WO2019169731A1 - 基于无数据辅助的knn算法的光纤非线性均衡方法 - Google Patents

基于无数据辅助的knn算法的光纤非线性均衡方法 Download PDF

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WO2019169731A1
WO2019169731A1 PCT/CN2018/086412 CN2018086412W WO2019169731A1 WO 2019169731 A1 WO2019169731 A1 WO 2019169731A1 CN 2018086412 W CN2018086412 W CN 2018086412W WO 2019169731 A1 WO2019169731 A1 WO 2019169731A1
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高明义
张俊峰
陈伟
沈纲祥
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苏州大学张家港工业技术研究院
苏州大学
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • 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
    • H04B10/60—Receivers
    • H04B10/61—Coherent receivers
    • H04B10/616—Details of the electronic signal processing in coherent optical receivers
    • H04B10/6161—Compensation of chromatic dispersion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • 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
    • H04B10/60—Receivers
    • H04B10/61—Coherent receivers
    • H04B10/616—Details of the electronic signal processing in coherent optical receivers
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03178—Arrangements involving sequence estimation techniques
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/38—Demodulator circuits; Receiver circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/38—Demodulator circuits; Receiver circuits
    • H04L27/3818—Demodulator circuits; Receiver circuits using coherent demodulation, i.e. using one or more nominally phase synchronous carriers

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  • the present invention relates to a fiber optic communication method, and in particular to a nonlinear equalization method for an optical fiber communication system.
  • M-PSK M-phase phase shift keying
  • M-QAM M-ary quadrature amplitude modulation
  • DSP coherent detection and digital signal processing
  • 16-QAM is commonly used in 200G channels and 64-QAM channels above 400G.
  • the nonlinear compensation method is to convert the optical signal into an electrical signal at the receiving end, and then perform digital signal processing (DSP) after sampling by the analog-to-digital converter.
  • DSP digital signal processing
  • a number of DSP algorithms have been developed to compensate for linear and nonlinear fiber transmission impairments to extend the transmission distance of higher order QAM signals.
  • Linear transmission impairments such as dispersion and polarization mode dispersion, can be effectively compensated in a limited digital domain based on an impulse equalization (FIR)-filter adaptive equalizer.
  • FIR impulse equalization
  • the Kerr effect in the fiber causes nonlinear waveform distortion to limit the maximum transmission distance of the high-order QAM signal. Therefore, nonlinearly balanced DSP technology is indispensable for mitigating fiber nonlinearity.
  • MAP maximum a posteriori probability
  • EM maximum expected value
  • MLE maximum likelihood estimation
  • DSP digital back propagation.
  • ANN artificial neural network
  • SVM support vector machine
  • k-means k-means
  • the proximity algorithm also known as the K nearest neighbor (KNN) algorithm, shown in Figure 2
  • KNN K nearest neighbor
  • the k value is too small, the classification result is susceptible to noise points; the k value is too large, and the neighbors may contain too many other categories of points.
  • the traditional KNN uses the voting method to make the decision, but the voting method does not consider the distance of the neighbors, which will affect the final classification performance.
  • the BER performance of the system is an object of the present invention to provide a fiber nonlinear equalization method based on a KNN algorithm without data assistance, which can reduce signal damage caused by fiber nonlinearity by reducing computational complexity and providing zero data redundancy to improve coherent optical communication.
  • the general idea of the present invention is to propose a low complexity blind density cluster tracking (DCT)-KNN algorithm, in which linear and nonlinear system noise has much greater influence on external constellation points than central constellation points.
  • the M-QAM signal therefore, uses the density function to extract less noisy data, label them in the first part of the training model, then use the marker data as a training sample, and apply the KNN algorithm to use more of the partial test model. Noise classifies data. Therefore, the method does not require additional training data, and can be called a non-data-assisted DCT-KNN algorithm, a self-training method, and extracts the label using the density function as the noise-free data of the training samples, which can completely solve the traditional KNN algorithm.
