applied sciences
Article Phase Noise Cancellation in Coherent Communication Systems Using a Radio Frequency Pilot Tone
Tianhua Xu 1,2,3,* , Cenqin Jin 2, Shuqing Zhang 4,*, Gunnar Jacobsen 5,6, Sergei Popov 6, Mark Leeson 2 and Tiegen Liu 1
1 Key Laboratory of Opto-Electronic Information Technology (MoE), School of Precision Instruments and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China; [email protected] 2 School of Engineering, University of Warwick, Coventry CV4 7AL, UK; [email protected] (C.J.); [email protected] (M.L.) 3 Optical Networks Group, University College London, London WC1E 7JE, UK 4 Department of Optical Engineering, Harbin Institute of Technology, Harbin 150001, China 5 NETLAB, RISE Research Institutes of Sweden, SE-16440 Stockholm, Sweden; [email protected] 6 Optics and Photonics Group, KTH Royal Institute of Technology, SE-16440 Stockholm, Sweden; [email protected] * Correspondence: [email protected] (T.X.); [email protected] (S.Z.)
Received: 26 September 2019; Accepted: 3 November 2019; Published: 5 November 2019
Featured Application: This work is performed for the compensation of the laser phase noise (LPN) and the equalization enhanced phase noise (EEPN) in high-capacity, long-haul, coherent optical fiber networks.
Abstract: Long-haul optical fiber communication employing digital signal processing (DSP)-based dispersion compensation can be distorted by the phenomenon of equalization-enhanced phase noise (EEPN), due to the reciprocities between the dispersion compensation unit and the local oscillator (LO) laser phase noise (LPN). The impact of EEPN scales increases with the increase of the fiber dispersion, laser linewidths, symbol rates, signal bandwidths, and the order of modulation formats. In this work, the phase noise cancellation (PNC) employing a radio frequency (RF) pilot tone in coherent optical transmission systems has been investigated. A 28-Gsym/s QPSK optical transmission system with a significant EEPN has been implemented, where the carrier phase recovery (CPR) was realized using the one-tap normalized least-mean-square (NLMS) estimation and the differential phase detection (DPD), respectively. It is shown that the RF pilot tone can entirely eliminate the LPN and efficiently suppress the EEPN when it is applied prior to the CPR.
Keywords: coherent optical fiber communication; laser phase noise (LPN); carrier phase recovery (CPR); phase noise cancellation (PNC); equalization enhanced phase noise (EEPN); radio frequency (RF) pilot tone
1. Introduction Long-haul optical communication is seriously deteriorated by transmission impairments, e.g., chromatic dispersion (CD), polarization mode dispersion (PMD), laser phase noise (LPN), and Kerr fiber nonlinearities [1,2]. The combination of coherent detection, digital signal processing (DSP), and advanced modulation formats offers a very promising solution for long-haul, high-capacity optical transmission, to offer great capabilities and flexibilities in the design, deployment, and operation of core telecommunication networks [3–5]. In the reported phase noise cancellation (PNC) methods, the radio frequency (RF) pilot tone scheme was verified to be an efficient approach to remove laser phase
Appl. Sci. 2019, 9, 4717; doi:10.3390/app9214717 www.mdpi.com/journal/applsci Appl. Sci. 20192019,, 99,, x 4717 FOR PEER REVIEW 22 of of 9 radio frequency (RF) pilot tone scheme was verified to be an efficient approach to remove laser phase fluctuationsfluctuations [6–9]. [6–9]. However, However, these these works only studied the the behaviors of RF pilot tones in short short-reach‐reach systems, where the enhancement effect effect of fiber fiber dispersion on the the LPN LPN was was neglected neglected [10,11]. [10,11]. Actually, Actually, due toto thethe interplay interplay between between the the electronic electronic dispersion dispersion compensation compensation (EDC) (EDC) module module and theand LPN the fromLPN fromthe local the local oscillator oscillator (LO), (LO), a phenomenon a phenomenon of equalization of equalization enhanced enhanced phase phase noise noise (EEPN) (EEPN) is induced is induced and andplays plays a significant a significant role in therole carrier in the phase carrier recovery phase (CPR) recovery in high-capacity (CPR) in opticalhigh‐capacity communication optical communicationsystems [10–16]. However,systems [10–16]. so far, no However, DSP-based so CPR far, has no been DSP developed‐based CPR to ehasffectively been compensatedeveloped forto effectivelyEEPN [16– 18compensate]. Therefore, for it EEPN will be [16–18]. of great Therefore, significance it to will study be theof great suppression significance of LPN to andstudy EEPN the suppressionusing an RF pilotof LPN tone and scheme. EEPN using an RF pilot tone scheme. In this work, the performance of an orthogonally polarized RF pilot tone scheme is investigated for eliminating both the LPN and the EEPN in long-haullong‐haul optical transmission systems. A 28 28-Gsym‐Gsym/s/s quadrature phase shift keying (QPSK) system is numerically implemented, where the CPR is realized realized using a one one-tap‐tap normalized least mean square (NLMS) estimation and a differential differential phase detection (DPD) scheme,scheme, respectively respectively [ 19[19–21].–21]. The The results results show show that that the the LPN LPN can becan fully be fully removed removed and the and EEPN the EEPNcan also can be also effectively be effectively suppressed, suppressed, when the when RF the pilot RF tone pilot scheme tone scheme is applied is applied prior to prior the CPR. to the CPR.
