Power amplifier digital pre-distortion optimization method based on complex convolutional neural network

Abstract

The invention discloses a power amplifier digital pre-distortion optimization method based on a complex convolutional neural network, and the method comprises the following steps: S1, collecting a plurality of groups of digital signals before and after passing through a power amplifier PA, and forming a sample set; s2, preprocessing the data in the sample set; s3, constructing a complex number time delay convolutional neural network containing a linear auxiliary branch and a nonlinear model as a digital pre-distortion model of the power amplifier; s4, training the digital pre-distortion model of the power amplifier by using the preprocessed data in the sample set to obtain maturely trained digital pre-distortion model parameters; and S5, when the digital pre-distortion of the power amplifier is actually carried out, sending a to-be-sent digital signal to the maturely trained digital pre-distortion model for processing. According to the method, the linearization capability is remarkably improved by introducing complex field processing and auxiliary linear branches while the low complexity characteristic is kept.

Description

Technical Field

[0001] The present invention relates to the field of digital predistortion, and particularly to a method for optimizing digital predistortion of a power amplifier based on a complex convolutional neural network. Background Art

[0002] With the development of 5G and future 6G communication systems, the demand for high data rate and wide bandwidth in communication systems is increasing continuously. However, when a power amplifier (PA) amplifies a radio frequency signal, due to its inherent nonlinearity and memory effect, signal distortion and adjacent channel interference will occur, thus reducing the transmission quality and spectral efficiency of the communication system. Digital predistortion (DPD) technology has attracted much attention in the field of amplifier linearization due to its advantages in linearization performance and stability and reliability. Its essence is to add a DPD module to generate a predistortion signal opposite to the nonlinear characteristics of the power amplifier to compensate for the nonlinear distortion of the power amplifier.

[0003] Constructing an accurate power amplifier behavior model is the basis for realizing digital predistortion technology. Traditional models, such as the Volterra model and the generalized memory polynomial (GMP) model, will significantly increase the model complexity in the application scenario of ultra-wideband, making it difficult to achieve a balance between implementation difficulty and accuracy. In recent years, neural networks (NNs) have been introduced into PA modeling due to their powerful nonlinear function approximation ability. Recurrent neural networks (RNNs) can effectively handle the memory effect of PAs due to their built-in memory structure and are first proven to be feasible in PA modeling. However, the linearization ability of RNNs is limited, and the network structure is complex, with a long training time. Subsequently, various deep neural networks (DNNs) have been introduced. These models use the in-phase and quadrature (I / Q) components with a specific memory depth and other envelope-related terms as inputs and exhibit good linearization ability. However, the fully connected (FC) network structure of DNNs results in a large number of model parameters and high computational complexity, especially when processing wideband signals. To reduce the model complexity, convolutional neural networks (CNNs) have been introduced. CNNs significantly reduce the number of model parameters through the weight sharing feature of the convolutional layer. The DPD method based on the real-valued time-delay convolutional neural network (RVTDCNN) extracts the nonlinear characteristics of the PA through the convolutional layer, reducing the number of parameters by 50% while maintaining linearization performance comparable to more complex models. However, there is still much room for improvement in the nonlinear compensation performance of existing RVTDCNN methods, especially when dealing with strongly nonlinear signals, where their linearization ability is limited. Summary of the Invention

[0004] The object of the present invention is to overcome the deficiencies of the prior art and provide a power amplifier digital predistortion optimization method based on a complex convolutional neural network, which significantly improves the linearization ability by introducing complex domain processing and an auxiliary linear branch while maintaining the low complexity characteristic.

[0005] The object of the present invention is achieved by the following technical solutions: A power amplifier digital predistortion optimization method based on a complex convolutional neural network, comprising the following steps:

[0006] S1. Collect multiple groups of digital signals before and after passing through the power amplifier PA to form a sample set;

[0007] In the step S1, the acquisition process of any group of digital signals before and after passing through the power amplifier PA is as follows:

[0008] The digital signal x(n) to be transmitted is transmitted to the power amplifier PA after passing through the DAC and the upconverter, and the signal received by the power amplifier PA is amplified and then transmitted; after the signal output by the power amplifier is downconverted by the downconverter, it is transmitted to the ADC for conversion to obtain the digital signal y(n); x(n) and y(n) are a group of digital signals before and after passing through the power amplifier PA.

