M-ary SVM非参数化解决光相干系统非线性相噪声

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本文主要探讨了在相干光通信系统中采用M-ary支持向量机（M-ary SVM）来改善非线性相位噪声（Nonlinear Phase Noise, NLPN）抑制的方法。NLPN是光纤通信系统中常见的噪声源，它会降低信号的传输质量，影响系统的性能。传统的检测技术如最大似然检测（Maximum Likelihood Detection, MLD）可能不足以有效处理这种复杂的非参数非线性噪声。 M-ary SVM作为一种无参数的机器学习方法，通过其二分类策略被引入到系统中，用于对受到光纤NLPN影响的信号进行分类。与传统方法不同，M-ary SVM利用训练数据构建每个分类器的分离超平面，从而实现对不同类别的信号进行精确区分。这种方法的优势在于，即使在没有预先定义的噪声模型情况下，也能自适应地学习并减少NLPN的影响，提高了系统的抗噪能力。研究者们，包括来自北京邮电大学的Minliang Li、Song Yu、Jie Yang、Zhixiao Chen、Yi Han和Wanyi Gu，针对这个问题进行了深入研究，并在2013年12月的《光学通信》期刊上发表了他们的成果。他们的工作得到了国家自然科学基金、国家基础研究计划（973计划）以及中央大学基础研究基金的支持。通过M-ary SVM的非参数化特性，该方案适用于各种类型的二次幅度调制（Quadratic Amplitude Modulations, QAM）系统，因为它们能够捕捉并适应不同强度的NLPN。这种方法不仅提升了系统的NLPN容忍度，还可能减少对精确噪声模型的依赖，使得系统的稳健性和灵活性有所增强。总结来说，这项研究提供了一种创新的解决方案，利用M-ary SVM在无先验知识的情况下有效地对抗相干光通信系统中的非线性相位噪声，为提高光纤通信系统的稳定性和信号质量提供了新的理论依据和技术手段。随着光通信技术的不断发展，这种基于机器学习的噪声抑制策略具有广阔的应用前景。

detector based on the Bayesian framework of factor graphs [11]. However, because of the

stochastic nature and nonlinear properties of the NLPN, above approaches to suppress NLPN are

all depends on the parameters of the transmission link. When the signal propagates through

dynamic optical network link instead of the fixed point-to-point link, the variation of link parameters

would lead these existing methods to become invalid [12], [13]. Hence, it is meaningful to

investigate techniques which are independent of the parameters of the link to mitigate the NLPN.

Machine learning algorithms are efficient non-parameter methods for their properties of getting

the characteristic of systems from data directly. The support vector machine (SVM) as one of

powerful and widely used machine learning algorithms [14], requires a small number of parameters

during establishing its model. Moreover, the priori information and heuristic assumptions are

unnecessary for the SVM. In this paper, we introduce the M-ary SVM [15] as a non-parameter

method to mitigate the NLPN in the signal-carrier 16-QAM coherent optical systems. By

transforming the NLPN mitigation problem for the QAM signal into a hypothesis test problem, the

decision for the received signal is conducted by the M-ary SVM through a series of binary

classification in this work. Moreover, because the model of each SVM of the M-ary SVM is obtained

by a certain amount of training data, this scheme need not any information about the transmission

link. By numerical simulation, the results show that the M-ary SVM scheme can achieve better

performance than the method proposed by Lau and Kahn [9].

The structure of this paper is as follows. In Section 2, we detail the mathematical model of SVM

as a binary classifier, the M-ary SVM for NLPN mitigation scheme is also illustrated. The simulation

scheme conducted in our study is described in the Section 3. The simulation results and

discussions are presented in the Section 4. Section 5 concludes this paper.

2. Theory of M-ary SVM

Nonlinear phase noise mitigation for multilevel modulation signal by using the M-ary SVM is

achieved via a number of parallel SVMs followed by a set of logical processing. Each SVM

classifies every received symbol into one of the two groups by a specific decision boundary, which

is obtained through a certain amount of training data. Accordingly, there is no need to know any

characteristic of the transmission channel. In the following of this part, we will firstly introduce the

principle of SVM, as it is the core component of the M-ary SVM. At last, a systematic description

about the M-ary SVM for 16-QAM detection is given.

2.1. SVM as Classifier

Based on statistical learning theory, SVM is developed from linear classifier which aims at finding

the optimal separating hyperplane that maximizes the margin (i.e., maximizes the smallest distance

between the hyperplane and any of the samples) [16]. Meanwhile, the kernel method is also

adopted by the SVM to solve the nonlinear separable situation [17]. For the two-class linearly

separable problem in an n-dimensional feature space, the optimal separating hyperplane f ðv Þ is

derived through training L vectors v

; v

; ...; v

where v

2 R

and each vector corresponds to a

category label y

2f1; þ1g. The form of f ðv Þ is given by

f ðv Þ¼!

 v þ b ¼ 0 (1)

where, the vector ! ¼ð!

; ...!

and the scalar b are the parameters of the hyperplane.

Assuming that all the training data are separated by (1) correctly, we have y

ð!

 v

þ bÞ 9 0

(this is because if y

¼þ1, f ðv

Þ 9 0; and if y

¼1, f ðv

Þ G 0) for every training instance-label

pair ðv

; y

Þ. So the Euclidean distance between vector v

and the hyperplane is



 v

þ bj

k!k

 f ðv

k!k

: (2)

IEEE Photonics Journal NLPN Mitigation Using M-ary SVM Systems

Vol. 5, No. 6, December 2013 7800312

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