  • DCT blind density cluster tracking
  • the technical solution adopted by the present invention is: a fiber nonlinear equalization method based on the KNN algorithm without data assistance, comprising the following steps:
  • step (1) the distribution density parameter is obtained by:
  • the function range is the numerical range of the data points, x and y represent the real and imaginary parts of the signal data, i represents the point in the data set, i is an integer from 1 to N, N is the number of data points in the data set, and k is the number The point in the data set.
  • the preset threshold is a value corresponding to one third of a range of values of dd(k).
  • step (2) the demodulation is demodulated using an M-QAM signal.
  • step (6) the specific method of the weighted sum voting rule is:
  • the present invention has the following advantages over the prior art:
  • the invention adopts a new blind KNN algorithm, firstly uses a density function to provide a high quality original cluster as a training set, and realizes without adding additional data.
  • the system is zero-redundant and, due to the high quality of the training clusters, can significantly improve the classification performance of the system.
  • the blind centroid tracking KNN method proposed by the invention has the following advantages: (1) Due to the particularity of the KNN algorithm, no additional training parameters are needed, and no iterative calculation is needed, which can greatly reduce the computational complexity; The blind center-of-kind tracking KNN method can provide high-quality training sets, and the optimal K-value selection and weighted voting method can significantly improve the classification results; (3) It provides the possibility for higher-speed optical communication transmission in the future. .
  • the fiber nonlinear convergence method of the present invention can improve the system error rate (BER) in 16-QAM and 64-QAM coherent optical communication systems, and has low computation cost and zero data redundancy. Sexual characteristics, scalability and rapid convergence of system noise.
  • BER system error rate
  • FIG. 1 is a schematic view of an apparatus according to an embodiment of the present invention.
  • 3 is a flow chart of a blind DCT-KNN algorithm in an embodiment
  • FIG. 5 is a graph showing OSNRvsBER experimental results of a blind DCT-KNN algorithm after a 16QAM signal is transmitted through an 800KM fiber;
  • FIG. 6 is a graph showing experimental results of a fiber-optic optical power vsBER of a blind DCT-KNN algorithm after a 16QAM signal is transmitted through a 240KM fiber;
  • FIG. 7 is a graph showing OSNRvsBER experimental results of a blind DCT-KNN algorithm after 64QAM signals are transmitted through an 80KM fiber;
  • Figure 9 is a graph showing the K-value vsBER experimental results of the blind DCT-KNN algorithm and the KNN algorithm with the training series after the 64QAM signal is transmitted through the 80KM fiber.
  • Embodiment 1 A fiber nonlinear equalization method based on the KNN algorithm without data assisting, the device used is as shown in FIG. 1 , after the signal sent by the transmitting end is transmitted through the long-distance optical fiber, the receiving light receives and receives the light. The signal is converted into an electrical signal, and after being recovered by the carrier phase, it enters the nonlinear equalizer (KNN detector) of the present embodiment to perform nonlinear equalization of the optical fiber.
  • KNN detector nonlinear equalizer
  • the optical fiber nonlinear equalization method is as follows: the data is divided into a training model and a test model, and the density function is used to extract the less noisy data and label them in the training model as a training sample, and the KNN algorithm is used to use more in the test model. Noise classifies data.
  • This part consists of three steps, the data extraction function by density, the demodulation function to mark the data and the recombination distance of the constellation clusters in the shortest order.
  • Step 1 Extract the data by the density function.
  • the function range is the numerical range of the data points
  • x and y represent the real and imaginary parts of the 64-QAM data
  • i represents the point in the data set
  • i is an integer from 1 to N
  • N is the data point in the data set.
  • the threshold is taken at one-third of the range of dd, and the obtained first-level data set is filtered according to the density function value dd(k), and the data with dd(k) exceeding the specified threshold is selected as The second level data set; step 2: labeling according to the demodulation function.
  • the second stage data set point on the constellation is demodulated with the M-QAM signal.
  • the obtained decimal data 0-(M-1) is attached as a label to the corresponding data point.
  • the data set of the second stage is divided into two parts, an M cluster and a centroid Ci obtained by the following formula.
  • Step 3 According to the obtained centroid Ci, the second stage data set will classify the corresponding cluster according to the nearest Euclidean distance to obtain the label y1st-output.
