Intelligent compensation method and system for nonlinear impairment of coherent optical communication

Abstract

This invention discloses an intelligent compensation method and system for nonlinear impairments in coherent optical communication, belonging to the fields of optical fiber communication and digital signal processing. The method employs a physically embedded unfolded network structure, mapping the iterative process of the step-by-step Fourier algorithm to a multi-layer neural network. Linear steps correspond to frequency domain compensation layers, and nonlinear steps correspond to learnable nonlinear activation layers. An adaptive depth control mechanism dynamically determines the number of unfolded network layers based on the optical signal-to-noise ratio and modulation format. A closed-loop parameter optimization mechanism is used, employing the mean square error between the transmitted symbol and the compensated signal as the loss function, updating network parameters through gradient backpropagation. This invention integrates prior knowledge of the physical model through a physically embedded network structure, reducing the number of learned parameters and improving training efficiency and generalization ability. Adaptive depth control automatically adjusts computational complexity under different channel conditions, achieving efficient nonlinear impairment compensation.

Description

Technical Field

[0001] This invention relates to the fields of optical fiber communication and digital signal processing technology, specifically to a method and system for intelligent compensation of nonlinear impairments in coherent optical communication. Background Technology

[0002] With the explosive growth of global data traffic, coherent optical communication systems have become a core technology for backbone network transmission. Coherent detection technology, combined with high-order modulation formats and polarization multiplexing, can achieve signal transmission rates of 400 Gbps or even higher per wavelength. However, one of the core challenges facing long-distance, high-speed optical transmission is the signal distortion problem caused by the Kerr nonlinearity of optical fibers.

[0003] Optical fiber, as a transmission medium, inherently possesses nonlinear characteristics. When the optical signal power is high, the refractive index of the fiber changes with the light intensity; this effect is known as the Kerr effect. In coherent optical communication systems, the Kerr effect mainly manifests as nonlinear impairments such as self-phase modulation, cross-phase modulation, and four-wave mixing. Self-phase modulation causes the signal phase to change with its instantaneous power, resulting in signal spectrum broadening; cross-phase modulation causes mutual interference between channels of different wavelengths; and four-wave mixing generates new frequency components in wavelength division multiplexing systems, causing inter-channel crosstalk. These nonlinear impairments interact with dispersion effects and accumulate with increasing transmission distance, severely limiting the system's transmission distance and capacity. In typical long-distance optical transmission systems, fiber nonlinearity and amplifier spontaneous emission noise jointly determine the system's maximum transmission capacity. As the input optical power increases, nonlinear impairments intensify, creating a trade-off between power and performance.

[0004] Chinese invention patent CN114285715B discloses a nonlinear equalization method based on bidirectional GRU-conditional random fields, which transforms the nonlinear equalization problem into a symbol classification problem. It extracts the temporal features of signal sequences by constructing a bidirectional GRU network and combines this with conditional random fields for joint prediction of symbol sequences. This method utilizes a machine learning model to directly learn the mapping relationship from received signals to transmitted symbols, without relying on precise parameter information of the fiber optic transmission link. However, this method has the following shortcomings: 1) The computational complexity of the bidirectional GRU network is high, making it difficult to meet the real-time processing requirements of systems with speeds of 400Gbps and above; 2) The network structure is designed as a purely data-driven form, failing to fully utilize the physical model information of fiber optic transmission, resulting in the network requiring more training data and longer training time to converge; 3) Using a fixed network depth, it is impossible to adaptively adjust the computational complexity according to different channel conditions, making it difficult to achieve a balance between compensation performance and computational overhead.

[0005] Traditional digital backpropagation algorithms rely on the split-step Fourier method to solve approximate solutions to the nonlinear Schrödinger equation, compensating for nonlinear impairments by simulating the fiber transmission process in the digital domain. The compensation accuracy of this algorithm is positively correlated with the number of steps, but increasing the number of steps leads to a sharp increase in computational complexity, making real-time processing difficult. For example, with a typical 50-step configuration per span, processing a single symbol requires performing 50 Fourier transform pairs and 50 nonlinear phase rotations. For a 64 Gbaud symbol rate system, this requires over 3 trillion complex operations per second, far exceeding the processing capabilities of current hardware platforms. Nonlinear compensation methods based on perturbation theory achieve compensation by analytically calculating nonlinear perturbation terms, but these rely on precise link parameters and still suffer from high computational complexity. In recent years, researchers have attempted to apply deep learning techniques to fiber nonlinear compensation, achieving some progress, but existing methods still have significant shortcomings in computational efficiency, training efficiency, and adaptability.

[0006] Therefore, there is an urgent need for an intelligent compensation method for fiber nonlinear damage that can integrate physical model knowledge and the advantages of deep learning, which can significantly reduce computational complexity while ensuring compensation performance, and can adaptively adjust processing resources according to channel conditions to meet the real-time processing requirements of high-speed coherent optical transmission systems. Summary of the Invention

[0007] To address the problems of excessive computational complexity in existing fiber optic nonlinear compensation algorithms, low training efficiency of purely data-driven methods, and difficulty in adaptively adjusting fixed network structures, this invention provides a coherent optical communication nonlinear damage intelligent compensation method and system. It expands the classic step-by-step Fourier algorithm into a learnable neural network structure, optimizes network parameters through a data-driven approach, and maintains the constraints of the physical model, thereby achieving efficient nonlinear damage compensation.

[0008] This invention adopts the following technical solution: a smart compensation method for nonlinear impairments in coherent optical communication, comprising the following steps:

[0009] Step 1, Signal Reception and Preprocessing: A coherent receiver is used to perform beat frequency detection with the received signal through a local oscillator laser, and outputs an electrical domain signal; the electrical domain signal is preprocessed to generate a linearly equalized signal;

[0010] Step 2: Construct a physically embedded unfolded network containing multiple cascaded compensation units, each of which contains a frequency domain compensation layer and a nonlinear activation layer in sequence.

[0011] The frequency domain compensation layer receives the linearly equalized signal and sequentially performs Fourier transform, frequency domain filtering, and inverse Fourier transform operations. The frequency domain filtering uses learnable frequency domain filter coefficients to weight the signal spectrum.

[0012] The nonlinear activation layer performs a point-by-point phase rotation operation on the time-domain signal based on a learnable nonlinear phase rotation coefficient, and outputs a nonlinear compensation signal.

[0013] Step 3, Adaptive Depth Control: Determine the number of unfolded layers of the physical embedded unfolded network based on the estimated optical signal-to-noise ratio of the received signal and the modulation format identification result;

[0014] Step 4, Parameter Optimization Feedback: Calculate the mean square error between the nonlinear compensation signal and the transmitted reference symbol, and update the frequency domain filter coefficients and nonlinear phase rotation coefficients based on the mean square error using the gradient backpropagation algorithm;

[0015] Step 5, Online Inference: Deploy the trained network parameters to the digital signal processing hardware platform, periodically estimate the channel conditions and select the corresponding network configuration through adaptive depth control, and use the pre-trained parameters to perform nonlinear compensation processing on the real-time received signal through physical embedded network expansion.

[0016] The present invention also provides: a coherent optical communication nonlinear impairment intelligent compensation system for implementing the aforementioned method, comprising:

[0017] The signal receiving preprocessing module includes a clock recovery unit, a carrier recovery unit, and a linear equalization unit. It is used to acquire the electrical domain signal output by the coherent receiver, perform clock recovery, carrier phase estimation, and linear equalization on the electrical domain signal, and generate a linearly equalized signal, which is then output to the physical embedded unfolded network module and the adaptive depth control module.