[0009] S2. Preprocess the data in the sample set, including:

[0010] S201. For any group of digital signals {x(n), y(n)} in the sample set, first perform normalization processing on y(n) to obtain where G is the ideal gain of the power amplifier PA;

[0011]

[0012] where I x [n] and Q x [n], I y [n] and Q y [n] are the in-phase and quadrature components of x(n) and y(n) respectively;

[0013] S202. Perform a sliding window process on y′(n), where the window length is L, to obtain window data Y n =[y′(n),y′(n - 1),…,y′(n - L + 1)] T ;

[0014] The window data Y n =[y′(n),y′(n - 1),…,y′(n - L + 1)] T preprocessed from y(n) is used as the window data corresponding to x(n);

[0015] S203. For each set of digital signals in the sample set, repeat steps S201 - S202 to complete the preprocessing of various digital signals in the sample set.

[0016] S3. Construct a complex time - delay convolutional neural network containing a linear auxiliary branch and a non - linear model as the digital pre - distortion model of the power amplifier;

[0017] In the complex time - delay convolutional neural network constructed in step S2;

[0018] The linear auxiliary branch consists of a fully - connected layer. The number of input features is L, and the number of output features is 1. It is used to perform a linear transformation on the complex input to generate an initial prediction value. The neuron parameters in the linear auxiliary branch are obtained by training with the gradient descent algorithm;

[0019] The non - linear model part consists of multiple cascaded one - dimensional complex convolutional layers and fully - connected layers, and is optimized using the Adam algorithm;

[0020] The outputs of the linear auxiliary branch and the non - linear model are combined by an adder and used as the final output of the complex time - delay convolutional neural network.

[0021] S4. Use the pre - processed data in the sample set to train the digital pre - distortion model of the power amplifier to obtain the parameters of the trained digital pre - distortion model;

[0022] The said step S4 includes:

[0023] S401. Train the linear auxiliary branch:

[0024] A1. For the window data Y n = [y′(n), y′(n - 1), …, y′(n - L + 1)] T obtained by pre - processing any set of digital signals in the sample set, input it into the linear auxiliary branch, and the result y linear (n) after linear transformation is output by the linear auxiliary branch;

[0025] A2. Use x(n) corresponding to the window data Y n to calculate the loss function loss1 with y linear :

[0026] loss1 = |x(n)-y linear (n)| 2

[0027] A3. According to the loss function loss1, use the gradient descent algorithm to update and optimize the linear auxiliary branch;

[0028] A4. For the window data obtained by digital signal processing of different samples in the sample set, repeat steps A1 - A3 until the linear auxiliary branch converges, that is, loss1 is less than the preset convergence threshold;

[0029] S402. Fix the parameters of the linear auxiliary branch and train the non - linear model:

[0030] B1. For the window data Y n = [y′(n), y′(n - 1), …, y′(n - L + 1)] T , which is obtained by pre - processing any group of digital signals in the sample set, input it into the linear auxiliary branch and the non - linear model respectively, and then the adder combines the results output from the linear auxiliary branch and the non - linear model to obtain the output result y DPD (n);

[0031] B2. Use the corresponding x(n) of the window data Y n to calculate the loss function loss2 with y DPD (n):

[0032] loss2 = |x(n) - y DPD (n)| 2

[0033] B3. According to the loss function loss2, use the Adam algorithm to update and optimize the non - linear model;

[0034] B4. For the window data obtained by digital signal processing of different samples in the sample set, repeat steps B1 - B3 until the model converges, that is, loss2 is less than the preset convergence threshold;

[0035] S5. When actually performing digital pre - distortion of the power amplifier, first send the digital signal to be transmitted into the trained digital pre - distortion model for processing, and then transmit it to the power amplifier PA through the DAC and the up - converter. The power amplifier PA amplifies the received signal and then transmits it.

[0036] The beneficial effects of the present invention are: while maintaining the low - complexity characteristics, the present invention significantly improves the linearization ability by introducing complex - domain processing and an auxiliary linear branch. Description of the Drawings

[0037] Figure 1 is the overall principle schematic diagram of the present invention;

[0038] Figure 2 is the schematic diagram of the spectrum comparison between CVTDCNN and other models;

[0039] Figure 3 is the schematic diagram of the experimental platform setting. Detailed implementation manners

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following description.