  • the cluster y1st output needs to be updated based on the obtained tags. Data sets with reach tags will be used as training samples in the following test models.
  • test model is also composed of three steps.
  • Step 1 Define the K nearest neighbors of the test data X from the training data set implemented in the training model. In this paper, 13 is the best K value.
  • Step 2 Calculate the tested KNN Euclidean distance data X and find the label cluster of the nearest K data points.
  • Step 3 Determine the category of the test data X using the weighted sum voting rule, and the transmitted data can be compared to obtain the final output label and the pre-stored label.
  • I is an indicator function.
  • the M-QAM constellation can be considered as M data clusters in two-dimensional (2D) space, and a KNN classification algorithm will be used to determine the cluster classification of all signal symbols.
  • the non-data assisted DCT-KNN scheme of the present invention is further explained by taking the 64-QAM signal as an example.
  • four constellation clusters are magnified in the 64-QAM signal constellation to explain the principles of the proposed method.
  • a distortion 64-QAM signal of ASE noise and fiber nonlinearity is used as the original input signal, in which the constellation points are widely dispersed with the rotational phase as shown in Fig. 4(a).
  • Second, four constellation clusters are extracted from the 64-QAM signal, as shown in Figure 4(b).
  • the density parameters of the data set are then defined and the spatial constellation clustering based on density is extracted.
  • the demodulation function is used to mark the input data set and estimate the position of the initial centroid, where the black snowflake represents the obtained centroid.
  • the distance between the centroid and each data is calculated, and reorganize the constellation cluster according to the shortest distance, as shown in Figure 4(d).
  • the extracted noise-free data is defined as a training data set, as shown in Fig. 4(e), and the residual noise data is represented by black dots as an unknown test data set.
