CN111800194B - Nonlinear compensation method for few-mode multi-core OAM optical fiber transmission probability distribution - Google Patents
Nonlinear compensation method for few-mode multi-core OAM optical fiber transmission probability distribution Download PDFInfo
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Abstract
The invention relates to a nonlinear compensation method for few-mode multi-core OAM optical fiber transmission probability distribution, and belongs to the technical field of optical fiber communication. The invention discloses a nonlinear compensation method for few-mode multi-core OAM optical fiber transmission probability distribution. Relating to the theory and principle of optical fiber communication. The method aims at the probability distribution characteristics of OAM optical fiber transmission, carries out nonlinear damage compensation on signals, greatly reduces the calculation complexity and the calculation complexity compared with the traditional nonlinear compensation algorithm, and enables the calculation complexity to be close to the requirement of an actual system, thereby realizing the nonlinear compensation method with low complexity and high precision.
Description
Technical Field
The invention relates to a nonlinear compensation method for few-mode multi-core OAM optical fiber transmission probability distribution, and belongs to the technical field of optical fiber communication.
Background
Since high rolls proposed optical fiber as a transmission medium in 1966, optical fiber communications have rapidly developed. Optical fibers have become the main transmission mode in communications, especially in long-distance transmission, due to their wide transmission band, high interference immunity and reduced signal attenuation, which are far superior to those of cables and microwave communications. Long-haul fiber transmission typically relies on high power lasers to transmit optical pulses over long distances to overcome attenuation, while at sufficiently high optical intensities, nonlinear refraction (kerr effect) occurs in the core, making nonlinear damage a critical issue in optical networks. Nonlinear impairments can be classified into two broad categories, the first category being deterministic nonlinear impairments that depend only on dispersion and nonlinear coefficients, such as self-phase modulation (SPM), intra-channel cross-phase modulation (IXPM) and four-wave mixing (IFWM), inter-channel cross-phase modulation (XPM) and four-wave mixing (FWM), etc.; the second category is random nonlinear impairments that rely on the interaction between nonlinearity, Amplified Spontaneous Emission (ASE) and dispersion.
A commonly used method of nonlinear compensation is Digital Back Propagation (DBP), which employs a virtual fiber of negative dispersion, loss, and nonlinear coefficient in the digital domain. DBP works well in compensating deterministic nonlinear impairments, but the DBP algorithm cannot compensate random nonlinear impairments. Therefore, researchers have introduced machine learning algorithms into the field of compensating for non-linearities, thereby compensating for deterministic and stochastic non-linear impairments, such as Support Vector Machines (SVMs), Support Vector Regression (SVR), neural networks, Parzen Window (PW) classifiers, KNNs, expectation-maximization (EM) algorithms, and k-means algorithms. Although these methods have good results, the algorithms are very complex and computationally expensive. Due to the explosive growth of various service requirements in recent years, the channel capacity and the information amount required by optical fiber transmission are larger and larger, and the nonlinear compensation method with high complexity and large calculation amount is more and more difficult to meet the transmission requirement, especially for OAM optical fiber transmission introducing Orbital Angular Momentum (OAM) into an optical fiber.
As a hot spot in the field of communications today, the field of Orbital Angular Momentum (OAM) has developed rapidly since OAM-bearing optical beams were proposed in 1992. Due to the infinite dimensional characteristic of OAM in Hilbert space, OAM is regarded as an important available resource in a communication system, and therefore has a wide application prospect. For a long time, however, OAM research in communications has been limited to transmissions in free space. OAM is considered unsuitable for transmission in an optical fiber because of the limitations of the conventional optical fiber, and until an optical fiber structure having a vortex is proposed, research into transmission of OAM in an optical fiber has gradually emerged. The optical fiber with the vortex structure is continuously researched and updated to become the existing ring core optical fiber, so that OAM modes capable of being transmitted are gradually increased. However, when the system capacity is increased, the influence of the nonlinear effect on the system is also increased, so that the nonlinear damage gradually becomes a main factor influencing the system performance, and therefore, it becomes important to realize a nonlinear compensation method with good compensation effect and low complexity.
Disclosure of Invention
The invention aims to provide a nonlinear compensation method aiming at the probability distribution of few-mode multi-core OAM optical fiber transmission, which can greatly reduce the calculation complexity of nonlinear compensation and correctly classify constellation points in a constellation diagram, thereby realizing the nonlinear compensation with low complexity and high precision.