[0041] As Figure 1 shown, a power amplifier digital predistortion optimization method based on a complex convolutional neural network is characterized in that it includes the following steps:

[0042] S1. Collect multiple groups of digital signals before and after passing through the power amplifier PA to form a sample set;

[0043] In the step S1, the acquisition process of any group of digital signals before and after passing through the power amplifier PA is as follows:

[0044] The digital signal x(n) to be transmitted is transmitted to the power amplifier PA after passing through the DAC and the upconverter, and the signal received by the power amplifier PA is amplified and then transmitted; after the signal output by the power amplifier is downconverted by the downconverter, it is transmitted to the ADC for conversion to obtain the digital signal y(n); x(n) and y(n) are a group of digital signals before and after passing through the power amplifier PA.

[0045] S2. Preprocess the data in the sample set;

[0046] In the step S2, preprocessing the data in the sample set includes:

[0047] S201. For any group of digital signals {x(n), y(n)} in the sample set, first normalize y(n) to obtain where G is the ideal gain of the power amplifier PA;

[0048]

[0049] where I x [n] and Q x [n], I y [n] and Q y [n] are the in-phase and quadrature components of x(n) and y(n), respectively;

[0050] S202. Perform a sliding window process on y′(n), where the window length is L, to obtain window data Y n =[y′(n), y′(n - 1), …, y′(n - L + 1)] T ;

[0051] The window data Y n =[y′(n), y′(n - 1), …, y′(n - L + 1)] T preprocessed from y(n) is used as the window data corresponding to x(n);

[0052] S203. For each group of digital signals in the sample set, repeat steps S201 - S202 to complete the preprocessing of various digital signals in the sample set.

[0053] S3. Construct a complex - valued time - delay convolutional neural network containing a linear auxiliary branch and a non - linear model as the digital pre - distortion model of the power amplifier.

[0054] The present invention uses CVNNs as the core modeling tool. Compared with traditional real - valued neural networks (RVNNs), CVNNs can directly process complex - valued inputs and outputs without decomposing complex - valued signals into real and imaginary parts. This not only reduces the preprocessing steps, but also improves the computational efficiency, reduces the number of model parameters, and thus significantly enhances the training and running efficiency of the model. At the same time, CVNNs can also make full use of the amplitude and phase information of the signal, thereby more effectively extracting features and improving the model performance.

[0055] In the present invention, CVNNs are applied to construct a complex - valued time - delay convolutional neural network (CVTDCNN). Through the complex - valued convolutional layer, CVTDCNN can directly extract the non - linear features of the input signal, maintain the low - complexity characteristics, and at the same time show superior performance when processing strongly non - linear signals.

[0056] To further improve the performance of the complex - valued time - delay convolutional neural network (CVTDCNN), the present invention introduces the Boosting algorithm. Boosting is an ensemble learning method that significantly improves the prediction ability and robustness of the model by iteratively training multiple weak learners and combining them into a strong learner. In the present invention, CVTDCNN combines a linear auxiliary branch and a non - linear model, where the linear auxiliary branch acts as a weak learner to generate an initial prediction value, and the non - linear model further fits the residuals of the linear auxiliary branch, focusing on processing the non - linear part of the signal. The final output is the sum of the two. By introducing the Boosting algorithm, CVTDCNN significantly reduces the adjacent - channel leakage ratio (ACLR) when processing strongly non - linear signals, improving the transmission quality and spectral efficiency of the communication system.

[0057] The network structure of CVTDCNN is as Figure 1 shown, including two main parts: a linear auxiliary branch and a non - linear model. The linear auxiliary branch uses a fully - connected (FC) layer (complex - valued linear layer) to generate an initial prediction value and process the linear part of the signal. The non - linear model consists of multiple cascaded one - dimensional complex - valued convolutional layers and fully - connected layers; this structure provides an efficient and reliable solution for the linearization of power amplifiers in future 6G and higher - generation communication systems.