2. EEPN EEPN in in Optical Optical Communication Communication Systems Figure 11 describesdescribes thethe blockblock diagramdiagram ofof a a long-haul, long‐haul, coherent coherent optical optical communication communication systemsystem with EDC EDC and and CPR. CPR. The The LPN LPN from from the the transmitter transmitter (Tx) (Tx) laser laser passes passes through through the the optical optical fiber fiber and and the dispersionthe dispersion compensation compensation unit, unit, and andthus thus the net the CD net CDexperienced experienced by the by Tx the LPN Tx LPN approaches approaches zero. zero. By contrast,By contrast, the the LO LO LPN LPN goes goes only only through through the the dispersion dispersion compensation compensation unit. unit. Consequently, Consequently, the the LO LPN interplaysinterplays with with the the dispersion dispersion compensation compensation component component in EDC in andEDC the and interactions the interactions will degrade will degradethe performance the performance of the optical of the communication optical communication system. Thissystem. effect This is called effect EEPNis called [10 EEPN–13]. [10–13].
Figure 1. BlockBlock diagram diagram of coherent transmission system and equalization-enhancedequalization‐enhanced phase noise (EEPN). ϕφTx:: Tx Tx laser laser phase phase noise noise (LPN), (LPN), ϕφLOLO: LO: LO LPN, LPN, ADCs: ADCs: analogue analogue-to-digital‐to‐digital converters. converters.
The variance of the EEPN distortion will increase with fiber fiber dispersion, local oscillator laser linewidth, and signal symbol rate. The noise variance of EEPN can be written as follows [10,19]: [10,19]:
2 2 2 πλ DD LL∆ ffLO 2 LO , (1) σEEPNEEPN= · · , (1) 2c2c· TTSS where λ is the central wavelength of the optical carrier, c is the speed of the light in vacuum, L is the length, D is the CD coecoefficientfficient of the fiber,fiber, TTSS isis thethe symbolsymbol periodperiod ofof thethe signal,signal, andand Δ∆ffLOLO isis the 3 3-dB‐dB linewidth of the LO laser. It is noted that the EEPN evaluation in Equation (1) only works for the static time-domaintime‐domain and frequencyfrequency-domain‐domain EDCs, which involve no phase noise compensation functionsfunctions [[22,23].22,23].
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3. CPR Using One‐Tap NLMS 3. CPR Using One-Tap NLMS A one‐tap NLMS filter could be effectively applied in the CPR [20], and its tap weight w(k) is expressedA one-tap using NLMS the following filter could equations: be effectively applied in the CPR [20], and its tap weight w(k) is expressed using the following equations: wk1 wk x* k ek, µ 2 (2) w(k + 1) = w(k) + xk x (k)e(k), (2) 2 ∗ x(k) ek dk wk xk , e(k) = d(k) w(k) x(k), (3) − · where x((k)) is the input signal, k is the symbol index, d(k) is is the the desired desired symbol, e(k) is is the the error error between between the output and the desired symbols, and µμ represents aa parameterparameter ofof thethe stepstep size.size. The schematic ofof the the NLMS NLMS CPR CPR is is illustrated illustrated in in Figure Figure2, which 2, which can can actually actually be implemented be implemented in a infeed-forward a feed‐forward structure structure and canand be can realized be realized in parallel in parallel in the fieldin the programmable field programmable gate array gate (FPGA) array (FPGA)circuits forcircuits a real-time for a real operation‐time operation [4]. [4].
Figure 2. BlockBlock diagram diagram of of the the one one-tap‐tap normalized normalized least least-mean-square‐mean‐square (NLMS) carrier phase recovery (CPR).
