Non-linear equalization compensation and multi-rate shaping factor identification method, system and apparatus

Abstract

The application discloses a nonlinear equalization compensation and multi-rate shaping factor identification method, system and device, relates to the technical field of optical fiber communication, and comprises the following steps: acquiring a received signal; acquiring an initial clustering centroid; calculating the Euclidean distance between the received signal and the initial clustering centroid; calculating a decision coefficient and a membership matrix; performing decision weighting clustering on the received signal again based on the membership matrix to obtain an equalization compensated signal; performing statistical probability calculation on each cluster of the equalization compensated signal to obtain the probability distribution of each cluster of the current signal; performing correlation processing on the probability distribution of each cluster of the current signal and standard probability characteristics under a plurality of shaping rates to obtain a certain shaping signal probability distribution; and selecting the shaping signal probability distribution with the largest correlation, namely the current signal shaping factor. The method can accurately obtain the current shaping factor, can provide a reliable, stable and flexible communication system, and has great potential and application prospect in the field of optical fiber communication.

Description

Technical Field

[0001] This invention relates to the field of optical fiber communication technology, and in particular to a method, system and apparatus for nonlinear equalization compensation and multi-rate shaping factor identification. Background Technology

[0002] To cope with the ever-increasing broadband traffic, applying high-order quadrature amplitude modulation (QAM) formats in optical communication systems can be a feasible solution to improve spectral efficiency and data rates without occupying additional spectrum. However, higher-level modulation formats require higher optical signal-to-noise ratios (OSNR), which limits transmission distance. Constellation shaping, as a method to improve achievable data rates and narrow the gap with Shannon capacity, has attracted widespread attention in the research community. Constellation shapes can be designed with constellation and symbol probabilities for different transmission system conditions, effectively optimizing OSNR sensitivity gain, increasing transmission distance, and providing flexible information rates. Probabilistic shaping balances the interaction between amplifier noise and fiber nonlinearity, improving transmission distance. It has also been demonstrated that constellation shaping, in addition to providing flexible information rates, can effectively generate OSNR gain and can be used for flexible rate adjustment.

[0003] The performance of high-speed, long-distance coherent optical communication systems is significantly degraded due to nonlinearities caused by equipment and transmission links. Therefore, suppressing system nonlinearity is considered a key technology for improving the capacity and performance of optical communication systems. Further research into advanced DSP algorithms for system nonlinearity compensation is of great significance. Many DSP algorithms have been proposed to compensate for nonlinearity, among which machine learning algorithms offer relatively better flexibility and adaptability because they do not require parameters of the fiber optic transmission link.

[0004] The combination of probabilistic shaping high-order modulation formats and machine learning-based clustering algorithms is widely considered to effectively improve long-distance transmission, increase transmission capacity, and enable flexible multi-rate transmission. However, an optimal decision compensation scheme is still lacking in the absence of prior information. To more accurately locate the optimal decision point and achieve multi-rate adaptive transmission, this invention studies a priori-free probabilistic equalization technique based on decision-weighted clustering, which can achieve multi-rate nonlinear compensation without requiring known prior shaping factors. Summary of the Invention

[0005] The purpose of this invention is to provide a nonlinear equalization compensation and multi-rate shaping factor identification method and system. By performing decision estimation on the signal, and then performing decision-weighted clustering, the nonlinear damage of the signal is compensated. Statistical probability features are extracted from the compensated signal and correlated with multiple standard probabilities to obtain the shaping factor of the current signal.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] In a first aspect, the present invention provides a method for nonlinear equilibrium compensation and multi-rate shaping factor identification, the method comprising:

[0008] Acquire received signals;

[0009] Obtain the initial cluster centroids;

[0010] Calculate the Euclidean distance between the received signal and the initial cluster centroid;

[0011] Decision coefficients are calculated based on the Euclidean distance.

