Nonlinear equalization method and device of digital subcarrier multiplexing signal and optical fiber communication system

Abstract

The invention discloses a nonlinear equalization method and device for digital subcarrier multiplexing signals and an optical fiber communication system. The method comprises the following steps: caching an original symbol of a transmitting end, and preprocessing a received signal to obtain a signal to be equalized; constructing a power model according to the link parameters and deducing a back propagation power model; inputting the data into an improved digital back transmission algorithm, and calculating a nonlinear accumulation amount in each equalization step length; determining an initial splitting ratio parameter by using a nonlinear symmetry principle, and embedding the initial splitting ratio parameter into the neural network as a trainable variable; inputting a received signal and an original symbol into a network, and optimizing a splitting ratio through gradient descent to obtain an optimal value; therefore, the position of a nonlinear operator in the improved digital back transmission algorithm is adjusted, linear and nonlinear combined compensation of the signal is realized, and a high-precision equalization result is output. According to the method, extra communication overhead is not needed, and the link power non-uniformity characteristic can be effectively adapted.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and more particularly, relates to a method and apparatus for non - linear equalization of digital sub - carrier multiplexing signals and an optical fiber communication system. Background Art

[0002] With the rapid development of emerging technologies such as fifth - generation mobile communication and industrial Internet, the demand for transmission rate and capacity of optical fiber communication systems has been continuously increasing. To meet the above requirements, optical fiber communication systems are continuously evolving towards higher transmission rates, larger capacities, and longer transmission distances. In this context, digital sub - carrier multiplexing technology decomposes high - speed single - carrier signals into multiple low - speed sub - carriers for parallel transmission, significantly reducing the complexity of digital signal processing (DSP) at the receiving end, and at the same time enhancing the robustness to linear transmission impairments such as dispersion and polarization mode dispersion. It has become the core solution for long - distance and large - capacity coherent optical transmission.

[0003] Although digital sub - carrier multiplexing technology has significant advantages in improving spectral utilization and transmission capacity, the signal multiplexing structure also introduces impairments such as self - sub - carrier non - linearity (SSN) and cross - sub - carrier non - linearity (CSN). These non - linear interferences are highly coupled in long - distance transmission links, seriously deteriorating the signal quality and becoming an important factor restricting the transmission performance of the system. To overcome the above non - linear impairments, the digital back - propagation algorithm (DBP), as the most widely used non - linear equalization method currently, in the receiving - end DSP, reversely models and jointly equalizes the dispersion and non - linear effects in the optical fiber through the split - step Fourier method (SSFM). In a digital sub - carrier multiplexing system, DBP can be generalized to an advanced digital back - propagation algorithm (ADBP) structure with parallel processing of each sub - carrier, whose goal is to significantly reduce the computational complexity while ensuring the equalization performance. Therefore, ADBP usually adopts fewer equalization steps, with each step corresponding to one or more optical fiber spans, resulting in significant performance differences from traditional single - carrier DBP.

[0004] Currently, ADBP generally adopts a symmetric split - step configuration, that is, placing the non - linear operator at the center of each compensation step (the splitting ratio is ρ = 0.5). This structure assumes that the optical power is evenly distributed along the transmission fiber path and achieves high - precision non - linear equalization through the cancellation of odd - symmetric error terms. It shows good equalization performance in single - step or short - distance transmission scenarios.

[0005] However, in an actual multi-span optical fiber transmission system, the optical signal power is affected by the combined action of fiber attenuation and the periodic gain of optical amplifiers, presenting an asymmetric sawtooth distribution. Especially when each equalization step spans multiple fiber segments, the non-linear cumulative amount is often no longer symmetric within the step size. At this time, the traditional fixed configuration (ρ = 0.5) will not be able to accurately match the non-linear evolution trajectory, resulting in a decrease in equalization accuracy and limiting the actual equalization ability of ADBP under complex link conditions.

[0006] The prior art patent with publication number CN119675783A proposed an optical transmission system based on an FEC extended perturbation optical fiber non-linear compensation technology. Its receiving end includes an adaptive perturbation equalization module, a soft decision demodulation module, a deinterleaving module, an FEC decoding module, an interleaving module, and a symbol reconstruction module based on soft information connected in sequence; the adaptive perturbation non-linear equalization module has a dual-input structure and is also connected to the output end of the symbol reconstruction module based on soft information in addition to receiving the signal; the data output by the interleaving module and the data output by the soft decision demodulation module are added and then input to the second input end of the soft decision demodulation module; the output end of the FEC decoding module uses the same coding pattern as the sending end for decoding and outputs the received bit result. This solution will inevitably introduce a certain communication overhead in the interleaving, deinterleaving, and soft decision decoding links, with a high overall implementation complexity and failing to fully match the actual state of the link. Summary of the Invention

[0007] In order to overcome the problems that the overall implementation complexity of the existing non-linear equalization algorithm is high and it fails to fully match the actual state of the link, the present invention provides a non-linear equalization method, device, and optical fiber communication system for digital subcarrier multiplexing signals.