  • KNN is applied to the weighted sum voting rule to classify the test data set, as shown in Figure 4(f).
  • FIG. 5 is a graph showing OSNRvsBER experimental results of a blind DCT-KNN algorithm after a 16QAM signal is transmitted through an 800KM fiber;
  • FIG. 6 is a graph showing experimental results of a fiber-optic optical power vsBER of a blind DCT-KNN algorithm after a 16QAM signal is transmitted through a 240KM fiber;
  • FIG. 7 is a graph showing OSNRvsBER experimental results of a blind DCT-KNN algorithm after 64QAM signals are transmitted through an 80KM fiber;
  • Figure 9 is a graph showing the K-value vsBER experimental results of the blind DCT-KNN algorithm and the KNN algorithm with the training series after the 64QAM signal is transmitted through the 80KM fiber.

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  • Computer Networks & Wireless Communication (AREA)
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Abstract

一种基于无数据辅助的KNN算法的光纤非线性均衡方法，包括：获取各数据点的分布密度参数，选取分布密度参数大于预设阈值的数据点进行信号解调，获得各数据点对应的标签，根据标签分成M个簇，获得对应的质心：根据获得的质心，将数据点按照欧几里得距离重新进行分类，构成训练样本集；取未获得标签的数据点X，从训练样本集中获取数据点X的K个最近邻点；计算数据点X的KNN欧氏距离数据，并找出K个最近邻点的标签簇；使用加权总和投票规则确定数据点X的预测标签，将X分配至对应簇；重复直至完成对所有数据点的处理。本方法大大降低计算复杂度，实现了系统的零冗余，能够显著地提升系统的分类性能，使系统误码率得以改善。

Description

基于无数据辅助的KNN算法的光纤非线性均衡方法 技术领域
本发明涉及一种光纤通信方法，具体涉及一种用于光纤通信系统的非线性均衡方法。
背景技术
对于远距离大容量光纤通信系统来说，系统的通信容量和通信距离是研发者追求的目标。为提升传输速率，这类系统通常具有高频谱效率的高阶调制信号，例如，M进制相移键控(M-PSK)和M进制正交幅度调制(M-QAM)都是竞争性候选的调制信号。当前，结合相干检测和数字信号处理(DSP)技术，16-QAM在200G通道中、64-QAM在400G以上的信道中被普遍采用。这些高阶调制信号提升了数据传输速率，但同时由于较高的光信噪比(OSNR)需求导致了实际传输距离的减小。
为提升传输距离，有必要对信号进行非线性补偿。目前，采用的非线性补偿方法是，在接收端将光信号转化为电信号，经过模数转换器采样后，再进行数字信号处理(DSP)。已经有许多DSP算法被开发用于补偿线性和非线性光纤传输损伤以延长高阶QAM信号的传输距离。线性传输损伤，如色散和偏振模色散都可以在有限的数字领域基于脉冲响应(FIR)-滤波器的自适应均衡器中得到有效的补偿。然而，光纤中的克尔效应会引起非线性波形失真从而限制高阶QAM信号的最大传输距离。因此，非线性均衡的DSP技术对于减轻光纤非线性来说是不可或缺的。
当前，一些非线性均衡DSP算法已经被提出，如最大后验概率(MAP)检测器、最大期望值(EM)、最大似然值估计(MLE)、非线性Volterra非线性均衡器、数字反向传播(DBP)、人工神经网络网络(ANN)、支持向量机(SVM)和k-means等。然而，其中大部分的算法具有较高的计算复杂性，同时有一些算法需要更长的训练序列，这无疑增加了额外的带宽需求。
