Nonlinear Impairment Compensation Method and Apparatus for High-Order Modulated Wavelength Division Multiplexing Systems

Abstract

This invention discloses a nonlinear impairment compensation method and apparatus suitable for high-order modulation wavelength division multiplexing (DMDM) systems, belonging to the field of optical fiber communication technology. The method includes: acquiring discrete sample signals collected by a coherent receiver corresponding to each channel in a high-speed coherent wavelength division multiplexing system; resampling the discrete sample signals of each channel to twice the sample value, forming a one-dimensional sample vector with a length of twice the number of symbols; performing dimension shaping preprocessing on the one-dimensional sample vector; inputting the preprocessed discrete sample signals into a cross-basis function neural network for training, obtaining a trained network model; preprocessing test data, and inputting the preprocessed test data into the trained network model, outputting a discrete sample signal that can effectively compensate for dispersion and nonlinear impairments. This invention solves the problems of complex nonlinear impairment compensation processes and unsatisfactory compensation effects in existing high-order modulation wavelength division multiplexing systems.

Description

Technical Field

[0001] This invention belongs to the field of optical fiber communication technology, and in particular relates to a nonlinear impairment compensation method suitable for high-order modulation wavelength division multiplexing systems. Background Technology

[0002] Currently, all kinds of information require communication networks for transmission. Fiber optic communication technology serves as the "main artery" connecting various communication networks. However, facing the explosive growth in network traffic, the capacity growth rate of fiber optic communication has decreased by about 50% in the past decade, failing to meet the rapidly growing demand for high-bandwidth network services. A "capacity crisis" is foreseeable in the future. To improve the transmission capacity of fiber optics, the introduction and application of technologies such as Wavelength Division Multiplexing (WDM), higher-order modulation, Polarization Demultiplexing (PDM), and Probabilistic Shaping (PS) have led to a rapid increase in the capacity of backbone fiber optic transmission networks, reaching Tb / s levels. However, in long-distance WDM transmission systems, noise from optical repeaters continuously increases. To maintain a constant signal-to-noise ratio, according to Shannon's formula, the signal power of each channel must be increased, thus increasing the total optical power entering the fiber. When the power entering the fiber is too high, it causes severe Kerr nonlinearity, leading to signal phase distortion or the generation of new frequency components, limiting the rapid growth of the capacity of current high-speed optical communication systems. Fiber nonlinear effects can be categorized into intra-channel and inter-channel types. Intra-channel fiber nonlinear effects mainly refer to the changes in the refractive index of the transmission medium caused by excessive input power, which affects the pulse shape due to the fiber being a nonlinear medium—this is known as self-phase modulation (SPM). Inter-channel nonlinear effects include cross-phase modulation (XPM), where one channel influences another, and four-wave mixing (FWM), which occurs only under certain conditions. For intra-channel self-phase modulation in single-carrier systems, the classic digital backpropagation (DBP) algorithm can be used for compensation. However, in wavelength division multiplexing (WDM) systems, where cross-phase modulation plays a dominant role, the classic DBP algorithm cannot achieve satisfactory compensation. Therefore, compensation for nonlinear impairments in WDM systems has attracted considerable attention and interest from researchers.

[0003] Current nonlinear impairment compensation methods in wavelength division multiplexing (WDM) systems can be broadly categorized into two types: nonlinear impairment compensation algorithms that improve upon the digital backpropagation (DBP) algorithm and machine learning-based nonlinear impairment compensation algorithms. While the classic DBP algorithm, after improvement, exhibits excellent compensation performance, its process involves numerous Fast Fourier Transform (FFT) operations, resulting in extremely high computational complexity, which is difficult for real-world hardware to meet. Machine learning-based nonlinear impairment compensation schemes primarily utilize different types of machine learning algorithms to extract signal amplitude, phase, and other features for regression or classification to compensate for nonlinear impairments. Due to the powerful learning capabilities of machine learning algorithms, they can be directly used to alleviate nonlinear impairments or extract features for precise compensation, offering significant advantages over traditional compensation methods.

[0004] Based on patent search results, the invention patent "Signal Transmission Nonlinear Effect Suppression Device and Method for Wavelength Division Multiplexing Fiber Optic Sensing System" (application number: 20211497888.0) achieves the effect of suppressing inter-channel nonlinear effects by designing an optical delay coil group, a waveband separator, and a waveband combiner to ensure that the number of channels contained in the transmission pulse at any transmission time of the transmitted optical signal is less than the total number of wavelength channels. However, this invention adopts an all-optical approach and is applied in the field of fiber optic sensing, resulting in high hardware costs. The invention patent "A Nonlinear Parameter Optimization Method Based on Gaussian Pulse Peak Power Distribution" (application number: 202111285736.4) optimizes the nonlinear parameters of the digital backpropagation method by solving for the Gaussian pulse peak power, making this invention perform better than the traditional constant digital backpropagation method. However, this invention inevitably involves a large number of Fourier transform operations, resulting in high computational complexity. Summary of the Invention