[0008] The primary object of the present invention is to solve the above technical problems, and the technical solution of the present invention is as follows:

[0009] The first aspect of the present invention provides a non-linear equalization method for digital subcarrier multiplexing signals, including the following steps:

[0010] Cache the original transmitted symbols generated by the transmitting end, preprocess the received signal to obtain a signal to be non-linearly equalized;

[0011] Establish a function model of the optical power along the transmission distance according to the link parameters, and derive a power model for backpropagation based on the function model;

[0012] Input the power model into an improved digital backward transmission algorithm, and calculate the integral area of the non-linear effect corresponding to each equalization step size in the improved digital backward transmission algorithm to obtain the cumulative amount of the non-linear effect within the equalization step size;

[0013] Using the principle of non - linear accumulation symmetry, determine the initial splitting ratio parameter in combination with the said cumulant, and embed the initial splitting ratio parameter as a trainable variable into a neural network model built with the improved digital backward transmission algorithm structure as the physical backbone;

[0014] Input the signal to be non - linearly equalized and the corresponding original transmitted symbol into the neural network model for training, optimize the initial splitting ratio parameter using the gradient descent algorithm, and determine the optimal splitting ratio parameter; adjust the non - linear equalization position of each equalization step length in the improved digital backward transmission algorithm using the optimal splitting ratio parameter;

[0015] Input the signal to be non - linearly equalized into the adjusted improved digital backward transmission algorithm, compensate for the linear and non - linear impairments of the signal, and output the equalized digital sub - carrier multiplexing signal.

[0016] Further, pre - process the received signal, including the following steps:

[0017] Input the received signal after fiber - optic link transmission into a demodulation module for coherent demodulation to obtain an analog electrical signal;

[0018] Input the analog electrical signal into an analog - to - digital conversion module for sampling to output the corresponding digital signal;

[0019] If there is a frequency offset between the transmit - end and receive - end lasers, perform frequency offset compensation on the digital signal to obtain the frequency - offset - compensated digital signal;

[0020] Perform filtering on the digital signal to remove out - of - band noise and interference components of the system;

[0021] Perform sub - carrier demultiplexing on the filtered signal to decompose the high - speed multiplexed signal into multiple low - speed sub - carrier signals;

[0022] Perform resampling on each sub - carrier signal to obtain the signal to be non - linearly equalized.

[0023] Further, the method for deriving the power model of back - propagation includes the following steps:

[0024] Obtain the key parameters of the fiber - optic link, including one or more of the following: span length, number of spans, fiber loss coefficient, input optical power, and optical amplifier gain;

[0025] Combined with the periodic gain and loss characteristics of the optical fiber, construct a forward power distribution model \(g(z)\) in which the signal power in each span decays exponentially along the transmission distance, and the expression is as follows:

[0026] \(g(z)=\exp(-\alpha z)\)

[0027] where \(\alpha\) is the fiber linear attenuation coefficient and \(z\) is the transmission distance;

[0028] Based on the backpropagation characteristics of the M-ADBP structure, using the symmetry principle of the forward power model, a backpropagation power model g'(z) is constructed, and the expression is as follows:

[0029]

[0030] where P in (dBm) represents the input optical power, in decibel-milliwatts; P in (mW) represents the input optical power, in milliwatts; L span represents the length of a single-span optical fiber, in km; represents the power attenuation factor of the signal within the length of a single span; mod(z,L span ) represents the result of taking the modulus of z with respect to the length L of a single-span optical fiber span .

[0031] Furthermore, the method for determining the initial splitting ratio parameter includes the following steps:

[0032] According to the calculated integral area of the nonlinear effect within each equalization step length, the expression is as follows:

[0033]

[0034] where L is the compensation step length, g'(z) is the backpropagation power model, and z is the transmission distance;

[0035] The current equalization step length is divided into two front and rear dispersion processing segments, denoted as [0,ρ] and [ρ,L] respectively, and the expressions for the nonlinear accumulation of the front and rear segments are defined as follows:

[0036]

[0037] where ρ is the initial splitting ratio, and the lengths of the two dispersion processing segments are set to make the intensity of the nonlinear effect as symmetric as possible. The optimization objective function expression is constructed as follows:

[0038]

[0039] where arg min represents finding the parameter value that minimizes the objective function, and the minimum parameter ρ0 is solved as the initial splitting ratio parameter.

