the signal before demapping at the receiving end in real time.

2. The method according to claim 1, characterized in that In the step 2, four 1D complex-valued convolutional layers are provided in the signal equalization model.

3. The method according to claim 1, characterized in that In step 3, when training the signal equalization model, the loss function is set to calculate the mean square error between the predicted value after input sample compensation and the label data.

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