因此，迫切需要提供一种改进的光纤非线性均衡方法，以在相对较低复杂情况下提供高效的非线性补偿，以降低计算成本，实现低数据冗余商业应用。
邻近算法，又称为K最近邻(KNN)算法，参见附图2所示，是一个分类和回归的非参数方法，同时也是一个简单的和有效的分类方法，对于类域的交 叉或重叠较多的待分样本集来说，KNN方法较其它方法更为适合。但是，在用于光纤通信后端的非线性均衡的DSP处理过程中时，存在以下问题：
(1)在传统的KNN算法中需要额外的训练序列，用有标签的训练序列通过计算最近的欧氏距离来预测未知的测试数据。但是因为较少的训练样本会导致错误的分类，即小规模的训练数据更容易受到噪声的影响，因此算法的性能高度取决于训练序列的长度，但更多的训练样本也意味着更大的系统冗余。
(2)对于传统的KNN而言，k值太小，分类结果易受噪声点影响；k值太大，近邻中又可能包含太多的其它类别的点。
(3)在进行类别判定时，传统的KNN使用投票法来进行判定，但是投票法并没有考虑近邻的距离的远近，这会影响最终的分类性能。
综上所述，如果在光通信DSP处理中采用传统的KNN聚类方法，那么就意味着需要额外添加辅助的训练系列进行聚类，在聚类过程中，毫无疑问地就增加了通信系统的数据冗余度。因此，这种应用不能解决目前遇到的问题。
技术解决方案
本发明的发明目的是提供一种基于无数据辅助的KNN算法的光纤非线性均衡方法，通过降低计算复杂度和提供零数据冗余度来减轻光纤非线性引起的信号损伤，以提高相干光通信系统的误码率性能。
为达到上述发明目的，本发明的总体构思是：提出一个复杂度低的盲密度集群跟踪(DCT)-KNN算法，线性和非线性系统噪声有对外星座点比中心星座点的影响要大得多的M-QAM信号，因此，使用密度函数来提取噪音较小的数据在第一部分的训练模型中标注它们，然后使用标记数据作为训练样本，并应用KNN算法在部分的测试模型中用更多的噪声对数据进行分类。因此，该方法不需要额外的训练数据，可以称为非数据辅助DCT-KNN算法，一种自我训练的方法，并提取标签采用密度函数作为训练样本的无噪数据，完全可以解决传统KNN算法中遇到的问题。
具体地，本发明采用的技术方案是：一种基于无数据辅助的KNN算法的光纤非线性均衡方法，包括以下步骤：
(1)接收待进行补偿的全体数据作为第一数据集，获取第一数据集中各数据点的分布密度参数，选取分布密度参数大于预设阈值的数据点作为第二数据集；
(2)对第二数据集中的数据点进行信号解调，获得各数据点对应的标签，根据标签，将第二数据集分成M个簇，获得对应的质心C i：
Figure PCTCN2018086412-appb-000001
其中，i＝1，2，…，M，s是第i个簇中的数据点数量，Dj是第i个簇的第j个数据；
(3)根据获得的质心C i，将第二阶段数据集中的数据点按照距离最近的欧几里得距离重新进行分类，相应的簇获得标签y1st-output，构成训练样本集；
(4)取第一数据集中未获得标签的数据点X，从训练样本集中获取数据点X的K个最近邻点，其中，K值为13；
(5)计算数据点X的KNN欧氏距离数据，并找出K个最近邻点的标签簇；
(6)使用加权总和投票规则确定数据点X的预测标签，将X分配至对应簇；
(7)输出最终的分类数据结果。
上述技术方案中，步骤(1)中，分布密度参数由下式获取：
Figure PCTCN2018086412-appb-000002
其中，
Figure PCTCN2018086412-appb-000003
函数range是数据点的数值范围，x和y分别表示信号数据的实部和虚部，i代表数据集中的点，i是1到N的整数，N是数据集中数据点的个数，k表示数据集中的点。
所述预设阈值为dd(k)取值范围的三分之一处对应的数值。
步骤(2)中，所述解调采用M-QAM信号解调。
步骤(4)中，优选地，K＝13。
步骤(6)中，加权总和投票规则的具体方法是：
给定训练样本集T＝{(x 1,y 1),(x 2,y 2),…,(x N,y N)}由N个训练数据点x i组成，其中x i对应着标签y i∈{C 1,C 2,C 3,…,C m},i＝1,2,…,N,m是簇的个数，在训练样本集T中找到与X最接近的K个点，在X的范围中，这些K个点被描述为N k(x)，根据N k(x)，得到与这K个点对应的K个标签，并返回这些标签的大部分作为预测标签：
Figure PCTCN2018086412-appb-000004
其中ω i＝1/D(x,x i),i＝1,2,…,N；j＝1,2,…,m，I是一个指示函数，当y i＝C j时，I等于1，否则I为0。
有益效果
由于上述技术方案运用，本发明与现有技术相比具有下列优点：
1、本发明在对相干光通信数据的处理过程中，采用了全新的盲KNN算法，首先利用密度函数来提供高质量的原始簇作为训练集，在不需要添加额外数据的情况下，实现了系统的零冗余，而且由于训练簇集的高质量，能够显著地提升系统的分类性能。