[0012] Calculate the membership matrix based on the decision coefficients;

[0013] Based on the membership matrix, the received signal is re-weighted and clustered to obtain a balanced and compensated signal.

[0014] Statistical probability calculations are performed on each cluster of the signal after equalization compensation to obtain the probability distribution of each cluster of the current signal.

[0015] The probability distribution of each cluster of the current signal is correlated with the standard probability characteristics under multiple shaping rates to obtain the probability distribution of a certain shaped signal.

[0016] Select the probability distribution of the shaped signal with the highest correlation, which is the current signal shaping factor.

[0017] Optionally, the received signal is a QAM signal that has undergone orthogonal balance, dispersion compensation, clock recovery, channel equalization, and frequency offset estimation.

[0018] Optionally, the method further includes the following step between "acquiring the received signal" and "acquiring the initial cluster centroid":

[0019] The received signal is scaled to match the amplitude of the transmitting signal.

[0020] Optionally, the Euclidean distance between the received signal and the initial cluster centroid is calculated using the following formula:

[0021]

[0022] Among them, S i (i∈[1,n]) represents the received signal, n is the total number of signals, and C j (j∈[1,c]) is the initial cluster centroid, and c is the number of points in the standard signal constellation.

[0023] Optionally, the decision coefficients are calculated based on the Euclidean distance using the following formula:

[0024]

[0025] Where, d ij d is the Euclidean distance between the received signal and the initial cluster centroid. ik Let m be the Euclidean distance from the i-th class to the k-th centroid, m be the decision index, c be the number of standard signal constellation points, and k be the current centroid ordinal number.

[0026] The membership matrix is ​​expressed as follows:

[0027] U = μ ij

[0028] Where, μ ij , where is the decision coefficient.

[0029] Optionally, re-judging and weighting the received signal based on the membership matrix specifically includes the following steps:

[0030] Initial cluster centers were set for the clusters based on the distribution of constellation points of different amplitudes in the standard constellation diagram under the transmission modulation format.

[0031] Based on the membership matrix, the weighted centroid is recalculated to obtain a new cluster centroid.

[0032] Calculate the Euclidean distance between the new cluster centroid and the received signal;

[0033] New decision coefficients and a new decision matrix are determined based on the Euclidean distance between the new cluster centroid and the received signal.

[0034] Repeat the above steps until the change in cluster centers is less than the set threshold.

[0035] Optionally, the expression for the new cluster centroid is as follows:

[0036] Where X j Let X represent the j-th cluster class. i Denotes the i-th cluster class, |X j | indicates that it is assigned to X j The total number of data objects, u kj Indicates in X j The decision coefficient S of the k-th data cluster in the membership matrix k To belong to X i The kth received signal of the cluster.

[0037] Optionally, the correlation processing between the probability distribution of each cluster of the current signal and the standard probability characteristics under multiple shaping rates is specifically performed using the following formula:

[0038] ρ t =cov(P,Pt )

[0039] Where, ρ t This represents the correlation between the currently received signal and the standard signal; a larger value indicates a stronger correlation, while 1 indicates perfect correlation. P represents the probability distribution vector of each cluster of the received signal. t denoted as the standard probability distribution vector of each cluster under each integer factor, and cov represents the calculation of the correlation function.

[0040] Secondly, based on the above-described method of this invention, this invention further provides a nonlinear equilibrium compensation and multi-rate shaping factor recognition system, the system comprising:

[0041] A signal acquisition module is used to acquire received signals;

[0042] The initial cluster centroid acquisition module is used to obtain the initial cluster centroids;

[0043] The Euclidean distance calculation module is used to calculate the Euclidean distance between the received signal and the initial cluster centroid.

[0044] The decision coefficient calculation module is used to calculate the decision coefficients based on the Euclidean distance;

[0045] The membership matrix calculation module is used to calculate the membership matrix based on the decision coefficients.

