JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008 1339
Influence of Tight Optical Filtering on Long-HaulTransmission Performance of Several
Advanced Signaling FormatsNatasa B. Pavlovic and Adolfo V. T. Cartaxo, Senior Member, IEEE
Abstract—In this paper, the influence of tight optical filtering(TOF) on dispersion-managed long-haul (LH) transmission perfor-mance of advanced signaling formats is analyzed through extensivenumerical simulation. The investigation is performed for duobi-nary, carrier-suppressed-return-to-zero (CS-RZ), and duobinaryCS-RZ (DCS-RZ) signaling formats, which were suggested for LHultradense wavelength division multiplexing systems previously.The simultaneous variation of pre-, inline, and postcompensationof dispersion amounts is performed to find out the optimum dis-persion map of each signaling format with and without TOF, andtheir dispersion tolerances. The tolerance to fiber nonlinearity ofeach signaling format is also analyzed. It is shown that the TOF af-fects differently the LH transmission performance of the three sig-naling formats. The TOF reduces the dispersion tolerances of theduobinary signaling format, but improves the maximum -factorand tolerance to nonlinear fiber effects due to the eye-opening im-provement. It improves the tolerance to inline dispersion and fibernonlinearity of the CS-RZ signaling format, but it reduces remark-ably the eye opening leading to a significant -factor degradation.It improves also the maximum -factor and the total residual dis-persion tolerance of DCS-RZ format due to the reduction of thesignal spectrum width, but it worsens the tolerance to pre- and in-line dispersion, and fiber nonlinearity.
Index Terms—Carrier-suppressed formats, dispersion com-pensation, duobinary format, nonlinear tolerance, tight opticalfiltering (TOF), ultradense wavelength division multiplexing.
I. INTRODUCTION
RECENTLY, investigation on optical transmission systemshas been focused on the increase of their distance and ca-
pacity [1], [2]. For long-haul (LH) transmission systems, highpowers are required at the fiber input to increase the opticalsignal-to-noise ratio (OSNR) reduced by accumulated ampli-fied spontaneous emission (ASE) noise of optical amplifiers. Asa consequence, some of the main impairments of LH transmis-sion are the nonlinear fiber effects. However, using the optimumdispersion map (ODM), signal degradation due to the nonlinearfiber effects can be reduced.
LH transmission performance can be improved by usingadvanced signaling formats. Signaling formats with low-cost
Manuscript received April 25, 2007; revised November 6, 2007. This workwas supported by Fundação para a Ciência e a Tecnologia (FCT), Portugal,FEDER and POSC within project POSC/EEA-CPS/56959/2004-SHOTS.The work of N. Pavlovic was supported by the FCT under ContractSFRH/BD/10162/2002.
The authors are with the Optical Communications Group, Instituto de Tele-comunicações, Department of Electrical and Computer Engineering, InstitutoSuperior Técnico, 1049-001 Lisboa, Portugal (e-mail: [email protected];[email protected]).
Digital Object Identifier 10.1109/JLT.2008.917347
transmitters and receivers are recommended for LH transmis-sion systems. Thus, the use of signaling formats that employinterferometric detection, such as those of the differentialphase-shift keying family, is questionable, particularly if di-rect-detection signaling formats show also good performancefor those systems. Several advanced signaling formats, such asduobinary [3], carrier-suppressed return-to-zero (CS-RZ) [4],and duobinary-CS-RZ (DCS-RZ) [5] have been proposed forLH transmission systems because they show improved perfor-mance compared to conventional nonreturn-to-zero (NRZ) andemploy the conventional and simple direct-detection receiver.Furthermore, the CS-RZ and DCS-RZ formats are very attrac-tive for use in spectrally efficient systems because they havethe narrowest signal spectra between others of RZ type.
