Multi-eigenvalues transmission with information encoded simultaneously in
both orthogonal polarizations is experimentally demonstrated. Performance below
the HD-FEC limit is demonstrated for 8-bits/symbol 1-GBd signals after
transmission up to 207 km of SSMF

Da Ros, Francesco

da Silva, Edson Porto

Gaiarin, Simone

Perego, Auro Michele

Zibar, Darko

English

arXiv

S. Gaiarin

A. M. Perego

E. P. da Silva

F. Da Ros

D. Zibar

Crossref

Experimental Demonstration of Dual Polarization Nonlinear Frequency Division Multiplexed Optical Transmission System

Multi-eigenvalues transmission with information encoded simultaneously in both orthogonal polarizations is experimentally demonstrated. Performance below the HD-FEC limit is demonstrated for 8-bits/symbol 1-GBd signals after transmission up to 207 km of SSM

Perego, A. M.

Porto da Silva, Edson

Online Research Database In Technology

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M.; Porto da Silva, Edson; Da Ros, Francesco; Zibar, DarkoPublished in:Proceedings of 43rd European Conference and Exhibition on Optical CommunicationsPublication date:2017Document VersionPeer reviewed versionLink back to DTU OrbitCitation (APA):Gaiarin, S., Perego, A. M., Porto da Silva, E., Da Ros, F., & Zibar, D. (2017). Experimental Demonstration ofDual Polarization Nonlinear Frequency Division Multiplexed Optical Transmission System. In Proceedings of43rd European Conference and Exhibition on Optical CommunicationsExperimental Demonstration of Dual Polarization NonlinearFrequency Division Multiplexed Optical Transmission SystemS. Gaiarin(1), A. M. Perego(2), E. P. da Silva(1), F. Da Ros(1), and D. Zibar(1)(1) DTU Fotonik, Technical University of Denmark, Lyngby, 2800, Denmark simga@fotonik.dtu.dk(2) AIPT, Aston University, Birmingham B4 7E7 UK, peregoa@aston.ac.ukAbstract Multi-eigenvalues transmission with information encoded simultaneously in both orthogonalpolarizations is experimentally demonstrated. Performance below the HD-FEC limit is demonstrated for8-bits/symbol 1-GBd signals after transmission up to 207 km of SSMF.IntroductionThe increasing demand for capacity and the limi-tations in achievable information rates imposed byfiber nonlinearities to the conventional coherenttransmission systems have pushed part of the re-search community to investigate new techniquesto encode and transmit information over the fiberchannel. Starting from the inverse scatteringtransform theory, the concept of nonlinear fre-quency division multiplexed (NFDM) system hasbeen introduced few years ago1.The first investi-gations focused on modulating only the position ofa few discrete eigenvalues and transmitting overshort distances. Further extensive research en-abled to demonstrate NFDM systems using multi-ple degrees of freedom (eigenvalue, spectral am-plitude) transmitting through thousands of kilome-ters2,3.Nevertheless, NFDM systems still suffer frommany challenges which have not yet allowed tomatch the spectral efficiencies achievable by thetechnologically mature linear coherent transmis-sion systems. One of the main limitations isthe inability of taking advantage of both polariza-tions supported by the standard single mode fiber(SMF), which can potentially double the spectralefficiency of such systems. A first preliminary at-tempt in this direction has been reported by thenumerical analysis of4.In this work, exploiting a rigurous mathemat-ical technique, we report, to the best of ourknowledge, the first experimental demonstrationof NFDM transmission independently modulatingthe two polarizations. The information data is en-coded in the phases of the four nonlinear Fourier(NF) coefficients b(λ) corresponding to two dis-crete eigenvalues, using quadrature phase shiftkeying (QPSK). The system is able to reach atransmission distance of 200 km and 160 km atthe hard-decision forward error correction (HD-FEC, BER=3.8×10−3) threshold, over a standardlink with EDFA amplification of 41.5 km and 83 kmSMF fiber spans, respectively.Eigenvalue Pol. X Pol. YRe{λ}Im{λ}Re{b1(λ)}Im{b1(λ)} Im{b2(λ)}Re{b2(λ)}0.3j0.6jFig. 1: Ideal eigenvalues and corresponding spectralamplitude constellations diagrams.Mathematical frameworkThe signal propagation in single mode fibers(SMFs) can be modeled by the so called Man-akov system (MS) which describes the evolutionof the pair of complex field amplitudes q1 and q2corresponding to the two polarizations of the fieldenvelope . The MS for the focusing regime in nor-malized form reads:∂q1∂z= i∂2q1∂t2+ i2q1(|q1|2 + q2|2) ,∂q2∂z= i∂2q2∂t2+ i2q2(|q1|2 + q2|2) , (1)where z and t are the normalized space and