2、本发明所提出的盲质心跟踪KNN方法具有以下优点：(1)由于KNN算法的特殊性，不需要额外的训练调参数，也不需要任何迭代计算，可以大大降低计算复杂度；(2)盲质心跟踪的KNN方法可以提供高质量的训练集，最优的K值选择和加权投票法的应用，都能够显著地提高分类结果；(3)为将来的更高速光通信传输提供了可能。
3、实验表明，采用本发明的光纤非线性均衡方法，会在16-QAM和64-QAM相干光通信系统中使系统误码率(BER)得以改善，并具有计算成本低、数据零冗余性的特点，对系统噪声有可拓展性和快速收敛性。
附图说明
图1是本发明实施例的装置示意图；
图2是KNN分类原理示意图；
图3是实施例中盲DCT-KNN算法的流程图；
图4是实施例中盲DCT-KNN算法的M-QAM信号聚类效果图；
图5是16QAM信号经过800KM光纤传输后盲DCT-KNN算法的OSNRvsBER实验结果图；
图6是16QAM信号经过240KM光纤传输后盲DCT-KNN算法的入纤光功率vsBER实验结果图；
图7是64QAM信号经过80KM光纤传输后盲DCT-KNN算法的OSNRvsBER实验结果图；
图8是64QAM信号经过80KM光纤传输后盲DCT-KNN算法的入纤光功率vsBER实验结果图；
图9是64QAM信号经过80KM光纤传输后盲DCT-KNN算法与有训练系列的KNN算法的K值vsBER实验结果图。
本发明的实施方式
下面结合附图及实施例对本发明作进一步描述：
实施例一：一种基于无数据辅助的KNN算法的光纤非线性均衡方法，采用的装置如附图1所示，发射端发出的信号经长距离光纤传输后，由接收接接收，接收的光信号转换成电信号，经载波相位恢复后，进入本实施例的非线性均衡器(KNN检测器)，进行光纤非线性均衡。
光纤非线性均衡方法为：将数据分为训练模型和测试模型，使用密度函数来提取噪音较小的数据在训练模型中标注它们，作为训练样本，并应用KNN算法在测试模型中用更多的噪声对数据进行分类。
参见附图3，具体包括以下步骤：
(a)训练模型
这部分包括三个步骤，按密度提取数据功能，用解调功能标记数据和按照最短的顺序对星座簇进行重组距离。
步骤1：通过密度函数提取数据。
使用以下公式计算各数据点的密度参数。
Figure PCTCN2018086412-appb-000005
其中，
Figure PCTCN2018086412-appb-000006
式中，函数range是数据点的数值范围，x和y分别表示64-QAM数据的实部和虚部，i代表数据集中的点，i是1到N的整数，N是数据集中数据点的个数；根据设定阈值,阈值取dd范围内的三分之一处,将获得的第一级数据集根据密度函数值dd(k)进行筛选，选择dd(k)超过指定阈值的数据作为第二级数据集；步骤2：根据解调函数进行贴标签。该星座图上的第二阶段数据集点是用M-QAM 信号解调。将获得十进制数据0-(M-1)作为标签附在相应的数据点上。根据标签，将第二阶段的数据集分为两部分，M集群和用下面公式获得的质心Ci。
Figure PCTCN2018086412-appb-000007
其中i＝1,2，3...，M，其中s是第i个簇中的数据数量Dj是第i个簇的第j个数据。
步骤3：根据获得的质心Ci，第二阶段数据集将按照距离最近的欧几里得距离进行分类相应的簇获得标签y1st-output。然后需要基于获得的标签来更新群集y1st输出。具有达到标签的数据集将被用作训练样本在以下测试模型中。
(b)测试模型
对于未标记的测试数据X，测试模型也是如此由三个步骤组成。
步骤1：定义测试数据X的K个最近邻从训练模型中实现的训练数据集中。在本文以13为最佳K值。
步骤2：计算测试的KNN欧氏距离数据X并找到最近的K个数据点的标签簇。
步骤3：使用加权总和投票规则确定测试数据X的类别，所传输的数据可以通过比较得出最后输出标签和预先存储的标签。
加权总和投票原则如下:给定训练数据集T＝{(x 1,y 1),(x 2,y 2),…,(x N,y N)}由N个训练数据点x i组成，其中x i对应着标签y i∈{C 1,C 2,C 3,…,C m},i＝1,2,…,N,m是簇的个数。根据给定的距离度量，可以在训练集T中找到与X最接近的K个点。在X的范围中，这些K个点被描述为N k(x)。根据N k(x)，可以得到与K个最近训练数据对应的K个标签，并返回这些K个标签的大部分作为预测标签：
Figure PCTCN2018086412-appb-000008
其中ω i＝1/D(x,x i),i＝1,2,…,N；j＝1,2,…,m。I是一个指示函数。当y i＝C j时，I等于1，否则I为0。
根据加权总和投票规则，在图2中，对于K＝1,5或9，X总是可以被分类到C1中。