[0046] The equalization compensation module is used to re-decision weighted cluster the received signal based on the membership matrix to obtain the equalized compensated signal.

[0047] The statistical probability calculation module is used to perform statistical probability calculations on each cluster of the signal after equalization compensation to obtain the probability distribution of each cluster of the current signal.

[0048] The correlation processing module is used to perform correlation processing on the probability distribution of each cluster of the current signal with the standard probability features under multiple shaping rates to obtain a certain shaped signal probability distribution.

[0049] The shaping factor determination module is used to select the probability distribution of the most correlated shaped signal, i.e., the shaping factor of the current signal.

[0050] Thirdly, the present invention also provides a nonlinear equilibrium compensation and multi-rate shaping factor identification device, the device comprising:

[0051] IQ quadrature module: The IQ quadrature module is connected to the analog-to-digital converter of the received signal. It is used to address the quadrature imbalance caused by the receiving device, ensure the orthogonality of the I and Q channels, and guarantee system performance.

[0052] Clock recovery module: The clock recovery module is connected to the IQ quadrature module and is used to eliminate the influence of chromatic dispersion and polarization mode dispersion introduced during optical fiber transmission on clock information;

[0053] Dispersion compensation module: The dispersion compensation module is connected to the clock recovery module and is used to perform dispersion compensation on the I and Q signals of the X and Y polarization states that are subject to dispersion interference in the channel;

[0054] Channel equalization module: The channel equalization module is connected to the dispersion compensation module and is used to eliminate the influence of polarization mode dispersion on the signal during optical fiber transmission;

[0055] Carrier phase recovery module: The carrier phase recovery module is connected to the channel equalization module and is used to remove frequency offset interference and laser phase noise.

[0056] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0057] This invention proposes a nonlinear equilibrium compensation and multi-rate shaping factor identification method and system based on decision coefficient weighted clustering. First, the Euclidean distance between the signal and the standard constellation is obtained, thus yielding the decision coefficients and membership matrix. Then, decision weighted clustering is performed on the signal. Finally, statistical probability and correlation are combined with the compensated signal to achieve shaping factor identification of the shaped signal, eliminating the influence of frequency offset and phase noise, and accurately obtaining the current shaping factor. This provides a reliable, stable, and flexible communication system with great potential and application prospects in the field of optical fiber communication. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 Flowchart of the nonlinear equilibrium compensation and multi-rate shaping factor identification method provided by the present invention;

[0060] Figure 2 A block diagram of a digital signal processing system for a nonlinear equilibrium compensation and multi-rate shaping factor identification method based on decision coefficient weighted clustering provided by this invention;

[0061] Figure 3The embodiment provided by the present invention shows the bit error rate as a function of OSNR after the PS-64QAM signal with v=0.05 has been transmitted for 375km. The nonlinear equalization compensation algorithm based on decision coefficient weighted clustering, the nonlinear equalization compensation algorithm based on kmeans clustering, and the algorithm without compensation are respectively shown.

[0062] Figure 4 The curves showing the change in bit error rate with power after 375km transmission of a PS-64QAM signal with v=0.05 in the embodiments provided by the present invention respectively demonstrate the nonlinear equalization compensation algorithm based on decision coefficient weighted clustering, the nonlinear equalization compensation algorithm based on kmeans clustering, and the algorithm without compensation.

[0063] Figure 5 The implementation example provided by this invention shows the probability correlation curves between the currently received transmitted signal and the signal from the PS-64QAM standard transmitter under different OSNR values ​​after the signal has been transmitted for 375km. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] The purpose of this invention is to provide a nonlinear equalization compensation and multi-rate shaping factor identification method and system. By performing decision estimation on the signal, and then performing decision-weighted clustering, the nonlinear damage of the signal is compensated. Statistical probability features are extracted from the compensated signal and correlated with multiple standard probabilities to obtain the shaping factor of the current signal.