timecoordinates respectively. The MS in Eqs. (1) isintegrable by the inverse scattering transform5,also called nonlinear Fourier transform (NFT). It istherefore possible to associate a Lax pair of oper-ators to the MS and define an eigenvalue problemwith eigenvalues λ and eigenvectors ψ. The timeevolution differential equation for ψ , induced bythe eigenvalue problem, is∂tψ1ψ2ψ3 =−iλ q1 q2−q∗1 iλ 0−q∗2 0 iλψ1ψ2ψ3 . (2)By integrating Eq. (2) using appropriate bound-ary conditions, the eigenvalues λ and theNF coefficients {a(λ), b1(λ), b2(λ)} can be ob-tained. Compared to the single-polarization case{a(λ), b1(λ)}), the MS has an additional NF co-efficient, b2(λ). This new degree of freedom canbe used in a NFDM communication system to en-QIRF Amp.PRBS generation and NFT mappingSignal predistortionINFTOptical Carrier IQ ModulationPol. diverse hybridRx DSPDSO 80 GSa/sCoherent frontendTx DSPBPDBPDBPDBPDAWG 64 GS/s, 20 GHzIQTransmission linkSMF 40kmEDFASMF 40kmEDFAPCDP-IQEigen. 1Eigen. 2Eigen. 1Eigen. 2 Fiber laser (Tx/Rx-LO)FLFig. 2: Experimental setup with transmitter and receiver DSP chain. Four constellations (two per polarization) associated to thetwo eigenvalues are shown at the transmitter side (top left) and after 360 km transmission with 41.5-km spans (top right).code twice as many information bits.The time domain waveform associated to aset of NF coefficients can be synthesized froma null field by using the Darboux transformation(DT) for the Manakov system. Such a powerfultechnique allows to add iteratively new eigenval-ues to the NF discrete spectrum by updating thetime domain signals correspondingly. The genericsolution ψ of (2) is transformed by the DT asψ˜ = (λ0I3 −G0)ψ, where G0 = ΨM0Ψ−1,9 withΨ =ψ1 ψ∗2 ψ∗3ψ2 −ψ∗1 0ψ3 0 −ψ∗1 . (3)The ψj are the components of the eigenvalueproblem solution that are being transformed,M0 = diag(λ0, λ∗0, λ∗0) and λ0 is the new eigen-value we want to add to the spectrum. The sig-nals are changed by the DT in the following way:q˜j = qj + 2i(λ∗0 − λ0)u∗j1 +∑2k=1 |uk|2, i = 1, 2 (4)being q˜j the modified component anduj = ψj+1/ψ1, where j = 1, 2 indicates oneof the two polarizations.Experimental setupIn order to demonstrate the advantage providedby the new degree of freedom b2(λ), the dual-polarization NFDM signaling depicted in Fig. 1 isimplemented by choosing two reference eigenval-ues λ1 = 0.3i and λ2 = 0.6i.Data symbols are generated at 1 GBd by map-ping the bits from a pseudo random bit sequenceof length 211 − 1 to the phases of each of theNFT coefficient pairs {b1(λi), b2(λi)} according toa QPSK constellation for b1,2(λ1) and to a QPSKconstellation rotated by pi/4 for b1,2(λ2), (Fig 1).The data so encoded are experimentally trans-mitted through the setup of Fig. 2. Inverse NFT(INFT) is used to generate time waveforms fromthe symbol {b1(λ1), b2(λ1), b1(λ2), b2(λ2)} usingan iterative algorithm based on the DT (see pre-vious section). The digital signal is pre-distortedto compensate for the Mach-Zehnder modulatornonlinear response and the waveforms are up-loaded to an arbitrary waveform generator (AWG,20-GHz analog bandwith and 64-GSa/s) whichdrives a dual polarization I/Q modulator. The opti-cal input of the modulator is a fiber laser (FL) with∼1 kHz linewidth, which is amplified after mod-ulation and transmitted to a fiber link of multiplespans of SMF with dispersionD = 17.5 ps/nm·km,nonlinear coefficient γ = 1.25 W−1km−1 and at-tenuation α = 0.195 dB/km.At the receiver, the polarization demultiplexingis performed manually through a polarization con-troller as no blind polarization demultiplexing al-gorithms for the NFT are yet available. The signalis then detected in homodyne configuration by us-ing a standard coherent receiver (33-GHz analogbandwidth, 80 GSa/s). The acquired digital signalis rescaled to the ideal power of the signal gener-ated by the INFT and low-pass filtered to removethe out of band noise. FFT-based coarse clockrecovery is used in order to align the pulse to thecenter of the processing time window. The sig-nal is then passed to the NFT block which firstlocates the eigenvalues λi (zeros of the NFT coef-ficient a(λi)) and then computes b1,2(λi). In orderto minimize numerical errors, the NFT coefficientsDistance [Km]10 15 20 25BER10-410-310-2 HD-FECPol. 1Pol. 2Avg. BERλ2λ1Fig. 3: BER as a function of the OSNR in back-to-back.Distance [Km]40 120 200 280 360BER10-410-310-210-1HD-FECPol. 1Pol. 2λ2λ1Distance [Km]80 240 400 560 720HD-FECPol. 1Pol. 2λ2λ1Distance [Km]40 200 360 520 680HD-FEC40km span80km spanFig. 4: BER as a function of the transmission distance for each individual eigenvalue for 41.5 km (a) and 83 km (b) spans.