[0018] The physically embedded unfolded network module contains K cascaded compensation units, each of which includes a frequency domain compensation layer and a nonlinear activation layer. It is used to receive the linearly equalized signal, perform nonlinear compensation processing on the signal through multiple cascaded frequency domain compensation layers and nonlinear activation layers, and output a nonlinear compensation signal. The output end is connected to the input end of the parameter optimization feedback module and also serves as the final output end of the system.

[0019] Adaptive Depth Control Module: Includes a signal-to-noise ratio estimation unit, a modulation format identification unit, and a layer number decision unit; used to dynamically determine the number of unfolded layers of the physically embedded unfolded network module based on the optical signal-to-noise ratio estimation value of the received signal and the modulation format identification result; the output end is connected to the control end of the physically embedded unfolded network module to transmit the unfolded layer number decision result;

[0020] The parameter optimization feedback module includes a loss calculation unit and a gradient backpropagation unit. It is used to calculate the mean square error between the nonlinear compensation signal and the transmitted reference symbol, and update the frequency domain filter coefficients and nonlinear phase rotation coefficients based on the mean square error using the gradient backpropagation algorithm. The output is connected to the parameter memory of each layer of the physically embedded unfolded network module to transmit the updated network parameters.

[0021] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0022] 1. The method of this invention integrates prior knowledge of physical models through a physically embedded network structure, which reduces the number of parameters that need to be learned and improves training efficiency and generalization ability; and automatically adjusts the computational complexity under different channel conditions through adaptive depth control. Under low signal-to-noise ratio conditions, a shallower network is used to save computational resources, while under high signal-to-noise ratio conditions, a deeper network is used to achieve better compensation effect.

[0023] 2. The overall solution of this invention extends the coherent optical transmission distance by more than 30%, reduces the computational complexity of nonlinear compensation by two orders of magnitude compared with the traditional digital backpropagation algorithm, and supports real-time online processing. It can be applied to various coherent optical communication scenarios such as backbone networks, metropolitan area networks and data center interconnection, and has broad application prospects. Attached Figure Description

[0024] Figure 1 This is a flowchart of the intelligent compensation method for nonlinear damage in coherent optical communication according to the present invention;

[0025] Figure 2 This is an architecture diagram of the intelligent compensation system for nonlinear damage in coherent optical communication according to the present invention;

[0026] Figure 3 This is a schematic diagram of the adaptive depth control module of the present invention;

[0027] Figure 4 This is the constellation diagram before optimization in the embodiments of the present invention;

[0028] Figure 5 This is an optimized constellation diagram according to an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in this invention. All non-innovative embodiments based on these embodiments by other researchers in the art are within the protection scope of this invention. Furthermore, the step numbers in the embodiments of this invention are only set for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0030] Example 1

[0031] A smart compensation method for nonlinear impairments in coherent optical communication is provided, which is applied to the digital signal processing link at the receiver end of a long-distance high-speed coherent optical transmission system.

[0032] Its core idea is to expand the classic split-step Fourier algorithm into a learnable neural network structure, optimize the network parameters through data-driven methods, and maintain the constraints of the physical model, thereby achieving efficient nonlinear damage compensation. The process is as follows: Figure 1 As shown, it includes the following steps:

[0033] Step 1: Signal Reception and Preprocessing

[0034] 1. Obtain the electrical domain signal output by the coherent receiver. The coherent receiver uses a local oscillator laser to perform beat frequency detection with the received signal, converting the optical domain signal into an electrical domain signal.

[0035] In this embodiment, the coherent receiver employs a polarization diversity and phase diversity structure, outputting an analog electrical signal containing four dual-polarization signals. Specifically, the receiver uses a polarization beamsplitter to separate the received optical signal into two orthogonal polarization components. Each polarization component coherently beats with the local oscillator light in a 90-degree optical mixer, generating two electrical signals: an in-phase component and a quadrature component. The four analog electrical signals are then conditioned by a transimpedance amplifier and an automatic gain control circuit to ensure that the signal amplitude is within the optimal operating range of the analog-to-digital converter.

[0036] 2. The analog-to-digital converter samples and quantizes the analog electrical signal at a sampling rate twice the signal symbol rate.

[0037] In this embodiment, for a 64 Gbaud signal, the sampling rate is set to 128 GSa / s, and the quantization precision is 8 bits. The sampling clock is provided by a high-precision clock source with a clock jitter of less than 100 femtoseconds to ensure sampling accuracy. The sampling time deviation between the four analog-to-digital converters is eliminated through a combination of hardware calibration and digital compensation, with a calibration accuracy better than 0.01 sampling periods.

[0038] 3. Perform clock recovery processing on the sampled digital signal.

[0039] In this embodiment, the clock recovery process uses the Gardner timing error detection algorithm to estimate the sampling clock deviation, and uses a multiphase filter to adjust the sampling time so that the sampling point is aligned with the optimal sampling position of the symbol.

[0040] The Gardner timing error detector calculates a timing error estimate using the sampled values ​​between adjacent symbols. This estimate is then smoothed by a loop filter and used to control a numerically controlled oscillator to adjust the sampling phase.

[0041] The loop filter adopts a proportional-integral structure with a proportional coefficient set to 0.01 and an integral coefficient set to 0.0001 to achieve a balance between tracking speed and steady-state jitter.

[0042] The polyphase filter uses a Farrow structure to achieve arbitrary fractional delay interpolation. The filter order is 4, which can realize timing adjustment with subsampling point precision.

[0043] 4. Perform carrier phase estimation processing on the signal after clock recovery.

[0044] The carrier phase estimation employs a fourth-power phase estimation algorithm for coarse frequency offset estimation and a decision-guided algorithm for fine phase tracking. In this embodiment, the search range for coarse frequency offset estimation is ±2 GHz, and the filter length for fine phase tracking is 16 symbols. The fourth-power frequency offset estimator first performs a fourth-power operation on the received symbols to eliminate modulation information, and then extracts the spectral peak position through a fast Fourier transform to estimate the carrier frequency offset.

[0045] For higher-order modulation formats such as 64QAM, a pre-decision process is required before the fourth power operation. This process pre-determines the symbol as the nearest constellation point before performing the fourth power operation to improve the accuracy of frequency offset estimation. After the frequency offset estimation is completed, the signal is shifted to baseband via digital down-conversion.

[0046] The decision-guided phase tracker adopts a first-order phase-locked loop structure, using the phase difference between the decision symbol and the received symbol as an error signal. With the loop gain set to 0.01, it can track phase changes at a rate of 0.1 degrees per symbol.

[0047] 5. Perform linear equalization processing on the signal after carrier recovery.

[0048] In this embodiment, the linear equalization process includes two sub-steps: dispersion compensation and polarization demultiplexing.

[0049] Dispersion compensation is achieved using a frequency-domain equalizer, whose transfer function is calculated based on the fiber dispersion coefficient and transmission distance. Specifically, assuming a standard single-mode fiber has a dispersion coefficient of 17 picoseconds per nanometer per kilometer at a wavelength of 1550 nanometers, and a transmission distance of L kilometers, the frequency-domain transfer function of the dispersion equalizer is an all-pass filter whose phase varies with the square of the frequency. Frequency-domain dispersion equalization converts the time-domain signal to the frequency domain using a Fast Fourier Transform (FFT), multiplies it by the equalizer transfer function, and then converts it back to the time domain using an Inverse Fast Fourier Transform (IFFT). The overlap-preservation method is used to process the continuous data stream, with each processing block having a length of 4096 points and an overlap length of 512 points.