[0005] To address the aforementioned shortcomings in the existing technology, this invention provides a nonlinear damage compensation method and apparatus suitable for high-order modulated wavelength division multiplexing systems, which solves the problems of complex nonlinear damage compensation processes and unsatisfactory compensation effects in existing technologies.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows: a nonlinear impairment compensation method suitable for high-order modulated wavelength division multiplexing systems, comprising the following steps:

[0007] S1. Obtain the discrete sample signals collected by the coherent receiver corresponding to each channel in the high-speed coherent wavelength division multiplexing system.

[0008] S2, regarding the acquisition C The discrete sampled signal of the i-th channel will be used to... l If a channel is used as the target channel, then the index l -1、l The +1 channel is an adjacent channel of the target channel. The discrete sample signals of the target channel and the adjacent channel are resampled to twice the sample value, forming a one-dimensional sample vector with a length of twice the number of symbols, where 1 ≤ l ≤ C The one-dimensional sample set of each discrete sample signal is: , S Represents discrete sample signals. N Represents a signed number. C This represents the total number of channels. T This represents the matrix transpose operation;

[0009] S3. Perform dimension reshaping preprocessing on the one-dimensional sample vector;

[0010] S4. Input the preprocessed discrete sample signal into the cross-basis function neural network for training to obtain the trained network model;

[0011] S5. Preprocess the test data using the methods in steps S1-S3, and input the preprocessed test data into the trained network model to output discrete sample signals that effectively compensate for dispersion and nonlinear damage.

[0012] The beneficial effects of this invention are as follows: The hidden layer of the proposed Cross Basis Function Neural Network (XBF-NN) consists of two parts: a linear layer and an activation function. In the linear layer, convolution operations are used to compensate for dispersion in the preprocessed data. Then, the activation function is used to compensate for nonlinear impairments. A key feature is the use of the coupled-channel enhanced distributed Fourier method to analyze the nonlinear phase rotation induced by different polarization components in different channels within the wavelength division multiplexing (WDM) system. This yields the interaction between cross-phase modulation and dispersion between different channels, thereby enhancing the activation function's ability to compensate for nonlinear impairments in the WDM system. This solves the problems of complex nonlinear impairment compensation processes and unsatisfactory compensation effects in existing methods.

[0013] Further, step S3 includes the following steps:

[0014] S301. Divide the one-dimensional sample set of the discrete sample signals of the target channel and adjacent channels into real and imaginary parts, with dimension . ,in, N Represents a signed number;

[0015] S302. Perform zero-padding on the one-dimensional sample vector to form... The integer transformation is performed in matrix form, where... , This represents the number of rows and columns of the matrix.

[0016] The beneficial effect of the above-mentioned further scheme is that it enables the original complex-valued discrete sample signal to be processed in real number form within the neural network.

[0017] Furthermore, step S4 includes the following steps:

[0018] S401. Network parameter initialization: Initialize the time-domain dispersion compensation filter. k Each tap coefficient, nonlinear phase shift correction factor, and activation function parameter are determined; the length of each optical fiber and the total number of optical fiber transmission segments are determined based on the transmission distance; the error vector amplitude is set as the loss function, and the Adam optimizer is set to update and optimize the tap coefficient, nonlinear phase shift correction factor, and activation function parameters, and the number of hidden layers in the cross-basis function neural network is kept consistent with the number of optical fiber transmission segments;

[0019] S402. Input characteristics of the network: The preprocessed channel discrete sample signal, together with the 1-times discrete sample signal output by the target channel transmitter, is input into the cross-basis function neural network.

[0020] S403, Time-Domain Dispersion Compensation: This applies the time-domain dispersion compensation filter... k Each tap coefficient is divided into real and imaginary parts. In the linear layer of each hidden layer in the cross-basis function neural network, the preprocessed discrete sample signals of the target channel and adjacent channels are combined with... k The real or imaginary part tap coefficients are convolved, and the optimal tap coefficients are obtained by iteratively updating the tap coefficients through the optimizer, so as to achieve dispersion compensation for each channel data.

[0021] S404, Nonlinear Impairment Compensation: Discrete sample signals of the target channel and adjacent channels that have undergone dispersion compensation in the linear layer are input into the activation function. The optimal nonlinear phase shift correction factor and activation function parameters are obtained by iteratively updating the nonlinear phase shift correction factor and activation function parameters through the optimizer, thereby realizing nonlinear impairment compensation of the target channel.

