CN111800194B - Nonlinear compensation method for transmission probability distribution of few-mode multi-core OAM fiber - Google Patents

Nonlinear compensation method for transmission probability distribution of few-mode multi-core OAM fiber Download PDF

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CN111800194B
CN111800194B CN202010576534.4A CN202010576534A CN111800194B CN 111800194 B CN111800194 B CN 111800194B CN 202010576534 A CN202010576534 A CN 202010576534A CN 111800194 B CN111800194 B CN 111800194B
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高然
忻向军
周思彤
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/25—Arrangements specific to fibre transmission
    • H04B10/2507—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion
    • H04B10/2543—Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion due to fibre non-linearities, e.g. Kerr effect
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    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
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    • H04L27/3461—Modifications of the signal space to allow the transmission of additional information in order to transmit a subchannel
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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

Nonlinear compensation method for few-mode multi-core OAM optical fiber transmission probability distribution
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,
Figure GDA0003017130750000021
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,
Figure GDA0003017130750000022
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,
Figure GDA0003017130750000031
wherein
Figure GDA0003017130750000032
s is the standard deviation of the training data, in the distribution of minimum values
Figure GDA0003017130750000033
Distribution of minimum value
Figure GDA0003017130750000034
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.
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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
Figure GDA0003017130750000041
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
Figure GDA0003017130750000051
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.针对少模多芯OAM光纤传输概率分布的非线性补偿方法，其特征在于：包括如下步骤：1. the nonlinear compensation method for the transmission probability distribution of few-mode multi-core OAM fiber, is characterized in that: comprise the steps: 步骤一：准备训练数据Step 1: Prepare training data 在发送端发送训练数据，数据长度为M；数据经过处理后形成星座图，星座图中含有坐标规整排布的N个星座点；再经过OAM传输，由于传输过程中所受到的非线性损伤，使得星座图上的点旋转弥散；得到一个格式为N*2的矩阵[[x1,y1]；[x2,y2]；...；[xn,yn]]，此矩阵的数据为训练数据；根据星座图确定坐标点的分类为i类；由于已知N个坐标点的原始坐标位置，根据已知分类将弥散的星座图中的坐标点分成i组，每组的格式为[[x1,y1]；[x2,y2]；...；[xn,yn]]；Send training data at the sending end, and the data length is M; after the data is processed, a constellation diagram is formed, and the constellation diagram contains N constellation points with regular coordinates; Disperse the rotation of the points on the constellation diagram; get a matrix of the form N*2 [[x 1 ,y 1 ];[x 2 ,y 2 ];...;[x n ,y n ]], this matrix The data is training data; according to the constellation diagram, the classification of the coordinate points is determined as the i category; since the original coordinate positions of the N coordinate points are known, the coordinate points in the diffuse constellation diagram are divided into i groups according to the known classification, and the The format is [[x 1 ,y 1 ];[x 2 ,y 2 ];...;[x n ,y n ]]; N为星座点个数，由M计算得到，且具体关系由传输过程中的调制格式决定；N is the number of constellation points, calculated by M, and the specific relationship is determined by the modulation format in the transmission process; 步骤二：训练模型Step 2: Train the model 选定分类模型，根据步骤一的i种类别下的训练数据进行求解，得到选定模型所需的参数；把参数带入模型中，求出i个所示模型的分类器；Select the classification model, solve according to the training data under the i categories in step 1, and obtain the parameters required by the selected model; bring the parameters into the model, and obtain the classifiers of the i shown models; 步骤三：预测Step 3: Predict 对于未知分类的坐标点(x,y)求分类，将x,y带入i个分类器中，得到i个数值，即该点属于i个分类的概率，对比出概率最大的一个，则判定坐标点(x,y)属于该分类；根据得到的分类，将坐标点判决为二进制数据，能够提高判决的准确度，降低误码率，以此达到补偿非线性损伤的效果；To classify the coordinate points (x, y) of unknown classification, bring x and y into i classifiers to get i values, that is, the probability that the point belongs to i classification, and compare the one with the highest probability, then determine The coordinate point (x, y) belongs to this classification; according to the obtained classification, the coordinate point is judged as binary data, which can improve the accuracy of the judgment and reduce the bit error rate, so as to achieve the effect of compensating for nonlinear damage; 步骤二中所述的分类模型包括：The classification model described in step 2 includes: 1)若为高斯分布模型，根据高斯分布模型的概率密度公式，
Figure FDA0003017130740000011
得知公式所需参数为平均值μ和方差σ2，求出训练数据的平均值和方差，带入公式得到高斯分布分类模型；1) If it is a Gaussian distribution model, according to the probability density formula of the Gaussian distribution model,
Figure FDA0003017130740000011
Knowing that the parameters required by the formula are the mean value μ and the variance σ 2 , obtain the mean value and variance of the training data, and bring them into the formula to obtain a Gaussian distribution classification model; 2)若为t分布模型，根据t分布模型的概率密度公式，
Figure FDA0003017130740000012
其中Gam为伽马函数，得知公式所需参数为自由度n、平均值μ和方差σ2，求出训练数据的自由度、平均值和方差，带入公式得到t分布分类模型；2) If it is a t distribution model, according to the probability density formula of the t distribution model,
Figure FDA0003017130740000012
Among them, Gam is the gamma function. It is known that the required parameters of the formula are the degree of freedom n, the mean value μ and the variance σ 2 , and the degrees of freedom, mean value and variance of the training data are obtained, and the t-distribution classification model is obtained by bringing it into the formula; 3)若为极值分布模型，根据极值分布模型的概率密度公式，
Figure FDA0003017130740000013
其中
Figure FDA0003017130740000014
s为训练数据标准差，极小值分布中
Figure FDA0003017130740000015
极小值分布中
Figure FDA0003017130740000021
Figure FDA0003017130740000022
为训练数据均值，得知公式所需参数为平均值和标准差，求出训练数据的平均值和标准差，带入公式得到极值分布分类模型；3) If it is an extreme value distribution model, according to the probability density formula of the extreme value distribution model,
Figure FDA0003017130740000013
in
Figure FDA0003017130740000014
s is the standard deviation of the training data, in the minimum value distribution
Figure FDA0003017130740000015
in the minimum distribution
Figure FDA0003017130740000021
Figure FDA0003017130740000022
For the mean value of the training data, it is known that the parameters required by the formula are the mean value and the standard deviation, and the mean value and standard deviation of the training data are obtained, and the extreme value distribution classification model is obtained by bringing it into the formula; 4)若根据系统概率分布特点拟合的系统概率分布模型，用训练数据画出概率密度分布，判断要使用的概率密度分布模型，然后用fittype和fit函数拟合出概率密度函数，并求出相应参数，带入到概率密度函数中，得到分类模型。4) If the system probability distribution model is fitted according to the characteristics of the system probability distribution, use the training data to draw the probability density distribution, determine the probability density distribution model to be used, and then use the fittype and fit functions to fit the probability density function, and find out The corresponding parameters are brought into the probability density function to obtain the classification model.
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