Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

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

Fernando P. Guiomar, Jacklyn D. Reis, António L. Teixeira, and Armando N. Pinto

Open Access Open Access

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.

© 2011 Optical Society of America

Full Article  |  PDF Article
More Like This
Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission

Fernando P. Guiomar, Jacklyn D. Reis, Andrea Carena, Gabriella Bosco, António L. Teixeira, and Armando N. Pinto
Opt. Express 21(1) 276-288 (2013)

Estimating the Volterra series transfer function over coherent optical OFDM for efficient monitoring of the fiber channel nonlinearity

Gal Shulkind and Moshe Nazarathy
Opt. Express 20(27) 29035-29062 (2012)

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

Mirko Gagni, Fernando P. Guiomar, Stefan Wabnitz, and Armando N. Pinto
Opt. Express 25(3) 2446-2459 (2017)

View More...

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)
Fig. 1
Fig. 1 FD-VSNE implementation for each fiber span. Black solid lines represent the equalizer operations; Blue dashed lines represent the equalizer control plan.

Download Full Size | PDF

Fig. 2
Fig. 2 Coherent NRZ-QPSK optical system model adopted in this work. DSP - Digital Signal Processor; ADC - Analog-to-Digital Converter; LPF - Low-Pass Filter.

Download Full Size | PDF

Fig. 3
Fig. 3 Equalization results (in terms of EVM) obtained for a 20 Gbaud NRZ-QPSK signal transmitted over 20 × 80 km. a) SSMF link with Nsp = 3; b) SSMF link with Nsp = 2; c) NZDSF link with Nsp = 3; d) NZDSF link with Nsp = 2. For simplicity, both FD-CDE and FD-VSNE have been abbreviated to CDE and VSNE respectively.

Download Full Size | PDF

Fig. 4
Fig. 4 EVM after nonlinear equalization as a function of the LPF cutoff frequency. a) Nsp = 3; b) Nsp = 2. Input optical power is 6 dBm.

Download Full Size | PDF

Fig. 5
Fig. 5 Optical spectra of the propagated signal before and after the LPF and after down-sampling at 3 samples per symbol. The LPF cutoff frequency is placed at 18 GHz.

Download Full Size | PDF

Fig. 6
Fig. 6 EVM as a function of the effective spectral support used to apply the FD-VSNE and LPF cutoff frequency (LPF3dB). The signal fed to the equalization block is sampled at 3 samples per symbol and the input power is 6 dBm.

Download Full Size | PDF

Fig. 7
Fig. 7 Number of complex multiplies required by FD-VSNE and BP-SSF as a function of the FFT block-size.

Download Full Size | PDF

Fig. 8
Fig. 8 Inter-block interference as a function of the FFT block-size. Red lines refer to the implementation of OS only at the link ends. Black lines are in respect with the span-by-span implementation of OS. Input power is 4 dBm; Nsp = 2.

Download Full Size | PDF

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

∂ A ∂ z = − α 2 A − i β 2 2 ∂ 2 A ∂ t 2 + i γ | A | 2 A ,
A ˜ in ( ω ) ≈ H 1 ′ ( ω ) A ˜ out ( ω ) + ∬ H 3 ′ ( ω 1 , ω 2 , ω − ω 1 + ω 2 )                                 × A ˜ out ( ω 1 ) A ˜ out * ( ω 2 ) A ˜ out ( ω − ω 1 + ω 2 ) d ω 1 d ω 2 ,
H 1 ′ ( ω ) = exp ( α 2 L span − i β 2 2 ω 2 L span ) ,
H 3 ′ ( ω 1 , ω 2 , ω − ω 1 + ω 2 ) = − i γ H 1 ′ ( ω ) 1 − exp ( α L span − i β 2 ( ω 1 − ω ) ( ω 1 − ω 2 ) L span ) − α + i β 2 ( ω 1 − ω ) ( ω 1 − ω 2 ) .
A ˜ ( ω n ) = 1 N F F T ∑ k = 1 N F F T A ( t k ) exp ( i 2 π ( n − 1 ) ( k − 1 ) N F F T ) ,
A ˜ e q N L ( ω n ) = ∑ n 2 = 1 N F F T ∑ n 1 = 1 N F F T H 3 ′ ( ω n 1 , ω n 2 , ω n − ω n 1 + ω n 2 ) A ˜ out ( ω n 1 ) A ˜ out * ( ω n 2 ) A ˜ out ( ω n − ω n 1 + ω n 2 ) ,
A e q = { A e q L I exp ( A e q N L A e q L I ) , if   | A e q N L | < | A e q L I | A e q L I + A e q N L , otherwise ,
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use