[0022] S405. Set the number of iterations to update the input features and network parameters: Based on the set number of iterations, determine whether the error vector amplitude has converged. If so, the input features and network parameters are considered to have reached the optimal value, and the trained network model is obtained. If the error vector amplitude continues to decrease after the iteration ends, increase the number of iterations and retrain the network model. If the EVM stabilizes at a certain value and no longer changes after the iteration ends, the network model training is completed.

[0023] The beneficial effect of the above-mentioned further scheme is that by optimizing the network parameters to construct a network model, the dispersion and nonlinearity impairments in discrete sample signals can be compensated.

[0024] Furthermore, the hidden layer of the cross-basis function neural network includes a linear layer and an activation function;

[0025] The linear layer uses the pre-obtained tap coefficients of the time-domain dispersion compensation filter to perform a convolution operation with the discrete sample signal to achieve dispersion compensation and obtain compensation data.

[0026] The activation function is constructed using the coupled signal enhancement distributed Fourier method to compensate for nonlinear impairments in the wavelength division multiplexing system.

[0027] Furthermore, the expression for the data to be compensated is as follows:

[0028]

[0029] in, This indicates the data to be compensated. Represents an exponential function. Represents the imaginary unit. This represents the nonlinear coefficient in the optical fiber. Indicates fiber input power. Indicates transmission distance. This indicates the trend of fiber insertion power over a certain distance. Indicates the integral symbol, This represents an optimizable coefficient. Indicates the target channel index. Indicates the first l Channel x Polarization data, Indicates the first l Channel y Polarization data, Indicates the target channel x / y Polarized data, Indicates the index of the discrete sample signal;

[0030] The expression for the activation function is as follows:

[0031]

[0032] in, Indicates the target channel l activation function, This represents an optimizable parameter in the activation function. This represents the data fed into the activation function, where the total number of channels is... C And the target channel l When the value equals 1, the adjacent channel is the second channel; when the target channel... l equal C When, the adjacent channel is the first.C -1 channel;

[0033] The expression for the time-domain dispersion compensation filter is as follows:

[0034]

[0035] in, This represents a time-domain dispersion compensation filter. Indicates the inverse Fourier transform. Represents the frequency domain dispersion compensation transfer function. Represents the dispersion coefficient. Indicates the wavelength of the target channel. Represents the speed of light in a vacuum. Indicates the angular frequency of the target channel.

[0036] The beneficial effects of the above-mentioned further scheme are: by considering the influence of adjacent channels on the target channel, nonlinear impairments in the target channel are compensated; in addition, by performing an inverse Fourier transform on the frequency domain dispersion compensation transfer function, dispersion is compensated in the time domain.

[0037] The present invention also provides a nonlinear impairment compensation device suitable for high-order modulated wavelength division multiplexing systems, comprising:

[0038] The first processing module is used to acquire discrete sample signals collected by the coherent receiver corresponding to each channel in the high-speed coherent wavelength division multiplexing system.

[0039] The second processing module is used for processing the acquired data. C The discrete sampled signal of the i-th channel will be used to... l If a channel is used as the target channel, then the index l -1、 l The +1 channel is an adjacent channel of the target channel. The discrete sample signals of the target channel and the adjacent channel are resampled to twice the sample value, forming a one-dimensional sample vector with a length of twice the number of symbols, where 1 ≤ l ≤ C The one-dimensional sample set of each discrete sample signal is: , S Represents discrete sample signals. N Represents a signed number. C This represents the total number of channels. T This represents the matrix transpose operation;

[0040] The third processing module is used to perform dimension reshaping preprocessing on the one-dimensional sample vector;

[0041] The fourth processing module is used to input the preprocessed discrete sample signals into the cross-basis function neural network for training, so as to obtain the trained network model.

[0042] The fifth processing module is used to preprocess the test data using the methods of the first to third processing modules, and input the preprocessed test data into the trained network model to output discrete sample signals that effectively compensate for dispersion and nonlinear damage.

[0043] The beneficial effects of this invention are as follows: The hidden layer of the proposed Cross Basis Function Neural Network (XBF-NN) consists of two parts: a linear layer and an activation function. In the linear layer, convolution operations are used to compensate for dispersion in the preprocessed data. Then, the activation function is used to compensate for nonlinear impairments. A key feature is the use of the coupled-channel enhanced distributed Fourier method to analyze the nonlinear phase rotation induced by different polarization components in different channels within the wavelength division multiplexing (WDM) system. This yields the interaction between cross-phase modulation and dispersion between different channels, thereby enhancing the activation function's ability to compensate for nonlinear impairments in the WDM system. This solves the problems of complex nonlinear impairment compensation processes and unsatisfactory compensation effects in existing methods. Attached Figure Description

[0044] Figure 1 This is a digital signal processing flowchart of the nonlinear damage compensation method based on cross-basis function neural networks in this embodiment.

[0045] Figure 2 This is a block diagram of the device of the present invention.

[0046] Figure 3 This is a flowchart of the method of the present invention.