[0066] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] Example 1

[0068] This embodiment uses a PS-64QAM signal with v=0.05 as an example to illustrate the specific implementation of the present invention.

[0069] Coherent optical communication systems can simultaneously achieve high spectral efficiency and long-distance transmission. However, the performance of high-speed, long-distance coherent optical communication systems is significantly degraded due to nonlinearities caused by equipment and transmission links. Furthermore, due to the nature of digital signal processing at the receiver, they are often unsuitable for shaped signals, and prior knowledge of the shaping factor is required when processing signals with different shaping rates. Therefore, system nonlinearity suppression and multi-shaping-rate shaping factor identification are considered key technologies for improving the capacity performance and flexible communication capabilities of optical communication systems.

[0070] This invention mainly designs the digital signal processing module of a coherent optical communication receiver. It focuses on using a decision-weighted clustering method based on fuzzy theory and the principle of statistical feature correlation to optimize the decision threshold, obtain the current signal shaping factor, realize nonlinear compensation of the signal and multi-rate shaping factor identification, eliminate the influence of frequency offset and phase noise, and realize flexible communication.

[0071] Figure 1 The flowchart of the nonlinear equilibrium compensation and multi-rate shaping factor identification method provided by the present invention is as follows: Figure 1 As shown, the method in this invention includes:

[0072] Step 101: Acquire the received signal.

[0073] The received signal is a PS-64QAM signal with v=0.05 after undergoing orthogonal balance, dispersion compensation, clock recovery, channel equalization, and frequency offset estimation.

[0074] Then the PS-64QAM signal is scaled up to standard. in

[0075] Step 102: Obtain the initial cluster centroids.

[0076] Specifically, the standard 64QAM constellation points are used as the initial cluster centroid C.

[0077] Step 103: Calculate the Euclidean distance between the received signal and the initial cluster centroid.

[0078] The specific calculation formula is as follows:

[0079]

[0080] Step 104: Calculate the decision coefficients based on the Euclidean distance.

[0081] Step 105: Calculate the membership matrix based on the decision coefficients.

[0082] Specifically, through decision coefficients The membership matrix U is calculated, U = μij .

[0083] Step 106: Based on the membership matrix, re-perform decision-weighted clustering of the received signal to obtain the balanced and compensated signal.

[0084] Using the membership matrix U obtained from PS-64QAM, the weighted centroids are recalculated to obtain new cluster centroids. Where X j Let |X| represent the j-th cluster class. j | indicates that it is assigned to X j The total number of data signals, u kj Indicates in X j The decision coefficients of the k-th data point in the cluster are represented in the membership matrix; the resulting new centroids and the signal are then used to recalculate the Euclidean distance. This yields the new membership matrix U' and decision coefficients μ. ij This process is repeated until the change in cluster centers is less than a set threshold. By optimizing the decision threshold, nonlinear compensation of the PS-64QAM signal is achieved.

[0085] Step 107: Perform statistical probability calculations on each cluster of the signal after equalization compensation to obtain the probability distribution of each cluster of the current signal.

[0086] Step 108: Perform correlation processing on the probability distribution of each cluster of the current signal and the standard probability characteristics under multiple shaping rates to obtain the probability distribution of a certain shaped signal.

[0087] Step 109: Select the probability distribution of the shaped signal with the highest correlation, i.e., the current signal shaping factor.

[0088] Statistical probability calculations are performed on each cluster of the equalized PS-64QAM signal. Obtain the probability distribution P of each cluster of the current signal; use the current signal probability P to perform correlation calculations with the PS-64QAM signal at v = 0.01 / v = 0.03 / v = 0.05 respectively: ρ t =cov(P,P t ), where P t This represents the known probability distribution of a certain shaped signal; the shaped probability distribution with the highest correlation, max(ρ), is taken, which is the current model's shaping factor v = 0.05.