The purpose of the invention is realized by the following technical scheme:
the nonlinear compensation method for the transmission probability distribution of the few-mode multi-core OAM optical fiber comprises the following steps:
the method comprises the following steps: preparing training data
Transmitting training data at the transmitting endA length of M; processing the data to form a constellation diagram, wherein the constellation diagram comprises N constellation points with regularly arranged coordinates; then, OAM transmission is carried out, and points on the constellation diagram are dispersed in a rotating mode due to nonlinear damage in the transmission process; obtaining a matrix with format of N x 2 [ [ x ]1,y1]；[x2,y2]；...；[xn,yn]]The data of this matrix is training data. And determining the classification of the coordinate points into i types according to the constellation diagram. Because the original coordinate positions of N coordinate points are known, the coordinate points in the dispersed constellation diagram are divided into i groups according to the known classification, and the format of each group is [ [ x ]1,y1]；[x2,y2]；...； [xn,yn]]。
N is the number of constellation points and is obtained by M calculation, and the specific relation is determined by the modulation format in the transmission process;
step two: training model
And (4) selecting a classification model, and solving according to the training data under the i types of the first step to obtain parameters required by the selected model. The parameters are substituted into the model to find i classifiers for the model shown.
Step three: prediction
And (3) solving the classification of the coordinate points (x, y) of unknown classification, bringing the x and y into i classifiers to obtain i numerical values, namely the probability that the point belongs to the i classifications, and comparing the probability with the maximum probability to judge that the coordinate points (x, y) belong to the classification. According to the obtained classification, the coordinate points are judged as binary data, so that the judgment accuracy can be improved, and the error rate can be reduced, thereby achieving the effect of compensating nonlinear damage.
The classifier model in the second step comprises:
1) if the model is a Gaussian distribution model, according to the probability density formula of the Gaussian distribution model,
the parameters required for the formula are the mean μ and the variance σ2And solving the average value and the variance of the training data, and substituting the average value and the variance into a formula to obtain a Gaussian distribution classifier model.
2) If the model is a t distribution model, according to the probability density formula of the t distribution model,
where Gam is a gamma function, the parameters required for the formula are n, the mean μ, and the variance σ2And solving the freedom degree, the average value and the variance of the training data, and substituting into a formula to obtain a t distribution classifier model.
3) If the extreme value distribution model is the extreme value distribution model, according to the probability density formula of the extreme value distribution model,
wherein
s is the standard deviation of the training data, in the distribution of minimum values
Distribution of minimum value
And (3) obtaining the mean value and standard deviation of the training data by knowing parameters required by a formula, and substituting the mean value and standard deviation of the training data into the formula to obtain an extreme value distribution classifier model.
4) And if the system probability distribution model is fitted according to the characteristics of the system probability distribution, drawing probability density distribution by using training data, judging the probability density distribution model to be used, fitting a probability density function by using fit type and fit functions, solving corresponding parameters, and bringing the parameters into the probability density function to obtain the classifier model.
Advantageous effects
The invention discloses a nonlinear compensation method for few-mode multi-core OAM optical fiber transmission probability distribution. Relating to the theory and principle of optical fiber communication. The method aims at the probability distribution characteristics of OAM optical fiber transmission, carries out nonlinear damage compensation on signals, greatly reduces the calculation complexity and the calculation complexity compared with the traditional nonlinear compensation algorithm, and enables the calculation complexity to be close to the requirement of an actual system, thereby realizing the nonlinear compensation method with low complexity and high precision.
