Method and apparatus for joint intra- and inter-channel nonlinear compensation in a wdm system

Abstract

The application provides a method and device for intra-channel and inter-channel nonlinear joint compensation of a WDM system based on an improved LDBP and electronic equipment, and belongs to the technical field of optical fiber communication. The method compensates dispersion by using a linear filter in the time domain, the corresponding network structure is designed as one-dimensional convolution, and the pulse broadening effect is combined in the overlap reservation method, the physical model of nonlinear compensation is improved by considering the interference of intra-channel dispersion pulse broadening and the walk-off effect between channels, and the purpose of intra-channel and inter-channel nonlinear joint compensation is achieved. The application fully utilizes the random interaction between inherent dispersion and nonlinearity in the optical fiber communication system to compensate the phase shift caused by the nonlinear effect, can effectively equalize the nonlinear distortion of the signal under the condition of controlling the calculation complexity and reducing the implementation cost, and is expected to play a better role in the long-distance transmission of the large-capacity WDM system.

Description

Technical Field

[0001] This invention belongs to the field of fault self-healing technology for traction substations, and particularly relates to an improved LDBP WDM system with intra-channel and inter-channel nonlinear joint compensation method, device and electronic equipment. Background Technology

[0002] In the rapidly developing digital age of the internet, the explosive growth of network traffic has placed higher demands on optical fiber communication networks in terms of both high speed and large capacity. However, the capacity and transmission rate of optical fiber communication are difficult to meet these requirements due to the influence of linear and nonlinear impairments. Among them, linear impairments, including chromatic dispersion (CD) and polarization mode dispersion (PMD), can be well compensated by digital signal processing (DSP) technology. However, nonlinear impairments caused by Kerr nonlinearity increase with the increase of signal power and baud rate. In particular, the nonlinear effects in wavelength division multiplexing (WDM) systems include not only self-phase modulation (SPM) from the same channel, but also cross-phase modulation (XPM) and four-wave mixing (FWM) from other channels. The nonlinear phase shifts caused by SPM and XPM can lead to severe signal distortion. Furthermore, since optical fiber communication systems are not simply linear or nonlinear systems, linear impairments during signal transmission can interfere with nonlinear effects to a certain extent. Therefore, overcoming optical fiber nonlinear effects is not only the key to optimizing system performance but also a major challenge.

[0003] To mitigate distortion caused by fiber nonlinearity, researchers have proposed several effective nonlinear compensation techniques. The digital back propagation (DBP) algorithm and its improved versions achieve alternating compensation for dispersion and nonlinearity by solving the fiber back propagation equation using the split-step Fourier method (SSFM). However, DBP iteration requires multiple Fourier transform pairs, and its performance improves with the number of steps per segment, meaning superior performance requires higher computational complexity. Furthermore, this algorithm is a theoretical method for compensating nonlinear distortion, requiring transparent fiber link parameters, making its direct practical application a significant challenge. In addition, optical phase conjugation (OPC) technology for nonlinear compensation in the optical domain, nonlinear equalization methods based on Volterra series, and nonlinear compensation algorithms based on perturbation theory have also proven effective. However, OPC is very expensive and has very low conversion efficiency in practical applications, which limits its performance. Since Volterra series requires a Fourier transform module, it faces the dilemma that the complexity increases with the accumulation of dispersion. Nonlinear compensation based on perturbation theory requires higher computational complexity to achieve the desired quantization accuracy.

[0004] In recent years, with the rapid development of machine learning, the powerful learning ability of neural networks (NNs) has attracted widespread attention. They can complete computations without requiring extensive prior information about the system's links. Therefore, artificial neural networks (ANNs) and convolutional neural networks (CNNs) have been introduced into the field of fiber optic nonlinear compensation to further improve system performance. The discovery of correlations between adjacent symbols in triplet arrays has made memory-based neural networks a research hotspot. Taking long short-term memory (LSTM) networks and their variants as examples, they effectively achieve nonlinear compensation in coherent optical communication systems by memorizing the correlations between adjacent symbols. However, most of the aforementioned neural network-based nonlinear compensation methods are black-box processes, focusing only on performance improvement, with output results and learning processes difficult to interpret. To address this, researchers combined theoretical models with neural networks, proposing interpretable learned digital backpropagation (LDBP). Its emergence solves the limitation of nonlinear compensation imposed by the black-box problem of neural networks.

[0005] Patent searches reveal that existing methods for nonlinear compensation in optical communication systems primarily include: First, compensation for signal dispersion and nonlinearity is performed, followed by regression analysis on the compensation signal to determine the final result. Second, existing research utilizes triples to enable a neural network to learn nonlinear impairment values, then subtracts these values ​​from the received signal to complete nonlinear compensation. Third, existing research employs optical phase conjugation algorithms to compensate for nonlinear impairments. However, these studies suffer from high computational complexity in nonlinear compensation for optical communication systems and do not comprehensively consider the complex correlation between linear and nonlinear impairments. They also neglect the disturbances to signal nonlinearity caused by intra-channel pulse broadening and inter-channel walk-off effects due to dispersion in WDM systems. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, this invention provides a method, apparatus, and electronic device for joint compensation of intra-channel and inter-channel nonlinearity in WDM systems based on improved LDBP, which can achieve performance improvement with lower computational complexity; and by using the forward error correction (FEC) threshold as a metric, it greatly extends the effective transmission distance.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] Firstly, this solution provides a joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system, comprising the following steps:

[0009] S1. Receive the signal of each channel in the WDM system individually using a coherent receiver, and resample the received signal to 2 samples / symbol;

[0010] S2. Based on the resampled signal, a one-dimensional convolution operation is performed in the time domain using the stepwise linear compensation layer of the improved LDBP neural network, and a pulse broadening effect is added to the overlap preservation method to compensate for the linear loss caused by dispersion.

[0011] S3. The signal after each step of dispersion compensation is passed to the step-by-step nonlinear compensation layer of the LDBP neural network. Considering the dispersion effect within the same channel, the weights are set in combination with the nonlinear interaction between adjacent symbols, and the nonlinear phase shift caused by the SPM effect is solved.