[0047] Figure 4 This is a schematic diagram illustrating the data dimensions of the input neural network in this embodiment.

[0048] Figure 5 The constellation diagrams before and after dispersion and nonlinear impairment compensation are shown for the 5-channel WDM system provided in this embodiment after transmitting 1200km of 28GBaud PDM-16QAM.

[0049] Figure 6 This is a simulation block diagram of the 5-channel 28GBaud WDM system in this embodiment.

[0050] Figure 7 This is a simulation bit error rate curve for a 5-channel 28GBaud WDM system with different modulation formats in this embodiment. Detailed Implementation

[0051] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0052] Example 1

[0053] To address the nonlinear impairment compensation problem in wavelength division multiplexing (WDM) systems, this invention proposes a nonlinear impairment compensation method based on a cross-basis function neural network. This method is applicable to various modulation formats, including Polarization Division Multiplexing (PDM) 16QAM and PDM-64QAM. Figure 1 As shown, during the training phase, this method first resamples the received signal samples by a factor of 2. Therefore, this invention is placed after the resampling module and before the time phase recovery module, and the testing and training phases follow the same process. The core idea of ​​this invention is to accurately compensate for cross-phase modulation and long-distance cumulative dispersion. The resampled signal samples are preprocessed using overlap-preservation technology to shape the data structure, and then fed into the linear layer of this method for dispersion compensation. Finally, the activation function optimized based on the coupled channel enhancement step-Fourier method proposed in this invention is used to compensate for nonlinear impairments in the wavelength division multiplexing system. Figure 3 As shown, a nonlinear impairment compensation method suitable for high-order modulated wavelength division multiplexing systems is implemented as follows:

[0054] S1. Obtain the discrete sample signals collected by the coherent receiver corresponding to each channel in the high-speed coherent wavelength division multiplexing system.

[0055] S2, regarding the acquisition C The discrete sampled signal of the i-th channel will be used to... l If a channel is used as the target channel, then the index l -1、 l The +1 channel is an adjacent channel of the target channel. The discrete sample signals of the target channel and the adjacent channel are resampled to twice the sample value, forming a one-dimensional sample vector with a length of twice the number of symbols, where 1 ≤ l ≤ C The one-dimensional sample set of each discrete sample signal is: , S Represents discrete sample signals. N Represents a signed number. C This represents the total number of channels. T This represents the matrix transpose operation;

[0056] S3. Perform dimension reshaping preprocessing on the one-dimensional sample vector, the implementation method of which is as follows:

[0057] S301. Divide the one-dimensional sample set of the discrete sample signals of the target channel and adjacent channels into real and imaginary parts, with dimension . ,in, N Represents a signed number;

[0058] S302. Perform zero-padding on the one-dimensional sample vector to form... The integer transformation is performed in matrix form, where... , This represents the number of rows and columns of the matrix.

[0059] In this embodiment, the specific method for data dimension shaping is the overlap preservation technique, such as... Figure 4 As shown, the specific method of its application is as follows: First, the complex dataset of the one-dimensional sample vector in step S2 is... Divided into real and imaginary parts, with dimension . The purpose of padding this vector with zeros at both ends is to form... The square formation, note It equals 2 N The present invention uses the first. The principle is explained using the column as an example, and the first column is used as an example. After the column m The signal sample value is added to the first... The head of the column will The front of the column m The signal sample value is added to the first... At the end of the column, this method is applied to each column, so that the length of each column becomes... n +2 m Finally, the number of rows was ( n +2 m ), number of columns is n The matrix is ​​used because a large amount of dispersion accumulates in long-distance transmission links, and severe crosstalk occurs between adjacent signal pulses. The crosstalk problem caused by dispersion is offset by considering the influence of adjacent symbols on the current symbol.

[0060] S4. Input the preprocessed discrete sample signal into the cross-basis function neural network for training to obtain the trained network model. The implementation method is as follows:

[0061] S401. Network parameter initialization: Initialize the time-domain dispersion compensation filter. kEach tap coefficient, nonlinear phase shift correction factor, and activation function parameter are determined; the length of each optical fiber and the total number of optical fiber transmission segments are determined based on the transmission distance; the error vector amplitude is set as the loss function, and the Adam optimizer is set to update and optimize the tap coefficient, nonlinear phase shift correction factor, and activation function parameters, and the number of hidden layers in the cross-basis function neural network is kept consistent with the number of optical fiber transmission segments;

[0062] S402. Input characteristics of the network: The preprocessed channel discrete sample signal, together with the 1-times discrete sample signal output by the target channel transmitter, is input into the cross-basis function neural network.