[0040] Furthermore, the method for determining the optimal splitting ratio parameter includes the following steps:

[0041] Using the signal to be nonlinearly equalized as the model input and the original transmitted symbol cached at the transmitter as the model label, a supervised learning data pair is constructed;

[0042] In the improved digital backward transmission algorithm structure, the splitting ratio parameter ρ0 to be optimized is introduced as a trainable variable in the neural network model built with the improved digital backward transmission algorithm structure as the physical backbone;

[0043] The loss function is defined as the mean square error between the received symbol and the reference transmitted symbol, and its form is

[0044]

[0045] where N is the total number of symbols, is the recovered ith symbol, x i is the corresponding transmitted reference signal,, are the X / Y polarization components of the recovered ith symbol respectively; x i (X) , x i (Y) are the X / Y polarization components of the corresponding transmitted reference signal respectively;

[0046] The optimization algorithm is used to iteratively optimize the loss function, and the splitting ratio parameter ρ is updated in the way of gradient descent until the loss function converges, and the optimal splitting ratio parameter ρ is output.

[0047] Furthermore, the method for compensating the linear and nonlinear damages to the non - linear equalized signal is as follows:

[0048] According to the different equalization step sizes and fiber link lengths, the initial splitting ratio will be dynamically adjusted. The single - step transfer expression of the improved digital backward transmission algorithm is as follows:

[0049]

[0050] where L is the compensation step size, ρ is the splitting ratio parameter, is a linear operator used to handle linear damages such as dispersion and polarization mode dispersion; is a non - linear operator used to handle the non - linear damages of each sub - carrier SSN and CSN. E(z,t) is the electric field signal at transmission distance z and time t, and E(z + L,t) is the electric field signal at transmission distance z + L and time t. The whole expression represents the compensation process of the electric field signal within a single equalization step size, including:

[0051] Compensate the dispersion effect of the first - stage length of ρL through the linear operator ;

[0052] Compensate the signal non - linear damage through the non - linear operator ;

[0053] Compensate the dispersion effect of the second - stage length of (1 - ρ)L through the linear operator ;

[0054] Preferably, the equalization of the subcarrier nonlinearity damage SSN is compensated by using a traditional single-wavelength DBP structure, and the equalization of the cross-subcarrier nonlinearity damage CSN is compensated by using the cross-phase modulation analysis model constructed in the wavelength-division multiplexing system.

[0055] Optionally, a phased static hidden layer optimization strategy is adopted to train the model, including the following steps:

[0056] Analyze the received signal by using a traditional digital signal processing module, and estimate the clock recovery parameter, the carrier frequency recovery parameter, and the carrier phase recovery parameter respectively;

[0057] Load the estimated parameters into the neural network in a static form to form a static hidden layer, and keep these parameters from participating in the update during the subsequent training process;

[0058] Input the received signal and the corresponding original transmitted symbols into a neural network model built with an improved digital backpropagation algorithm structure as the physical backbone, and optimize the splitting ratio parameter in the improved digital backpropagation algorithm structure by driving the training with an objective function of minimizing the error; during the training process, shield the influence of time-varying interference on the model gradient update through the static hidden layer;

[0059] When the network training converges and the optimal splitting ratio parameter is obtained, remove the static hidden layer and restore the complete digital signal processing flow to compensate for the residual signal damage and output the restored signal.

[0060] The second aspect of the present invention provides a nonlinear equalization device for digital subcarrier multiplexing signals. The device includes a program for the nonlinear equalization method of digital subcarrier multiplexing signals. When the program for the nonlinear equalization method of digital subcarrier multiplexing signals is executed by the device, the steps of a nonlinear equalization method for digital subcarrier multiplexing signals are realized.

[0061] The third aspect of the present invention provides an optical fiber communication system, which includes:

[0062] A transmitter, including a DSP processing module, a subcarrier multiplexing module, a DAC module, and an IQ modulator, for generating a modulated signal multiplexed with multiple subcarriers;

[0063] A transmission link, including a single-mode optical fiber and an optical amplifier, for optical signal transmission;

[0064] A receiver, including a coherent receiver, an ADC module, a frequency offset compensation, a subcarrier demultiplexing module, and the above-mentioned nonlinear equalization device for digital subcarrier multiplexing signals, for receiving, restoring, and compensating for damaged signals.