Similar to the definition of the Tx and the LO, a concept of effective linewidth ∆f is employed Similar to the definition of the Tx and the LO, a concept of effective linewidth ΔfEEffff is employed here to describe the total phase noise in coherent transmissiontransmission systemssystems consideringconsidering EEPNEEPN [[17,19]:17,19]: σ222+σ2 + σ 22 f TxTx LO EEPNEEPN ∆ fE fEff f (4)(4) ≈ 22πTTSS
2 2 σTx = 2π∆ fTx TS (5) Tx 2fTx ·TS (5) 2 σLO = 2π∆ fLO TS (6) 2 · LO 2f LO TS (6) 2 2 where σTx and σLO are the LPN variance of the Tx and LO lasers, respectively, and ∆fTx is the 3-dB 2 2 wherelinewidth Tx of and the Tx LO laser. are the LPN variance of the Tx and LO lasers, respectively, and ΔfTx is the 3‐ dB linewidthIt has been of establishedthe Tx laser. that the step size µ can be optimized to enhance the performance of NLMS CPRIt [19 has]. Therefore,been established it is significant that the step to find size theμ can optimal be optimized step size to forenhance NLMS the CPR, performance when the of EEPN NLMS is CPRconsidered [19]. Therefore, in coherent it opticalis significant communication to find the systems. optimal Figure step size3 shows for NLMS the optimal CPR, step when size the parameter EEPN is consideredfor various einffective coherent linewidths optical in communication the 28-Gsym/s QPSK systems. system, Figure applicable 3 shows to the the time-domain optimal step and size the parameterfrequency-domain for various static effective dispersion linewidths equalizations in the [2822‐,Gsym/s23]. In all QPSK numerical system, simulations applicable in to this the paper,time‐ domainthe NLMS and algorithm the frequency is operated‐domain with itsstatic corresponding dispersion optimal equalizations value of the[22,23]. step size.In all numerical simulations in this paper, the NLMS algorithm is operated with its corresponding optimal value of the step size. Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 9 Appl.Appl. Sci. Sci.2019 2019, 9,, 9 4717, x FOR PEER REVIEW 44 of of 9 9
FigureFigureFigure 3. 3.The 3.The optimalThe optimal optimal step step stepsize size parameter size parameter parameter in inthe inthe NLMS the NLMS NLMS CPR CPR CPR for for various for various various effective effective effective linewidths. linewidths. linewidths. 4. Differential Carrier Phase Recovery 4. 4.Differential Differential Carrier Carrier Phase Phase Recovery Recovery Differential phase detection (DPD) can also be employed for recovering the carrier phase in DifferentialDifferential phase phase detection detection (DPD) (DPD) can can also also be be employed employed for for recovering recovering the the carrier carrier phase phase in in coherent communication systems. In the DPD scheme, signal data are encoded in and extracted from coherentcoherent communication communication systems. systems. In In the the DPD DPD scheme, scheme, signal signal data data are are encoded encoded in in and and extracted extracted from from the phase differences between consecutive transmitted signal symbols [21]. For instance, the phase thethe phase phase differences differences between between consecutive consecutive transmitted transmitted signal signal symbols symbols [21]. [21]. For For instance, instance, the the phase phase information of the k-th symbol can be extracted according to the phase difference between the k-th informationinformation of of the the k‐ thk‐th symbol symbol can can be be extracted extracted according according to to the the phase phase difference difference between between the the k‐ thk‐th and the (k + 1)-th symbols. Therefore, the CPR error is determined by the phase fluctuation between andand the the (k (+k 1)+ ‐1)th‐th symbols. symbols. Therefore, Therefore, the the CPR CPR error error is isdetermined determined by by the the phase phase fluctuation fluctuation between between the k-th and the (k + 1)-th symbols within a symbol period [19]. It is noted that DPD does not require thethe k‐ thk‐th and and the the (k (+k 1)+ ‐1)th‐th symbols symbols within within a symbola symbol period period [19]. [19]. It Itis isnoted noted that that DPD DPD does does not not require require additional computations such as the n-power, the averaging, and the phase unwrapping, compared to additionaladditional computations computations such such as as the the n‐ npower,‐power, the the averaging, averaging, and and the the phase phase unwrapping, unwrapping, compared compared other CPR methods [20,24–26]. Therefore, it can be easily implemented in DSP hardware for a real-time toto other other CPR CPR methods methods [20,24–26]. [20,24–26]. Therefore, Therefore, it canit can be be easily easily implemented implemented in in DSP DSP hardware hardware for for a reala real‐ ‐ operation. The block diagram of DPD CPR is provided in Figure4. timetime operation. operation. The The block block diagram diagram of of DPD DPD CPR CPR is isprovided provided in in Figure Figure 4. 4.
FigureFigure 4. 4.SchematicSchematic Schematic of of ofthe the the differential di differentialfferential phase phase detection. detection. 5. Transmission Setup with RF Pilot Tone Scheme 5. 5.Transmission Transmission Setup Setup with with RF RF Pilot Pilot Tone Tone Scheme Scheme Figure5 depicts a 28-Gsym /s QPSK coherent optical fiber transmission system using an RF pilot FigureFigure 5 depicts5 depicts a 28a 28‐Gsym/s‐Gsym/s QPSK QPSK coherent coherent optical optical fiber fiber transmission transmission system system using using an an RF RF pilot pilot tone orthogonally polarized against the transmitted signals. The electrical data were converted into tonetone orthogonally orthogonally polarized polarized against against the the transmitted transmitted signals. signals. The The electrical electrical data data were were converted converted into into 28-Gsym/s QPSK signals using an in-phase and quadrature (I-Q) optical modulator. The modulated 2828‐Gsym/s‐Gsym/s QPSK QPSK signals signals using using an an in in‐phase‐phase and and quadrature quadrature (I ‐(IQ)‐Q) optical optical modulator. modulator. The The modulated modulated signals occupied one polarization state, and the RF pilot tone was transmitted in the orthogonal signalssignals occupied occupied one one polarization polarization state, state, and and the the RF RF pilot pilot tone tone was was transmitted transmitted in in the the orthogonal orthogonal polarization state. The signals and the RF pilot tone are integrated into the fiber via a polarization polarizationpolarization state. state. The The signals signals and and the