[0050] Polarization demultiplexing is implemented using a constant-mode algorithm adaptive equalizer. The equalizer has a butterfly structure, with each branch having a filter length of 21 taps and a convergence factor of 0.001. The butterfly equalizer contains four finite impulse response (FIR) filters, which handle coupling and crosstalk between the two polarization states respectively. The filter coefficients are updated online adaptively using the constant-mode algorithm, which uses the square of the difference between the received symbol modulus and the desired modulus as a cost function, and minimizes the cost function using stochastic gradient descent. For non-constant-mode modulation formats such as 64QAM, after initial convergence, the constant-mode algorithm switches to a decision-guided algorithm for fine-tuning.

[0051] After the above preprocessing, the output signal is linearly equalized. The linearly equalized signal has compensated for linear impairments such as dispersion and polarization mode dispersion, but it still contains nonlinear impairments caused by the fiber Kerr nonlinearity effect. These nonlinear impairments manifest as rotation and diffusion of symbols on the constellation diagram, with mutual interference between adjacent symbols, leading to an increase in the bit error rate. For long-distance, high-power transmission scenarios, nonlinear impairments become a major factor limiting system performance and must be addressed using specialized nonlinear compensation algorithms.

[0052] Step 2: Physically Embedded Deployment of Network Processing

[0053] The linearly equalized signal is received, and nonlinear compensation processing is performed on the signal through a multi-layer cascaded compensation unit.

[0054] The design concept of physically embedded unfolded networks originates from a deep unfolding of the split-step Fourier algorithm. The traditional split-step Fourier algorithm discretizes the optical fiber transmission process into multiple small steps, and processes linear and nonlinear effects sequentially within each step.

[0055] This embodiment unfolds this iterative structure into a neural network, with linear processing steps corresponding to frequency domain compensation layers, nonlinear processing steps corresponding to nonlinear activation layers, and the number of iterations corresponding to the number of network layers. This design retains the physical rationality of the split-step Fourier algorithm while introducing data-driven parameter optimization capabilities, achieving an organic integration of physical models and machine learning.

[0056] Compared with traditional data-driven neural network methods, physically embedded unfolded networks have the following advantages: the network structure directly corresponds to the physical process, the parameters have clear physical meanings, and are easy to understand and debug; the initial values ​​of parameters are calculated using physical models, which greatly reduces the amount of parameter adjustment that needs to be learned and reduces the training data requirements; physical constraints ensure the rationality of the network output and avoid abnormal results that violate physical laws; the network depth corresponds to the number of steps and can be flexibly adjusted according to the compensation accuracy requirements.

[0057] In this embodiment, each compensation unit includes a frequency domain compensation layer and a nonlinear activation layer, which are cascaded sequentially. If the number of layers in the physically embedded unfolded network is K, then it contains a total of K compensation units. The layers are sequentially connected, with the output of the previous compensation unit directly serving as the input of the next compensation unit.

[0058] This cascaded structure simulates the process of multiple iterations in the split-step Fourier algorithm, with each compensation unit equivalent to compensating for dispersion and nonlinear effects over a short fiber transmission distance.

[0059] 1. The processing procedure of the frequency domain compensation layer is as follows:

[0060] Let the first The input signal of the layer compensation unit is ,in Indicates the index of the time sampling point. Representation layer index, The input signal of the first compensation unit is the linearly equalized signal. The signal is represented in complex form, with the real part corresponding to the in-phase component and the imaginary part corresponding to the quadrature component.

[0061] First, perform a Fast Fourier Transform on the input signal to convert the time-domain signal to the frequency domain:

[0062] ;

[0063] in: This represents the frequency domain of the input signal at the k-th layer. This indicates the Fast Fourier Transform operation; The length of the signal sequence; For frequency index, ; The imaginary unit is used. The Fast Fourier Transform (FFT) is implemented using the Cooley-Tukey radix-2 algorithm. When the sequence length N is a power of 2, the computational complexity is O(n^2). In this embodiment, the length of each processing block is set to 4096 points, corresponding to 32768 complex multiplication operations.

[0064] Then, point-by-point complex multiplication is performed between the frequency domain signal and the learnable frequency domain filter coefficients:

[0065] ;

[0066] in: This is the signal after frequency domain filtering; Let be the frequency domain filter coefficients of the k-th layer, which is a variable of length . The complex vector is learned through a training process. The physical meaning of frequency domain filtering is to apply different amplitude gains and phase delays to each frequency component of the signal, thereby altering the signal's spectral characteristics. In dispersion compensation applications, the phase response of the frequency domain filter is designed as a quadratic function of frequency to compensate for dispersion phase distortion introduced by fiber optic transmission.

[0067] Specifically, in this embodiment, the initial values ​​of the frequency domain filter coefficients are calculated based on the physical model of optical fiber transmission. Let the dispersion coefficient of the optical fiber be... The transmission distance is The center wavelength is The speed of light is Then the initial values ​​of the frequency domain filter coefficients are:

[0068] ;

[0069] in: These are the initial values ​​for the coefficients of the k-th layer frequency domain filter; The sampling frequency; This represents the total number of expanded layers.

[0070] The above initialization method enables each layer of frequency domain filter to compensate for total dispersion. In part, the initial state of the entire network corresponds to the dispersion compensation function of the traditional split-step Fourier algorithm. Taking a 1000 km standard single-mode fiber transmission as an example, with a dispersion coefficient of 17 picoseconds per nanometer per kilometer and a center wavelength of 1550 nanometers, the total dispersion is 17000 picoseconds per nanometer. If the number of unfolded layers is set to 10, each layer compensates for 1700 picoseconds per nanometer of dispersion. The phase response of the frequency domain filter is maximum at the edge of the signal bandwidth; for a 64 Gbaud signal, the phase rotation of the edge frequency components is approximately 10 radians per layer.

[0071] Finally, perform a fast inverse Fourier transform on the frequency domain filtered signal to convert the signal back to the time domain:

[0072] ;

[0073] in: This is the output signal of the frequency domain compensation layer; This represents the Inverse Fast Fourier Transform (IFFT) operation. The computational structure of the IFFT is the same as that of the Fast Fourier Transform (FFT), except that the signs of the twiddle factors are reversed. By reusing the same hardware module, the Fourier transform and inverse transform can share computational resources.

[0074] 2. The processing procedure for the nonlinear activation layer is as follows:

[0075] The nonlinear activation layer receives the output signal from the frequency domain compensation layer. It performs learnable nonlinear phase rotation operations. The design of the nonlinear activation layer is based on a mathematical model of the fiber self-phase modulation effect. In self-phase modulation, the phase of the signal changes with its instantaneous power; the phase rotation is large at high power and small at low power. By applying a phase rotation opposite to the signal transmission process, the phase distortion introduced by self-phase modulation can be compensated.

[0076] First, calculate the instantaneous power value at each sampling point of the input signal:

[0077] ;

[0078] in: This represents the instantaneous power value at the t-th sampling point in the k-th layer; This represents taking the modulus of a complex number. Instantaneous power is calculated by multiplying the complex signal by its conjugate, and the result is a non-negative real number. For a normalized signal, the average instantaneous power is equal to the average power of the signal.

[0079] The nonlinear activation layer then multiplies the instantaneous power value by a learnable nonlinear phase rotation coefficient to obtain the phase rotation amount:

[0080] ;

[0081] in: This represents the phase rotation amount at the t-th sampling point in the k-th layer; Let be the nonlinear phase rotation coefficient of the k-th layer, a scalar parameter learned through the training process. The physical meaning of the nonlinear phase rotation coefficient is the product of the nonlinear coefficient and the effective length, which determines the phase rotation rate of a unit power signal.