[0063] S403, Time-Domain Dispersion Compensation: This applies the time-domain dispersion compensation filter... k Each tap coefficient is divided into real and imaginary parts. In the linear layer of each hidden layer in the cross-basis function neural network, the preprocessed discrete sample signals of the target channel and adjacent channels are combined with... k The real or imaginary part tap coefficients are convolved, and the optimal tap coefficients are obtained by iteratively updating the tap coefficients through the optimizer, so as to achieve dispersion compensation for each channel data.

[0064] S404, Nonlinear Impairment Compensation: Discrete sample signals of the target channel and adjacent channels that have undergone dispersion compensation in the linear layer are input into the activation function. The optimal nonlinear phase shift correction factor and activation function parameters are obtained by iteratively updating the nonlinear phase shift correction factor and activation function parameters through the optimizer, thereby realizing nonlinear impairment compensation of the target channel.

[0065] S405. Set the number of iterations to update the input features and network parameters: Based on the set number of iterations, determine whether the error vector amplitude has converged. If so, the input features and network parameters are considered to have reached the optimal value, and the trained network model is obtained. If the error vector amplitude continues to decrease after the iteration ends, increase the number of iterations and retrain the network model. If the EVM stabilizes at a certain value and no longer changes after the iteration ends, the network model training is completed.

[0066] In this embodiment, an appropriate number of iterations is set to update the parameters involved in the input feature parameters. When the EVM index gradually converges, each parameter in the input feature parameters also reaches its optimal value, which means that the scheme has achieved the compensation effect for dispersion and nonlinear damage.

[0067] In this embodiment, the modulation format of the signal sample input to the cross-basis function neural network includes PDM-16QAM and PDM-64QAM, but is not limited to these two modulation formats.

[0068] In this embodiment, the hidden layer of the cross-basis function neural network includes a linear layer and an activation function;

[0069] The linear layer uses the pre-obtained tap coefficients of the time-domain dispersion compensation filter to perform a convolution operation with the discrete sample signal to achieve dispersion compensation and obtain compensation data.

[0070] The activation function is constructed using the coupled signal enhancement distributed Fourier method to compensate for nonlinear impairments in the wavelength division multiplexing system.

[0071] In this embodiment, the discrete sample signal structure after shaping preprocessing is fed into the cross-basis function neural network proposed in this invention. The hidden layer of this cross-basis function neural network consists of a linear layer and an activation function. Dispersion compensation is achieved in the linear layer by convolving the sample signal with the pre-obtained tap coefficients of the time-domain dispersion compensation filter. Since the coupled channel enhancement step-by-step Fourier method considers the cross-phase modulation effect between different polarization components of different channels and their interaction with dispersion, the expression for the data to be compensated can be obtained as follows:

[0072]

[0073] in, This indicates the data to be compensated. Represents an exponential function. Represents the imaginary unit. This represents the nonlinear coefficient in the optical fiber. Indicates fiber input power. Indicates transmission distance. This indicates the trend of fiber insertion power over a certain distance. Indicates the integral symbol, This represents an optimizable coefficient. Indicates the target channel index. Indicates the first l Channel x Polarization data, Indicates the first l Channel y Polarization data, Indicates the target channel x / y Polarized data, Indicates the index of the discrete sample signal;

[0074] The expression for the activation function is as follows:

[0075]

[0076] in, Indicates the target channel l activation function, This represents an optimizable parameter in the activation function. This represents the data fed into the activation function, where the total number of channels is...C And the target channel l When the value equals 1, the adjacent channel is the second channel; when the target channel... l equal C When, the adjacent channel is the first. C -1 channel;

[0077] In this embodiment, some additional parameters need to be fed into the cross-basis function neural network along with the received samples, including the original symbols output by the transmitter and the tap coefficients of the time-domain dispersion compensation filter. h_cdc Length of each fiber optic cable L Total number of segments Span Nonlinear phase shift correction factor a and activation function parameters These parameters, after initialization, are fed into the cross-basis function neural network to achieve fast network convergence. The hidden layer of this cross-basis function neural network is divided into a linear compensation part and an activation function part. In the linear compensation, dispersion is compensated by updating the tap coefficients of the time-domain dispersion compensation filter. The expression for the time-domain dispersion compensation filter is:

[0078]

[0079] in, This represents a time-domain dispersion compensation filter. Indicates the inverse Fourier transform. Represents the frequency domain dispersion compensation transfer function. Represents the dispersion coefficient. Indicates the wavelength of the target channel. Represents the speed of light in a vacuum. This represents the angular frequency of the target channel. To reduce network computation, this invention performs a cyclic shift on the tap coefficients of the time-domain dispersion compensation filter, taking the first... k Each tap coefficient is used for L Column copying, composition k * L coefficient matrix h _ cdc This completes the initialization of the dispersion compensation tap coefficients for each hidden layer.

[0080] S5. Preprocess the test data using the methods in steps S1-S3, and input the preprocessed test data into the trained network model to output discrete sample signals that effectively compensate for dispersion and nonlinear damage.