the RF RF pilot pilot tone tone are are integrated integrated into into the the fiber fiber via via a polarizationa polarization beam combiner (PBC). At the receiver side, both the received signals and the RF pilot tone are mixed beambeam combiner combiner (PBC). (PBC). At At the the receiver receiver side, side, both both the the received received signals signals and and the the RF RF pilot pilot tone tone are are mixed mixed with the LO laser, respectively, and are then detected by balanced photodiodes after the 90 hybrid. withwith the the LO LO laser, laser, respectively, respectively, and and are are then then detected detected by by balanced balanced photodiodes photodiodes after after the the 90° 90°◦ hybrid. hybrid. After that, both the received signals and the RF pilot tone are digitized using 8-bit analogue-to-digital AfterAfter that, that, both both the the received received signals signals and and the the RF RF pilot pilot tone tone are are digitized digitized using using 8‐ bit8‐bit analogue analogue‐to‐to‐digital‐digital converters (ADCs) at 56 Gsym/s and are then equalized using the EDC module. The signals are further convertersconverters (ADCs) (ADCs) at at56 56 Gsym/s Gsym/s and and are are then then equalized equalized using using the the EDC EDC module. module. The The signals signals are are multiplied with a conjugate of the processed RF pilot tone to suppress the impact of both LPN and furtherfurther multiplied multiplied with with a conjugatea conjugate of of the the processed processed RF RF pilot pilot tone tone to to suppress suppress the the impact impact of of both both LPN LPN EEPN. The central wavelengths of both the transmitter and the local oscillator lasers are 1553.6 nm, andand EEPN. EEPN. The The central central wavelengths wavelengths of of both both the the transmitter transmitter and and the the local local oscillator oscillator lasers lasers are are 1553.6 1553.6 1 −1 1−1 nm,and and the fiberthe fiber dispersion dispersion coe fficoefficientcient is 16 is ps16 nmpsnm− km km−1− .. Here,− Here,1 we we havehave neglected fiber fiber attenuation, attenuation, nm, and the fiber dispersion coefficient is 16· psnm km . Here, we have neglected fiber attenuation, PMD,PMD, and and Kerr Kerr nonlinearities nonlinearities [27,28]. [27,28]. The The EDC EDC is isimplemented implemented in in the the frequency frequency domain domain [23]. [23]. The The CPRCPR is isperformed performed using using the the one one‐tap‐tap NLMS NLMS and and DPD DPD methods, methods, respectively. respectively. Appl. Sci. 2019, 9, 4717 5 of 9
PMD,Appl. Sci. and 2019 Kerr, 9, x nonlinearitiesFOR PEER REVIEW [27 ,28]. The EDC is implemented in the frequency domain [23]. The5 CPR of 9 isAppl. performed Sci. 2019, 9, using x FOR thePEER one-tap REVIEW NLMS and DPD methods, respectively. 5 of 9
Figure 5. High‐speed coherent communication system with an orthogonally‐polarized RF pilot tone. Figure 5. HighHigh-speed‐speed coherent communication system with an orthogonally-polarizedorthogonally‐polarized RF pilot tone. 6. Results and Analyses 6. Results Figure and 6 shows Analyses the results of PNC using the RF pilot tone in a 2000 km coherent communication system,Figure where6 6 shows shows the CPR the the results isresults realized of of PNC PNC using using using the NLMS the the RF RF algorithm. pilot pilot tone tone in inIn a aFigure 20002000 kmkm 6a, coherent coherentthe effective communicationcommunication linewidth is system,170 MHz where and thethere the CPR CPR is nois is realized realizedEEPN, usingsince using the the NLMSlinewidth NLMS algorithm. algorithm. of the transmitterIn In Figure Figure 6a, 6lasera, the the effectiveis e 170ffective MHz linewidth linewidth and the is is170linewidth 170 MHz MHz andof and the there thereLO islaser isno no EEPN,is EEPN, 0 Hz. since sinceIt is the thefound linewidth linewidth that both of of the thethe transmitter transmitterTx and the laser laserLO LPNis is 170 170 can MHz be and entirely the linewidthsuppressed. of In the Figure LO laserlaser 6b, the isis 0linewidths Hz.Hz. It It is is foundof found both that that the Txboth both and the the the Tx LO and lasers the areLO 5LPN MHz. can According be entirely to suppressed.Equations (1) In In and Figure (4), 6the6b,b, theEEPNthe linewidthslinewidths is quite significant ofof bothboth thethe in TxTx such andand a the the case, LO LO and lasers lasers the are areeffective 5 5 MHz. MHz. linewidth According According is the to to Equationssame (170 (1)MHz) andand as (4)(4), that, thethe in EEPNEEPN Figure isis quitequite6a. It significantsignificantis found in inin Figure suchsuch a 6b case,case, that and the the theBER eeffectiveff performanceective linewidth improves is the −4 −4 sameconsiderably (170 MHz) (around as that half inin an FigureFigure order6 6a. a.of ItmagnitudeIt isis foundfound ininin Figure theFigure BER6 b6b floor, that that thefrom the BER BER8 × performance10 performance to 3 × 10 improves) improvesusing the 4 4 considerablyRF pilot tone, (around compared half to an the order case of of magnitude NLMS CPR in theonly. BER The floor, results from in 8 Figure10 − 4to6a,b 3 demonstrate10 −4) using the considerably (around half an order of magnitude in the BER floor, from ×8 × 10− to 3× × 10− ) using the RFefficiency pilot tone, of the compared RF pilot totone the in case compensating of NLMS CPR for both only. LPN The and results EEPN. in Figure It can6 6a,bbea,b found demonstrate demonstrate that the theusethe eefficiencyofffi RFciency pilot ofof tone thethe can RFRF pilot pilotentirely tone tone mitigate in in compensating compensating the LPN from for for both bothboth LPN LPNthe andTx and and EEPN. EEPN. the LO It It can lasers.can be be found However, found that that the it the cannot use use of RFoffully RF pilot pilotcompensate tone tone can can entirely for entirely the mitigate EEPN mitigate in the theoptical LPN LPN from fromfiber both bothtransmission the the Tx Tx and and systems the the LO LO lasers. lasers.since However,theHowever, EEPN ititactually cannot fullyrepresents compensatecompensate a complicated for for the the EEPN EEPNintegration in optical in optical fiberof the transmissionfiber phase, transmission the systems amplitude, systems since the and since EEPN the the actuallytime EEPN jitter represents actually noise arepresents[10,12,16,29]. complicated a complicated integration of integration the phase, theof amplitude,the phase, and the the amplitude, time jitter noiseand the [10, 12time,16, 29jitter]. noise [10,12,16,29].