[0012] S4. Considering the inter-channel walk-off effect, solve the nonlinear phase shift caused by the XPM effect in the frequency domain, and transfer the XPM nonlinear phase shift obtained in the frequency domain to the time domain.

[0013] S5. Add the nonlinear phase shift caused by the XPM effect in the time domain and the nonlinear phase shift caused by the SPM effect to perform joint nonlinear compensation for the signal within and between channels.

[0014] S6. The polarization-related nonlinear interaction of the signal after joint compensation is compensated by an adaptive filter;

[0015] S7. The signal compensated in step S6 is used by the DSP to restore the damaged signal, thus completing the nonlinear joint compensation of the WDM system within and between channels.

[0016] The beneficial effects of this invention are: by optimizing the physical model of signal transmission, this invention alternately compensates for dispersion and nonlinear effects at the receiving end. In the case of unknown specific parameters, by combining neural networks and an improved nonlinear compensation physical model, it achieves joint compensation of intra-channel and inter-channel nonlinearity in WDM systems. This can effectively balance signal nonlinear distortion while controlling computational complexity and reducing implementation costs, and is expected to play a better role in high-capacity WDM systems with long-distance transmission.

[0017] Further, step S1 includes the following steps:

[0018] S101. In the WDW system, a coherent receiver is used to receive the discrete signals of each channel individually.

[0019] S102, Resample the discrete signal to 2 samples / symbol.

[0020] Furthermore, the improved LDBP neural network includes:

[0021] The input layer is used to receive resampled signals;

[0022] The linear compensation layer is used to perform a one-dimensional convolution operation in the time domain based on the resampled signal, and to add a pulse broadening effect to the overlap preservation method to compensate for the linear loss caused by dispersion.

[0023] The nonlinear joint compensation layer for intra-channel and inter-channel signals is used to set weights based on the dispersion-compensated signal at each step, taking into account the dispersion effect within the same channel and the nonlinear interaction between adjacent symbols, and to solve for the nonlinear phase shift caused by the SPM effect; considering the walk-off effect between channels, it solves for the nonlinear phase shift caused by the XPM effect in the frequency domain, and transfers the XPM nonlinear phase shift obtained in the frequency domain to the time domain; the XPM nonlinear phase shift in the time domain and the nonlinear phase shift caused by the SPM effect are added together to perform joint nonlinear compensation for the signal within and between channels.

[0024] An adaptive filter is used to compensate for the polarization-dependent nonlinear interactions of the jointly compensated signal.

[0025] The output layer is used to output the signal after adaptive filter compensation.

[0026] Furthermore, step S2 includes the following steps:

[0027] S201. Adjust the input characteristics of two orthogonal discrete polarization signals according to the signal time series and dispersion properties to achieve a combination of overlap preservation method and pulse broadening effect;

[0028] S202. Send the input features to the stepwise linear compensation layer of the improved LDBP neural network;

[0029] S203. Using the stepwise linear compensation layer of the LDBP neural network, a one-dimensional convolution operation is used in the time domain to compensate for the linear loss caused by dispersion.

[0030] The beneficial effects of the above-mentioned further solutions are as follows: the neural network of the present invention uses one-dimensional convolution operation in the time domain and adds pulse broadening effect in the overlap preservation method, which more accurately compensates for the linear damage caused by dispersion, does not require additional Fourier transform operations, and greatly reduces the computational complexity.

[0031] Furthermore, the expression for the nonlinear phase shift caused by the SPM effect in step S3 is as follows:

[0032]

[0033] in, g represents the nonlinear phase shift caused by the SPM effect. SPM,k Let S represent the nonlinear parameters within the target channel k, S represent the range of correlated symbols within the same channel, i.e., the interval of symbols correlated with symbol p is [pS, p+S], p represents the symbol that needs to be equalized at the current time, i represents the position of the correlated symbol, and δ represents the nonlinear parameters within the target channel k. i u represents the training weights corresponding to different symbols. k,x / y,i and u k,y / x,i The values ​​of x / y and y / x represent the amplitudes of x or y at point i in the target channel k, respectively, where x and y represent two orthogonal polarization signals, and γ... kk l represents the nonlinear coefficient within the same channel. eff The effective length of the nonlinearity in the optical fiber is represented by , and u represents the complex envelope of the electrical signal.

[0034] The time-domain XPM nonlinear phase shift expression in step S4 is as follows:

[0035]

[0036]

[0037] d nk =β2(ω n -ω k )

[0038] in, Let F represent the XPM nonlinear phase shift in the time domain, k represent the index of the target channel, t represent time, l represent the signal transmission length, and F represent the time domain. -1 U represents the inverse Fourier transform, F represents the Fourier transform, u n,x / y u n,y / x Based on the different values ​​of x / y and y / x, g represents the x or y polarization signal of channel n. XMP,nk γ represents the optimization parameters, including go-away parameters and nonlinear coefficients, when link information is unknown. nk The nonlinear coefficients between different channels are represented by exp(·), which represents the exponential operation, α represents the loss coefficient, i' represents the imaginary number, and d nk The walk-off parameter represents the distance between the non-target channel n and the target channel k, ω represents the frequency, and β² represents the second-order group velocity dispersion GVD coefficient. n ω represents the carrier frequency of the non-target channel n. k This represents the carrier frequency of the non-target channel k.

[0039] The beneficial effects of the above-mentioned further scheme are as follows: Based on the enhanced split-step Fourier method, the interaction between dispersion and nonlinearity is introduced into the signal after dispersion compensation in each step. A more accurate nonlinear compensation model is constructed along each step of the optical fiber, considering the nonlinear interaction between adjacent symbols, thus mitigating interference caused by pulse broadening while compensating for nonlinear impairments. Simultaneously, by decomposing the walk-off effect between multiple channels, the inter-channel XPM compensation model is improved, effectively solving the problem of signal pulse transmission asynchrony.