[0082] Specifically, in this embodiment, the initial value of the nonlinear phase rotation coefficient is calculated based on the physical model of optical fiber transmission. Let the nonlinear coefficient of the optical fiber be... The effective length is The initial value of the nonlinear phase rotation coefficient is:

[0083] ;

[0084] in: This represents the initial value of the nonlinear phase rotation coefficient for the k-th layer; the negative sign indicates that reverse compensation is performed.

[0085] The above initialization method enables each nonlinear activation layer to compensate for the total nonlinear phase shift. Partially. Taking typical standard single-mode fiber parameters as an example, the nonlinear coefficient is taken as 1.3 watts per kilometer, and the effective length is determined by the fiber attenuation coefficient. When the attenuation coefficient is taken as 0.2 dB per kilometer, the effective length is approximately 21.7 kilometers. For a long-distance transmission system with a span length of 80 kilometers and multiple spans cascaded, the effective length of each span is approximately equal.

[0086] Finally, a phase rotation operation is performed on each sampling point of the input signal:

[0087] ;

[0088] in: This is the output signal of the k-th compensation unit, and also the input signal of the (k+1)-th compensation unit. The phase rotation operation is implemented through complex multiplication, and the phase rotation factor is... Since the modulus is always 1, phase rotation does not change the signal amplitude, only the phase. The complex exponential function is calculated using the CORDIC algorithm, which approximates the signal with a series of angles to obtain accurate sine and cosine values.

[0089] After cascading processing by K compensation units, the physically embedded unfolded network finally outputs a nonlinear compensation signal. .

[0090] 3. Treatment of cross-layer connection structures:

[0091] In this embodiment, the physically embedded unfolded network also includes a cross-layer connection structure. The cross-layer connection structure performs a weighted summation of the input signal of the first compensation unit and the output signal of the last compensation unit:

[0092] ;

[0093] in: This is the final output nonlinear compensation signal; The cross-layer connection weight coefficients range from 0 to 1 and are learned through the training process, with an initial value of 0.1.

[0094] The role of cross-layer connections is to establish a direct path from input to output, which facilitates backpropagation of gradients and accelerates network training convergence. From a signal processing perspective, cross-layer connections are equivalent to retaining a certain proportion of the original signal components in the compensated signal. When the nonlinear impairment is minor, overcompensation can be reduced by increasing the cross-layer weights.

[0095] 4. Handling of group processing mechanism:

[0096] In this embodiment, the physically embedded unfolded network also supports a group processing mechanism. For long sequence signals, the signal is divided into multiple overlapping processing blocks. Each processing block is independently compensated by the network. After processing, the effective parts of each block are spliced ​​together to obtain the complete output signal.

[0097] Grouping reduces storage requirements per processing run and enables pipelined parallel processing to improve throughput. In this embodiment, the length of each processing block is set to 4096 symbols, and the overlap length between adjacent blocks is set to 512 symbols to eliminate block boundary effects.

[0098] Step 3: Adaptive Depth Control

[0099] Based on the optical signal-to-noise ratio (SNR) estimate of the received signal and the modulation format identification result, the number of unfolded layers of the physically embedded unfolded network is determined, including: SNR estimation, modulation format identification, and layer number decision.

[0100] 1. Signal-to-noise ratio estimation: Calculate the estimated optical signal-to-noise ratio based on the constellation distribution of the signal after linear equalization.

[0101] This embodiment uses the error vector magnitude method for signal-to-noise ratio estimation. Let the received i-th symbol be... The symbol after the judgment is The error vector magnitude is then defined as:

[0102] ;

[0103] in: The magnitude of the error vector; In this embodiment, the number of symbols used for estimation is set to 10,000.

[0104] The optical signal-to-noise ratio estimate is calculated based on the error vector magnitude:

[0105] ;

[0106] in: This is an estimated optical signal-to-noise ratio, in dB. For the 16QAM modulation format, a correction factor is used that is related to the modulation format. dB for 64QAM modulation format dB.

[0107] 2. Modulation format identification: Identify the modulation format based on the statistical characteristics of the signal after linear equalization.

[0108] This embodiment uses the higher-order cumulant method for modulation format identification, calculating the fourth-order and sixth-order cumulants of the received signal:

[0109] ;

[0110] ;

[0111] in: It is a fourth-order cumulant; It is a sixth-order cumulant; Represents the mathematical expectation; Indicates the received symbol.

[0112] The modulation format is determined by comparing the ratio of the fourth-order cumulant to the sixth-order cumulant with a preset decision threshold. This embodiment supports the recognition of four modulation formats: QPSK, 16QAM, 32QAM, and 64QAM.

[0113] 3. Layer number decision: Based on the optical signal-to-noise ratio estimate and modulation format identification results, the corresponding number of unfolded layers is queried from the preset layer number mapping table.

[0114] The structure of the layer mapping table in this embodiment is as follows:

[0115] For QPSK modulation format: when the optical signal-to-noise ratio is below 12dB, the number of unfolded layers is 2; when the optical signal-to-noise ratio is between 12dB and 16dB, the number of unfolded layers is 4; when the optical signal-to-noise ratio is between 16dB and 20dB, the number of unfolded layers is 6; and when the optical signal-to-noise ratio is above 20dB, the number of unfolded layers is 8.

[0116] For the 16QAM modulation format: when the optical signal-to-noise ratio is below 18dB, the number of unfolded layers is 4; when the optical signal-to-noise ratio is between 18dB and 22dB, the number of unfolded layers is 6; when the optical signal-to-noise ratio is between 22dB and 26dB, the number of unfolded layers is 10; and when the optical signal-to-noise ratio is above 26dB, the number of unfolded layers is 12.

[0117] For the 64QAM modulation format: when the optical signal-to-noise ratio is below 24dB, the number of unfolded layers is 6; when the optical signal-to-noise ratio is between 24dB and 28dB, the number of unfolded layers is 10; when the optical signal-to-noise ratio is between 28dB and 32dB, the number of unfolded layers is 14; and when the optical signal-to-noise ratio is above 32dB, the number of unfolded layers is 20.

[0118] The design principle of the layer mapping table is as follows: under low signal-to-noise ratio conditions, nonlinear impairments have a relatively small impact on system performance, and shallower networks can meet the compensation requirements while saving computational resources; under high signal-to-noise ratio conditions, nonlinear impairments become the main factor limiting system performance, and deeper networks are needed to obtain more refined compensation effects.

[0119] In summary, adaptive depth control sends the determined number of unfolded layers to the physically embedded unfolded network, controlling the number of compensation units actually involved in processing. During the training phase, a set of network parameters needs to be trained separately for each possible number of unfolded layers. During the inference phase, the corresponding number of layers and parameters are selected for processing based on the real-time estimated channel conditions.

[0120] Step 4: Parameter Optimization Feedback

[0121] The mean square error between the nonlinear compensation signal and the transmitted reference symbol is calculated. Based on this mean square error, the frequency domain filter coefficients and the nonlinear phase rotation coefficients are updated using a gradient backpropagation algorithm. Parameter optimization feedback is processed during the training phase, and the training data includes the known sequence of reference symbols from the transmitter and the corresponding received signals.

[0122] 1. Loss Calculation:

[0123] The symbol positions in the nonlinear compensation signal corresponding to the transmitted reference symbols are obtained. In this embodiment, training symbols are inserted into the data stream in blocks, with each training block containing 128 symbols and a spacing of 1024 data symbols between training blocks.