(a) (b)
Figure 6.6. Phase noise cancellation(a) (PNC) results of the 2000 kmkm coherentcoherent(b) transmissiontransmission systemsystem (the(the one-tapFigureone‐tap 6. NLMS Phase CPR). noise Ideal:cancellation linewidth linewidth (PNC) of of bothresults both Tx Tx ofand and the LO LO2000 lasers lasers km iscoherent is 0 0Hz. Hz. w/o: transmission w/ o:without, without, w/:system w with./: with. (the (a) (oneTransmitter:a) Transmitter:‐tap NLMS 170 CPR). 170 MHz, MHz, Ideal: local local linewidthoscillator: oscillator: 0of Hz; both 0 Hz; (b )Tx (Transmitterb )and Transmitter LO lasers = local= islocal 0oscillator: Hz. oscillator: w/o: 5 without, MHz. 5 MHz. w/: with. (a) Transmitter: 170 MHz, local oscillator: 0 Hz; (b) Transmitter = local oscillator: 5 MHz. When the CPR is implemented using DPD, the results of the PNC using the RF pilot tone in the sameWhen 2000 km the coherent CPR is implemented systemsystem areare illustratedillustrated using DPD, inin FigureFigure the results7 7.. In In Figure Figureof the7 PNC a,7a, the the using linewidth linewidth the RF of of pilot the the transmitter transmittertone in the lasersamelaser is is2000 170 170 km MHz MHz coherent and and the the system linewidth linewidth are illustrated of theof the LO LO laser in laserFigure is 0 is Hz, 7.0 In representingHz, Figure representing 7a, the an absencelinewidth an absence of of EEPN. the of transmitterEEPN. It is found It is laserfound is that 170 the MHz full and suppression the linewidth of LPN of canthe beLO performed laser is 0 Hz,with representing the use of the an RF absence pilot tone, of EEPN. compared It is foundto the thatscheme the fullof DPD suppression only. In ofFigure LPN 7b,can the be performedlinewidths withof both the theuse transmitter of the RF pilot and tone, local compared oscillator tolasers the schemeare 5 MHz, of DPD so that only. the In EEPNFigure is 7b, significant the linewidths again of(with both an the effective transmitter linewidth and local of 170 oscillator MHz). lasers are 5 MHz, so that the EEPN is significant again (with an effective linewidth of 170 MHz). Appl. Sci. 2019, 9, 4717 6 of 9 that the full suppression of LPN can be performed with the use of the RF pilot tone, compared to the schemeAppl. Sci. 2019 of DPD, 9, x FOR only. PEER In REVIEW Figure7 b, the linewidths of both the transmitter and local oscillator lasers6 of 9 are 5 MHz, so that the EEPN is significant again (with an effective linewidth of 170 MHz). Similar toSimilar Figure to6 b,Figure a considerable 6b, a considerable improvement improvement of BER performance of BER performance is also achieved is also achieved with half with an order half ofan magnitudeorder of magnitude in the BER in floorthe BER (from floor 6.5 (from10 46.5to × 1.5 10−4 10to 1.54), when× 10−4), the when RF pilot the RF tone pilot scheme tone isscheme applied is × − × − priorapplied to theprior DPD. to the DPD.
(a) (b)
Figure 7. PNC results of the 20002000 kmkm coherentcoherent transmissiontransmission systemsystem (DPD(DPD CPR).CPR). Ideal:Ideal: linewidth of both Tx and LO lasers are 0 Hz. ( a) Transmitter: 170 MHz, local oscillator: 0 Hz; (b) Transmitter == local oscillator: 5 MHz.