[0081] Based on the above, the results obtained by simultaneously compensating for dispersion and nonlinear impairment in the received signal samples are as follows: Figure 5 As shown, Figure 5 (Left) shows the original constellation diagram without the cross-basis function neural network. Figure 5 (Right) is a constellation diagram of a neural network with cross-basis functions.

[0082] To verify the effectiveness of this invention, a simulation platform is used for verification in this embodiment:

[0083] This invention utilizes VPI and MATLAB to build, as follows Figure 6 The coherent optical transmission system shown can be used for high-speed coherent polarization multiplexing WDM system simulation. Detailed parameters are as follows: Five PDM transmitters transmit 28GBaud PDM-16QAM / 64QAM signals of different wavelengths. To fully verify the phase damage caused by nonlinear effects, the simulation embodiment of this invention does not consider the influence of laser linewidth. The input power range is -7dBm to 4dBm, increasing by 1dB each time. A lossless optical multiplexer couples the optical signals from the five transmitters into the fiber loop. In the fiber loop, this invention uses single-mode fiber with a span of 100km, a loss coefficient of 0.2 dB / km, a dispersion coefficient of 17 ps / (nm·km), a polarization mode dispersion of 0.2 ps / sqrt(km), and a nonlinear coefficient of 1.3W. -1 / km. Subsequently, an EDFA with a noise figure of 4dB is used to compensate for the loss of the fiber optic link and introduce ASE noise, transmitting 5-channel PDM-16QAM / 64QAM signals for 1200km or 400km respectively. After the fiber loop, a demultiplexer is first used to demultiplex the WDM signal, and five coherent receivers are used to collect the signal. Inside the coherent receivers, the signal light and local oscillator light are mixed at 90° and passed through balanced detection to obtain four electrical signals. These signals are then filtered by a low-pass filter and sampled in real time by an analog-to-digital converter. The acquired data is then resampled to twice the sample value and fed into the nonlinear impairment compensation module based on a cross-basis function neural network proposed in this invention. After a series of DSP processing steps, including time phase recovery, polarization demultiplexing, and carrier phase recovery, symbol inverse mapping and bit error rate calculation are finally performed. It should also be noted that, for the 5-channel WDM 28GBaud PDM-16QAM / 64QAM system built in this invention, the signal of the 3rd channel is used as an example for explanation, where the channel spacing is 50GHz and the wavelength is 1550nm.

[0084] After the complete DSP process is completed, demapping and bit error rate calculation are performed. In this embodiment, the bit error rate is used to measure the effectiveness of the invention. Figure 7The BER curves of the third channel were selected after transmitting PDM-16QAM / 64QAM signals for 1200km and 400km respectively through a 5-channel WDM system and processing them with a series of DSP algorithms. From the PDM-16QAM curves in the left figure, it can be seen that the black rectangular dotted line represents the curve after only frequency domain dispersion compensation; the circular dashed line represents the DBP curve per 10 steps; the gray rectangular dotted line represents the DBP curve per 50 steps; and the black triangular solid line represents the BER curve after a cross-basis function neural network per 1 step. As can be seen from the left figure, the BER performance of the method of this invention is significantly improved compared to frequency domain dispersion compensation, and the performance level is between that of DBP per 10 steps and DBP per 50 steps. At 1dBm, the BER of this method can be significantly improved. Down to At a higher fiber input power of 4dBm, the BER can be increased from... Down to The input power range is expanded by approximately 2 dB. The right figure shows the nonlinear impairment compensation curve after 400km transmission of a 5-channel WDM system using PDM-64QAM. As can be seen from the figure, due to the smaller spacing between PDM-64QAM constellation points, it is more susceptible to ASE noise and nonlinear effects in WDM systems, resulting in overall signal quality degradation. Therefore, for PDM-64QAM, this invention uses a 20% FEC value as the BER threshold. At the optimal transmit power of 1 dBm, the BER increases from... Down to At a higher fiber input power of 4dBm, BER from Down to The fiber input power range has been expanded by approximately 2 dB.

[0085] The BER curves of both modulation formats show that this method can compensate for ASE noise to some extent, thus providing a slight performance improvement compared to the other three curves when the input power is low. As the input power increases, the nonlinear effect becomes more pronounced. This method can shift the optimal input power of PDM-16QAM from 0dBm to 1dBm and effectively expand the input power range of both modulation formats. After exceeding the optimal power point, this method can achieve similar results to the DBP algorithm with 50 steps per step, albeit with lower complexity.

[0086] Simulation results demonstrate that this invention significantly compensates for accumulated dispersion and nonlinear impairments under different conditions in wavelength division multiplexing (WDM) systems. Specifically, this invention provides good compensation for nonlinear impairments caused by different high-order modulation formats transmitted over different distances in WDM systems, expands the input fiber power range, and its compensation performance falls between that of the 10-step and 50-step DBP algorithms. Furthermore, under the same performance conditions, its complexity is reduced by more than two orders of magnitude compared to the 50-step DBP algorithm.