[0040] Furthermore, in step S5, the signal undergoes joint nonlinear compensation both within and between channels, the expression of which is as follows:

[0041]

[0042] Where x and y represent two orthogonal polarization signals, u k,x / y (0,t) represents the received x / y polarization signal of the target channel k, u k,x / y (l,t) represents the x / y polarization signal transmitted in the target channel k, t represents time, exp(·) represents exponential operation, and j represents the imaginary number. and denoted as SPM effect and XPM effect respectively, and l represents the signal transmission length.

[0043] The beneficial effects of the above-mentioned further solutions are as follows: The present invention, through the theoretical model for calculating the joint nonlinear compensation within and between channels, starts from the perspective of interpretable neural networks and realizes nonlinear compensation based on an improved physical model, effectively achieving the purpose of joint nonlinear compensation within and between channels.

[0044] Furthermore, step S6 specifically includes:

[0045] Based on the jointly compensated signal, an adaptive time-domain filter located at the back end of the LDBP neural network is used to compensate for polarization-related nonlinear interactions.

[0046] Furthermore, step S7 specifically includes:

[0047] Based on the signal compensated in step S6, the damaged signal with carrier phase recovery is obtained through DSP processing.

[0048] The bit error rate is calculated for the damaged signal of carrier phase recovery, and nonlinear joint compensation within and between channels of the WDM system is completed.

[0049] The advantages of the above-mentioned further solutions are: the present invention completes nonlinear compensation before polarization demultiplexing by simulating the transmission physical model; when the precise link conditions are unknown, the neural network makes the learning process clearer and the learning results easier to interpret. Furthermore, the processing by other digital signal processing modules more closely approximates the recovery of distorted signals in practical applications.

[0050] In a second aspect, the present invention provides a joint compensation device for intra-channel and inter-channel nonlinearity in a WDM system, the device comprising:

[0051] The first processing module is used to receive the signal of each channel in the WDM system individually using a coherent receiver, and resample the received signal to 2 samples / symbol; the second processing module is used to apply a one-dimensional convolution operation in the time domain using the step-by-step linear compensation layer of the LDBP neural network based on the resampled signal, and add a pulse broadening effect in the overlap-preserving method to compensate for the linear loss caused by dispersion; the third processing module is used to pass the signal after each step-by-step dispersion compensation to the step-by-step nonlinear compensation layer of the LDBP neural network, and set weights in combination with the nonlinear interaction between adjacent symbols while considering the dispersion effect within the same channel, and solve for the nonlinear phase shift caused by the SPM effect; the fourth... The first processing module is used to solve the nonlinear phase shift caused by the XPM effect in the frequency domain, considering the inter-channel walk-off effect, and then transfer the XPM nonlinear phase shift obtained in the frequency domain to the time domain. The second processing module is used to add the nonlinear phase shift caused by the XPM effect and the nonlinear phase shift caused by the SPM effect in the time domain, and perform joint compensation for intra-channel and inter-channel nonlinearities of the signal. The third processing module is used to compensate for the polarization-related nonlinear interactions of the jointly compensated signal by an adaptive filter. The fourth processing module is used to recover the damaged signal from the signal compensated by the sixth processing module by a DSP, thus completing the joint compensation for intra-channel and inter-channel nonlinearities of the WDM system.

[0052] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps of a joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system. Attached Figure Description

[0053] Figure 1 This is a flowchart of the method of the present invention.

[0054] Figure 2 This is a diagram of the overall neural network structure of the present invention, taking three channels as an example.

[0055] Figure 3 This is an expanded diagram of the nonlinear compensation part of the LDBP neural network in this embodiment.

[0056] Figure 4 This is the DSP flowchart in this embodiment.

[0057] Figure 5 This is a block diagram of the 11-channel WDM simulation system in this embodiment.

[0058] Figure 6 This is a Q-factor performance curve of different equalization schemes in an 11-channel WDM simulation system with 36GBaud DP-16QAM at 1600km, as shown in this embodiment.

[0059] Figure 7 This is a Q-factor performance curve of different equalization schemes in an 11-channel WDM simulation system with 64GBaud DP-64QAM 400km, as shown in this embodiment.

[0060] Figure 8 This diagram illustrates the relationship between the Q-factor performance and transmission distance of different equalization schemes under the DP-16QAM modulation format in an 11-channel WDM simulation system according to this embodiment.

[0061] Figure 9 This diagram illustrates the relationship between the Q-factor performance and transmission distance of different equalization schemes under the DP-64QAM modulation format in an 11-channel WDM simulation system according to this embodiment.

[0062] Figure 10 This is a block diagram of the 5-channel WDM experimental system in this embodiment.

[0063] Figure 11 This is a Q-factor performance curve of different equalization schemes for the 28GBaud DP-16QAM 806.4km channel WDM experimental system in this embodiment.

[0064] Figure 12 This is a schematic diagram of the device structure of the present invention. Detailed Implementation

[0065] 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.

[0066] Example 1

[0067] like Figure 1 As shown, this invention provides a joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system, the implementation of which is as follows:

[0068] S1. Utilize a coherent receiver to individually receive the signal from each channel in the WDM system, and resample the received signal to 2 samples / symbol. The implementation method is as follows:

[0069] S101. In the WDW system, a coherent receiver is used to receive the discrete signals of each channel individually.

[0070] S102, Resample the discrete signal to 2 samples / symbol.

[0071] S2. Based on the resampled signal, a one-dimensional convolution operation is performed in the time domain using the stepwise linear compensation layer of the improved LDBP neural network. Pulse broadening is added to the overlap-preserving method to compensate for the linear loss caused by dispersion. The implementation method is as follows:

[0072] S201. Adjust the input characteristics of two orthogonal discrete polarization signals according to the signal time series and dispersion properties to achieve a combination of overlap preservation method and pulse broadening effect;

[0073] S202. Send the input features to the stepwise linear compensation layer of the improved LDBP neural network;

[0074] S203. Using the stepwise linear compensation layer of the LDBP neural network, a one-dimensional convolution operation is used in the time domain to compensate for the linear loss caused by dispersion.