[0065] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0066] In each equalization step length of the present invention, an adjustable splitting ratio parameter is introduced. By flexibly adjusting the position of the non-linear operator, the non-uniform optical power distribution in the link is effectively matched, and the equalization error caused by the traditional symmetric configuration is avoided, thereby improving the accuracy of non-linear equalization and the overall transmission performance of the system; on the basis of the existing equalization structure implementation, no additional module needs to be added, which not only maintains the controllability of the computational complexity, but also has good engineering realizability and system compatibility, and is applicable to digital subcarrier multiplexing coherent optical fiber communication systems, especially suitable for multi-span link scenarios with long transmission distances and significant power fluctuations. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to make the objectives and technical solutions of the present invention clearer, the present invention provides the following drawings and descriptions:

[0068] Figure 1 It is a flowchart of a non-linear equalization method for a digital subcarrier multiplexing signal provided by an embodiment of the present invention;

[0069] Figure 2 It is a flowchart of machine learning optimization of the splitting ratio parameter in the M-ADBP structure provided by an embodiment of the present invention;

[0070] Figure 3 It is a schematic diagram of a non-linear equalization device for a digital subcarrier multiplexing signal provided by an embodiment of the present invention;

[0071] Figure 4 It is a schematic diagram of an optical fiber communication system provided by an embodiment of the present invention;

[0072] Figure 5 It is a Q-factor performance comparison diagram of different schemes under different input optical powers provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0073] In order to be able to more clearly understand the above-mentioned objectives, features and advantages of the present invention, the present invention will be further described in detail below with reference to the drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present application and the features in the embodiments may be combined with each other.

[0074] Many specific details are set forth in the following description in order to provide a thorough understanding of the present invention. However, the present invention may be practiced in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0075] Embodiment 1:

[0076] The present invention provides a non-linear equalization method for a digital subcarrier multiplexing signal, asFigure 1 Shown is a flowchart of a non - linear equalization method for digital sub - carrier multiplexing signals. The specific steps are as follows:

[0077] S1: Cache the original transmitted symbols generated at the transmitting end, and pre - process the received signal to obtain the signal to be non - linearly equalized.

[0078] The pre - processing of the received signal includes the following steps:

[0079] Input the received signal after fiber - optic link transmission into a demodulation module for coherent demodulation to obtain an analog electrical signal;

[0080] Input the analog electrical signal into an analog - to - digital conversion module for sampling and output the corresponding digital signal;

[0081] If there is a frequency offset between the lasers at the transmitting end and the receiving end, perform frequency offset compensation on the digital signal to obtain the frequency - offset - compensated digital signal;

[0082] Perform filtering on the digital signal to remove out - of - band noise and interference components of the system;

[0083] Perform sub - carrier demultiplexing on the filtered signal to decompose the high - speed multiplexed signal into multiple low - speed sub - carrier signals;

[0084] Perform resampling on each sub - carrier signal to adapt to the time - domain processing requirements of the subsequent equalization module and obtain the signal to be non - linearly equalized.

[0085] S2: Establish a function model of optical power along the transmission distance according to the link parameters, and derive the power model for back - propagation based on the function model. The specific process is as follows:

[0086] Obtain the key parameters of the fiber - optic link, including one or more of the following: span length, number of spans, fiber loss coefficient, input optical power, and optical amplifier gain;

[0087] Combined with the periodic gain and loss characteristics of the fiber, construct a forward power distribution model g(z) in which the signal power in each span decays exponentially along the transmission distance. The expression is as follows:

[0088] g(z)=exp(-αz)

[0089] Where α is the fiber linear attenuation coefficient and z is the transmission distance;

[0090] Based on the back - propagation characteristics of the improved digital back - propagation algorithm (M - ADBP) structure, utilize the symmetry principle of the forward power model to construct the back - propagation power model g'(z). The expression is as follows:

[0091]

[0092] Among them, P in (dBm) represents the input optical power, in decibel-milliwatts (dBm); P in (mW) represents the input optical power, in milliwatts (mW); L span represents the length of a single-span optical fiber, in km; represents the power attenuation factor of the signal within the length of a single span; mod(z, L span ) represents the result of taking the modulus of z with respect to the length L of a single-span optical fiber span , which is used to convert the input power from the dBm unit to mW and consider the attenuation after one-span transmission.

[0093] S3: Input the power model into M-ADBP, and use the integral calculation method to calculate the integral area of the nonlinear effect corresponding to each equalization step length in M-ADBP, obtaining the cumulative amount of the nonlinear effect within the equalization step length. The expression is as follows:

[0094]

[0095] Among them, L is the equalization step length, g'(z) is the power model of backpropagation, and z is the transmission distance;

[0096] S4: Utilize the principle of nonlinear accumulation symmetry, combine the cumulative amount to determine the initial splitting ratio parameter, and embed the initial splitting ratio parameter as a trainable variable into a neural network model built with the improved digital backward transmission algorithm structure as the physical backbone.