[0087] Example 2

[0088] like Figure 2 As shown, the present invention provides a device for nonlinear impairment compensation suitable for high-order modulated wavelength division multiplexing systems, comprising:

[0089] The first processing module is used to acquire discrete sample signals collected by the coherent receiver corresponding to each channel in the high-speed coherent wavelength division multiplexing system.

[0090] The second processing module is used for processing the acquired data. C The discrete sampled signal of the i-th channel will be used to... l If a channel is used as the target channel, then the index l -1、 l The +1 channel is an adjacent channel of the target channel. The discrete sample signals of the target channel and the adjacent channel are resampled to twice the sample value, forming a one-dimensional sample vector with a length of twice the number of symbols, where 1 ≤ l ≤ C The one-dimensional sample set of each discrete sample signal is: , S Represents discrete sample signals. N Represents a signed number. C This represents the total number of channels. T This represents the matrix transpose operation;

[0091] The third processing module is used to perform dimension reshaping preprocessing on the one-dimensional sample vector;

[0092] The fourth processing module is used to input the preprocessed discrete sample signals into the cross-basis function neural network for training, so as to obtain the trained network model.

[0093] The fifth processing module is used to preprocess the test data using the methods of the first to third processing modules, and input the preprocessed test data into the trained network model to output discrete sample signals that effectively compensate for dispersion and nonlinear damage.

[0094] like Figure 2 The apparatus for compensating for nonlinear impairments in a high-order modulation wavelength division multiplexing system provided in the embodiment shown can execute the technical solution shown in the method embodiment above for compensating for nonlinear impairments in a high-order modulation wavelength division multiplexing system. Its implementation principle and beneficial effects are similar, and will not be repeated here.

[0095] In this embodiment, the functional units can be divided according to the method for compensating nonlinear impairments in a high-order modulated wavelength division multiplexing system. For example, each function can be divided into its own functional unit, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this invention is illustrative and represents only a logical division; other division methods may be used in actual implementation.

[0096] In this embodiment, the device for compensating for nonlinear impairments in a high-order modulation wavelength division multiplexing (HDWDM) system, in order to realize the principle and beneficial effects of a method for compensating for nonlinear impairments in a HDWDM system, includes hardware structures and / or software modules corresponding to the execution of various functions. Those skilled in the art should readily recognize that, based on the illustrative units and algorithm steps described in conjunction with the embodiments disclosed in this invention, the present invention can be implemented in hardware and / or a combination of hardware and computer software. Whether a function is executed in a hardware-driven or computer software-driven manner depends on the specific application and design constraints of the technical solution. Different methods can be used to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

Claims

1. A nonlinear impairment compensation method suitable for high-order modulated wavelength division multiplexing systems, characterized in that, Includes the following steps: S1. Obtain the discrete sample signals collected by the coherent receiver corresponding to each channel in the high-speed coherent wavelength division multiplexing system. S2, regarding the acquisition C The discrete sampled signal of the i-th channel will be the i-th channel. l If a channel is used as the target channel, then the index l -1、 l The +1 channel is an adjacent channel of the target channel. The discrete sample signals of the target channel and the adjacent channel are resampled to twice the sample value, forming a one-dimensional sample vector with a length of twice the number of symbols, where 1 ≤ l ≤ C The one-dimensional sample set of each discrete sample signal is: , S Represents discrete sample signals. N Represents a signed number. C This represents the total number of channels. T This represents the matrix transpose operation; S3. Perform dimension reshaping preprocessing on the one-dimensional sample vector; S4. Input the preprocessed discrete sample signal into the cross-basis function neural network for training to obtain the trained network model; S5. Preprocess the test data using the methods in steps S1-S3, and input the preprocessed test data into the trained network model to output discrete sample signals that effectively compensate for dispersion and nonlinear damage.

2. The nonlinear impairment compensation method for high-order modulated wavelength division multiplexing systems according to claim 1, characterized in that, Step S3 includes the following steps: S301. Divide the one-dimensional sample set of the discrete sample signals of the target channel and adjacent channels into real and imaginary parts, with dimension . ,in, N Represents a signed number; S302. Perform zero-padding on the one-dimensional sample vector to form... The integer transformation is performed in matrix form, where... , This represents the number of rows and columns of the matrix.