[0075] In this embodiment, the resampled signal enters the stepwise linear compensation stage of the LDBP neural network. The compensation layer uses one-dimensional convolution in the time domain and incorporates pulse broadening in the overlap-preservation method to more accurately compensate for linear damage caused by dispersion. The input features of two orthogonal discrete polarized electrical signals are adjusted according to the signal's time series and dispersion properties to achieve a combination of overlap preservation and pulse broadening. Then, the input features are fed into the linear compensation layer of the LDBP neural network. The linear compensation layer uses one-dimensional convolution in the time domain, and the convolution kernel of the linear compensation layer is equivalent to a symmetrical filter in the time domain. Linear damage compensation is achieved by multiplying the optimized filter weights with the convolution of the damaged signal. This method does not require additional Fourier transform operations, significantly reducing computational complexity.

[0076] The improved LDBP neural network includes: an input layer for receiving resampled signals;

[0077] The linear compensation layer performs a one-dimensional convolution operation in the time domain based on the resampled signal and incorporates pulse broadening in the overlap-preservation method to compensate for the linear loss caused by dispersion. The intra-channel and inter-channel nonlinear joint compensation layer calculates the nonlinear phase shift caused by the SPM effect based on the dispersion-compensated signal at each step, considering the intra-channel dispersion effect and the nonlinear interactions between adjacent symbols. Considering the inter-channel walk-off effect, it solves for the nonlinear phase shift caused by the XPM effect in the frequency domain and transfers the frequency-domain XPM nonlinear phase shift to the time domain. The time-domain XPM nonlinear phase shift and the nonlinear phase shift caused by the SPM effect are added together to perform intra-channel and inter-channel nonlinear joint compensation. An adaptive filter compensates for the polarization-related nonlinear interactions of the jointly compensated signal. The output layer outputs the signal compensated by the adaptive filter.

[0078] In this embodiment, the input signal to the convolutional layer is configured with features based on time series and dispersion properties: 65,536 training samples are divided into training data blocks composed of input vectors, with each data block having a batch size of 32 and a layer width of 128. To more effectively compensate for accumulated dispersion in the temporal convolutional layer, adjacent data affected by the dispersion pulse broadening effect are added to both ends of each original data block. These adjacent data are then combined into input features and fed into the neural network for training and learning, achieving a proper combination of overlap preservation and pulse broadening effects. The stepwise linear compensation layer employs a one-dimensional convolution operation in the temporal domain. The convolution kernel of the stepwise linear compensation layer is equivalent to a symmetric filter in the temporal domain, and linear damage compensation is achieved by multiplying the optimized filter weights with the damage signal through convolution.

[0079] S3. The signal after each step of dispersion compensation is passed to the step-by-step nonlinear compensation layer of the LDBP neural network. Considering the dispersion effect within the same channel, the weights are set in combination with the nonlinear interaction between adjacent symbols, and the nonlinear phase shift caused by the SPM effect is solved.

[0080] In this embodiment, based on the enhanced split-step Fourier method, the interaction between dispersion and nonlinearity is introduced into the signal after dispersion compensation in each step, constructing a more accurate nonlinear compensation model along each step of the optical fiber. Considering the nonlinear interaction between adjacent symbols, the interference caused by pulse broadening is mitigated while compensating for nonlinear impairments, resulting in the formula for the nonlinear phase shift caused by the SPM effect:

[0081]

[0082] Among them, g SPM,k =γ kk l eff γ kk l represents the nonlinear coefficient within the same channel. eff Let represent the effective length of the nonlinearity in the optical fiber, u represent the complex envelope of the electrical signal, the subscripts x and y of u represent two orthogonal polarization signals, k represent the subscript of the target channel, p represent the symbol that needs to be equalized at the current moment, and S represent the range of related symbols within the same channel, i.e., the interval of symbols related to symbol p is [pS, p+S]. If the vector ξ reflects the degree of correlation between adjacent symbols, then ξ = [δ p-S ,δ p-S+1 ,...,δ p ,...,δ p+S ], where δ i (i = pS...p+S) represents the training weights for different symbols, which are real-valued parameters, where i represents the position of the relevant symbol, i.e., δ. p-S ,δp-S+1 ,...,δ p ,...,δ p+S Let u represent the training weights between the symbols pS, p-S+1, ..., p, ..., p+S and the symbol p, respectively. k,x / y,i u k,y / x,i The difference between x / y and y / x represents the amplitude of the x or y polarized signal of the target channel k at point i.

[0083] S4. Considering the inter-channel walk-off effect, solve the nonlinear phase shift caused by the XPM effect in the frequency domain, and transfer the XPM nonlinear phase shift obtained in the frequency domain to the time domain.

[0084] In this embodiment, if channel k is taken as the target channel and the focus is on the XPM effect, the time-domain XPM nonlinear phase shift is obtained while considering the inter-channel walk-off effect.

[0085]

[0086] Where z represents distance and t represents time. d represents the distance variable in the integral; nk =β2(ω n -ω k ) represents the walk-off effect between different channels per unit length, n and k are used to distinguish different channels, ω n ω represents the carrier frequency of the non-target channel n. k Let βk represent the carrier frequency of the non-target channel k, β2 represent the second-order group velocity dispersion (GVD) coefficient, l represent the signal transmission length, and γk represent the signal propagation length. nk The nonlinear coefficients between different channels are represented by u, which represents the complex envelope of the electrical signal. The subscripts x and y of u represent two orthogonal polarization signals. n,x / y u n,y / x The x / y and y / x represent the x or y polarization signal of channel n, respectively, and α represents the loss coefficient. This represents parameters related to losses.

[0087] Taking a Fourier transform of the above formula yields the nonlinear phase shift in the frequency domain:

[0088]

[0089] Where F represents the Fourier transform, and ω represents the frequency. Here, 'e' represents the distance variable in the integral, and 'e' represents the exponential operation. To make it applicable to discrete signals, the integral of the above equation is expressed as an approximation:

[0090]

[0091] Where exp(·) represents exponentiation and i' represents the imaginary number. Since both the transmitted signal and the SPM nonlinear phase shift are in the time domain, the XPM phase shift given in the above equation needs to be transformed to the time domain, as shown below:

[0092]

[0093] in, F is an optimization parameter that includes go-away parameters and nonlinear coefficients when link information is unknown. -1 This represents the inverse Fourier transform.