Drawings
Fig. 1 is a flow chart of a nonlinear compensation method for few-mode multi-core OAM fiber transmission probability distribution according to the present invention;
fig. 2 is a schematic diagram of an OAM optical fiber transmission system as described in the embodiment;
fig. 3 is a constellation diagram of training data in the embodiment, where fig. 3(a) is a data constellation diagram before transmission, and fig. 3(b) is a constellation diagram of received nonlinear impairments after transmission;
FIG. 4 is a binary probability density distribution diagram of training data after transmission in example 2;
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1
As shown in fig. 1, the nonlinear compensation method for the transmission probability distribution of the few-mode multi-core OAM fiber includes the following steps:
the method comprises the following steps: preparing training data with the length of 64000 bits, sequentially processing the data by 16QAM, training sequence addition, DFT, complex conjugation, cyclic prefix, super Nyquist, PDM and ETDM to form a constellation diagram, wherein the constellation diagram contains 16000 constellation points with regularly arranged coordinates, as shown in fig. 3 (a); after passing through the OAM transmission system, due to the nonlinear damage suffered in the transmission process, the points on the constellation diagram are dispersed rotationally, as shown in fig. 3 (b); at this time, the coordinate points of the constellation points are a matrix of 16000 × 2 [ [ x ]1,y1]；[x2,y2]；...；[x16000,y16000]]The classification of the coordinate points into 16 classes is determined according to the constellation diagram. Since the original coordinate positions of 16000 coordinate points are known, the coordinate points in FIG. 2(b) can be divided into 16 groups according to known classifications, each group having the format [ [ x ] x [ ]1,y1]；[x2,y2]；...；[xn,yn]]。
The OAM fiber transmission system is shown in fig. 2, wherein the transmission line consists of a ring core fiber, an EDFA, an OSNR, a filter, a local oscillator light source, an oscilloscope, and a module for generating an OAM mode. Mode group characteristics within the fiber form a mode group from the same order of OAM modes. Each mode group has 4 sub-modes inside according to the OAM phase rotation direction and polarization state. (ii) a
Step two: selecting classification model as naive Gauss Bayes
Establishing a model through the mean value and the variance;
respectively calculating the average value mu of the x coordinates of the 16 groups of training data obtained in the step onexSum variance σxThat is, 16 groups of mean values μ were obtainedxSum variance σx(ii) a Respectively calculating the average value mu of the y coordinates of the 16 groups of training data obtained in the step oneySum variance σy(ii) a And (4) substituting all obtained average values and variances into the model to obtain 16 classified classifiers, namely p 1-p 16.
Step three: the detection data are 16384 coordinate points after transmission, the original data before transmission is known, the length of the original data is 65536 bits, coordinates (x, y) of the coordinate points are brought into a formula of a classifier model one by one, classification and judgment are judged, the classification and judgment are compared with the original data, 72 data judgment results in the obtained results are wrong, the error rate is one thousandth, the calculation time is far shorter than other nonlinear compensation algorithms, and the method is an effective compensation method with low complexity and high accuracy. When solving unknown classified data of the same transmission system, the coordinate point (x, y) is brought into 16 classifiers to obtain 16P values, namely the probability that the point belongs to the 16 classifications is compared to obtain the one with the maximum probability, and then the coordinate point (x, y) is judged to belong to the classification.
Example 2
The nonlinear compensation method for the transmission probability distribution of the few-mode multi-core OAM optical fiber comprises the following steps:
the method comprises the following steps: preparing training data with length of 64000 bits, sequentially processing the data by 16QAM, training sequence addition, DFT, complex conjugation, cyclic prefix, super-Nyquist and PDForming a constellation diagram after the M and ETDM processing, wherein the constellation diagram contains 16000 constellation points with regularly arranged coordinates, as shown in fig. 3 (a); after passing through the OAM transmission system, due to the nonlinear damage suffered in the transmission process, the points on the constellation diagram are dispersed rotationally, as shown in fig. 3 (b); at this time, the coordinate points of the constellation points are a matrix of 16000 × 2 [ [ x ]1,y1]；[x2,y2]；...；[x16000,y16000]]The classification of the coordinate points into 16 classes is determined according to the constellation diagram. Since the original coordinate positions of 16000 coordinate points are known, the coordinate points in FIG. 3(b) can be divided into 16 groups according to known classifications, each group having the format [ [ x ] x [ ]1,y1]；[x2,y2]；...；[xn,yn]]。
The OAM fiber transmission system is shown in fig. 2, wherein the transmission line consists of a ring core fiber, an EDFA, an OSNR, a filter, a local oscillator light source, an oscilloscope, and a module for generating an OAM mode. Mode group characteristics within the fiber form a mode group from the same order of OAM modes. Each mode group has 4 sub-modes inside according to the OAM phase rotation direction and polarization state. (ii) a
Step two: drawing binary probability density distribution of each group of coordinate points, wherein the probability distribution of the first group of data is shown in figure 4, and determining a classifier model as superposition of two Gaussian Bayesian distributions according to the characteristics of the probability density distribution, wherein the formula is
The mean value μ in 16 classes was found using the fittype and fit functionsxSum variance σxThen, the obtained parameters are substituted into the model to obtain 16 classified classifiers, i.e., p1 to p 16.
