Digital Nonlinearity Compensation in High-Capacity Optical Fibre Communication Systems: Performance and Optimisation

Digital Nonlinearity Compensation in High- Capacity Optical Fibre Communication Systems: Performance and Optimisation Tianhua Xu Connected Systems Group, School of Engineering University of Warwick Coventry, UK tianhua.xu@warwick.ac.uk Nikita A. Shevchenko Optical Networks Group, Department of Electronic & Electrical Engineering University College London London, UK mykyta.shevchenko.13@ucl.a c.uk Boris Karanov Optical Networks Group, Department of Electronic & Electrical Engineering University College London London, UK boris.karanov.16@ucl.ac.uk Gabriele Liga Optical Networks Group, Department of Electronic & Electrical Engineering University College London London, UK gabriele.liga.11@ucl.ac.uk Domaniç Lavery Optical Networks Group, Department of Electronic & Electrical Engineering University College London London, UK d.lavery@ucl.ac.uk Robert I. Killey Optical Networks Group, Department of Electronic & Electrical Engineering University College London London, UK r.killey@ucl.ac.uk (In vited) Polina Bayvel Optical Networks Group, Department of Electronic & Electrical Engineering University College London London, UK p.bayvel@ucl.ac.uk Abstract — Meeting the ever-growing information rate demands has become of utmost importance for optical communication systems. However, it has proven to be a challenging task due to the presence o f Kerr effects, which have largely been regarded as a major bottleneck for enhancing the achievable information rates in modern optical communications. In this work, the optimisation and performance of digital nonlinearity compensation are discussed for maximising the achievable info rmation rates in spectrally-efficient optical fib re communication systems. It is found that, for an y given target information rate , there exists a trade-off between modulation format and compensat ed bandwidth to reduce the computational complexity requirement of digital nonlinearity compensation. Keywords — optical communication, achievable information rate, digital nonlinearity compensation, modulation format, digital back-propagation I. I NTRODUCTION Optic al ne twor ks f orm an int egra l pa rt o f the worl d-wide comm unic ation infras truc tur e and n owada ys ove r 95% of all digit al da ta tr affi c is ca rrie d over optica l fibr es . Achi eva ble inform ati on rat es (A IRs), whi ch ar e natur al f igures of m erit in coded commun ica tion syst ems for demons trati ng the net data rate s achieve d [1 -4], ha ve increa sed grea tly over the past few decade s with the deve lopm ent of multi plexi ng tech nique s, impr oved opti cal fibres and ampli fier s, advanc ed modul atio n form ats, detecti on schem es and di gita l signa l proce ssi ng (DSP) [5 -14]. These technol ogie s togethe r facili tate d the revol ution of the commun icati on system s and the ra pid growt h of the Int erne t. Curre ntly , optica l fibre comm unic ation s are challeng ed to meet the massi ve surge of inform ati on ra te dem ands . Howe ver, the prese nce of Ker r effec ts in fibr e medium is widely believe d to impose an ultim ate lim it on furthe r enhancem ent of the achieva ble inform ati on ra tes in optic al comm uni catio n system s. The signa l di stort ions as an effe ct of the fibr e nonlinea rity are mor e signif icant in the system s that util i se large r transm is sion bandw idths , clos er channel spacing as well as highe r-ord er modul ati on for ma ts [15 - 20 ] . Signi fica nt researc h effo rts have been conc entrat ed on the miti gati on of the nonlinea rit y-induc ed degradat ions in optical transm is sion. A numbe r of nonl inea r c ompe nsat ion (NL C) techn iques have been inves tiga ted, such as digit al back- propa gati on (DBP), nonline ar pre-di stor tion, Volter ra equal isat ion , optical phase conjugati on, nonline ar Fourier trans form and twin-wave