[0094] S5. Add the nonlinear phase shift caused by the XPM effect in the time domain and the nonlinear phase shift caused by the SPM effect to perform joint nonlinear compensation for the signal within and between channels.

[0095] In this embodiment, merging and The overall nonlinear phase shift of channel k in the WDM system is obtained, nonlinear compensation is performed, and the corrected signal is output. The theoretical model for calculating joint intra-channel and inter-channel nonlinear compensation is expressed as follows:

[0096]

[0097] Where x and y represent two orthogonal polarization signals, u k,x / y (0,t) represents the received x / y polarization signal of the target channel k, u k,x / y (l,t) represents the x / y polarization signal transmitted in the target channel k, t represents time, exp(·) represents exponential operation, and j represents the imaginary number. and denoted as SPM effect and XPM effect respectively, and l represents the signal transmission length.

[0098] S6. The polarization-related nonlinear interaction of the jointly compensated signal is compensated by an adaptive filter. Specifically, the polarization-related nonlinear interaction is compensated by an adaptive time-domain filter located at the back end of the LDBP neural network based on the jointly compensated signal.

[0099] In this embodiment, an adaptive filter is added to the back end of the neural network after nonlinear compensation to compensate for polarization-related nonlinear interactions and reduce the random influence of polarization-related damage on LDBP. The time-domain filter used is similar to the filter of the blind constant mode algorithm.

[0100] In this embodiment, steps S2-S6 complete signal compensation in the neural network, such as... Figure 2 As shown; the fiber nonlinear equalization model obtained in steps S3-S5 is the theoretical basis for the nonlinear layer of the neural network, such as Figure 3 As shown.

[0101] S7. The signal compensated in step S6 is used by the DSP to recover the damaged signal, completing the joint nonlinear compensation of the WDM system within and between channels. Specifically:

[0102] Based on the signal compensated in step S6, the damaged signal with carrier phase recovery is obtained through DSP processing; the bit error rate of the damaged signal with carrier phase recovery is calculated to complete the nonlinear joint compensation within and between channels of the WDM system.

[0103] In this embodiment, as Figure 4 As shown, the improved LDBP neural network model is located before polarization demultiplexing. In step S6, the signal output after neural network dispersion compensation and nonlinear compensation is processed by other algorithms in the DSP, including polarization demultiplexing, downsampling, frequency offset estimation and carrier phase recovery. Finally, the bit error rate is calculated on the output of the carrier phase recovery.

[0104] This embodiment constructs an 11-channel WDM system with 36GBaud DP-16QAM 1600km and 64GBaud DP-64QAM 400km based on VPIDesign Suite 11.1 and Matlab co-simulation, such as... Figure 5 As shown. To avoid the neural network learning the data generation pattern, the bit sequence was randomly generated using Matlab's `random` function, with a symbol length of 65536 for each polarization. The frequency offset and laser linewidth were set to 100MHz and 100kHz, respectively. Each transmission span of the system consisted of 80km of standard single-mode fiber (SSMF) and an erbium-doped fiber amplifier (EDFA). The waveform of the modulated signal was formed by a root-raised-cosine (RRC) filter with a roll-off factor of 0.1. The wavelength of the center channel of the WDM system was 1550nm, and the channel spacing for DP-16QAM and DP-64QAM was 50GHz and 75GHz, respectively. The fiber loss, dispersion coefficient, nonlinearity coefficient, and polarization mode dispersion coefficient were set to 0.2dB / km, 16ps / nm / km, and 1.3W, respectively. -1 / km, 0.1 The dispersion slope was set to 0.08 ps / nm. 2 / km. The EDFA operates in gain control mode, with noise figures of 5dB (DP-16QAM) and 4dB (DP-64QAM). At the receiving end, this embodiment uses a coherent receiver to receive the signal, followed by offline processing.

[0105] In this embodiment, for the received discrete data, whether DP-16QAM or DP-64QAM, the data length for each channel is 131,072 samples. The first 50% (65,536 samples) is used for training, and the remaining 65,536 samples are used for testing. In this embodiment, the number of alternating linear and nonlinear layers in the neural network compensation layer used to train 16QAM is 10, equivalent to 0.5 steps per span in classic DBP; the number of neural network layers used to train 64QAM is also 10, equivalent to 2 steps per span in classic DBP.

[0106] In this embodiment, to train the neural network, the Adam optimizer, which has a relatively fast convergence speed, is simple to implement, and is suitable for large-scale data and parameter scenarios, is selected. The learner rate of the optimizer is set to 0.001 to ensure the stability of the neural network training performance. Mean squared error (MSE) is used as the loss function to measure the closeness between the data obtained from neural network training and the labels. For DP-16QAM and DP-64QAM, the width of the dispersion compensation filter is 81, the width of the filter used for polarization-related interference compensation is 3, and the width of the SPM filter corresponding to the number of correlation samples of nonlinear and dispersion interactions within the same channel is 11.

[0107] In this embodiment, the effectiveness of the method of the present invention in compensating for channel nonlinear impairments is analyzed and compared in detail. Under the same parameter conditions, the performance is compared with other typical schemes from two perspectives: considering only SPM and considering both SPM and XPM. The specific analysis is as follows.

[0108] In this embodiment, Figure 6 The curves showing the relationship between different transmit powers and Q factors on the target channel of interest after 1600 km transmission of a WDM system with 36 GBaud DP-16QAM are presented. Figure 6It can be seen that, for the DP-16QAM transmission scenario, compared with the linear compensation scheme, the optimal transmit power of the LDBP scheme, which only compensates for the SPM within the channel every 0.5 steps, is increased from -1dBm to 0dBm, and its performance is better than DBP-1StPs. When considering both SPM and XPM, the optimal transmit power of the improved LDBP method is increased from -1dBm to 0dBm compared to the linear compensation scheme. Compared to the linear compensation scheme and the deep convolutional neural network (DCNN) scheme, the signal-to-noise ratio at the optimal transmit power can be improved by approximately 3.1dB and 1dB, respectively, with Q-factor gains of approximately 0.75dB and 0.15dB. Moreover, the overall performance of the joint compensation scheme of this invention is better than that of DBP-5StPs. Compared to DBP-5StPs, the signal-to-noise ratio at the optimal transmit power can be improved by approximately 1dB, with a Q-factor gain of approximately 0.15dB. In the 16QAM transmission scenario, the transmit power range per channel where the Q-factor of this scheme satisfies the 7% FEC threshold is -2.5dBm to 2.5dBm.

