Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer

Abstract

We address the issue of intra-channel nonlinear compensation using a Volterra series nonlinear equalizer based on an analytical closed-form solution for the 3rd order Volterra kernel in frequency-domain. The performance of the method is investigated through numerical simulations for a single-channel optical system using a 20 Gbaud NRZ-QPSK test signal propagated over 1600 km of both standard single-mode fiber and non-zero dispersion shifted fiber. We carry on performance and computational effort comparisons with the well-known backward propagation split-step Fourier (BP-SSF) method. The alias-free frequency-domain implementation of the Volterra series nonlinear equalizer makes it an attractive approach to work at low sampling rates, enabling to surpass the maximum performance of BP-SSF at 2× oversampling. Linear and nonlinear equalization can be treated independently, providing more flexibility to the equalization subsystem. The parallel structure of the algorithm is also a key advantage in terms of real-time implementation.

Simplified high-order Volterra series transfer function for optical transmission links

“…The split-step Fourier method (SSFM) is the most commonly used numerical technique to solve the NLSE [6]. The SSFM was proposed to implement DBP in order to post-compensate for both linear and nonlinear fiber impairments [1,2].…”

“…The VSNE approach provides an accuracy which is comparable with that of the SSFM, under the hypothesis of using a single step per span [4]. In [3,6], it was suggested to use an inverse modified VSTF in order to compensate for fiber propagation impairments in DBP. The VSTF can improve the nonlinear tolerance by almost 2 dB when is operating at the Nyquist rate [3], if compared with the SSFM.…”

Volterra Series Digital Backpropagation Accounting for PMD

“…Digital backpropagation (DBP) is a universal technique used to compensate for such nonlinear distortions. It involves digitally solving the nonlinear Schrödinger equation using the split-step Fourier method (SSFM) 1 or using perturbation analysis in the time domain 2 or frequency domain 3 . The latter approach is often referred to as Volterra series (VS) 4 DBP.…”

Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission

“…Recently, new algorithms based on Volterra series theory have been reported either in time 2 or frequency-domain 3 . In 3 , an intra-channel Volterra series nonlinear equalizer (VSNE) applied in frequency-domain has been proposed and assessed through numerical simulations.…”

“…Recently, new algorithms based on Volterra series theory have been reported either in time 2 or frequency-domain 3 . In 3 , an intra-channel Volterra series nonlinear equalizer (VSNE) applied in frequency-domain has been proposed and assessed through numerical simulations. The VSNE algorithm can be beneficial for real-time implementation due to its parallel structure, while maintaining very high equalization performance even at 2 samples per symbol 3 .…”