[0058] S4. Use the preprocessed data in the sample set to train the digital predistortion model of the power amplifier, and obtain the parameters of the trained digital predistortion model;

[0059] The training process of the digital predistortion model adopts an indirect learning method, that is, the output signal of the power amplifier is converted into a digital signal, and after normalization and window processing, it is used as the input of the predistortion model, and the digital signal x(n) to be transmitted is used as the output of the model for training. Specifically: The step S4 includes:

[0060] S401. Train the linear auxiliary branch:

[0061] A1. For the window data Y obtained by preprocessing any set of digital signals in the sample set n = [y′(n), y′(n - 1), …, y′(n - L + 1)] T , input it into the linear auxiliary branch, and the linearly transformed result y linear (n) is output by the linear auxiliary branch;

[0062] A2. Use the x(n) corresponding to the window data Y n to calculate the loss function loss1 with y linear :

[0063] loss1 = |x(n) - y linear (n)| 2

[0064] A3. According to the loss function loss1, use the gradient descent algorithm to update and optimize the linear auxiliary branch;

[0065] A4. For the window data obtained by processing different digital signals in the sample set, repeat steps A1 - A3 until the linear auxiliary branch converges, that is, loss1 is less than the preset convergence threshold;

[0066] S402. Fix the parameters of the linear auxiliary branch and train the non - linear model:

[0067] B1. For the window data Y obtained by preprocessing any set of digital signals in the sample set n = [y′(n), y′(n - 1), …, y′(n - L + 1)] T , input it into the linear auxiliary branch and the non - linear model respectively, and then the adder combines the results output by the linear auxiliary branch and the non - linear model to obtain the output result y DPD (n) of the digital predistortion model;

[0068] B2. Use the x(n) corresponding to the window data Y n to calculate the loss function loss2 with y DPD(n) Calculate the loss function loss2:

[0069] loss2 = |x(n) - y DPD (n)| 2

[0070] B3. According to the loss function loss2, use the Adam algorithm to update and optimize the non - linear model;

[0071] B4. For the window data obtained from different digital signal processing in the sample set, repeat steps B1 - B3 until the model converges, that is, loss2 is less than the preset convergence threshold;

[0072] S5. When actually performing digital pre - distortion of the power amplifier, first send the digital signal to be transmitted into the trained digital pre - distortion model for processing, and then transmit it to the power amplifier PA through the DAC and up - converter. The power amplifier PA amplifies the received signal and then transmits it.

[0073] In some embodiments, the sample set can be divided into a training set, a test set, and a validation set. The training process of the above - mentioned step S4 can use the training set obtained by dividing the sample set, while the validation set and the test set are used to verify and test the training results.

[0074] In the embodiments of the present application, in the present invention, in order to verify the effectiveness of the CVTDCNN model in the digital pre - distortion (DPD) application of the power amplifier (PA), we adopted two main performance evaluation indicators: the normalized mean square error (NMSE) and the adjacent - channel leakage ratio (ACLR). The lower the NMSE value, the smaller the error between the output of the model and the ideal output, and the better the linearization performance of the model. The lower the ACLR value, the less the signal leaks into the adjacent channels, the higher the spectral efficiency, and the less the interference to other channels. These two indicators can comprehensively reflect the linearization performance of the model and the impact on the signal spectrum. NMSE and ACLR are respectively defined as:

[0075]

[0076] ACLR (dB) = P Adj(dB) - P Main(dB) .

[0077] In machine learning, when the model scale is small, the initial values of the parameters have a greater impact on the final result of the solution. In order to reduce the impact of random parameter initialization on the performance evaluation results, this application trains the model 3 times, each time using different randomly initialized parameters, and independently trains on the same data set to reduce the accidental results caused by specific initialization. Calculate the average value and variance of all the NMSE and ACLR obtained from the training.

[0078] 1. Data preparation:

[0079] The data is orthogonal frequency division multiplexing (OFDM) data obtained by sampling. The data sampled at the PA transmitter is x(n), and the data obtained at the receiver is y(n);

[0080] Perform normalization processing on y(n) to obtain y′(n);

[0081] Divide the data into a training set, a validation set, and a test set according to the ratio of 8:1:1;

[0082] Perform a sliding window process on y′(n), where the window length is L, to obtain window data Y n =[y′(n), y′(n - 1), …, y′(n - L + 1)] T , as the network input.

[0083] 2. Model initialization:

[0084] First, create the network structure of the CVTDCNN model;

[0085] Use the Kaiming initialization method to initialize the neuron parameters in the model. This method helps prevent gradient vanishing or explosion in the initial stage of training, thus accelerating the convergence speed and improving the model performance.

[0086] 3. Calculate the parameters of the linear auxiliary branch:

[0087] Use the gradient descent (GD) algorithm to calculate and update the neuron parameters in the model.

