Experimental demonstration of a dual-polarization Volterra series nonlinear equalizer applied in frequency-domain is carried out for 100G polarization-multiplexed QPSK test signals. We were able to reduce the BER by a factor of ~2.5x relatively to the single-polarization approach, with a 1 dB increase in the optimum power

A. N. Pinto

A. Teixeira

BOSCO, GABRIELLA

CARENA, Andrea

F. P. Guiomar

J. D. Reis

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEExperimental Demonstration of a Frequency-Domain Volterra Series Nonlinear Equalizer in Polarization-MultiplexedTransmission / F.P. Guiomar; J.D. Reis; A. Carena; G. Bosco; A.N.Pinto; A. Teixeira. - ELETTRONICO. - (2012), pp. 1-3.((Intervento presentato al convegno European Conference on Optical Communication (ECOC) tenutosi a Amsterdam nelSeptember 2012.OriginalExperimental Demonstration of a Frequency-Domain Volterra Series Nonlinear Equalizer in Polarization-Multiplexed TransmissionPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2503770 since:The Optical Society of America (OSA)Th.1.D.1.pdf ECOC Technical Digest © 2012 OSAExperimental Demonstration of a Frequency-Domain VolterraSeries Nonlinear Equalizer in Polarization-MultiplexedTransmissionFernando P. Guiomar(1), Jacklyn D. Reis (1), Andrea Carena (2), Gabriella Bosco (2),António L. Teixeira (1,3), Armando N. Pinto (1)(1) Department of Electronics, Telecommunications and Informatics, University of Aveiro and Instituto deTelecomunicações, 3810-193, Aveiro, Portugal B guiomar@av.it.pt(2) Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino, Corso Duca degli Abruzzi, 24,10129 Torino, Italy(3) Nokia Siemens Networks Portugal S.A., IE WSM, 2720-093 Amadora, PortugalAbstract Experimental demonstration of a dual-polarization Volterra series nonlinear equalizer appliedin frequency-domain is carried out for 100G polarization-multiplexed QPSK test signals. We were able toreduce the BER by a factor of ∼2.5× relatively to the single-polarization approach, with a 1 dB increasein the optimum power.IntroductionThanks to coherent detection, digital equalizationof linear fibre impairments can nowadaysbe performed with negligible penalty. Theultimate limits of fibre capacity are then set bynonlinearities and their interaction with noise. Thedevelopment of efficient nonlinear compensationalgorithms is therefore of utmost importance. Theissue of nonlinear compensation has been mostcommonly approached through digital backwardpropagation (DBP) employing split-step Fourier(SSF) methods1. Recently, new algorithmsbased on Volterra series theory have beenreported either in time2 or frequency-domain3.In3, an intra-channel Volterra series nonlinearequalizer (VSNE) applied in frequency-domainhas been proposed and assessed throughnumerical simulations. The VSNE algorithm canbe beneficial for real-time implementation due toits parallel structure, while maintaining very highequalization performance even at 2 samples persymbol3.Digital compensation of single-polarizationinter-channel4 and dual-polarization (dual-pol) intra-channel5 effects has been alreadyexperimentally demonstrated using SSFapproaches. Time-domain Volterra seriesfiltering has been demonstrated in single-polarization QPSK transmission6 at 10 Gbaud,using 5 samples per symbol. A recentexperimental demonstration of the single-polarization VSNE algorithm has been reportedfor a 28 Gbaud polarization-multiplexed (PM)-16QAM transmission over 250 km of ultra-largearea fibre7. However, these performanceassessments of Volterra series equalizationare limited by their underlying scalar model.Although a dual-pol VSNE based on theregular perturbation method has been recentlyproposed8, its performance is only assessedthrough simulations.In this paper we experimentally demonstratethe validity of the dual-pol VSNE in differentPM-QPSK transmission links and data rates,providing direct comparisons with the well-knownSSF method. Significative gains in terms of BERand optimal input power are shown, relatively tothe single-polarization version.Volterra Series Nonlinear EqualizerThe propagation of polarization-multiplexedoptical signals can be analytically modeled bythe nonlinear Schrödinger (NLS) equation in itsvectorial form. However, being a complex andcomputationally expensive model, the vector NLSequation is not adequate for DBP. To overcomethis complexity issue, the vectorial model canbe replaced by the Manakov equation. Thissimplified approach