[0097] The method for determining the initial splitting ratio parameter includes the following steps:

[0098] According to the calculated integral area of the nonlinear effect within each equalization step length;

[0099] Divide the current equalization step length into two dispersion processing segments, denoted as [0, σ] and [σ, L] respectively, and define the expressions for the nonlinear accumulation of the front and back segments as follows:

[0100]

[0101] Among them, ρ is the initial splitting ratio. Set the lengths of the two dispersion processing segments to make the intensity of the nonlinear effect as symmetric as possible, and construct the optimization objective function expression as follows:

[0102]

[0103] Among them, arg min represents finding the parameter value that makes the objective function (here the absolute value of the difference between the front and back areas) the smallest, and solving for the smallest parameter σ0 as the initial splitting ratio parameter.

[0104] S5: Input the signal to be nonlinearly equalized and the corresponding original transmitted symbols into the neural network model for training. Use the gradient descent algorithm to optimize the initial splitting ratio parameter and determine the optimal splitting ratio parameter. Adjust the nonlinear equalization positions of each equalization step size in M-ADBP using the optimal splitting ratio parameter.

[0105] The process of determining the optimal splitting ratio parameter is as follows:

[0106] Take the signal to be nonlinearly equalized as the model input and the original transmitted symbols cached at the transmitter as the model labels to construct a supervised learning data pair;

[0107] Introduce the splitting ratio parameter σ0 to be optimized in the M-ADBP structure as a trainable variable in the neural network model built with M-ADBP as the physical backbone;

[0108] Define the loss function as the mean square error between the received symbols and the reference transmitted symbols, and its form is

[0109]

[0110] where N is the total number of symbols, is the i-th symbol recovered, x i is the corresponding transmitted reference signal, is the X / Y polarization component of the i-th symbol recovered; x i (X) ,x i (Y) is the X / Y polarization component of the corresponding transmitted reference signal;

[0111] Use the Adam optimization algorithm to iteratively optimize the loss function and update the splitting ratio parameter ρ in the way of gradient descent. The learning rate is set to 1×10 -4 , until the loss function converges and output the optimal splitting ratio parameter ρ.

[0112] S6: Input the signal to be nonlinearly equalized into the adjusted M-ADBP to compensate for the linear and nonlinear impairments of the signal and output the equalized digital subcarrier multiplexing signal.

[0113] The method for compensating the linear and nonlinear impairments of the signal to be nonlinearly equalized is:

[0114] According to different equalization step sizes and fiber link lengths, the initial splitting ratio will be dynamically adjusted. The single-step transfer expression of M-ADBP is as follows:

[0115]

[0116] For equalizing linear and nonlinear transmission impairments for each subcarrier, where L is the compensation step size and ρ is the splitting ratio parameter, is a linear operator for handling linear impairments such as dispersion and polarization mode dispersion; is a nonlinear operator for handling the nonlinear impairments of SSN and CSN for each subcarrier. E(z,t) is the electric field signal at transmission distance z and time t, and E(z+L,t) is the electric field signal at transmission distance z+L and time t. The overall expression represents the compensation process of the electric field signal within a single equalization step, including:

[0117] Compensate for the dispersion effect of the first segment with a length of ρL through the linear operator ;

[0118] Compensate for the signal nonlinear impairment through the nonlinear operator ;

[0119] Compensate for the dispersion effect of the second segment with a length of (1-ρ)L through the linear operator ;

[0120] It should be noted that the equalization of the subcarrier nonlinear impairment SSN is compensated by using the traditional single-wavelength DBP structure, and the equalization of the cross-subcarrier nonlinear impairment CSN is compensated by using the cross-phase modulation analysis model constructed in the wavelength-division multiplexing system.

[0121] More specifically, the model is trained by adopting a phased static hidden layer optimization strategy, including the following steps:

[0122] Analyze the received signal by using the traditional digital signal processing module, and respectively estimate the clock recovery parameter, carrier frequency recovery parameter, and carrier phase recovery parameter;

[0123] Load the estimated parameters into the neural network in a static form to form a static hidden layer, and keep these parameters from participating in the update during the subsequent training process;

[0124] Input the received signal and the corresponding original transmitted symbols into the neural network built with M-ADBP as the physical backbone, and optimize the splitting ratio parameter in the M-ADBP structure by driving the training with the objective function of minimizing the error; during the training process, shield the influence of time-varying interference on the model gradient update through the static hidden layer, and improve the training convergence speed and equalization accuracy;

[0125] When the network training converges and obtains the optimal splitting ratio parameter, remove the static hidden layer and restore the complete digital signal processing flow to compensate for the residual signal impairment and output the restored signal.