7. Discussions It has to be clarifiedclarified that the use of the RF pilot tone for the PNC in this work has occupied one polarization state state in in the the fiber, fiber, since since here here we we aim aim to investigate to investigate and and discuss discuss the e thefficiency efficiency of the of use the of use an RF of pilotan RF tone pilot for tone PNC for in PNC a simplified in a simplified transceiver transceiver structure. structure. In fact, the In RF fact, pilot the tone RF can pilot also tone be transmittedcan also be usingtransmitted the same using polarization the same polarization state as the opticalstate as data the signals,optical data which signals, requires which a more requires complicated a more implementationcomplicated implementation to perform the to generation perform the and generation recovery ofand the recovery RF pilot of tone the [ RF7,30 pilot,31]. tone In such [7,30,31]. systems, In asuch pilot-carrier systems, vector a pilot modulation‐carrier vector (PCVM) modulation scheme has(PCVM) been applied,scheme wherehas been the transverseapplied, where magnetic the (TM)transverse component magnetic is loaded (TM) component with the signal is loaded data in with X-polarization the signal data and thein X transverse‐polarization electric and (TE)the componenttransverse electric is employed (TE) component to carry both is the employed signal data to carry in Y-polarization both the signal and thedata RF in pilot Y‐polarization tone [7]. It wasand reportedthe RF pilot that tone the PNC[7]. It in was such reported PCVM that transmission the PNC schemesin such PCVM can also transmission provide a good schemes performance can also forprovide an eff aective good linewidth performance of up for to 30an MHzeffective [7,31 linewidth]. The performance of up to 30 comparison MHz [7,31]. between The performance such PCVM transmissioncomparison between scheme andsuch our PCVM proposed transmission RF pilot scheme tone-PNC and scheme our proposed will be investigated RF pilot tone in‐PNC future scheme work. Inwill addition, be investigated for orthogonal in future frequency work. divisionIn addition, multiplexing for orthogonal (OFDM) frequency optical transmission division multiplexing systems it will(OFDM) be straightforward optical transmission to employ systems one it subcarrier will be straightforward as the RF pilot toneto employ within one the subcarrier OFDM spectrum as the RF to removepilot tone the within influence the OFDM of laser spectrum phase noise to remove and EEPN the [influence32]. of laser phase noise and EEPN [32]. To studystudy thethe impact of PMD on the proposed RF pilot tone PNC scheme, numerical simulations using the same 28-Gsym28‐Gsym/s/s QPSK coherent transmission setup have been implemented with a PMD coecoefficientfficient of 0.1 ps𝑝𝑠/⁄√√km𝑘𝑚.. TheThe didifferentialfferential groupgroup delaydelay (DGD)(DGD) and the random rotations between the transmitted data and the RF pilot tone (due to effect effect of PMD) are mitigated using a constant modulus algorithm CMACMA equalizerequalizer [ [5,33,34].5,33,34]. TheThe CPR CPR is is performed performed using using the the one-tap one‐tap NLMS NLMS approach. approach. Figure Figure8 shows8 shows the the PNC PNC results results of of the the same same 2000 2000 km km coherent coherent system, system, with with and and without without including including the the impact impact of PMD.of PMD. Similarly, Similarly, the the linewidth linewidth of theof the Tx Tx laser laser is 170 is 170 MHz MHz and and the the linewidth linewidth of theof the LO LO laser laser is 0is Hz 0 Hz in Figurein Figure8a, and8a, and the linewidths the linewidths of both of theboth Tx the and Tx the and LO the lasers LO are lasers 5 MHz are in 5 FigureMHz 8inb. Figure Both scenarios 8b. Both indicatescenarios an indicate effective an linewidth effective oflinewidth 170 MHz, of and 170 there MHz, is and no EEPN there inis Figureno EEPN8a. Itin can Figure be clearly 8a. It foundcan be that,clearly for found both that, transmission for both transmission scenarios, the scenarios, impact of the PMD impact can of be PMD fully can suppressed be fully suppressed using the CMAusing equalizerthe CMA andequalizer the performance and the performance of the RF pilot of tone-basedthe RF pilot PNC tone (both‐based with PNC and (both without with EEPN) and without will not beEEPN) affected will due not tobe theaffected introduction due to the of PMD.introduction of PMD. Appl. Sci. 2019,, 9,, x 4717 FOR PEER REVIEW 77 of of 9
(a) (b)
Figure 8. PNC performance of the 2000 km coherent transmission systems with and without PMD, when the NLMS-CPRNLMS‐CPR is applied. Ideal: linewidth linewidth of of both both Tx Tx and and LO LO lasers lasers are are 0 0 Hz. Hz. ( (aa)) Transmitter: Transmitter: 170 MHz, local oscillator: 0 Hz; ( b) Transmitter = local oscillator: 5 5 MHz. MHz.
8. Conclusions Conclusions In thisthis work,work, an an orthogonally orthogonally polarized polarized RF RF pilot pilot tone tone is investigated is investigated to suppress to suppress the LPN the and LPN EEPN and EEPNin long-haul in long coherent‐haul coherent optical fiber optical communication fiber communication systems. A systems. 28-Gsym /As QPSK28‐Gsym/s optical QPSK transmission optical transmissionsystem is numerically system is implemented, numerically whereimplemented, the CPR where is performed the CPR using is performed the one-tap using NLMS the and one DPD‐tap NLMSmethods, and respectively. DPD methods, Our respectively. results demonstrate Our results that demonstrate the LPN in that the communicationthe LPN in the communication system can be systemcompletely can eliminatedbe completely and eliminated the EEPN can and also the be EEPN effectively can also suppressed, be effectively when suppressed, the RF pilot when tone scheme the RF pilotis applied tone scheme prior to is the applied CPR. prior to the CPR.