[0089] Example 2

[0090] In addition, this invention also provides a nonlinear equilibrium compensation and multi-rate shaping factor identification device for decision coefficient weighted clustering, such as... Figure 2 As shown. The digital signal processing (DSP) module includes:

[0091] IQ quadrature module: The IQ quadrature module is connected to the analog-to-digital converter of the received signal. It is used to address the quadrature imbalance caused by the receiving device, ensure the orthogonality of the I and Q channels, and guarantee system performance.

[0092] Clock recovery module: The clock recovery module is connected to the IQ quadrature module and is used to eliminate the influence of chromatic dispersion and polarization mode dispersion introduced during optical fiber transmission on clock information;

[0093] Dispersion compensation module: The dispersion compensation module is connected to the clock recovery module and is used to perform dispersion compensation on the I and Q signals of the X and Y polarization states that are subject to dispersion interference in the channel.

[0094] Channel equalization module: The channel equalization module is connected to the dispersion compensation module and is used to eliminate the influence of polarization mode dispersion on the signal during optical fiber transmission;

[0095] Carrier phase recovery module: The carrier phase recovery module is connected to the channel equalization module and is used to remove frequency offset interference and laser phase noise.

[0096] like Figure 2 As shown, after the DSP system signal is received by zero-difference coherent reception, the analog-to-digital converter outputs the signal to the IQ quadrature module for orthogonal balancing, and then inputs it to the clock recovery module to eliminate the influence of chromatic dispersion and polarization mode dispersion introduced during fiber transmission on the clock information. Next, a dispersion compensator compensates for the dispersion interference in the X and Y polarization states of the I and Q signals in the channel. The dispersion-compensated signal is connected to the channel equalizer to eliminate the effects of differential group delay and fiber Kerr effect received during fiber transmission. The channel-equalized signal is output to the carrier phase recovery module to remove interference caused by frequency offset and phase noise. A nonlinear compensation module eliminates interference caused by signal phase offset and laser phase noise, achieving signal compensation. Finally, a multi-rate shaping factor identification module identifies the shaping factor of the current transmitted signal.

[0097] See Figure 3 The figure shows the bit error rate as a function of power after transmitting a PS-64QAM signal with v=0.05 for 375km. It also shows the nonlinear equalization compensation algorithm based on decision coefficient weighted clustering (ber-the-proposed), the nonlinear equalization compensation algorithm based on kmeans clustering (ber-kmeans), and the algorithm without compensation (ber).

[0098] The bit error rate (BER) curves of PS-64QAM signals with v=0.05 at different optical signal-to-noise ratios (SNRs) after processing by a nonlinear equalization compensation algorithm based on decision coefficient weighted clustering and a nonlinear impairment compensation algorithm based on k-means clustering, and the BER curve without algorithm compensation are shown below. Figure 4As shown, compared with the nonlinear equalization compensation algorithm based on k-means clustering and the unprocessed signal bit error rate, the equalization compensation algorithm based on nonlinear constraints proposed in this invention has better nonlinear compensation effect and significant performance advantages.

[0099] The bit error rate (BER) curves of PS-64QAM signals with v=0.05 at different optical transmit powers after processing by a nonlinear equalization compensation algorithm based on decision coefficient weighted clustering and a nonlinear impairment compensation algorithm based on k-means clustering, and the BER curve of the uncompensated signal are shown below. Figure 4 As shown, compared with the nonlinear equilibrium compensation algorithm based on k-means clustering and the signal to be compensated, the equilibrium compensation algorithm based on nonlinear constraints proposed in this invention has a better nonlinear compensation effect and a significant performance advantage.

[0100] The PS-64QAM signal with v=0.05 under different optical signal-to-noise ratios is correlated with the probability distribution of standard PS-64QAM with v=0.01 / v=0.03 / v=0.05 by a multi-rate shaping factor identification algorithm, which can accurately obtain the shaping factor of the current transmitted signal.