phase conjuga tion , etc. [ 21 - 28 ]. Singl e-cha nnel DBP, i.e. compens ati ng only for intra-c hann el nonli near iti es (self-ph ase modula tion ), has bee n suggest ed as a low-com plexi ty compe nsat ion schem e which may reali se potent ial cos t s aving s i n ne wly depl oyed sy stem s [ 29 - 31 ]. Nevert hel ess , for a subs tant ial i ncrea se in the achievabl e inform ati on rates, mul ti-c hanne l DBP (MC -DBP ) has been widel y considere d as a promi sing approac h as it compe nsates for both int ra-c hanne l and int er-cha nne l fibre nonli neari tie s in dense wavele ngt h divis ion multipl exe d (WDM) opti cal comm unic ation syst ems [32- 39]. In thi s paper, the perfor ma nce and the optimi sati on of MC-DBP is dis cusse d from the perspec tive s of signal-t o-nois e ratio (SNR) and AIR enhanc em ent in the compe nsat ed fibre-op tic communic ation syst ems, where different high-c ardi nali ty modul ati on form ats such as dual-pol aris ati on quadrat ure phase shif t keying (DP- QPSK) , dual-pol aris ati on 16-level quadr atur e amplitud e modul ati on (DP-16QAM) , DP-64QAM and DP -25 6QA M, are appli ed. Both num erica l simula tions and anal yti cal mode lling have been carr ied out in a represent at ive comm unic ation system consist ing of nine 32 -Gbaud Nyquist - space d WDM cha nnels t ransm itt ed over a standard sing le- mode fibr e (SS MF) link. In the c ase wh ere ful l-fiel d DBP is appli ed to com pensa te for all nonline ar si gnal-si gnal inter acti ons our inv esti gatio n shows that the remaini ng distor tions due to sign al-noi se beat ing become mod ulat ion format independent. On the other hand, the pres enc e of sig nal-s ignal nonli near ity , when onl y an elec troni c di spersi on com pe nsat ion (E DC) or a pa rtia l- bandw idth DB P is utilised, exhibit s a conside rabl e depen dence on the m odul ati on for mat appl ied. Rega rding the backpro pagat ion optim isati on, when AIRs are conside red the m inim um requir ed number of ste ps per span (M RNS PS) pa ram eter i n the DBP algorit hm dem onstr ates a stron g depend ence on the modul ati on forma t for differe nt back-prop aga ted bandwi dths. This is in contra st to the obtaine d MRNSPS wit h respect to SNR optimis ation which does not show any mod ulat ion form at dependenc e in the m ulti -cha nnel D BP sc hem es un der i nves tiga tion. Our study indic ates that for any given target inform ation rate t he compl exity requirem ent of the MC-DBP com pensa tion can potenti ally reduce , benefi tting from the exis ting trade- off between modul ati on format and ba ck- propa gate d ban dwidt h. II. T RANSMISSION S ETUP T he nume rica l setup of the 9-channe l 32-Gb aud Nyquist - space d superch annel optic al transm issi on system is illust rated in Fig. 1. The app lie d modula tion form ats are DP -QPSK, DP- 16QAM , DP-64QAM and DP-256Q AM. The phase-l ocke d optic al carri ers in the transmitt er are generated using a 9-li ne 32 -GHz spaced lase r comb, and are de -multi ple xed before I- Q optica l modula tors. The data in each channel are indepe ndent a nd ra ndom , and t he sy mbo ls are furt her de - corre late d with a delay of half the seque nce length in the two ortho gonal polari sat ions . The Nyquis t pulse shaping (NPS) is real ised using a root -raised cosi ne (RRC) filter with a roll-off of 0.1%. The SSMF span is simul ated using the Mana kov equat ion sol ved by the spl it- step Fourier method with a logar ithm ic distribut ion of the step size [40,41]. The erbium - doped optica l fibre amplifi er (EDF A) is applied to com pensa te for the loss in ea ch fibr e spa n. A t t he rec eiver end , the optic al signal s are mixed with the local oscill ator ( LO ) lase r to im pleme nt a n ide al cohe re nt det ect ion. TABLE I. T RANSMISSION S YSTEM P ARAME TERS Parameter Value Symbol rate 32 Gbaud Channel spacing 32 GHz Central wavelengths (both Tx and LO) 1550 nm Number