[0124] The loss calculation unit calculates the mean square error between the nonlinear compensation signal and the transmitted reference symbol:

[0125] ;

[0126] in: This is the mean square error value; The number of training symbols; This is the nonlinear compensation signal for the i-th training position; Send the reference symbol for the i-th symbol.

[0127] Calculate the regularization term to constrain the deviation of network parameters from the initial values ​​of the physical model:

[0128] ;

[0129] in: For regularization terms; and In this embodiment, the regularization weight coefficient is set to... , .

[0130] The total loss function is a weighted sum of the mean squared error term and the regularization term:

[0131] .

[0132] 2. Gradient backpropagation:

[0133] The gradients with respect to the frequency domain filter coefficients and nonlinear phase rotation coefficients are calculated based on the total loss function. Since each operation of the physically embedded unfolded network is differentiable, the gradients can be directly calculated using an automatic differentiation framework.

[0134] The gradient calculation expression for the frequency domain filter coefficients is as follows:

[0135] ;

[0136] in: express The conjugate of complex numbers.

[0137] The expression for calculating the gradient of the nonlinear phase rotation coefficient is as follows:

[0138] ;

[0139] in: This indicates taking the real part of a complex number.

[0140] 3. Update network parameters:

[0141] The network parameters are updated based on the calculated gradient and the preset learning rate. In this embodiment, the Adam optimization algorithm is used for parameter updates. The initial learning rate is set to 0.001, and a cosine annealing strategy is used to dynamically adjust the learning rate.

[0142] ;

[0143] in: Let be the learning rate for the nth training cycle; The maximum learning rate; Minimum learning rate; This represents the total number of training cycles, which is set to 100 in this embodiment.

[0144] The update formula for the frequency domain filter coefficients is:

[0145] ;

[0146] The update formula for the nonlinear phase rotation coefficient is:

[0147] ;

[0148] The training process continues until the convergence condition is met. The convergence condition is that the change in the loss function value is less than 0.001 for 10 consecutive training epochs, or the maximum number of training epochs is reached.

[0149] The training environment configuration in this embodiment is as follows: AMD EPYC 7742 processor, NVIDIA A100 graphics card, and PyTorch 2.0 deep learning framework. For a network configuration with 64QAM modulation format and 20 unfolded layers, a single forward propagation takes approximately 0.8 milliseconds, and the complete training process takes approximately 30 minutes. The training dataset contains 100,000 training symbols and 20,000 validation symbols, which are randomly partitioned to ensure consistent data distribution. During training, performance is evaluated on the validation set every 10 epochs. If the loss function value on the validation set does not decrease after 5 consecutive evaluations, training is terminated early to prevent overfitting.

[0150] Step 5: Online Inference Processing

[0151] After offline training is completed, the trained network parameters are deployed to a digital signal processing hardware platform. During the online inference phase, channel conditions are periodically estimated and the corresponding network configuration is selected through adaptive depth control. The physically embedded unfolded network uses the pre-trained parameters to perform nonlinear compensation processing on the real-time received signal.

[0152] The hardware implementation in this embodiment uses an FPGA platform. For the Fourier transform operation of the frequency domain compensation layer, a radix-4 fast Fourier transform algorithm is used, and a pipelined structure is employed to improve throughput. For the phase rotation operation of the nonlinear activation layer, the CORDIC algorithm is used to implement complex multiplication, reducing multiplier resource consumption.

[0153] The performance test results of this embodiment are as follows: In a 64Gbaud, 64QAM modulation format, 2000km standard single-mode fiber transmission scenario, using a network configuration with a 12-layer unfolding depth, this method achieved an equivalent signal-to-noise ratio gain of 0.8dB, and reduced the bit error rate from 3.2×10⁻⁶. -2 Reduced to 1.8×10 -3 This achieves a hard-decision forward error correction code threshold below 7%. Compared to the traditional 50-step digital backpropagation algorithm, this method reduces computational complexity by approximately 98%, and single-symbol processing latency is reduced from 12.5 microseconds to 0.15 microseconds.

[0154] Example 2

[0155] A public coherent optical communication nonlinear damage intelligent compensation system is provided, the structure of which is as follows: Figure 2 As shown, it includes: a signal receiving preprocessing module, a physically embedded unfolded network module, an adaptive depth control module, and a parameter optimization feedback module.

[0156] The system in this embodiment can be integrated into the digital signal processing unit of a coherent optical receiver, or it can be deployed as a stand-alone signal processing device at the receiving end.

[0157] The signal receiving preprocessing module is connected to the output of the analog-to-digital converter of the coherent receiver. It acquires the electrical domain signal output by the coherent receiver and performs clock recovery, carrier phase estimation, and linear equalization on the electrical domain signal to generate a linearly equalized signal. The output of the signal receiving preprocessing module is connected to the input of the physically embedded unfolded network module and also to the input of the adaptive depth control module. The processing delay of the signal receiving preprocessing module directly affects the overall delay performance of the system. This embodiment uses a pipelined parallel structure to control the processing delay to within 1 microsecond.

[0158] The signal receiving preprocessing module includes: a clock recovery unit, a carrier recovery unit, and a linear equalization unit.

[0159] The clock recovery unit employs a Gardner timing error detector and a polyphase filter to achieve sampling clock synchronization. The Gardner timing error detector outputs an error estimate every two symbol periods, which, after being smoothed by a loop filter, drives a numerically controlled oscillator to adjust the sampling phase. The polyphase filter, implemented using a Farrow architecture, includes four parallel fixed-coefficient filters and a polynomial interpolation unit, enabling adjustment of sampling times with arbitrary fractional delays. The clock recovery unit has a synchronization range of ±500 ppm and a synchronization accuracy better than 0.01 symbol periods.

[0160] The carrier recovery unit employs a fourth-order frequency offset estimator and a decision-guided phase tracker to achieve carrier recovery. The fourth-order frequency offset estimator first performs pre-decision processing on the received symbols, mapping them to the nearest standard constellation point. Then, it performs a fourth-order operation on the pre-decision symbols to eliminate modulation information. Finally, it extracts the spectral peak position using a fast Fourier transform to estimate the frequency offset. After frequency offset estimation, the signal is down-converted to baseband using a digital oscillator and a complex multiplier. The decision-guided phase tracker uses a first-order phase-locked loop structure, utilizing the phase difference between the decision and received symbols as an error signal to drive the loop filter. The carrier recovery unit has a frequency offset acquisition range of ±2 GHz and a phase tracking accuracy better than 1 degree.

[0161] The linear equalization unit comprises a frequency-domain dispersion equalizer and an adaptive polarization demultiplexing equalizer, implementing dispersion compensation and polarization demultiplexing functions, respectively. The frequency-domain dispersion equalizer uses an overlap-preservation method to process continuous data streams, with each processing block having a length of 4096 points and an overlap length of 512 points. The equalizer's transfer function is pre-calculated based on the fiber dispersion coefficient and transmission distance and stored in read-only memory. The adaptive polarization demultiplexing equalizer employs a butterfly structure, containing four 21-tap finite impulse response filters. The filter coefficients are adaptively updated online using a constant modulus algorithm. For higher-order modulation formats, after the constant modulus algorithm converges, a decision-guided algorithm is used for fine-tuning. The linear equalization unit has a processing delay of approximately 0.5 microseconds and can compensate for cumulative dispersion up to 50,000 picoseconds per nanometer.