[0101] See Figure 5 After the signal has traveled 375km, the probability correlation curves between the currently received transmitted signal and the signal from the PS-64QAM standard transmitter under different OSNR values ​​are shown.

[0102] The horizontal axis represents OSNR, and the vertical axis represents correlation. The theoretical correlation is the ideal case (the theoretical correlation is 1, which means perfect correlation). The maximum correlation is the value that is closest to the theoretical correlation.

[0103] Example 3

[0104] To implement the method corresponding to Embodiment 1 above and achieve the corresponding functions and technical effects, a nonlinear equilibrium compensation and multi-rate shaping factor recognition system is provided below, including:

[0105] A signal acquisition module is used to acquire received signals;

[0106] The initial cluster centroid acquisition module is used to obtain the initial cluster centroids;

[0107] The Euclidean distance calculation module is used to calculate the Euclidean distance between the received signal and the initial cluster centroid.

[0108] The decision coefficient calculation module is used to calculate the decision coefficients based on the Euclidean distance;

[0109] The membership matrix calculation module is used to calculate the membership matrix based on the decision coefficients.

[0110] The equalization compensation module is used to re-decision weighted cluster the received signal based on the membership matrix to obtain the equalized compensated signal.

[0111] The statistical probability calculation module is used to perform statistical probability calculations on each cluster of the signal after equalization compensation to obtain the probability distribution of each cluster of the current signal.

[0112] The correlation processing module is used to perform correlation processing on the probability distribution of each cluster of the current signal with the standard probability features under multiple shaping rates to obtain a certain shaped signal probability distribution.

[0113] The shaping factor determination module is used to select the probability distribution of the most correlated shaped signal, i.e., the shaping factor of the current signal.

[0114] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0115] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for nonlinear equilibrium compensation and multi-rate shaping factor identification, characterized in that, The method includes: Acquire the received signal; the received signal is a QAM signal that has undergone orthogonal balance, dispersion compensation, clock recovery, channel equalization and frequency offset estimation; Obtain the initial cluster centroids; Calculate the Euclidean distance between the received signal and the initial cluster centroid; Decision coefficients are calculated based on the Euclidean distance. Calculate the membership matrix based on the decision coefficients; Based on the membership matrix, the received signal is re-weighted and clustered to obtain a balanced and compensated signal. Statistical probability calculations are performed on each cluster of the signal after equalization compensation to obtain the probability distribution of each cluster of the current signal. The probability distribution of each cluster of the current signal is correlated with the standard probability characteristics under multiple shaping rates to obtain the probability distribution of a certain shaped signal. Select the probability distribution of the most correlated signal, i.e., the current signal shaping factor; The Euclidean distance between the received signal and the initial cluster centroid is calculated using the following formula: ； in, In order to receive signals, The total number of signals, As the initial cluster centroid, This refers to the number of points in the standard signal constellation. The decision coefficients are calculated based on the Euclidean distance using the following formula: ； in, The Euclidean distance between the received signal and the initial cluster centroid. For the first Class to the k Euclidean distance between the centroids As a decision index, For standard signal constellation points, The current centroid ordinal number; The membership matrix is ​​expressed as follows: ； in, , where is the decision coefficient.

2. The nonlinear equilibrium compensation and multi-rate shaping factor identification method according to claim 1, characterized in that, The re-decision weighted clustering of the received signal based on the membership matrix specifically includes the following steps: Initial cluster centroids are set for the clusters based on the distribution of constellation points of different amplitudes in the standard constellation diagram under the transmission modulation format. Based on the membership matrix, the weighted centroid is recalculated to obtain a new cluster centroid. Calculate the Euclidean distance between the new cluster centroid and the received signal; New decision coefficients and a new membership matrix are determined based on the Euclidean distance between the new cluster centroid and the received signal. Repeat the above steps until the change in cluster centroids is less than the set threshold.