of channels 9 Roll-off 0.1 % Attenuation coefficient 0.2 dB /km Chromatic dispersion coefficient 17 ps/nm/km Nonlinear coefficient 1.2 /W/km Span length 80 km Number of spans 25 SS MF steps per span (logarithmic step -size) 800 EDFA noise figure 4.5 dB In the DSP part, EDC is realise d using freque ncy-d om ain equal isat ion [42,43] , and the MC-DBP is perform ed using an rever se split -ste p Fouri er solut ion of the Manakov equa ti on [21 ,33,3 5]. An ide al RRC filter is furthe r empl oyed to cha nge the back-pr opa gate d bandwidt h in the MC-DBP modul e. The consi dered back-p ropa gate d band widt hs ran ge from 32 -GHz (1-cha nnel NLC) to 288-GHz (full-fie ld NLC). The matche d filt er the n sel ects the cent ral cha nnel and re mov es th e cross talk f rom neigh bour ing c hannel s. The SNR of the c entr al channe l is eva luat ed over 2 18 sym bol s, and the m utual inform ati on (MI ) i s c alc ulat ed from t he obta ined SN R, as Fig. 1. Schematic of Nyquist-sp aced optical communication system using multi -channel digital nonlinearity compensatio n (MC -NLC). disc ussed in [2, 31,38] . A digita l re solut ion is 2 sampl e/sym bol/ cha nnel to guara ntee the accura cy of nume rical simul ati ons. The phase noise fro m the transm itt er and LO lase rs, the frequency offset between them, as well as the polaris ation mode dispersi on (PMD) in the opti cal fibres are ne glec ted. Tabl e 1 shows sy stem param ete rs in deta il. III. O PTIMISATION OF M ULTI - CHANNEL D IGITAL B ACK - PROPAGATION Traditionally, the optimisation of MC -DBP algorithm wa s performed in terms of Q 2 factors and SNR performance [ 32 - 34 ]. However, in coded transmission systems, AIR s are more useful indicators which give a measure of the net data rates that can be achieved [1-4]. I n this work, the m ulti- channel DBP algorithm is optimised in terms of both SNR and AIR values, w here the m inimum required number of steps per span for different back-propagated bandwidths and modulation formats are investigated in the considered 9- channel 32-Gbaud Nyquist-spaced optical communication system. Table 2 summarises the minimum required number of steps per span under bot h AIR and S NR optimisation criteria. The obtained results indicate that for a given back- propagated bandwidth in the MC-DBP scheme, the minimum required number of steps per span that achieves the highest possible A IR is depe ndent on the m odulation format applied . Therefore, when optimisation is carried out for maximising the information rates, the choice of modulation format has an integral role. On the other hand, if MC -DBP is optimised with resp ect to the SN R, there is no modulation format dependence. As a consequence, the implications of the AIR optimisation are significant reductions of MRNSPS with decreasing order of modulation cardinality as compared to the SNR -optimised cases. F or instance, full-field DBP maximises the AIR of the DP -QPSK systems when it is performed with 100 steps/span, while the SNR is maximised at 500 steps/span. The comparison between the AIR- and SNR-optimised MRNSPS suggests that the conventional SNR optimisation often overestimates the system requirements. Therefore, in practice the complexity of applying MC-DBP may be considerably reduced if the AI Rs instead of the SNRs are maximised for given m odulation format. TABLE II. M INIMUM R EQUIRED N UMBER O F S TEPS P ER S PAN MRNSPS in terms of AIRs Formats 32 -GHz 96 -GHz 160 -GHz 224 -GHz 288 -GHz DP -QPSK 1 2 5 25 100 DP -16QAM 1 10 25 75 200 DP -64QAM 5 25 75 150 250 DP -256QAM 5 25 75 150 500 MRNSPS in terms of SNRs DP -QPSK 5 25 75 150 500 DP -16QAM 5 25 75 150 500 DP -64QAM 5 25 75 150 500 DP -256QAM 5 25 75 150 500 IV. R ESULTS A ND D ISCUSSIONS In this section, the performance of MC-DBP is studied with respect to both SNR and AIR. The transmission link is 2000 km (25 span× 80 km) SSMF. The nonlinear coefficient and the number of steps per span in the MC-DBP module are always the same as those in the transmission fibre to guarantee an optimal operation of MC -DBP. Simulation results of SNR versus optical signal power per channel at different back-propagated bandwidths and modulation formats are shown in Fig. 2. The results show that in the cases of EDC and up to 7 -channel NLC, the DP- Fig. 2. Signal- to -noise ratio (SNR) v ersus optical launch power fo r systems with linear and multi-channel nonlinear ity compensation. 