Author Contributions: Theoretical analyses and numerical simulations were implemented by T.X. The paper Author Contributions: Theoretical analyses and numerical simulations were implemented by T.X. The paper was mainly written by T.X., C.J. wrote some parts and edited the manuscript. S.Z. and M.L. made modifications. Allwas authors mainly reviewedwritten by and T.X. discussed C.J. wrote the some paper. parts and edited the manuscript. S.Z. and M.L. made modifications. All authors reviewed and discussed the paper. Funding: This work is in parts supported by the EU H2020 RISE Grant DAWN4IoE (778305) and the UK EPSRC Funding:Program Grant This work TRANSNET is in parts (EP supported/R035342/ 1).by the EU H2020 RISE Grant DAWN4IoE (778305) and the UK EPSRC ProgramConflicts Grant of Interest: TRANSNETThe authors (EP/R035342/1). declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. References References 1. Kaminow, I.; Li, T.; Willner, A.E. Optical Fiber Telecommunications VIA: Components and Subsystems, 6th ed.; 1. Kaminow,Academic PressI.; Li, Publisher:T.; Willner, Oxford, A. E. Optical UK, 2013. fiber telecommunications VIA: Components and subsystems, 6th ed.; 2. AcademicIp, E.; Lau, Press A.P.T.; Publisher: Barros, D.J.F.; Oxford, Kahn, UK, J.M. 2013. Coherent detection in optical fiber systems. Opt. Express 2008, 16, 2. Ip,753–791. E.; Lau, [CrossRef A.P.T.; Barros,][PubMed D.J.F.;] Kahn, J.M. Coherent detection in optical fiber systems. Opt. Express 2008, 3. 16Winzer,, 753–791. P.J.; Essiambre, R.J. Advanced modulation formats for high-capacity optical transport networks. 3. Winzer,J. Lightwave P.J.; Technol. Essiambre,2006 R.J., 24 Advanced, 4711–4728. modulation [CrossRef] formats for high‐capacity optical transport networks. J. 4. LightwaveSavory, S.J. Technol Digital. coherent2006, 24, optical4711–4728. receivers: Algorithms and subsystems. IEEE J. Sel. Top. Quantum Electron. 4. Savory,2010, 16 ,S.J. 1164–1179. Digital coherent [CrossRef optical] receivers: Algorithms and subsystems. IEEE J. Sel. Top. Quantum 5. ElectronZhao, J.;. 2010 Liu,, Y.; 16, Xu, 1164–1179. T. Advanced DSP for coherent optical fiber communication. App. Sci. 2019, 9, 4192. 5. Zhao,[CrossRef J.; Liu,] Y.; Xu, T. Advanced DSP for coherent optical fiber communication. App. Sci. 2019, 9, 4192. 6. Mori, Y.; Zhang, Zhang, C.; C.; Igarashi, Igarashi, K.; K.; Katoh, Katoh, K.; K.; Kikuchi, Kikuchi, K. UnrepeatedK. Unrepeated 200 200 km transmissionkm transmission of 40-Gbit of 40/‐sGbit/s 16-QAM 16‐ QAMsignals signals using digitalusing digital coherent coherent receiver. receiver.Opt. Express Opt. Express2009, 172009, 1435–1441., 17, 1435–1441. [CrossRef ] 7. Nakamura, M.;M.; Kamio,Kamio, Y.; Y.; Miyazaki, Miyazaki, T. T. Pilot-carrier Pilot‐carrier based based linewidth-tolerant linewidth‐tolerant 8PSK 8PSK self-homodyne self‐homodyne using using only onlyone modulator. one modulator. In Proceedings In Proceedings of the 33rd of European the 33rd Conference European andConference Exhibition and of Optical Exhibition Communication, of Optical Communication,Berlin, Germany, Berlin, 16–20 September Germany, 2007.16–20 September 2007. 8. Cai, Y.; Gao, X.; Ling, Y.; Xu,Xu, B.;B.; Qiu, K. RFRF pilotpilot tonetone phasephase noisenoise cancellation based on DD-MZMDD‐MZM SSB modulation for optical heterodyne RoF link. Opt. Commun Commun.. 20202020,, 454454,, 124502. 124502. [CrossRef] 9. Jacobsen, G.;G.; Xu,Xu, T.; T.; Popov, Popov, S.; S.; Li, Li, J.; J.; Friberg, Friberg, A.T.; A.T.; Zhang, Zhang, Y. Receiver Y. Receiver implemented implemented RF pilot RF pilot tone phasetone phase noise noisemitigation mitigation in coherent in coherent optical optical nPSK nPSK and nQAM and nQAM systems. systems.Opt. Express Opt. Express2011, 201119, 14487–14494., 19, 14487–14494. [CrossRef ] 10. Shieh, W.; Ho, K.P. Equalization‐enhanced phase noise for coherent detection systems using electronic digital signal processing. Opt. Express 2008, 16, 15718–15727. Appl. Sci. 2019, 9, 4717 8 of 9