[0088] 4. Train the non - linear model:

[0089] Fix the linear auxiliary branch coefficients to ensure that the non - linear model focuses on learning the non - linear part of the signal and improves the overall performance of the model;

[0090] Train the non - linear model on the dataset, and update the model parameters through the backpropagation algorithm to further optimize the MSE loss function.

[0091] 5. Output:

[0092] After training is completed, output the final digital predistortion (DPD) model.

[0093] Such as Figure 2As shown, in the embodiments of the present application, a specific hardware and software platform is adopted to verify the performance of the CVTDCNN model. The test signal used in the experiment is an OFDM signal with a bandwidth of 20 MHz and a peak-to-average power ratio (PAPR) of 13.2 dB. The signal is generated in MATLAB on a personal computer (PC), using 8PSK modulation and having 2048 subcarriers. The generated test signal is processed through a software-defined radio (SDR) platform and the baseband signal is up-converted to a center frequency of 2.3 GHz, and then transmitted to a PA system, which consists of two cascaded ZX60-V82-S+PAs with a frequency range of 20 MHz - 6 GHz. The SDR captures 65536 output samples, and together with the transmitted data, the network is trained on the PC using Python. In the embodiments of the present application, after power control, analog-to-digital conversion, and up-conversion processing of the digital signal through the SDR (software defined radio platform), it is transmitted to the power amplifier; by controlling the signal power before the PA input, corresponding to various degrees of nonlinear distortion, different scenarios of nonlinear distortion can be simulated according to the method of the present application. The parameter settings in the CVTDCNN network are shown in the following table:

[0094] Table 1 Parameter Settings in the CVTDCNN Network

[0095]

[0096] The CVTDCNN training parameter settings are as described in the following table:

[0097] Table 2 CVTDCNN Training Parameter Settings

[0098]

[0099] After testing the CVTDCNN model, it is noted that the ACLR does not improve significantly with the increase of the memory depth M, but instead shows an increasing trend, as shown in the following table:

[0100] Table 3 Effects of Different Memory Depths on NMSE and ACLR of the CVTDCNN Model

[0101]

[0102] Therefore, considering the balance between model performance and computational complexity, this patent sets M = 4 as the memory depth for subsequent experiments.

[0103] When the transmit signal power is set from 7 dBm to 11 dBm, different transmission power requirements that may be encountered in an actual communication system can be simulated. The CVTDCNN model with a linear auxiliary branch improves the ACLR by an average of 1.5 dB, as shown in the following table:

[0104] Table 4 Influence of having a linear auxiliary branch on the NMSE and ACLR of the model

[0105]

[0106] This table shows that the linear auxiliary branch helps to further reduce the leakage of signals in adjacent channels, thereby improving the spectral efficiency and communication quality.

[0107] To verify the performance of the CVTDCNN model proposed in the present invention, this patent conducts a detailed comparative analysis of it with several other neural network-based models. These models are divided into: traditional methods and neural network methods. Traditional methods include the Generalized Memory Polynomial (GMP) model, and neural network methods include the Real-Valued Time-Delay Convolutional Neural Network (RVTDCNN), the Gated Recurrent Unit (GRU), and the Deep Gated Recurrent Unit (DGRU). The purpose of the comparative analysis is to evaluate the differences in the Digital Predistortion (DPD) performance of different models, especially the performance in the key indicator of ACLR.

[0108] As can be seen from Table 5, CVTDCNN exhibits superior linearization performance at all tested signal powers, and its ACLR value is significantly lower than that of other models. Compared with RVTDCNN, the average ACLR of the CVTDCNN model is reduced by 1.7 dB, and at a transmit power of 9 dBm, the maximum reduction reaches 2.2 dB, showing its superior performance in processing strongly non-linear signals. At this power level, Figure 3 The spectrum of the received signal after various processing methods is shown, clearly demonstrating the superior ability of the CVTDCNN model in suppressing the sideband power.

[0109] Table 5 Comparison of ALCR between CVTDCNN and other models

[0110]

[0111] The above is the preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, should not be regarded as excluding other embodiments, but can be used in other combinations, modifications, and environments, and can be changed within the scope of the concept described herein through the above teachings or the technology or knowledge in related fields. And any changes and variations made by those skilled in the art without departing from the spirit and scope of the present invention shall fall within the protection scope of the appended claims of the present invention.

