Nonparameter Nonlinear Phase Noise Mitigation by Using M-ary Support Vector Machine for Coherent Optical Systems

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.

An SVM-Based Detection for Coherent Optical APSK Systems With Nonlinear Phase Noise

“…Classification for the received signals as a kind of feasible detection way has been used to mitigate the NLPN [8]. The SVM is a useful technique for nonlinear data classification.…”

“…Then under the established classification strategies, SVM conducts classification in the testing stage. The detailed principle of the SVM and the detailed derivation used for classification is shown in [8], [17], and [18].…”

“…For convenience, fþ1; À1g is used to represent fC þ i ; C À i g. Then the separating hyperplane of each SVM is obtained through the quadratic programming. Based on the established separating hyperplane, the received symbols in testing stage are classified by the ith SVM according to the discriminant function given as [8] …”

“…We learn from [19] that when the radii of the constellation are uniformly distributed, the system is highly immune to the nonlinear phase noise. So for simplicity, the radii of the ring constellations are set as (0.64, 1 In the fiber transmission subsystem, we first follow the model in [8], [10], and [11], in which we focus on the impacts of fiber NLPN and neglect the chromatic dispersion. The fiber link consists of N Â 80 km of dispersion shift fiber (DSF) with the nonlinear coefficient ¼ 1:3 W À1 km À1 and the loss coefficient ¼ 0:2 dB/km.…”

“…Among the fiber-induced impairments, nonlinear phase noise (NLPN) is a primary obstacle and severely limits the transmission distance as well as the capacity [3]. Various approaches have been investigated for combating the effect of NLPN in optical QAM systems, e.g., phase pre- [4] and post-compensation [5] in electric field, the maximum likelihood (ML) detector [6], maximum likelihood sequence estimation (MLSE) [7] and M-ary support vector machine (SVM) [8].…”