[0109] In this embodiment, Figure 7 For 64GBaud DP-64QAM transmission scenarios, compared to linear compensation schemes, the optimal transmit power of the LDBP scheme, which compensates only for SPM every two steps, increases from 1dBm to 2dBm, achieving performance comparable to DBP-10StPs. When considering both SPM and XPM, the optimal transmit power of the method in this invention increases from 1dBm to 2dBm compared to linear compensation schemes. Compared to linear compensation schemes and DCNN schemes, the signal-to-noise ratio (SNR) at optimal transmit power can be improved by approximately 3dB and 1dB respectively, with Q-factor gains of approximately 0.54dB and 0.1dB. The overall performance of the joint compensation scheme in this invention surpasses that of DBP-10tPs. Compared to DBP-10tPs, the improved LDBP scheme can improve the SNR by approximately 1.5dB and Q-factor gain by approximately 0.2dB at optimal transmit power. In 64QAM transmission scenarios, the transmit power range per channel where the Q-factor of this scheme satisfies the 20% FEC threshold is -3dBm to 6dBm.

[0110] In this embodiment, the above analysis and discussion reflect that the LDBP scheme that compensates for SPM alone can reduce the number of steps and lower computational complexity while achieving the same performance as the classic DBP. The method of this invention not only outperforms LDBP that only considers SPM compensation in terms of joint compensation performance for intra-channel and inter-channel nonlinear impairments, but also outperforms DBP with more steps compared to LDBP that only considers SPM compensation, with a significant reduction in computational complexity.

[0111] In this embodiment, Figure 8The relationship between the Q-factor performance of DP-16QAM at optimal transmit power and different transmission distances is presented. The figure shows that the linear compensation scheme performs the worst, with 16QAM achieving a transmission distance of 1720 km under the 7% FEC threshold condition. In contrast, under the same conditions, the present invention achieves approximately 2080 km for 16QAM, representing an increase of about 360 km in effective transmission distance compared to the linear compensation scheme, and 160 km more than the LDBP scheme that only compensates for SPM. Figure 9 As shown, the DP-64QAM linear compensation scheme with a 20% FEC threshold has a transmission distance of only about 700km, while the present invention can effectively transmit about 880km, which is about 180km longer than the linear compensation scheme and about 120km longer than the LDBP scheme that only compensates for SPM.

[0112] In this embodiment, the total number of real multiplications required for the neural network training process is used as the metric for complexity analysis. For 16QAM with a 0.5-step span, this invention outperforms DBP-5StPs but has only 43.58% of its complexity. For 64QAM with a 2-step span, it outperforms DBP-10StPs but has 87.17% of its complexity.

[0113] To further verify the effectiveness of the present invention, Example 2 constructed a 28GBaud DP-16QAM 806.4km 5-channel WDM experimental transmission system, as follows: Figure 10As shown. At the transmitting end, five external cavity lasers (ECLs) with center frequencies of 193.3 THz, 193.35 THz, 193.4 THz, 193.45 THz, and 193.5 THz, respectively, have their emitted signals multiplexed by a multiplexer. The frequency offset and linewidth of the lasers are approximately 100 MHz and 100 kHz, respectively. Similar to the simulation, the symbol length is 65536. A random bit sequence is constructed using the built-in Matlab function `Random`. The signal is generated by a 65 GSa / s arbitrary waveform generator (AWG, Keysight M8195A). The signal pulse waveform is formed by an RRC filter with a roll-off factor of 0.1, and then modulated using an IQ modulator. Each transmission span of the fiber optic link consists of a 100.8km SSMF (Silent Fiber Motion Filter), an EDFA (Optical Fiber Optic Amplifier) ​​with a noise figure of 6.5dB, an optical band-pass filter (OBPF), and a variable optical attenuator (VOA). Additionally, the signal passes through an EDFA and a variable optical attenuator (VOA) before entering the fiber optic link to adjust to the appropriate input optical power. The fiber loss, dispersion coefficient, nonlinearity coefficient, and polarization mode dispersion coefficient are 0.19dB / km, 16.7ps / nm / km, and 1.27W, respectively. -1 / km、 Before entering the receiver, the five multiplexed waveforms are demultiplexed according to different center frequencies, enabling the coherent receiver to receive individual channel signals separately. At the receiving end, the received optical signal is sampled by a real-time oscilloscope with a sampling rate of 80 GSa / s to obtain discrete signals, which are then processed offline by a DSP.

[0114] In this embodiment, for the received discrete data, for a 28GBaud DP-16QAM transmission over 806.4km, the data length for each channel is 131,072 samples. The first 50% (65,536 samples) is used for training, and the remaining 65,536 samples are used for testing. In this embodiment, the number of alternating linear and nonlinear layers in the neural network compensation layer used to train 16QAM is 4, equivalent to 0.5 steps per span in classical DBP; the width of the dispersion compensation filter is 61, the width of the filter used for polarization-dependent interference compensation is 3, and the width of the SPM filter corresponding to the number of correlation samples of nonlinear and dispersion interactions within the same channel is 9.

[0115] This embodiment further verifies the effectiveness of the improved method of the present invention in an experimental system, and the results are as follows: Figure 11 As shown. Compared to the linear compensation scheme, the optimal transmit power of the method in this invention is increased from -1dBm to 0dBm, and the signal-to-noise ratio (SNR) can be improved by about 3.5dB and the Q factor gain by about 0.86dB at the optimal transmit power. Compared with the DCNN scheme, the SNR and Q factor can be improved by about 1dB and 0.16dB respectively at the optimal transmit power. The overall performance of this invention is better than DBP-5StPs. Compared with DBP-5StPs, the SNR can be improved by about 1dB and the Q factor gain by about 0.2dB at the optimal transmit power. In the scenario of 28GBaud DP-16QAM transmission over 806.4km, the transmit power range per channel in which the Q factor of this scheme meets the 7% FEC threshold condition is -2.5dBm to 1.8dBm. This experimental system transmits DP-16QAM 806.4km based on an improved LDBP scheme. Under the same conditions, it can achieve or even exceed the performance of DBP-5StPs with only 0.5 steps per span, while the complexity is only 27.29% of that of DBP-5StPs.