Claims

1. A power amplifier digital predistortion optimization method based on complex convolutional neural network, characterized in that: The following steps are involved: S1. Collect multiple groups of digital signals before and after the power amplifier PA to form a sample set; S2. Preprocess the data in the sample set; S3. Construct a complex time-delay convolutional neural network including a linear auxiliary branch and a nonlinear model as a digital pre-distortion model of the power amplifier; S4. Using the preprocessed data in the sample set to train the digital predistortion model of the power amplifier, the parameters of the trained mature digital predistortion model are obtained; S5. When actually performing digital pre-distortion of the power amplifier, the digital signal to be sent is first sent to a well-trained digital pre-distortion model for processing, and then transmitted to the power amplifier PA through a DAC and an up-converter. The power amplifier PA amplifies the received signal and then transmits it.

2. The power amplifier digital predistortion optimization method based on complex convolutional neural network according to claim 1, characterized in that: In step S1, the collection process of any group of digital signals before and after passing through the power amplifier PA is as follows: The digital signal x(n) to be sent is transmitted to the power amplifier PA after passing through the DAC and the up-converter, and the power amplifier PA amplifies the received signal and then transmits it; the signal output by the power amplifier is down-converted by the down-converter and then transmitted to the ADC for conversion to obtain the digital signal y(n); {x(n), y(n)} is a set of digital signals before and after passing through the power amplifier PA.

3. The power amplifier digital predistortion optimization method based on complex convolutional neural network according to claim 2, characterized in that: In step S2, preprocessing the data in the sample set includes: S201. For any set of digital signals {x(n), y(n)} in the sample set, first normalize y(n) to obtain Where G is the ideal gain of the power amplifier PA; Among them I x [n] and Q x [n],I y [n] and Q y [n], are the in-phase and quadrature components of x(n) and y(n), respectively; S202. Perform sliding window processing on y′(n), where the window length is L, to obtain window data Y n =[y′(n),y′(n-1),…,y′(n-L+1)] T ; The window data T obtained by preprocessing y(n) n =[y′(n),y′(n-1),…,y′(n-L+1)] T , as the window data corresponding to x(n); S203. For each group of digital signals in the sample set, steps S201 to S202 are repeatedly executed to complete the preprocessing of various digital signals in the sample set.

4. The power amplifier digital predistortion optimization method based on complex convolutional neural network according to claim 3, characterized in that: In the complex time-delay convolutional neural network constructed in step S3; The linear auxiliary branch consists of a fully connected layer with L input features and 1 output feature, which is used to perform a linear transformation of the complex input and generate the initial prediction value; The parameters in the linear auxiliary branch are trained by the gradient descent algorithm; The nonlinear model part consists of multiple cascaded one-dimensional complex convolutional layers and fully connected layers, optimized using the Adam algorithm; The outputs of the linear auxiliary branch and the nonlinear model are combined through an adder as the final output of the complex time-delay convolutional neural network.

5. The power amplifier digital predistortion optimization method based on complex convolutional neural network according to claim 4, characterized in that: The step S4 comprises: S401. Training linear auxiliary branch: A1. Window data Y obtained by preprocessing any set of digital signals in the sample set n =[y′(n),y′(n-1),…,y′(n-L+1)] T , input it into the linear auxiliary branch, and the linear auxiliary branch outputs the linearly transformed result y linear (n); A2. Using window data Y n The corresponding x(n) and y linear Calculate the loss function loss1: loss1=|x(n)-y linear (n)| 2 A3. According to the loss function loss1, the linear auxiliary branch is updated and optimized using the gradient descent algorithm; A4. Repeat steps A1 to A3 for window data obtained by different digital signal processing in the sample set until the linear auxiliary branch converges, that is, loss1 is less than a preset convergence threshold; S402. Fix the parameters of the linear auxiliary branch and train the nonlinear model: B1. Window data Y obtained by preprocessing any set of digital signals in the sample set n =[y′(n),y′(n-1),…,y′(n-L+1)] T , and input them into the linear auxiliary branch and the nonlinear model respectively, and then the adder combines the output results of the linear auxiliary branch and the nonlinear model to obtain the output result y of the digital pre-distortion model DPD (n); B2. Using window data Y n The corresponding x(n) and y DPD (n) Calculate the loss function loss2: loss2=|x(n)-y DPD (n)| 2 B3. According to the loss function loss2, the Adam algorithm is used to update and optimize the nonlinear model; B4. Repeat steps B1 to B3 for window data obtained by processing different digital signals in the sample set until the model converges, that is, loss2 is less than a preset convergence threshold.

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