3. The nonlinear impairment compensation method for high-order modulated wavelength division multiplexing systems according to claim 1, characterized in that, Step S4 includes the following steps: S401. Network parameter initialization: Initialize the time-domain dispersion compensation filter. k Each tap coefficient, nonlinear phase shift correction factor, and activation function parameter are determined; the length of each optical fiber and the total number of optical fiber transmission segments are determined based on the transmission distance; the error vector amplitude is set as the loss function, and the Adam optimizer is set to update and optimize the tap coefficient, nonlinear phase shift correction factor, and activation function parameters, and the number of hidden layers in the cross-basis function neural network is kept consistent with the number of optical fiber transmission segments; S402. Input characteristics of the network: The preprocessed channel discrete sample signal, together with the 1-times discrete sample signal output by the target channel transmitter, is input into the cross-basis function neural network. S403, Time-Domain Dispersion Compensation: This applies the time-domain dispersion compensation filter... k Each tap coefficient is divided into real and imaginary parts. In the linear layer of each hidden layer in the cross-basis function neural network, the preprocessed discrete sample signals of the target channel and adjacent channels are combined with... k The real or imaginary part tap coefficients are convolved, and the optimal tap coefficients are obtained by iteratively updating the tap coefficients through the optimizer, so as to achieve dispersion compensation for each channel data. S404, Nonlinear Impairment Compensation: Discrete sample signals of the target channel and adjacent channels that have undergone dispersion compensation in the linear layer are input into the activation function. The optimal nonlinear phase shift correction factor and activation function parameters are obtained by iteratively updating the nonlinear phase shift correction factor and activation function parameters through the optimizer, thereby realizing nonlinear impairment compensation of the target channel. S405. Set the number of iterations to update the input features and network parameters: Based on the set number of iterations, determine whether the error vector amplitude has converged. If so, the input features and network parameters are considered to have reached the optimal value, and the trained network model is obtained. If the error vector amplitude continues to decrease after the iteration ends, increase the number of iterations and retrain the network model. If the EVM stabilizes at a certain value and no longer changes after the iteration ends, the network model training is completed.

4. The nonlinear impairment compensation method for high-order modulated wavelength division multiplexing systems according to claim 3, characterized in that, The hidden layer of the cross-basis function neural network includes a linear layer and an activation function; The linear layer uses the pre-obtained tap coefficients of the time-domain dispersion compensation filter to perform a convolution operation with the discrete sample signal to achieve dispersion compensation and obtain compensation data. The activation function is constructed using the coupled signal enhancement distributed Fourier method to compensate for nonlinear impairments in the wavelength division multiplexing system.

5. The nonlinear impairment compensation method for high-order modulated wavelength division multiplexing systems according to claim 4, characterized in that, The expression for the compensation data is as follows: in, Indicates compensation data, Represents an exponential function. Represents the imaginary unit. This represents the nonlinear coefficient in the optical fiber. Indicates fiber input power. Indicates transmission distance. This indicates the trend of fiber insertion power over a certain distance. Indicates the integral symbol, This represents an optimizable coefficient. Indicates the target channel index. Indicates the first l Channel x Polarization data, Indicates the first l channel y Polarization data, Indicates the target channel x / y Polarized data, Indicates the index of the discrete sample signal; The expression for the activation function is as follows: in, Indicates the target channel l Activation function, This represents an optimizable parameter in the activation function. This represents the data fed into the activation function, where the total number of channels is... C And the target channel l When the value equals 1, the adjacent channel is the second channel; when the target channel... l equal C When, the adjacent channel is the first. C -1 channel; The expression for the time-domain dispersion compensation filter is as follows: in, This represents a time-domain dispersion compensation filter. Indicates the inverse Fourier transform. Represents the frequency domain dispersion compensation transfer function. Represents the dispersion coefficient. Indicates the wavelength of the target channel. Represents the speed of light in a vacuum. Indicates the angular frequency of the target channel.

6. A nonlinear impairment compensation device suitable for high-order modulated wavelength division multiplexing systems, characterized in that, include: The first processing module is used to acquire discrete sample signals collected by the coherent receiver corresponding to each channel in the high-speed coherent wavelength division multiplexing system. The second processing module is used for processing the acquired data. C The discrete sampled signal of the i-th channel will be the i-th channel. l If a channel is used as the target channel, then the index l -1、 l The +1 channel is an adjacent channel of the target channel. The discrete sample signals of the target channel and the adjacent channel are resampled to twice the sample value, forming a one-dimensional sample vector with a length of twice the number of symbols, where 1 ≤ l ≤ C The one-dimensional sample set of each discrete sample signal is: , S Represents discrete sample signals. N Represents a signed number. C This represents the total number of channels. T This represents the matrix transpose operation; The third processing module is used to perform dimension reshaping preprocessing on the one-dimensional sample vector; The fourth processing module is used to input the preprocessed discrete sample signals into the cross-basis function neural network for training, so as to obtain the trained network model. The fifth processing module is used to preprocess the test data using the methods of the first to third processing modules, and input the preprocessed test data into the trained network model to output discrete sample signals that effectively compensate for dispersion and nonlinear damage.

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