[0116] Based on the above analysis, simulation and experimental verification show that the joint compensation method for intra-channel and inter-channel nonlinearity in WDM systems based on the improved LDBP can improve the accuracy of nonlinear compensation and greatly reduce the required computational complexity. It is an effective method for balancing signal nonlinear distortion while controlling computational complexity and reducing implementation costs, and is expected to have good application prospects in long-distance, high-capacity WDM systems.

[0117] Example 2

[0118] like Figure 12 As shown, the present invention provides a joint compensation device for intra-channel and inter-channel nonlinearity in a WDM system, the device comprising:

[0119] The first processing module is used to receive the signal of each channel in the WDM system individually using a coherent receiver, and resample the received signal to 2 samples / symbol; the second processing module is used to apply a one-dimensional convolution operation in the time domain using the step-by-step linear compensation layer of the LDBP neural network based on the resampled signal, and add a pulse broadening effect in the overlap-preserving method to compensate for the linear loss caused by dispersion; the third processing module is used to pass the signal after each step-by-step dispersion compensation to the step-by-step nonlinear compensation layer of the LDBP neural network, and set weights in combination with the nonlinear interaction between adjacent symbols while considering the dispersion effect within the same channel, and solve for the nonlinear phase shift caused by the SPM effect; the fourth... The first processing module is used to solve the nonlinear phase shift caused by the XPM effect in the frequency domain, considering the inter-channel walk-off effect, and then transfer the XPM nonlinear phase shift obtained in the frequency domain to the time domain. The second processing module is used to add the nonlinear phase shift caused by the XPM effect and the nonlinear phase shift caused by the SPM effect in the time domain, and perform joint compensation for intra-channel and inter-channel nonlinearities of the signal. The third processing module is used to compensate for the polarization-related nonlinear interactions of the jointly compensated signal by an adaptive filter. The fourth processing module is used to recover the damaged signal from the signal compensated by the sixth processing module by a DSP, thus completing the joint compensation for intra-channel and inter-channel nonlinearities of the WDM system.

[0120] In this embodiment, the main structure of the improved LDBP neural network is constructed using the Adam optimizer, which has a relatively fast convergence speed, is simple to implement, and is suitable for large-scale data and parameter scenarios. The learner rate of the optimizer is set to 0.001 to ensure the stability of the neural network training performance. The mean squared error (MSE) is used as the loss function to measure the closeness between the data obtained from the neural network training and the labels.

[0121] like Figure 12 The WDM system intra-channel and inter-channel nonlinear joint compensation device provided in the embodiment shown can execute the technical solution shown in the above-described method embodiment of the WDM system intra-channel and inter-channel nonlinear joint compensation method. Its implementation principle and beneficial effects are similar, and will not be repeated here.

[0122] In this embodiment, the functional units can be divided according to the joint compensation method for intra-channel and inter-channel nonlinearity in WDM systems. For example, each function can be divided into its own functional units, 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.

[0123] In this embodiment, the WDM system's intra-channel and inter-channel nonlinear joint compensation system, in order to realize its principle and beneficial effects, 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.

[0124] In this embodiment, the present invention makes full use of the random interaction between dispersion and nonlinearity inherent in optical fiber communication systems to compensate for the phase shift caused by nonlinear effects. It can effectively balance signal nonlinear distortion while controlling computational complexity and reducing implementation costs, and is expected to play a better role in high-capacity WDM systems for long-distance transmission.

[0125] Example 3

[0126] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps of the joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system as described in Embodiment 1.

[0127] In this embodiment, the electronic device may include: a processor, a memory, a bus, and a communication interface. The processor, the communication interface, and the memory are connected via the bus. The memory stores a computer program that can run on the processor. When the processor runs the computer program, it executes some or all of the steps of the joint compensation method for intra-channel and inter-channel nonlinearity of WDM system based on improved LDBP provided in Embodiment 1 of this application.

Claims

1. A method for joint compensation of intra-channel and inter-channel nonlinearity in a WDM system, characterized in that, Includes the following steps: S1. Receive the signal of each channel in the WDM system individually using a coherent receiver, and resample the received signal to 2 samples / symbol; S2. Based on the resampled signal, a one-dimensional convolution operation is performed in the time domain using the stepwise linear compensation layer of the improved LDBP neural network, and a pulse broadening effect is added to the overlap preservation method to compensate for the linear loss caused by dispersion. S3. The signal after each step of dispersion compensation is passed to the step-by-step nonlinear compensation layer of the LDBP neural network. Considering the dispersion effect within the same channel, the weights are set in combination with the nonlinear interaction between adjacent symbols, and the nonlinear phase shift caused by the SPM effect is solved. S4. Considering the inter-channel walk-off effect, solve the nonlinear phase shift caused by the XPM effect in the frequency domain, and transfer the XPM nonlinear phase shift obtained in the frequency domain to the time domain. S5. Add the nonlinear phase shift caused by the XPM effect in the time domain and the nonlinear phase shift caused by the SPM effect to perform joint nonlinear compensation for the signal within and between channels. S6. The polarization-related nonlinear interaction of the signal after joint compensation is compensated by an adaptive filter; S7. The signal compensated in step S6 is used by the DSP to restore the damaged signal, thus completing the nonlinear joint compensation of the WDM system within and between channels.

2. The joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to claim 1, characterized in that, Step S1 includes the following steps: S101. In the WDW system, a coherent receiver is used to receive the discrete signals of each channel individually. S102, Resample the discrete signal to 2 samples / symbol.