[0126] The present invention introduces an adjustable splitting ratio parameter within each equalization step length. By flexibly adjusting the position of the nonlinear operator, it effectively matches the non-uniform optical power distribution in the link, avoids the equalization error caused by the traditional symmetric configuration, thereby improving the accuracy of nonlinear equalization and the overall transmission performance of the system. Based on the existing equalization structure implementation, without adding additional modules, it not only maintains the controllability of the computational complexity but also has good engineering feasibility and system compatibility. It is applicable to digital subcarrier multiplexing coherent optical fiber communication systems, especially suitable for multi-span link scenarios with long transmission distances and significant power fluctuations. As Figure 5 shown, the figure shows the comparison curves of the system Q factor between the traditional symmetric configuration ADBP method and the nonlinear position optimization type M-ADBP method proposed by the present invention under different input optical power conditions. Among them, CDC represents the reference scheme that only performs linear impairment compensation and does not perform nonlinear equalization. The results show that both the ADBP and M-ADBP methods achieve nonlinear compensation gain, and the M-ADBP method is always superior to the traditional ADBP under various input optical powers, demonstrating stronger nonlinear equalization ability and system performance improvement effect.

[0127] Embodiment 2:

[0128] This embodiment provides a nonlinear equalization device for digital subcarrier multiplexing signals, which is used to jointly compensate for dispersion and nonlinearity of the received signal.

[0129] As Figure 3 shown, the device includes:

[0130] A demodulation module, which is used to perform coherent demodulation on the received optical signal and convert it into an analog electrical signal.

[0131] An analog-to-digital conversion module, which is used to sample the analog electrical signal into a digital signal for subsequent module processing.

[0132] A preprocessing module, which is used to complete operations such as frequency offset compensation, filtering, and subcarrier demultiplexing, demultiplex the received high-speed multiplexed signal into M low-speed subcarrier signals, and input them into subsequent modules for parallel processing.

[0133] A nonlinear equalization module, based on the M-ADBP structure proposed in Embodiment 1, jointly compensates for linear and nonlinear impairments in each subcarrier signal. This module further includes:

[0134] An initial value calculation sub-module, which generates an initial splitting ratio value according to the fiber link modeling result;

[0135] A training and optimization sub-module, which uses a physics-driven machine learning method to train and update the parameters.

[0136] A collaborative optimization module that receives subcarrier signals after non - linear equalization and implements collaborative optimization based on a static hidden - layer optimization mechanism, where relevant parameters are loaded as static parameters during the training phase and remain unchanged during the training phase to improve the convergence of machine learning and anti - interference ability. This module further includes:

[0137] A clock recovery module for estimating the symbol timing information of the received signal to achieve sampling synchronization and clock error correction.

[0138] A carrier frequency recovery module for compensating the frequency error caused by laser offset;

[0139] A carrier phase recovery module for estimating and compensating the carrier phase offset caused by laser phase noise, etc.

[0140] An output module for outputting the M - path subcarrier signals after equalization processing for subsequent transmission performance evaluation and bit - error rate analysis.

[0141] Embodiment 3:

[0142] This embodiment provides an optical fiber communication system, as Figure 4 shown, the optical fiber communication system includes:

[0143] A transmitter, including a DSP processing module, a sub - carrier multiplexing module, a DAC module, and an IQ modulator, for generating a modulated signal with multi - sub - carrier multiplexing;

[0144] A transmission link, including a single - mode optical fiber and an optical amplifier, for optical signal transmission;

[0145] A receiver, including a coherent receiver, an ADC module, frequency offset compensation, a sub - carrier demultiplexing module, and the non - linear equalization device for a digital sub - carrier multiplexing signal described in Embodiment 2, for receiving, recovering, and compensating the damaged signal.

[0146] More specifically, at the transmitting end, the binary bit sequence to be transmitted passes through the DSP processing module, and after performing precoding, constellation mapping, pulse shaping, sub - carrier generation, and frequency offset in sequence, it is multiplexed into a high - speed digital sub - carrier multiplexing signal through sub - carrier multiplexing. After this signal is converted into an electrical signal, it is modulated onto an optical carrier through an IQ modulator and then injected into the optical fiber link for transmission.

[0147] The transmission link includes multiple optical fiber spans, and an erbium - doped fiber amplifier (EDFA) is configured after each span to compensate for the signal loss during transmission.

[0148] At the receiving end, the optical signal is received by a coherent receiver, sampled by an ADC, and then enters the receiving-end DSP module. The receiver DSP first performs subcarrier demultiplexing. After forming multiple parallel subcarriers, operations such as matched filtering, resampling, dispersion and nonlinear equalization, clock recovery, and carrier phase recovery are performed respectively. The nonlinear equalization device for a digital subcarrier multiplexing signal described in Embodiment 2 is embedded in the dispersion and nonlinear equalization stage of the receiving-end DSP.