is based on the observationthat, since the polarization scattering lengthis much shorter than the typical nonlinearinteraction length, the resulting nonlinearities canbe determined with small penalty by averagingthe fast polarization changes along the fibre.Then, using the Manakov equation we mayanalytically describe DBP as1∂Ax/y∂(−z) =α2Ax/y + iβ22∂2Ax/y∂t2− i8γ9(|Ax|2 + |Ay|2)Ax/y, (1)where Ax/y is the slowly varying complex fieldenvelope in x/y states of polarization, z and t arethe spatial and temporal coordinates respectively,β2 accounts for chromatic dispersion and γ is thenonlinearity parameter.Th.1.D.1.pdf ECOC Technical Digest © 2012 OSAStarting from equation (1) we may redefinethe frequency-domain Volterra series nonlinearequalizer derived in3 in order to account forpolarization-dependent nonlinear crosstalk:A˜eqx/y (ωn) ==89NFFT∑n2=1NFFT∑n1=1H′3(ωn1 , ωn2 , ωn − ωn1 + ωn2)× P (ωn1 , ωn2)A˜rxx/y (ωn − ωn1 + ωn2), (2)where A˜rxx/y and A˜eqx/y are the Fouriertransforms of the received and nonlinearlyequalized electrical fields after each fibre span,in both states of polarization. The inverse third-order Volterra kernel, H′3(ωn1 , ωn2 , ωn−ωn1+ωn2)is defined in3. The P (ωn1 , ωn2) term refers to thecoherent cross-polarization power transfer, and itis given byP (ωn1 , ωn2) = A˜rxx(ωn1)A˜∗rxx(ωn2)+ A˜rxy (ωn1)A˜∗rxy (ωn2). (3)Expression (2) is applied span-by-span for eachangular frequency, ωn, composing the signalspectrum. By scanning the spectrum of interestwith the auxiliary angular frequencies, ωn1 andωn2 , the nonlinear equalizer is evaluated over amemory range of NFFT samples, correspondingto the length of each fast-Fourier transform (FFT)block. Regarding numerical complexity, onlyan extra N2FFT complex additions per sampleare required, relatively to the single-polarizationVSNE.Experimental SetupIn terms of experimental setup we will considertwo single-channel PM-QPSK scenarios: i)transmission at 30 Gbaud over non-zerodispersion shifted fibre (NZDSF) and ii)transmission at 25 Gbaud over standard single-mode fibre (SSMF). In both cases, multi-spanpropagation is achieved using a recirculatingloop composed of a single fibre span. Analog-to-digital conversion is performed at 50 GSa/susing a Tektronix DPO71604 oscilloscope, whosemeasured -3 dB analog bandwidth is ∼13 GHz.The most relevant experimental parameters forboth experimental scenarios are shown in Tab. 1,where Rs is the symbol rate, Lspan is the fibrespan length and SpS denotes the number ofsamples per symbol at the receiver. Furtherdetails about the experimental setup i) employingNZDSF fibre can be found in9, but we usea different transmission rate (30 Gbaud) andsingle-channel propagation. In turn, scenario ii)is a single-channel trial of the experiment detailedTab. 1: Experimental setup parameters.i) ii)Tx Rs =30 Gbaud Rs =25 GbaudFibreNZDSF SSMFα = 0.22 dB/km α = 0.20 dB/kmβ2 =-3.29 ps2/km β2 =-21.37 ps2/kmγ =2.01 W−1km−1 γ =1.35 W−1km−1Lspan = 100 km Lspan = 63.6 kmRx SpS =1.6 SpS =2in10, which uses a recirculating loop composedof an SSMF installed span in the city of Torino.Experimental ResultsOff-line processing for BER evaluation has beencarried out on 217 bits. We employ theoverlap-save method to process the signal infrequency-domain, using an FFT block length,NFFT , of 128 samples. Linear equalizationis performed by a frequency-domain chromaticdispersion equalizer (CDE). Digital nonlinearequalization is performed using both the SSFand VSNE methods. The SSF method withN steps per span is denoted as SSFN .Single- and dual-pol approaches have alsobeen compared. Polarization demultiplexing andresidual dispersion compensation are performedby a 25 taps adaptive filter driven by the constantmodulus algorithm (CMA). Phase estimation isimplemented by the Viterbi-Viterbi algorithm.Finally, BER evaluation is carried out after symboldecoding.In Fig. 1 we show the evolution of BER as afunction of input power in scenario i), propagatedover 16 (Fig. 1(a)) and 31 spans (Fig. 1(b)).For both models, we have observed that themaximum SSF performance is attained with only1 step per span. This stems from the low temporalresolution (1.6 samples per symbol) associatedwith narrow electrical filtering at the oscilloscope,imposing severe limitations on the performanceof nonlinear equalization. The same limitation issetting the performance of VSNE. On the otherhand, for both transmission distances we observethat the dual-pol versions of SSF and VSNEenable to increase the optimum input power byabout 0.7 dB, simultaneously reducing the BERby a factor of 2.5× and 2.2× for the 16 and 31spans cases, respectively.In Fig. 2 we provide a similar analysis forscenario ii) composed of 50 spans with a25 Gbaud PM-QPSK input signal. Advantagesof scenario ii) are twofold: temporal resolutionis increased to 2 samples per symbol and theoscilloscope bandwidth limitation is less stringentat 25 Gbaud. In this scenario, the best SSFTh.1.D.1.pdf ECOC Technical Digest © 2012 OSA- 4 - 3 - 2 - 1 0 11 0 - 41 0 - 31 0 - 20 . 