3. The nonlinear equilibrium compensation and multi-rate shaping factor identification method according to claim 1, characterized in that, The expression for the new cluster centroid is as follows: ,in Indicates the first j Each cluster class X i Indicates the first i Each cluster class Indicates assignment to The total number of data objects, Indicates in No. 1 in the cluster k The decision coefficients in the membership matrix corresponding to each data cluster S k For belonging X i The kth received signal of the cluster.

4. The nonlinear equilibrium compensation and multi-rate shaping factor identification method according to claim 1, characterized in that, The correlation processing between the probability distribution of each cluster of the current signal and the standard probability characteristics under multiple shaping rates is specifically performed using the following formula: in, ρ t This indicates the degree of correlation between the currently received signal and the standard signal. A higher value indicates a stronger correlation, while a value of 1 indicates perfect correlation. P This represents the probability distribution vector of each cluster of the received signal. P t This represents the standard probability distribution vector of each cluster under each integer factor. cov This indicates the calculation of the relevant function.

5. A nonlinear equilibrium compensation and multi-rate shaping factor identification system, characterized in that, The system includes: A received signal acquisition module is used to acquire a received signal; the received signal is a QAM signal that has undergone orthogonal balance, dispersion compensation, clock recovery, channel equalization and frequency offset estimation. The initial cluster centroid acquisition module is used to obtain the initial cluster centroids; The Euclidean distance calculation module is used to calculate the Euclidean distance between the received signal and the initial cluster centroid. The decision coefficient calculation module is used to calculate the decision coefficients based on the Euclidean distance. The membership matrix calculation module is used to calculate the membership matrix based on the decision coefficients. The equalization compensation module is used to re-decision weighted cluster the received signal based on the membership matrix to obtain the equalized compensated signal. The statistical probability calculation module is used to perform statistical probability calculations on each cluster of the signal after equalization compensation to obtain the probability distribution of each cluster of the current signal. The correlation processing module is used to perform correlation processing on the probability distribution of each cluster of the current signal with the standard probability features under multiple shaping rates to obtain a certain shaped signal probability distribution. The shaping factor determination module is used to select the probability distribution of the most correlated shaping signal, i.e., the shaping factor of the current signal; The Euclidean distance between the received signal and the initial cluster centroid is calculated using the following formula: ； in, In order to receive signals, The total number of signals, As the initial cluster centroid, This refers to the number of points in the standard signal constellation. The decision coefficients are calculated based on the Euclidean distance using the following formula: ； in, The Euclidean distance between the received signal and the initial cluster centroid. For the first Class to the k Euclidean distance between the centroids As a decision index, For standard signal constellation points, The current centroid ordinal number; The membership matrix is ​​expressed as follows: ； in, , where is the decision coefficient.

6. A nonlinear equilibrium compensation and multi-rate shaping factor identification device, characterized in that, The nonlinear equalization compensation and multi-rate shaping factor identification device is applied to the nonlinear equalization compensation and multi-rate shaping factor identification method as described in any one of claims 1-4, wherein the nonlinear equalization compensation and multi-rate shaping factor identification device comprises: IQ quadrature module: The IQ quadrature module is connected to the analog-to-digital converter of the received signal. It is used to address the quadrature imbalance caused by the receiving device, ensure the orthogonality of the I and Q channels, and guarantee system performance. Clock recovery module: The clock recovery module is connected to the IQ quadrature module and is used to eliminate the influence of chromatic dispersion and polarization mode dispersion introduced during optical fiber transmission on clock information; Dispersion compensation module: The dispersion compensation module is connected to the clock recovery module and is used to perform dispersion compensation on the I and Q signals of the X and Y polarization states that are subject to dispersion interference in the channel; Channel equalization module: The channel equalization module is connected to the dispersion compensation module and is used to eliminate the influence of polarization mode dispersion on the signal during optical fiber transmission; Carrier phase recovery module: The carrier phase recovery module is connected to the channel equalization module and is used to remove frequency offset interference and laser phase noise.

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