[0162] The input of the physically embedded unfolded network module is connected to the output of the signal receiving and preprocessing module. It receives the linearly equalized signal and performs nonlinear compensation processing on the signal through a multi-layered cascaded frequency domain compensation layer and nonlinear activation layer, outputting a nonlinear compensated signal. The output of the physically embedded unfolded network module is connected to the input of the parameter optimization feedback module, serving as the system's final output. The physically embedded unfolded network module supports a configurable unfolding depth of 2 to 20 layers; the actual number of layers used is determined by the adaptive depth control module.

[0163] The physically embedded unfolded network module contains K cascaded compensation units, where K is the number of unfolded layers, determined by the adaptive depth control module. Each compensation unit contains a frequency domain compensation layer and a nonlinear activation layer. The frequency domain compensation layer contains a Fourier transform, a frequency domain multiplier, and an inverse Fourier transform. The Fourier transform converts the time-domain signal to the frequency domain, the frequency domain multiplier multiplies the frequency-domain signal with learnable frequency-domain filter coefficients, and the inverse Fourier transform converts the frequency-domain signal back to the time domain. The Fourier transform and inverse Fourier transform are implemented using the radix-4 Fast Fourier Transform algorithm. When the processing block length is 4096 points, six stages of butterfly operations are required, with each stage containing 1024 radix-4 butterfly units. The frequency domain multiplier is implemented using a complex multiplier array; 4096 complex multipliers operate in parallel, completing all frequency domain multiplication operations in a single cycle.

[0164] The nonlinear activation layer comprises a power calculator, a phase calculator, and a phase rotator. The power calculator calculates the instantaneous power of the input signal. The phase calculator multiplies the instantaneous power by a learnable nonlinear phase rotation coefficient to obtain the phase rotation amount. The phase rotator performs the phase rotation operation on the input signal. The power calculator is implemented using a complex modulo-squaring circuit, which squares the real and imaginary parts of the complex signal respectively and then adds them to obtain the instantaneous power. The phase calculator is implemented using a fixed-point multiplier, and the nonlinear phase rotation coefficients are stored in a 16-bit fixed-point format. The phase rotator is implemented using the CORDIC algorithm, which obtains sine and cosine values ​​with an accuracy better than 0.01 radians through 12 iterations, and then performs complex multiplication with the input signal to complete the phase rotation.

[0165] Specifically, the physically embedded unfolded network module also includes a cross-layer connection structure that performs a weighted summation of the input of the first compensation unit and the output of the last compensation unit. The cross-layer connection is implemented through a weighted summation unit containing two scalar multipliers and one complex adder. The cross-layer connection weights are stored in a configurable register and can be updated based on training results. This cross-layer connection structure helps maintain gradient magnitude during gradient backpropagation, avoiding the vanishing gradient problem that occurs during the training of deep networks.

[0166] The input of the adaptive depth control module is connected to the output of the signal receiving preprocessing module. It determines the number of unfolded layers in the physically embedded unfolded network module based on the estimated optical signal-to-noise ratio (SNR) of the received signal and the modulation format identification result. The output of the adaptive depth control module is connected to the control terminal of the physically embedded unfolded network module, transmitting the unfolded layer decision result. The decision cycle of the adaptive depth control module is set to update once every 1000 symbols, ensuring timely response to changes in channel conditions without causing processing instability due to frequent switching.

[0167] The structure of the adaptive depth control module is as follows: Figure 3 As shown, it includes: a signal-to-noise ratio estimation unit, a modulation format identification unit, and a layer number decision unit.

[0168] The signal-to-noise ratio (SNR) estimation unit uses the error vector magnitude method to estimate the optical SNR. Internally, it includes a symbol decision unit, an error calculator, and an SNR converter. The symbol decision unit employs a minimum Euclidean distance decision algorithm, mapping the received symbol to the nearest standard constellation point. The error calculator calculates the average Euclidean distance between the received symbol and the decision symbol. The SNR converter calculates the estimated optical SNR based on the error vector magnitude and modulation format; the conversion formula is stored in a lookup table. The SNR estimation unit achieves an estimation accuracy better than 0.5 dB, with an estimation period of 1000 symbols.

[0169] The modulation format identification unit uses a high-order cumulant method to identify the modulation format, and internally includes a cumulant calculator and a format classifier. The cumulant calculator calculates the fourth-order and sixth-order cumulants of the received signal using a sliding window accumulator with a window length of 10,000 symbols. The format classifier determines the modulation format based on the comparison between the cumulant ratio and a preset threshold, supporting the identification of four modulation formats: QPSK, 16QAM, 32QAM, and 64QAM. The modulation format identification unit has an accuracy rate higher than 99.9% and an identification period of 10,000 symbols.

[0170] The layer number decision unit internally stores a layer number mapping table. Based on the signal-to-noise ratio (SNR) estimate and modulation format identification result, it queries the corresponding expanded layer number. The layer number mapping table is implemented in read-only memory, with entries organized according to modulation format and SNR intervals, containing a total of 16 entries. The query process first selects the corresponding sub-table based on the modulation format, then determines the interval based on the SNR estimate, and finally reads the corresponding expanded layer number. The layer number decision unit also includes a smoothing filter to avoid frequent layer switching caused by SNR estimate fluctuations. The filter uses a median filtering algorithm with a window length of 5 decision cycles.

[0171] The input of the parameter optimization feedback module is connected to the output of the physically embedded unfolded network module. It calculates the mean square error between the nonlinear compensation signal and the transmitted reference symbol, and updates the frequency domain filter coefficients and nonlinear phase rotation coefficients based on this mean square error using a gradient backpropagation algorithm. The output of the parameter optimization feedback module is connected to the parameter memory of each layer of the physically embedded unfolded network module, transmitting the updated network parameters. The parameter optimization feedback module operates during the offline training phase, and after training is complete, it stores the optimized parameters in the parameter memory of the physically embedded unfolded network module.

[0172] The parameter optimization feedback module includes a loss calculation unit and a gradient backpropagation unit.

[0173] The loss calculation unit includes a training symbol extractor, a mean square error (MSE) calculator, and a regularization calculator. The training symbol extractor extracts the symbol positions corresponding to the transmitted reference symbols from the received signal. The MSE calculator calculates the MSE error between the compensation signal and the reference symbol. The regularization calculator calculates the regularization penalty term for parameter deviation from the initial value. The MSE calculator is implemented using a complex subtractor and a modulo-square circuit, while the regularization calculator is implemented using a difference accumulator.

[0174] The gradient backpropagation unit comprises a gradient calculator and a parameter updater. The gradient calculator uses an automatic differentiation algorithm to calculate the gradient of the loss function with respect to the network parameters, while the parameter updater uses the Adam optimization algorithm to update the network parameters based on the gradients. The gradient calculator is implemented using the backpropagation algorithm, calculating and accumulating local gradients layer by layer from the output layer to the input layer. The parameter updater maintains the first-order moment estimate and second-order moment estimate for each parameter, calculates the adaptive learning rate according to the Adam algorithm formula, and updates the parameters.

[0175] The hardware implementation of this system can utilize FPGA or ASIC chips. In the FPGA implementation, the signal receiving preprocessing module and the physically embedded unfolded network module employ a pipelined structure to achieve high-throughput processing, while the adaptive depth control module uses a parallel lookup table structure for low-latency decision-making. The parameter optimization feedback module's functionality is completed by the host computer software during the offline training phase. This embodiment uses a Xilinx VU13P FPGA chip with a clock frequency of 250MHz, supporting real-time processing of 64Gbaud signals. Regarding resource utilization, the lookup table utilization is approximately 45%, the register utilization is approximately 30%, and the digital signal processing unit utilization is approximately 60%. In terms of power consumption, the overall power consumption under typical operating conditions is approximately 35 watts.