10. Shieh, W.; Ho, K.P. Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing. Opt. Express 2008, 16, 15718–15727. [CrossRef] 11. Xie, C. Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation. In Proceedings of the 2009 Conference on Optical Fiber Communication-Incudes post deadline papers, San Diego, CA, USA, 29 May 2009. 12. Lau, A.P.T.; Shen, T.S.R.; Shieh, W.; Ho, K.P. Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection. Opt. Express 2010, 18, 17239–17251. [CrossRef] 13. Xu, T.; Liga, G.; Lavery, D.; Thomsen, B.C.; Savory, S.J.; Killey, R.I.; Bayvel, P. Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multi-channel digital back-propagation. Sci. Rep. 2015, 5.[CrossRef] 14. Zhuge, Q.; Xu, X.; El-Sahn, Z.A.; Mousa-Pasandi, M.E.; Morsy-Osman, M.; Chagnon, M.; Qiu, M.; Plant, D.V. Experimental investigation of the equalization-enhanced phase noise in long haul 56 Gbaud DP-QPSK systems. Opt. Express 2012, 20, 13841–13846. [CrossRef][PubMed] 15. Fatadin, I.; Savory, S.J. Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation. Opt. Express 2010, 18, 16273–16278. [CrossRef][PubMed] 16. Kakkar, A.; Navarro, J.R.; Schatz, R.; Louchet, H.; Pang, X.; Ozolins, O.; Jacobsen, G.; Popov, S. Comprehensive study of equalization-enhanced phase noise in coherent optical systems. J. Lightwave Technol. 2015, 33, 4834–4841. [CrossRef] 17. Xu, T.; Jacobsen, G.; Popov, S.; Li, J.; Friberg, A.T.; Zhang, Y. Carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise. Opt. Commun. 2013, 293, 54–60. [CrossRef] 18. Colavolpe, G.; Foggi, T.; Forestieri, E.; Secondini, M. Impact of phase noise and compensation techniques in coherent optical systems. J. Lightwave Technol. 2011, 29, 2790–2800. [CrossRef] 19. Xu, T.; Jacobsen, G.; Popov, S.; Li, J.; Friberg, A.T.; Zhang, Y. Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization. Opt. Express 2011, 19, 7756–7768. [CrossRef] 20. Xu, T.; Jacobsen, G.; Popov, S.; Li, J.; Wang, K.; Friberg, A.T. Normalized LMS digital filter for chromatic dispersion equalization in 112-Gbit/s PDM-QPSK coherent optical transmission system. Opt. Commun. 2010, 283, 963–967. [CrossRef] 21. Fatadin, I.; Ives, D.; Savory, S.J. Differential carrier phase recovery for QPSK optical coherent systems with integrated tunable lasers. Opt. Express 2013, 21, 10166–10171. [CrossRef] 22. Savory, S.J. Digital filters for coherent optical receivers. Opt. Express 2008, 16, 804–817. [CrossRef] 23. Kudo, R.; Kobayashi, T.; Ishihara, K.; Takatori, Y.; Sano, A.; Miyamoto, Y. Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems. J. Lightwave Technol. 2009, 27, 3721–3728. [CrossRef] 24. Jacobsen, G.; Xu, T.; Popov, S.; Sergeyev, S. Study of EEPN mitigation using modified RF pilot and Viterbi-Viterbi based phase noise compensation. Opt. Express 2013, 21, 12351–12362. [CrossRef][PubMed] 25. Ly-Gagnon, D.S.; Tsukamoto, S.; Katoh, K.; Kikuchi, K. Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation. J. Lightwave Technol. 2006, 24, 12–21. [CrossRef] 26. Viterbi, A.J.; Viterbi, A.M. Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission. IEEE Trans. Inf. Theory 1983, 29, 543–551. [CrossRef] 27. Liga, G.; Xu, T.; Alvarado, A.; Killey, R.I.; Bayvel, P. On the performance of multichannel digital backpropagation in high-capacity long-haul optical transmission. Opt. Express 2014, 22, 30053–30062. [CrossRef][PubMed] 28. Maher, R.; Xu, T.; Galdion, L.; Sato, M. Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back propagation. Sci. Rep. 2015, 5, 08214. [CrossRef][PubMed] 29. Ho, K.P.; Lau, A.P.T.; Shieh, W. Equalization-enhanced phase noise induced timing jitter. Opt. Lett. 2011, 36, 585–587. [CrossRef] 30. Nakamura, M.; Kamio, Y.; Miyazaki, T. Linewidth-tolerant real-time 40-Gbit⁄s 16-QAM self-homodyne detection using a pilot carrier and ISI suppression based on electronic digital processing. Opt. Lett. 2010, 35, 13–15. [CrossRef] 31. Nakamura, M.; Kamio, Y.; Miyazaki, T. Linewidth-tolerant real-time 10-Gbit⁄s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique. Opt. Express 2008, 16, 10611–10616. [CrossRef] Appl. Sci. 2019, 9, 4717 9 of 9
32. Randel, S.; Adhikari, S.; Jansen, S.L. Analysis of RF-pilot-based phase noise compensation for coherent optical OFDM systems. IEEE Photon. Technol. Lett. 2010, 22, 1288–1290. [CrossRef] 33. Ip, E.; Kahn, J.M. Digital equalization of chromatic dispersion and polarization mode dispersion. J. Lightwave Technol. 2007, 25, 2033–2043. [CrossRef] 34. Liga, G.; Czegledi, C.B.; Xu, T.; Agrell, E.; Killey, R.I.; Bayvel, P. Ultra-wideband nonlinearity compensation performance in the presence of PMD. In Proceedings of the 42nd European Conference on Optical Communication, Dusseldorf, Germany, 5 December 2016.
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