3. The joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to claim 1, characterized in that, The improved LDBP neural network includes: The input layer is used to receive resampled signals; The linear compensation layer is used to perform a one-dimensional convolution operation in the time domain based on the resampled signal, and to add a pulse broadening effect to the overlap preservation method to compensate for the linear loss caused by dispersion. The nonlinear joint compensation layer for intra-channel and inter-channel signals is used to set weights based on the dispersion-compensated signal at each step, taking into account the dispersion effect within the same channel and the nonlinear interaction between adjacent symbols, and to solve for the nonlinear phase shift caused by the SPM effect; taking into account the walk-off effect between channels, it solves for the nonlinear phase shift caused by the XPM effect in the frequency domain, and transfers the XPM nonlinear phase shift obtained in the frequency domain to the time domain; the XPM nonlinear phase shift in the time domain and the nonlinear phase shift caused by the SPM effect are added together to perform joint nonlinear compensation for the signal within and between channels. An adaptive filter is used to compensate for the polarization-dependent nonlinear interactions of the jointly compensated signal. The output layer is used to output the signal after adaptive filter compensation.

4. The joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to claim 1, characterized in that, Step S2 includes the following steps: S201. Adjust the input characteristics of two orthogonal discrete polarization signals according to the signal time series and dispersion properties to achieve a combination of overlap preservation method and pulse broadening effect; S202. Send the input features to the stepwise linear compensation layer of the improved LDBP neural network; S203. Using the stepwise linear compensation layer of the LDBP neural network, a one-dimensional convolution operation is used in the time domain to compensate for the linear loss caused by dispersion.

5. The joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to claim 1, characterized in that, The expression for the nonlinear phase shift caused by the SPM effect in step S3 is as follows: g SPM,k =c kk l eff in, g represents the nonlinear phase shift caused by the SPM effect. SPM,k Let S represent the nonlinear parameters within the target channel k, S represent the range of correlated symbols within the same channel, i.e., the interval of symbols correlated with symbol p is [pS, p+S], p represents the symbol that needs to be equalized at the current time, i represents the position of the correlated symbol, and δ represents the nonlinear parameters within the target channel k. i u represents the training weights corresponding to different symbols. k,x / y,i and u k,y / x,i The values ​​of x / y and y / x represent the amplitudes of x or y at point i in the target channel k, respectively, where x and y represent two orthogonal polarization signals, and γ... kk l represents the nonlinear coefficient within the same channel. eff The effective length of the nonlinearity in the optical fiber is represented by , and u represents the complex envelope of the electrical signal. The time-domain XPM nonlinear phase shift expression in step S4 is as follows: d nk =β2(ω n -oh k ) in, Let F represent the XPM nonlinear phase shift in the time domain, k represent the index of the target channel, t represent time, l represent the signal transmission length, and F represent the time domain. -1 U represents the inverse Fourier transform, F represents the Fourier transform, u n,x / y u n,y / x Based on the different values ​​of x / y and y / x, g represents the x or y polarization signal of channel n. XMP,nk γ represents the optimization parameters, including go-away parameters and nonlinear coefficients, when link information is unknown. nk The nonlinear coefficients between different channels are represented by exp(·), α represents the loss coefficient, i' represents the imaginary number, and d nk The walk-off parameter represents the distance between the non-target channel n and the target channel k, ω represents the frequency, and β² represents the second-order group velocity dispersion GVD coefficient. n ω represents the carrier frequency of the non-target channel n. k This represents the carrier frequency of the non-target channel k.

6. The joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to claim 1, characterized in that, In step S5, the signal undergoes joint nonlinear compensation both within and between channels, as expressed below: Where x and y represent two orthogonal polarization signals, u k,x / y (0,t) represents the received x / y polarization signal of the target channel k, u k,x / y (l,t) represents the x / y polarization signal transmitted in the target channel k, t represents time, exp(·) represents exponential operation, and j represents the imaginary number. and denoted as SPM effect and XPM effect respectively, and l represents the signal transmission length.

7. The joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to claim 1, characterized in that, Step S6 specifically involves: Based on the jointly compensated signal, an adaptive time-domain filter located at the back end of the LDBP neural network is used to compensate for polarization-related nonlinear interactions.

8. The joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to claim 1, characterized in that, Step S7 specifically involves: Based on the signal compensated in step S6, the damaged signal with carrier phase recovery is obtained through DSP processing. The bit error rate is calculated for the damaged signal of carrier phase recovery, and nonlinear joint compensation within and between channels of the WDM system is completed.

9. An apparatus for implementing the joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system according to any one of claims 1-8, characterized in that, The device includes: The first processing module is used to receive the signal of each channel in the WDM system individually using a coherent receiver, and resample the received signal to 2 samples / symbol; The second processing module is used to perform one-dimensional convolution operation in the time domain using the step-by-step linear compensation layer of the LDBP neural network based on the resampled signal, and to add pulse broadening effect in the overlap preservation method to compensate for the linear loss caused by dispersion. The third processing module is used to transmit the signal after each step of dispersion compensation to the step-by-step nonlinear compensation layer of the LDBP neural network. Considering the dispersion effect within the same channel, the module sets the weights in combination with the nonlinear interaction between adjacent symbols and solves the nonlinear phase shift caused by the SPM effect. The fourth processing module is used to solve the nonlinear phase shift caused by the XPM effect in the frequency domain, taking into account the inter-channel walk-off effect, and to transfer the XPM nonlinear phase shift obtained in the frequency domain to the time domain. The fifth processing module is used to add the nonlinear phase shift caused by the XPM effect in the time domain and the nonlinear phase shift caused by the SPM effect, and to perform joint nonlinear compensation for the signal within and between channels. The sixth processing module is used to compensate the polarization-related nonlinear interactions of the jointly compensated signal using an adaptive filter; The seventh processing module is used to recover the damaged signal from the signal compensated by the sixth processing module via the DSP, thus completing the nonlinear joint compensation within and between channels of the WDM system.

10. An electronic device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory and running on the processor, the processor executing the program to implement the steps of the joint compensation method for intra-channel and inter-channel nonlinearity in a WDM system as described in any one of claims 1-8.

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