Step three: the detection data are 16384 coordinate points after transmission, the original data before transmission is known, the length of the original data is 65536 bits, coordinates (x, y) of the coordinate points are brought into a formula of a classifier model one by one, classification and judgment are judged, the classification and judgment are compared with the original data, 16 data judgment results in the obtained results are wrong, the error rate is two ten thousandth, the calculation time is far shorter than that of other nonlinear compensation algorithms, and the method is an effective compensation method with low complexity and high accuracy. When solving unknown classified data of the same transmission system, the coordinate point (x, y) is brought into 16 classifiers to obtain 16P values, namely the probability that the point belongs to the 16 classifications is compared to obtain the one with the maximum probability, and then the coordinate point (x, y) is judged to belong to the classification.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (1)
1. The nonlinear compensation method for the transmission probability distribution of the few-mode multi-core OAM optical fiber is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: preparing training data
Transmitting training data at a transmitting end, wherein the data length is M; processing the data to form a constellation diagram, wherein the constellation diagram comprises N constellation points with regularly arranged coordinates; then, OAM transmission is carried out, and points on the constellation diagram are dispersed in a rotating mode due to nonlinear damage in the transmission process; obtaining a matrix with format of N x 2 [ [ x ]1,y1]；[x2,y2]；...；[xn,yn]]The data of the matrix is training data; determining the classification of the coordinate points into i types according to the constellation diagram; because the original coordinate positions of N coordinate points are known, the coordinate points in the dispersed constellation diagram are divided into i groups according to the known classification, and the format of each group is [ [ x ]1,y1]；[x2,y2]；...；[xn,yn]]；
N is the number of constellation points and is obtained by M calculation, and the specific relation is determined by the modulation format in the transmission process;
step two: training model
Selecting a classification model, and solving according to the training data under the i types of the first step to obtain parameters required by the selected model; substituting the parameters into the model to obtain i classifiers of the model;
step three: prediction
Solving the classification of coordinate points (x, y) of unknown classification, bringing the x, y into i classifiers to obtain i numerical values, namely the probability that the point belongs to the i classifications, comparing out the one with the maximum probability, and judging that the coordinate points (x, y) belong to the classification; according to the obtained classification, the coordinate points are judged as binary data, so that the judgment accuracy can be improved, and the error rate is reduced, thereby achieving the effect of compensating nonlinear damage;
the classification model in the second step comprises:
1) if the model is a Gaussian distribution model, according to the probability density formula of the Gaussian distribution model,
the parameters required to know the formula are the mean value mu and the variance sigma2Calculating the average value and variance of the training data, and substituting the average value and variance into a formula to obtain a Gaussian distribution classification model;
2) if the model is a t distribution model, according to the probability density formula of the t distribution model,
where Gam is a gamma function, the parameters required for the formula are n, μ, the mean and σ2Solving the degree of freedom, the average value and the variance of the training data, and substituting the degrees of freedom, the average value and the variance into a formula to obtain a t distribution classification model;
3) if the extreme value distribution model is the extreme value distribution model, according to the probability density formula of the extreme value distribution model,
wherein
s is the standard deviation of the training data, in the distribution of minimum values
Distribution of minimum value
Obtaining the mean value and standard deviation of the training data by learning the parameters required by the formula as the mean value and standard deviation of the training data, and substituting the mean value and standard deviation into the formula to obtain an extreme value distribution classification model;
4) if the system probability distribution model is fitted according to the characteristics of the system probability distribution, the probability density distribution is drawn by using training data, the probability density distribution model to be used is judged, then the probability density function is fitted by using fit type and fit functions, corresponding parameters are solved and are brought into the probability density function, and the classification model is obtained.
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| CN113114422A (en) * | 2021-04-13 | 2021-07-13 | 兰州理工大学 | Deep learning detection-super-Nyquist rate atmospheric optical transmission method |
| CN113346957B (en) * | 2021-06-01 | 2022-08-05 | 北京理工大学 | Clustering nonlinear compensation method for OAM-QPSK transmission |
| CN113534454A (en) * | 2021-07-12 | 2021-10-22 | 北京邮电大学 | Multi-core optical fiber channel damage equalization method and system |
| CN114039670B (en) * | 2021-10-18 | 2023-09-12 | 北京理工大学 | Nonlinear damage compensation method for mode division multiplexing communication system |
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