Nonparameter Nonlinear Phase Noise
Mitigation by Using M-ary Support Vector
Machine for Coherent Optical Systems
Minliang Li, Song Yu, Jie Yang, Zhixiao Chen, Yi Han, and Wanyi Gu
State Key Laboratory of Information Photonics and Optical Communications,
Beijing University of Posts and Telecommunications, Beijing 100876, China
DOI: 10.1109/JPHOT.2013.2287565
1943-0655 Ó 2013 IEEE
Manuscript received August 3, 2013; revised October 7, 2013; accepted October 15, 2013. Date of
publication October 28, 2013; date of current version November 1, 2013. This work was supported in
part by the National Basic Research Program of China (973 Program) under Grant 2012CB315605; by
the National Natural Science Foundation under Grants 61271191, 61271193, and 61072054; by the
Fundamental Research Funds for the Central Universities; and by the State Key Laboratory of
Information Photonics and Optical Communications (Beijing University of Posts and Telecommunica-
tions). Corresponding author: S. Yu (e-mail: yusong@bupt.edu.cn).
Abstract: The M-ary support vector machine (SVM) is introduced as a nonparameter
nonlinear phase noise (NLPN) mitigation approach for the coherent optical systems. The
NLPN tolerance of the system can be improved by using the M-ary SVM to conduct
nonlinear detection. In this scheme, SVMs with different classification strategies are utilized
to execute binary classification for signals impaired by fiber NLPN. Since the separating
hyperplane of each SVM is constructed by training data, this scheme is independent from
the knowledge of the transmission link. In numerical simulation, the M-ary SVM performs
better than the method of amplitude-dependent phase rotation at the transmitter and
receiver, as well as the maximum likelihood detection with back rotation.
Index Terms: Nonlinear phase noise, quadratic amplitude modulation (QAM), support
vector machine (SVM), M-ary SVM.
1. Introduction
The fiber nonlinearities have been identified as the limiting factors for enhancing the capacity and
transmission length of coherent optical system. Recently, multilevel quadratic amplitude modulation
(QAM) has been applied as a promising technology to meet the growing requirement on the spectral
efficiency [1]. However, in QAM system, higher launch power is required to obtain increased signal-
to-noise ratio (SNR), resulting in more notable fiber nonlinear impairments [2]. Nonlinear phase
noise (NLPN) is one of the major distortion factors, which is caused by the interaction between the
signal and the amplified spontaneous emission (ASE) noise from inline optical amplifiers via fiber
Kerr nonlinearity [3], [4]. The NLPN has attracted attention since it was firstly introduced by Gordon
and Mollenauer [5].
To eliminate NLPN, many optical and electronic methods have been proposed. Compared with
the optical phase conjugation schemes [6], [7], which insert hardware in transmission link, electronic
methods have the advantages of being flexible and less costly. Recently, various lumped electronic
processing methods have been proposed to mitigate the effect of nonlinear phase noise. The
amplitude-dependent phase rotation for transmitted or received signals can reduce the NLPN
variance effectively [8], [9]. Based on constructing the likelihood function, a close-form maximum
likelihood-based data detection algorithm was proposed [10], as well as a maximum a posteriori
Vol. 5, No. 6, December 2013 7800312
IEEE Photonics Journal NLPN Mitigation Using M-ary SVM Systems