[0176] In ASIC implementations, all modules can be integrated onto a single chip, further reducing power consumption and cost. When implemented using a 28nm CMOS process, the chip area is approximately 25 square millimeters, and the power consumption is approximately 8 watts, representing a power reduction of about 77% compared to FPGA implementations. ASIC implementations can also employ more aggressive pipeline partitioning and parallelism configurations to further improve processing performance.

[0177] Furthermore, the method of the present invention is compared with the traditional method in terms of suppressing nonlinear damage. The constellation diagram before optimization is shown in the traditional method. Figure 4 As shown, the constellation diagram optimized using the method of this invention is as follows: Figure 5 As shown.

[0178] from Figure 4 It can be seen that without the nonlinear compensation of this invention or with only traditional linear equalization, the constellation points of the received signal exhibit significant divergence and rotation. Due to the Kerr effect in fiber optic transmission (such as self-phase modulation (SPM) and cross-phase modulation (XPM), the signal is severely affected by nonlinear phase noise. The four clusters in the constellation diagram have large areas, blurred edges, and large Euclidean distances between the points and their ideal center positions. This diffusion of constellation points leads to unclear decision boundaries between adjacent symbols, making them highly susceptible to bit errors.

[0179] from Figure 5As can be seen, after processing with the physically embedded unfolded network proposed in this invention, the constellation diagram quality is significantly improved, the convergence of constellation points is significantly enhanced, the four signal clusters become more compact and clear, and the deviation from the ideal constellation points is greatly reduced. This indicates that the present invention, through the frequency domain compensation layer and nonlinear activation layer driven by the physical model, effectively performs reverse phase rotation and spectral correction on the signal, accurately offsetting the nonlinear impairments accumulated in the transmission link.

[0180] The comparison shows that the method of this invention significantly reduces the error vector amplitude (EVM) of the signal and increases the decision margin between symbols. The visual "clustering convergence" is highly consistent with the experimental data: that is, through the intelligent compensation of this invention, the signal-to-noise ratio (Q factor) is effectively improved, and the bit error rate (BER) is reduced from a relatively high level before optimization to below the hard decision threshold. This intuitively demonstrates that this invention has superior nonlinear impairment compensation capability and higher signal recovery quality compared with traditional algorithms in long-distance, high-speed coherent optical communication systems.

[0181] In summary, this invention integrates the physical prior knowledge of the step-by-step Fourier algorithm through a physically embedded unfolded network structure. The initial values ​​of the network parameters already possess good compensation capabilities, significantly reducing the amount of parameter adjustment required for learning and improving training convergence speed by 5 to 10 times. Through an adaptive depth control mechanism, the computational complexity is dynamically adjusted under different channel conditions, reducing computational complexity by more than 60% in low signal-to-noise ratio scenarios while maintaining system performance. The overall solution supports the real-time processing requirements of coherent optical transmission systems with speeds of 400Gbps and above, extending transmission distance by more than 30% compared to the uncompensated case. This invention's system can be applied to various coherent optical communication scenarios such as backbone networks, metropolitan area networks, and data center interconnections, demonstrating broad application prospects.

[0182] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for intelligent compensation of nonlinear impairments in coherent optical communication, characterized in that, Includes the following steps: Step 1, Signal Reception and Preprocessing: A coherent receiver is used to perform beat frequency detection with the received signal through a local oscillator laser, and outputs an electrical domain signal; the electrical domain signal is preprocessed to generate a linearly equalized signal; Step 2: Construct a physically embedded unfolded network containing multiple cascaded compensation units, each of which contains a frequency domain compensation layer and a nonlinear activation layer in sequence. The frequency domain compensation layer receives the linearly equalized signal and sequentially performs Fourier transform, frequency domain filtering, and inverse Fourier transform operations. The frequency domain filtering uses learnable frequency domain filter coefficients to weight the signal spectrum. The nonlinear activation layer performs a point-by-point phase rotation operation on the time-domain signal based on a learnable nonlinear phase rotation coefficient, and outputs a nonlinear compensation signal. Step 3, Adaptive Depth Control: Determine the number of unfolded layers of the physical embedded unfolded network based on the estimated optical signal-to-noise ratio of the received signal and the modulation format identification result; Step 4, Parameter Optimization Feedback: Calculate the mean square error between the nonlinear compensation signal and the transmitted reference symbol, and update the frequency domain filter coefficients and nonlinear phase rotation coefficients based on the mean square error using the gradient backpropagation algorithm; Step 5, Online Inference: Deploy the trained network parameters to the digital signal processing hardware platform, periodically estimate the channel conditions and select the corresponding network configuration through adaptive depth control, and use the pre-trained parameters to perform nonlinear compensation processing on the real-time received signal through physical embedded network expansion.

2. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 1, characterized in that, The signal reception and preprocessing described in step 1 includes the following sub-steps: Step 1.1: The coherent receiver adopts a polarization diversity and phase diversity structure. The receiving end is equipped with a polarization beam splitter to separate the received optical signal into two orthogonal polarization state components. Each polarization state component and the local oscillator light are coherently beat in a 90-degree optical mixer to generate two electrical signal outputs: an in-phase component and an orthogonal component. Step 1.2: The four analog electrical signals are conditioned by transimpedance amplifiers and automatic gain control circuits, and then sampled and quantized by analog-to-digital converters. Step 1.3: Preprocess the electrical domain signal, including clock recovery processing, carrier phase estimation, and linear equalization processing.

3. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 2, characterized in that, The clock recovery process uses a Gardner timing error detector to calculate the timing error estimate using the sampled values ​​between adjacent symbols. After the estimate is smoothed by a loop filter, the numerically controlled oscillator is used to adjust the sampling phase. Then, the sampling time is adjusted by a multiphase filter so that the sampling point is aligned with the optimal sampling position of the symbol. The carrier phase estimation employs a fourth-power frequency offset estimator to remove modulation information from the received symbols, extracts the peak position of the spectrum through fast Fourier transform, performs coarse frequency offset estimation, and shifts the signal to the baseband through digital down-conversion; a decision-guided phase tracker is used to perform fine phase tracking by using the phase difference between the decision symbol and the received symbol as an error signal. The linear equalization process includes dispersion compensation and polarization demultiplexing. Dispersion compensation is implemented using a frequency-domain equalizer, with the transfer function calculated based on the fiber dispersion coefficient and transmission distance. Frequency-domain dispersion equalization converts the time-domain signal to the frequency domain using a Fast Fourier Transform (FFT), multiplies it by the equalizer's transfer function, and then converts it back to the time domain using an Inverse Fast Fourier Transform (IFFT). Polarization demultiplexing is implemented using a constant-modulus algorithm adaptive equalizer. The equalizer has a butterfly structure and contains four finite impulse response (FIR) filters to handle coupling and crosstalk between the two polarization states. The filter coefficients are updated online adaptively using a constant-modulus algorithm. The constant-modulus algorithm uses the square of the difference between the received symbol modulus and the desired modulus as the cost function, which is minimized using a stochastic gradient descent algorithm.

4. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 1, characterized in that, The frequency domain compensation layer described in step 2 is processed as follows: Step 2.1: Perform a Fast Fourier Transform on the input signal to convert the time-domain signal to the frequency domain: ； in, Indicates the index of the time sampling point; Representation layer index, , This represents the total number of unfolded layers; For the first Frequency domain representation of the layer input signal; This indicates the Fast Fourier Transform operation; For the first Input signal of the layer compensation unit; The length of the signal sequence; For frequency index, ; The imaginary unit; Step 2.2: Perform point-by-point complex multiplication on the frequency domain signal and the learnable frequency domain filter coefficients to obtain the frequency domain filtered signal. : ； in, For the first The frequency domain filter coefficients of the layer; Step 2.3: Perform a fast inverse Fourier transform on the frequency-domain filtered signal to convert the signal back to the time domain. ； in, This is the output signal of the frequency domain compensation layer; This indicates the Inverse Fast Fourier Transform operation.

5. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 4, characterized in that, The nonlinear activation layer described in step 2 is processed as follows: Step 2.4: Receive the output signal of the frequency domain compensation layer. Calculate the instantaneous power value at each sampling point: ； in, For the first Layer The instantaneous power value at each sampling point; Indicates taking the modulus of a complex number; Step 2.5: Multiply the instantaneous power value by the learnable nonlinear phase rotation coefficient to obtain the phase rotation amount: ； in: For the first Layer Phase rotation amount at each sampling point; For the first The nonlinear phase rotation coefficient of the layer; Step 2.6: Perform a phase rotation operation on each sampling point of the input signal: ； in, For the first The output signal of the layer compensation unit is also the first The input signal of the layer compensation unit; the phase rotation operation is implemented through complex multiplication, and the phase rotation factor. The modulus is always 1.

6. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 5, characterized in that, The frequency domain filter coefficients are of length [missing information]. The complex vector, with initial values ​​calculated based on the physical model of optical fiber transmission: ； in, For the first Initial values ​​for the coefficients of the layer frequency domain filter; The dispersion coefficient of the optical fiber; For transmission distance; The center wavelength; The speed of light; The sampling frequency; The nonlinear phase rotation coefficient is a scalar parameter, and its initial value is calculated based on the physical model of optical fiber transmission. ； in, For the first Initial values ​​for the layer nonlinear phase rotation coefficient; Let be the nonlinear coefficient of the optical fiber, and let be the effective length. The negative sign indicates that reverse compensation is performed. The frequency domain filter coefficients and nonlinear phase rotation coefficients are all learned through a training process, and each frequency domain compensation layer compensates for the total dispersion. Partially, each nonlinear activation layer compensates for the total nonlinear phase shift. In part, after being processed by K cascaded compensation units, the physically embedded unfolded network outputs a nonlinear compensation signal. .

7. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 5, characterized in that, The physically embedded unfolded network also includes a cross-layer connection structure to establish a direct path from input to output, which performs a weighted summation of the input signal of the first compensation unit and the output signal of the last compensation unit. ； in, This is the final output nonlinear compensation signal; This is the cross-layer connection weight coefficient, with a value ranging from 0 to 1.

8. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 5, characterized in that, The adaptive depth control described in step 3 is processed as follows: Step 3.1: Based on the constellation distribution of the linearly equalized signal, calculate the optical signal-to-noise ratio estimate using the error vector amplitude method. The error vector amplitude is defined as: ； in, For the i-th received symbol, The symbol following the judgment. The magnitude of the error vector; The number of symbols used for estimation; The optical signal-to-noise ratio estimate is calculated based on the error vector magnitude: ； in, This is an estimate of the optical signal-to-noise ratio; This is a correction factor related to the modulation format; Step 3.2: Based on the statistical characteristics of the signal after linear equalization, the modulation format is identified using the higher-order cumulant method, and the fourth-order and sixth-order cumulants of the received signal are calculated: ； ； in, It is a fourth-order cumulant; It is a sixth-order cumulant; Represents the mathematical expectation; Indicates the received symbol; The ratio of the fourth-order cumulant to the sixth-order cumulant is compared with a preset decision threshold to determine the modulation format, including: QPSK, 16QAM, 32QAM and 64QAM; Step 3.3: Based on the optical signal-to-noise ratio estimate and modulation format identification results, query the corresponding unfolded layer number from the preset layer number mapping table.

9. The intelligent compensation method for nonlinear impairments in coherent optical communication according to claim 8, characterized in that, The parameter optimization feedback described in step 4 is performed during the training phase, and the processing procedure is as follows: Step 4.1: Obtain the symbol position in the nonlinear compensation signal corresponding to the transmitted reference symbol, and calculate the mean square error between the nonlinear compensation signal and the transmitted reference symbol. ； in, This is the mean square error value; The number of training symbols; This is the nonlinear compensation signal for the i-th training position; Send the reference symbol for the i-th symbol; Step 4.2: Calculate the regularization term to constrain the deviation of network parameters from the initial values ​​of the physical model. ； in, For regularization terms; and These are the regularization weight coefficients; Step 4.3: The total loss function is a weighted sum of the mean squared error term and the regularization term. ； Step 4.4: Calculate the gradients with respect to the frequency domain filter coefficients and nonlinear phase rotation coefficients based on the total loss function, and directly calculate the gradients using the automatic differentiation framework; The gradient calculation expression for the frequency domain filter coefficients is as follows: ； in, express The conjugate of complex numbers; The expression for calculating the gradient of the nonlinear phase rotation coefficient is as follows: ； in, This indicates taking the real part of a complex number; Step 4.5: Update the network parameters based on the calculated gradient and the preset learning rate. The Adam optimization algorithm is used for parameter updates, and the cosine annealing strategy is used to dynamically adjust the learning rate. ； in: Let be the learning rate for the nth training cycle; The maximum learning rate; Minimum learning rate; This represents the total number of training cycles; Step 4.6, the update formula for the frequency domain filter coefficients is: ； The update formula for the nonlinear phase rotation coefficient is: ； Step 4.7: Repeat steps 4.1 to 4.6 of the training process until the convergence condition is met.

10. A coherent optical communication nonlinear impairment intelligent compensation system, used to implement the method according to any one of claims 1 to 9, characterized in that, include: The signal receiving preprocessing module includes a clock recovery unit, a carrier recovery unit, and a linear equalization unit. It is used to acquire the electrical domain signal output by the coherent receiver, perform clock recovery, carrier phase estimation, and linear equalization on the electrical domain signal, and generate a linearly equalized signal, which is then output to the physical embedded unfolded network module and the adaptive depth control module. Physically embedded unfolded network module: contains K cascaded compensation units, each of which contains a frequency domain compensation layer and a nonlinear activation layer; It is used to receive the linearly equalized signal, and performs nonlinear compensation processing on the signal through a multi-layer cascaded frequency domain compensation layer and nonlinear activation layer to output a nonlinear compensation signal. The output is connected to the input of the parameter optimization feedback module and also serves as the final output of the system. Adaptive depth control module: includes signal-to-noise ratio estimation unit, modulation format recognition unit, and layer number decision unit; It is used to dynamically determine the number of unfolded layers of the physically embedded unfolded network module based on the estimated optical signal-to-noise ratio of the received signal and the modulation format identification result; the output end is connected to the control end of the physically embedded unfolded network module to transmit the unfolded layer decision result; The parameter optimization feedback module includes a loss calculation unit and a gradient backpropagation unit. It is used to calculate the mean square error between the nonlinear compensation signal and the transmitted reference symbol, and update the frequency domain filter coefficients and nonlinear phase rotation coefficients based on the mean square error using the gradient backpropagation algorithm. The output is connected to the parameter memory of each layer of the physically embedded unfolded network module to transmit the updated network parameters.

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