参见附图4，在M-QAM系统中，可以将M-QAM星座视为二维(2D) 空间中的M个数据簇，并且将使用KNN分类算法来确定所有信号符号的聚类分类。以64-QAM信号为例，对本发明的非数据辅助的DCT-KNN方案作进一步解释。为了方便起见，在64-QAM信号星座图中放大了四个星座簇，来解释所提出的方法的原理。首先，使用ASE噪声和光纤非线性的失真64-QAM信号作为原始输入信号，其中星座点随着旋转相位而广泛分散，如图4(a)所示。其次，在64-QAM信号中提取四个星座聚类，如图4(b)所示。然后定义数据集的密度参数，并提取基于密度的空间星座聚类。如图4(c)所示，解调函数用于标记输入数据集并估计初始质心的位置，其中黑色的雪花表示获得的质心。第三，计算质心与每个数据之间的距离，并按照最短距离对星座簇进行重组，如图4(d)所示。提取的无噪声数据定义为训练数据集，如图4(e)所示的有色点，剩余噪声数据以黑点表示为未知测试数据集。最后，将KNN应用于加权总和投票规则来对测试数据集进行分类，如图4(f)所示。
采用本实施例的方法，获得的效果可以从图5至图9显示。
图5是16QAM信号经过800KM光纤传输后盲DCT-KNN算法的OSNRvsBER实验结果图；
图6是16QAM信号经过240KM光纤传输后盲DCT-KNN算法的入纤光功率vsBER实验结果图；
图7是64QAM信号经过80KM光纤传输后盲DCT-KNN算法的OSNRvsBER实验结果图；
图8是64QAM信号经过80KM光纤传输后盲DCT-KNN算法的入纤光功率vsBER实验结果图；
图9是64QAM信号经过80KM光纤传输后盲DCT-KNN算法与有训练系列的KNN算法的K值vsBER实验结果图。
由图可知，采用本发明实施例的方法，经过长距离传输，信号的误码率明显得到很大的改善。

Claims (6)

  1. 一种基于无数据辅助的KNN算法的光纤非线性均衡方法，其特征在于，包括以下步骤：
    (1)接收待进行补偿的全体数据作为第一数据集，获取第一数据集中各数据点的分布密度参数，选取分布密度参数大于预设阈值的数据点作为第二数据集；
    (2)对第二数据集中的数据点进行信号解调，获得各数据点对应的标签，根据标签，将第二数据集分成M个簇，获得对应的质心C i：
    Figure PCTCN2018086412-appb-100001
    其中，i＝1，2，…，M，s是第i个簇中的数据点数量，Dj是第i个簇的第j个数据；
    (3)根据获得的质心C i，将第二阶段数据集中的数据点按照距离最近的欧几里得距离重新进行分类，相应的簇获得标签y1st-output，构成训练样本集；
    (4)取第一数据集中未获得标签的数据点X，从训练样本集中获取数据点X的K个最近邻点，其中，K为13；
    (5)计算数据点X的KNN欧氏距离数据，并找出K个最近邻点的标签簇；
    (6)使用加权总和投票规则确定数据点X的预测标签，将X分配至对应簇；
    (7)重复步骤(4)至(6)直至完成对所有数据点的处理；
    (8)输出最终的分类数据结果。
  2. 根据权利要求1所述的基于无数据辅助的KNN算法的光纤非线性均衡方法，其特征在于：步骤(1)中，分布密度参数由下式获取：
    Figure PCTCN2018086412-appb-100002
    其中，
    Figure PCTCN2018086412-appb-100003
    函数range是数据点的数值范围，x和y分别表示信号数据的实部和虚部，i代表数据集中的点，i是1到N的整数，N是数据集中数据点的个数，k表示数据集中的点。
  3. 根据权利要求2所述的基于无数据辅助的KNN算法的光纤非线性均衡方法，其特征在于：所述预设阈值为dd(k)取值范围的三分之一处对应的数值。
  4. 根据权利要求1所述的基于无数据辅助的KNN算法的光纤非线性均衡方法，其特征在于：步骤(2)中，所述解调采用M-QAM信号解调。
  5. 根据权利要求1所述的基于无数据辅助的KNN算法的光纤非线性均衡方法，其特征在于：步骤(4)中，K＝13。
  6. 根据权利要求1所述的基于无数据辅助的KNN算法的光纤非线性均衡方法，其特征在于：步骤(6)中，加权总和投票规则的具体方法是：
    给定训练样本集T＝{(x 1,y 1),(x 2,y 2),…,(x N,y N)}由N个训练数据点x i组成，其中x i对应着标签y i∈{C 1,C 2,C 3,…,C m},i＝1,2,…,N,m是簇的个数，在训练样本集T中找到与X最接近的K个点，在X的范围中，这些K个点被描述为N k(x)，根据N k(x)，得到与这K个点对应的K个标签，并返回这些标签的大部分作为预测标签：
    Figure PCTCN2018086412-appb-100004
    其中ω i＝1/D(x,x i),i＝1,2,…,N；j＝1,2,…,m，I是一个指示函数，当y i＝C j时，I等于1，否则I为0。
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