[0149] It should be noted that this system can achieve nonlinear equalization based on the M-ADBP structure at the receiving end without modifying the traditional transmitter or the fiber link structure, and is particularly suitable for multi-span optical fiber transmission scenarios with a long transmission link and significant power fluctuations.

[0150] In this embodiment, the system uses 8 subcarriers, each subcarrier is in 64QAM modulation format, the symbol rate is 11.95Gbaud, and the overall signal rate after subcarrier multiplexing is 95.6Gbaud. The optical fiber transmission link contains 15 spans. Each span is 80km of standard single-mode optical fiber, the loss coefficient is about 0.2dB / km, the dispersion coefficient is 17ps / nm / km, the nonlinear coefficient is 1.3 / W / km, and each span is configured with an EDFA to compensate for signal loss, with a total length of 1200km.

[0151] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, rather than limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A non - linear equalization method for digital sub - carrier multiplexing signals, characterized in that, It includes the following steps: Cache the original transmission symbols generated by the transmitter, preprocess the received signal to obtain the signal to be nonlinearly equalized; Establish a function model of the optical power along the transmission distance based on the link parameters, and derive the power model for backpropagation according to the function model; Input the power model into the improved digital backward transmission algorithm, and calculate the integral area of the nonlinear effect corresponding to each equalization step length in the improved digital backward transmission algorithm to obtain the cumulative amount of the nonlinear effect within the equalization step length; Utilize the principle of nonlinear accumulation symmetry, determine the initial splitting ratio parameter in combination with the cumulative amount, and embed the initial splitting ratio parameter as a trainable variable into a neural network model built with the improved digital backward transmission algorithm structure as the physical backbone; Input the signal to be nonlinearly equalized and the corresponding original transmission symbols into the neural network model for training, optimize the initial splitting ratio parameter using the gradient descent algorithm to determine the optimal splitting ratio parameter; adjust the nonlinear equalization position of each equalization step length in the improved digital backward transmission algorithm using the optimal splitting ratio parameter; Input the signal to be nonlinearly equalized into the adjusted improved digital backward transmission algorithm, compensate for the linear and nonlinear impairments of the signal, and output the equalized digital subcarrier multiplexing signal.

2. The non - linear equalization method for a digital sub - carrier multiplexing signal according to claim 1, characterized in that, Preprocess the received signal, including the following steps: Input the received signal after fiber optic link transmission into a demodulation module for coherent demodulation to obtain an analog electrical signal; Input the analog electrical signal into an analog-to-digital conversion module for sampling and output the corresponding digital signal; If there is a frequency offset between the transmit and receive lasers, perform frequency offset compensation on the digital signal to obtain the frequency offset compensated digital signal; Perform filtering processing on the digital signal to remove out-of-band noise and interference components of the system; Perform subcarrier demultiplexing on the filtered signal to decompose the high-speed multiplexed signal into multiple low-speed subcarrier signals; Resample each subcarrier signal to obtain the signal to be nonlinearly equalized.

3. The non-linear equalization method for a digital subcarrier multiplexing signal according to claim 1, wherein, The method for deriving the power model for backpropagation includes the following steps: Obtain the key parameters of the fiber optic link, including one or more of the following: span length, number of spans, fiber loss coefficient, input optical power, and optical amplifier gain; Combined with the periodic gain and loss characteristics of the optical fiber, construct a forward power distribution model g(z) in which the signal power decays exponentially along the transmission distance within each span, and the expression is as follows: g(z) = exp(-αz) where α is the fiber linear attenuation coefficient and z is the transmission distance; Based on the backpropagation characteristics of the M-ADBP structure, utilize the symmetry principle of the forward power model to construct the backpropagation power model g'(z), and the expression is as follows: Among them, P in (dBm) represents the input optical power, in decibel-milliwatts; P in (mW) represents the input optical power, in milliwatts; L span represents the length of a single-span optical fiber, in km; represents the power attenuation factor of the signal within the length of a single span; mod(z, L span ) represents the result of taking the modulus of z with respect to the length L span of a single-span optical fiber.

4. A non - linear equalization method for a digital sub - carrier multiplexing signal according to claim 1, characterized in that, The method for determining the initial splitting ratio parameter includes the following steps: According to the calculated integral area of the nonlinear effect within each equalization step length, the expression is as follows: where L is the compensation step length, g'(z) is the backpropagation power model, and z is the transmission distance; Divide the current equalization step length into two dispersion processing segments before and after, denoted as [0,ρ] and [ρ,L] respectively, and define the expressions for the nonlinear accumulation of the front and rear segments as follows: Among them, ρ is the initial splitting ratio. By setting the lengths of two dispersion processing sections to make the non - linear action intensity as symmetric as possible, the expression of the optimization objective function is constructed as follows: Among them, arg min represents finding the parameter value that minimizes the objective function, and solving for the minimum parameter ρ0 as the initial splitting ratio parameter.