16QAM, DP-64QAM and DP-256QAM systems have identical SNR perform ance, while the DP-QPSK system outperforms the other three modulation formats. This indicates that the nonlinear distortions in the cases of EDC and partial-bandwidth NLC, which are mainly from signal- signal interactions, depend on m odulation format, and signal- signal interactions in the DP-QPSK system are smaller than in the systems using oth er higher -level modulation formats. This conclusion is consistent with earlier reports [4 4-46]. However, in the case of full-field NLC, all systems show similar SNR behaviour independent of the modulation formats applied. This demonstrates that the remaining nonlinear distortions for full-field NLC, which are mainly signal-noise interactions, do no t depend on modulation formats. Fig. 3 shows the simulated AIRs as a function of optical signal power per channel for the investigate d transmission system at different back-propagated bandwidths, where different modulation formats are applied. I t is found that in terms of AIRs the highest gain for full-field NLC is achieved at the highest-orde r modulation format (DP -256QAM), and is 1.34 Tbit/s (from 2 .86 Tbit/s at -2 dBm in EDC to 4.20 Tbit/s at 6.5 dBm in full-field NLC) . Furthermore, it can be observed in Fig. 3 that the AIR of the DP- 25 6QAM system using 7-channel NLC is higher than that in the DP-64QAM system using full-field NLC, if the signal power is less than 3.5 dBm. For any examined power, the AIR of the DP- 256QAM system using 7- channel NLC exceeds the AI Rs of the fu ll -field NLC cases in the DP -16QAM and DP-QPSK systems. Therefore, to achieve a given target AIR, a compromise could be made between the modulation format selection and the back-propagated bandwidth. Th e complexity of signal processing schemes may be traded for modulation generation complexity. In general, the effects of such a trade-off will depend on the particular transmission distance. V. C ONCLUSIONS In this pape r, both the optim is ation and perform ance of digit al MC-NLC was studied from the perspe cti ves of SNR and AIR in the long-haul optic al fibre comm unica tion syst ems, when diffe rent modula tion format s are appli ed . Nume rical simul ati ons were carri ed out in a 9-channe l 32 - Gbaud Nyquis t-s pace d optical comm unica tion system base d on the SSMF transmi ssion . Our results show that no nli near dist orti ons in the case of full-fi eld NLC , which arise from signa l-noi se interac tion s, exhibit no modulat ion forma t depen dence . On the othe r hand , no nline ar distorti ons in the syst em using EDC and partia l-bandwi dth NLC, which mai nly aris es from signa l- si gna l inter acti ons, show consi dera ble depen dence on the m odul ati on for mat s appl ied. Furthe rm ore, the mi nim um required numbe r of steps per span in the MC-NLC algorithm has been invest igat ed in term s of the AIRs in the compens ated commun icati on syst ems and were compa red to the cases where the SNRs are optim ise d. It is observed tha t in the AI R optim is ation the mini mum requi red num ber of st eps pe r spa n at di ffer ent bac k- propa gate d bandwi dths str ongl y depends on the modul atio n form at ap plie d, in c ontra st to th e sche me of SNR opt imi sati on where for a given back- prop agat ed bandwi dth th e numbe r of steps per s pan requi red i s t he s ame for al l m odulat ion form ats . 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