7  d B1  d B1 . 7  d B5  ×  BERI n p u t  P o w e r  [ d B m ] C D E  C D E  +  V S N E S S F 1  d u a l - p o l  S S F 1 C D E  +  d u a l - p o l  V S N Ea )2 . 5  ×2  ×- 3 - 2 - 1 01 0 - 31 0 - 21 0 - 11 . 6  d B0 . 7  d B0 . 9  d B3 . 5  ×1 . 6  ×2 . 2  ×b )  BERI n p u t  P o w e r  [ d B m ] C D E  C D E  +  V S N E   S S F 1  d u a l - p o l  S S F 1 C D E  +  d u a l - p o l  V S N EFig. 1: BER results obtained for scenario i) composedof: a) 16 spans; b) 31 spans. Solid/dashed lines areobtained by third-order polynomial fittings of data.performance is now attained at 4 steps per span(for clarity reasons, SSF1 is not show in thegraph). The dual-pol equalizers provide around1 dB improvement in terms of optimal inputpower and a BER reduction of ∼2.7×. However,the negligible improvement of VSNE over SSF4denotes that the equalization accuracy is stillbeing limited by the available electrical bandwidth.In fact, besides limiting the accuracy of nonlinearequalization in general, a low receiver bandwidthalso works as an anti-aliasing filter, reducing theVSNE performance gain over SSF, as reportedin3. In this sense, the use of lower symbol ratescan be beneficial for nonlinear equalization.ConclusionsRecurring to experimental data, we havedemonstrated the high performance of a dual-pol VSNE in different propagation scenarios.The dual-pol VSNE has shown to attain themaximum accuracy of its SSF counterpart.Being intrinsically single-step, the VSNEis most beneficial in scenarios with lessstringent temporal resolution and electricalbandwidth limitations, where the maximumSSF performance is attained at several stepsper span. In comparison with the previoussingle-polarization approach, we have shown animprovement of up to 2.7× in BER and 1 dB in- 3 - 2 - 1 0 1 2 3 41 0 - 41 0 - 31 0 - 21 0 - 11  d B3  d B2  d B2 . 7  ×6 . 6  ×  BERI n p u t  P o w e r  [ d B m ] C D E  C D E  +  V S N E    S S F 4  d u a l - p o l  S S F 4 C D E  +  d u a l - p o l  V S N EFig. 2: BER results obtained for scenario ii) composedof 50 spans. Solid/dashed lines are obtained bythird-order polynomial fittings of data.optimum power, with negligible added numericalcomplexity. Although the reported simulation-based nonlinear tolerance improvement3 overSSF could not be achieved in realistic PM-QPSK 100 Gb/s links due to limited electricalbandwidth and sampling rate, the dual-polVSNE has proved its robustness in polarization-multiplexed transmission, enabling linear andnonlinear compensation to be performed inparallel independent stages.AcknowledgmentsThis work was supported in part by the FCT- Fundação para a Ciência e a Tecnologia,through the Ph.D. Grant SFRH/BD/74049/2010,by EURO-FOS, a Network of Excellence fundedby the European Union through the 7th ICT-Framework Programme, by PT Inovação, SA,through the project “AdaptDig” and by the FCTand the Instituto de Telecomunicações, under thePEst-OE/EEI/LA0008/2011 program, project NG-COS.References[1] F. Yaman et al., J. Lightwave Technol. 2, 816(2010).[2] Z. Pan et al., Proc. OFC’11, JThA40 (2011).[3] F. Guiomar et al., Opt. Express 20, 1360(2012).[4] L. Zhu et al., Electron. Lett. 16, 1140 (2010).[5] S. Savory et al., IEEE Photon. Technol. Lett.22, 673 (2010).[6] F. Zhang et al., Electron. Lett. 46, 353 (2010).[7] H.-M. Chin et al., Proc. OFC’12, JW2A.61(2012).[8] L. Liu et al., J. Lightwave Technol. 30, 310(2012).[9] G. Gavioli et al., IEEE Photon. Technol. Lett.22, 1419 (2010).[10] G. Gavioli et al., IEEE Photon. Technol. Lett.22, 371 (2010).

Experimental Demonstration of a Frequency-Domain Volterra Series Nonlinear Equalizer in Polarization-Multiplexed Transmission

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Experimental Demonstration of a Frequency-Domain Volterra Series Nonlinear Equalizer in Polarization-Multiplexed Transmission

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