(c) Comparison of the average BER versus transmission distance between links of the two different span lengths.are computed by integrating (2) using a general-ized version of the forward-backward trapezoidalalgorithm7. The standard blind phase search al-gorithm is used independently on each of the con-stellations to perform carrier phase estimation.Experimental resultsThe proposed system is first tested in a back-to-back (BTB) configuration by removing the trans-mission link and varying the optical signal to noiseratio (OSNR) at the receiver input through noiseloading. The measured signal bit error rate (BER)is shown in Fig. 3. The BER averaged over thefour constellations saturates toward a value of5×10−4 as the OSNR is increased. The maincontribution of errors comes from the two con-stellations of λ2. As shown in Fig. 2 (top left) atmaximum OSNR, both constellations related toλ2 are more noisy and distorted at the transmit-ter due to the higher peak-to-average power ra-tio of the λ2-pulse portion, and the limited digitalto analog converter resolution. Additionally, im-perfections in the digital signal processing (DSP)chain at the receiver can introduce further degra-dation. For example, sub-optimum timing recov-ery due to noise, results in distortions of the re-ceived constellations, and an increment in BER.Such a transceiver-induced penalty could be im-proved by more sophisticated DSP schemes.The system is then tested by transmitting overa link of SMF fibers spans, first with spans of41.5 km and then with spans of 83 km. InFig. 4 (a) and (b) the BER curves for the four dif-ferent b(λ) are shown as a function of the trans-mission distance for the 41.5 km and 83 km spanscase respectively. As in Fig. 3, the BER is sensi-bly higher for b1,2(λ2) as already hinted by the re-ceived constellations after a 360-km transmission(Fig. 2). The constellations associated to λ2 aremore degraded while those associated to λ1 arestill well defined. The performance of b1(λi) andb2(λi), which are associated to the two polariza-tions, are instead similar for the same eigenvaluei. In Fig. 4 (c) we compare the average BER forthe two span lengths. Theoretically, worse per-formance may be expected for the longer spans(further away from lossless transmission). Theresults of Fig. 4 (c) instead, do not show a rele-vant difference and the performance are similarin the two cases at the same transmission dis-tance. This is probably due to the performancebeing mainly limited by transceivers impairments,so that the losses play a minor role. Transmissiondistances up to 200 km for the configuration using41.5 km long spans and up to 160 km for the oneusing spans of 83 km are achievable with a BERbelow the HD-FEC threshold of 3.8×10−3.ConclusionsThe results presented in the paper demonstratethat polarization multiplexing in NFDM systems isfeasible and can lead to a potential increase of thespectral efficiency achieved up to now. The per-formance of the two polarizations fields reportedare similar, while there is a clear difference inBER between constellations associated to differ-ent eigenvalues.AcknowledgementsThis work is supported by the Marie Curie Actionsthrough ICONE Project (no. 608099). We thank M.Kamalian for the stimulating discussions.References[1] Y. I. Mansoor, F. Kschischang, ”Information Trans-mission Using the Nonlinear Fourier Transform, PartI:MathematicalTools,” IEEE Trans on Inf. Theory, Vol.60(7), p. 4312-4328 (2014).[2] S. K. Turitsyn et al. “Nonlinear Fourier transform for opti-cal data processing and transmission: advances and per-spectives,” Optica, Vol. 4(3), p. 307 (2017).[3] V. Aref, S. T. Le, and H. Buelow, “Demonstration of FullyNonlinear Spectrum Modulated System in the Highly Non-linear Optical Transmission Regime,” ECOC, Th.3.B.2,Du¨sseldorf (2016).[4] A. Maruta, Y. Matsuda, “Polarization division multiplexedoptical eigenvalue modulation”, PS, Florence, 2015[5] S. V. Manakov, “On the theory of two-dimensional station-ary self-focussing of electromagnetic waves”, Sov. Phys.-JETP Vol. 38, no.2 p. 248 (1974).[6] O. C. Wright, “The Darboux transformation of some Man-akov systems,” Applied Mathematics Letters Vol.16, p. 647(2003).[7] V. Aref, “Control and detection of discrete spectral ampli-tudes in nonlinear fourier transform,” arxiv:1605.06328v1(2016).

Experimental Demonstration of Dual Polarization Nonlinear Frequency
  Division Multiplexed Optical Transmission System

Experimental Demonstration of Dual Polarization Nonlinear Frequency Division Multiplexed Optical Transmission System

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