5. A non - linear equalization method for a digital sub - carrier multiplexing signal according to claim 1, characterized in that, The method for determining the optimal splitting ratio parameter includes the following steps: Taking the signal to be non - linearly equalized as the model input and the original transmitted symbols cached at the transmitter as the model label, a supervised learning data pair is constructed; Introducing the splitting ratio parameter ρ0 to be optimized into the improved digital back - propagation algorithm structure as a trainable variable in the neural network model built with the improved digital back - propagation algorithm structure as the physical backbone; Defining the loss function as the mean square error between the received symbols and the reference transmitted symbols, and its form is where N is the total number of symbols, is the i-th symbol recovered, and x i is the corresponding transmitted reference signal, are the X / Y polarization components of the i-th symbol recovered, respectively; x i ( X ), x i ( Y ) are the X / Y polarization components of the corresponding transmitted reference signal, respectively; Using an optimization algorithm to iteratively optimize the loss function, updating the splitting ratio parameter ρ in the way of gradient descent until the loss function converges, and outputting the optimal splitting ratio parameter ρ.

6. The non - linear equalization method for a digital sub - carrier multiplexing signal according to claim 1, characterized in that, The method for compensating the linear and non - linear impairments of the signal to be non - linearly equalized is as follows: According to different equalization step sizes and fiber - optic link lengths, the initial splitting ratio will be dynamically adjusted. The single - step transfer expression of the improved digital back - propagation algorithm is as follows: where L is the compensation step size, ρ is the splitting ratio parameter, is a linear operator for processing linear impairments such as dispersion and polarization mode dispersion; is a nonlinear operator for processing the nonlinear impairments of each sub-carrier's SSN and CSN. E(z,t) is the electric field signal at transmission distance z and time t, and E(z + L,t) is the electric field signal at transmission distance z + L and time t. The whole expression represents the compensation process of the electric field signal within a single equalization step size, including: Compensate for the dispersion effect of the front section with a length of ρL through a linear operator ​ Compensate for the non - linear damage of the signal through a non - linear operator Compensate for the non - linear damage of the signal Compensate for the dispersion effect of the latter segment with a length of (1 - ρ)L through a linear operator ​ 7. A non - linear equalization method for a digital sub - carrier multiplexing signal according to claim 6, characterized in that, The equalization of the self - sub - carrier non - linear impairment SSN is compensated by using the traditional single - wavelength DBP structure, and the equalization of the cross - sub - carrier non - linear impairment CSN is compensated by using the cross - phase - modulation analysis model constructed in the wavelength - division multiplexing system.

8. A non-linear equalization method for a digital subcarrier multiplexing signal according to claim 1, characterized in that, The model is trained using a phased static hidden - layer optimization strategy, including the following steps: Using a traditional digital signal processing module to analyze the signal to be non - linearly equalized, and respectively estimating the clock recovery parameter, carrier frequency recovery parameter, and carrier phase recovery parameter; Loading the estimated parameters into the neural network in a static form to form a static hidden layer, and keeping these parameters from participating in the update during the subsequent training process; Inputting the signal to be non - linearly equalized and the corresponding original transmitted symbols into the neural network model built with the improved digital back - propagation algorithm structure as the physical backbone, driving the training through the objective function of error minimization, and optimizing the splitting ratio parameter in the improved digital back - propagation algorithm structure; during the training process, shielding the influence of time - varying interference on the model gradient update through the static hidden layer; When the network training converges and the optimal splitting ratio parameter is obtained, removing the static hidden layer and restoring the complete digital signal processing flow to compensate for the residual signal impairment and output the restored signal.

9. A non - linear equalization device for digital sub - carrier multiplexing signals, characterized in that, This device is used to implement the steps of a non - linear equalization method for a digital sub - carrier multiplexing signal as described in any one of claims 1 to 8.

10. An optical fiber communication system, characterized in that, This system includes: A transmitter, including a DSP processing module, a sub - carrier multiplexing module, a DAC module, and an IQ modulator, for generating a modulated signal of multi - sub - carrier multiplexing; A transmission link, including a single - mode optical fiber and an optical amplifier, for optical signal transmission; A receiver, including a coherent receiver, an ADC module, a frequency offset compensation, a sub - carrier demultiplexing module, and a non - linear equalization device for a digital sub - carrier multiplexing signal as described in claim 9, for receiving, restoring, and compensating the damaged signal.

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