Tight optical filtering (TOF) can improve the transmissioncapacity by increasing the spectral efficiency, leading to ultra-dense wavelength-division-multiplexing (UDWDM) systems.TOF can be realized as bandwidth-limited (BL), centered onthe carrier frequency, or as single-sideband (SSB) filtering,centered off the carrier frequency. The combination of TOFwith advanced signaling formats has been shown to lead togood performance of 40-Gb/s UDWDM systems with 50 GHzof channel spacing [1], [2], [4]–[8]. However, depending onthe advanced signaling format, such combination may degradeor improve the transmission performance, namely, the per-formance achieved at the ODM, and the dispersion and fibernonlinearity tolerances. Therefore, it is important to analyzeand compare the influence of TOF on the ODM, and tolerancesto dispersion and fiber nonlinearity of these advanced signalingformats.
The dispersion map of LH UDWDM systems at 40 Gb/s andabove is usually optimized in single-channel operation becausethe intrachannel nonlinear fiber effects, mainly intrachannelfour-wave mixing (IFWM), are the dominating nonlinearities[9]. This was reported in several papers [8], [10], where similarODM for single-channel and UDWDM systems was found. Inmost of the studies of UDWDM systems [1], [8] and of theinfluence of TOF on dispersion tolerance [11]–[13], the dis-persion map considers only inline and/or postcompensations.However, the use of precompensation can significantly im-prove the LH transmission performance by reducing the signaldegradation caused by IFWM and intrachannel cross-phasemodulation, as explained in [10]. The ODM consisting ofpre-, inline, and postcompensation of dispersion was analyzedfor several formats without TOF in [14], and for other fibertype than standard single-mode fiber (SSMF). To the authors’knowledge, the influence of TOF on the ODM and dispersion
1340 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Fig. 1. Generation scheme of (a) duobinary, (b) DCS-RZ, and (c) CS-RZ signals. � is the bit period and � is the bit rate.
tolerances of advanced signaling formats still remains to beassessed.
In this paper, we perform an extensive numerical optimiza-tion and analysis of the duobinary, BL-duobinary, CS-RZ,BL-CS-RZ, DCS-RZ, and SSB-DCS-RZ signaling formats forLH systems at a bit rate of 43 Gb/s. We analyze the optimumdispersion map and tolerances to pre-, inline, and total residualdispersion, and fiber nonlinearity of those signaling formats.Signaling formats of RZ and NRZ types are investigated toget more insight on the impact of TOF on the transmissionperformance and draw more general conclusions. The re-mainder of this paper is organized as follows. In Section II,the system model is presented. In Section III, the filters op-timization is analyzed. In Section IV, the ODM is presentedand analyzed. In Section V, the pre-, inline, and total residualdispersion tolerances are discussed. In Section VI, the toleranceto fiber nonlinearity of these signaling formats is investigated.Section VII presents the main conclusions.
II. SYSTEM DESCRIPTION
Three advanced signaling formats are investigated withoutand with TOF: duobinary, DCS-RZ, and CS-RZ. The genera-tion schemes of the investigated formats are shown in Fig. 1.The duobinary signal is generated as described in [6]. TheDCS-RZ signal is generated as described in [5]. The duty cycle
of DCS-RZ signal is set to 53% by choosing adequately thedriving voltages swing. The CS-RZ signal with an extinctionratio of 12 dB and a duty cycle of 67% is used, and it isgenerated as described in [4].
The TOF is optimized for UDWDM system with 50 GHzof channel spacing and is performed by a second-order super-Gaussian filter. This optical filter type showed better perfor-mance for UDWDM systems compared to the Gaussian filter[15] and similar performance to “flat-top” arrayed waveguidegrating filter [16], often used in experimental works as mul-tiplexer and demultiplexer. Analysis and discussion of the as-sumptions and parameters of the optical and electrical filtersconsidered in this study are presented in Section III.
The setup of the 43-Gb/s single-channel LH transmissionsystem operating at 1552.52 nm is shown in Fig. 2. The LH linkconsists of ten spans of 80 km (transmission distance of 800km) of SSMF, unless indicated otherwise. The spans are sep-arated by repeaters incorporating double-stage erbium-dopedfiber amplifiers (EDFA) with a dispersion compensating fiber(DCF) between the two stages. Each EDFA stage has a noisefigure of 6 dB, which is typical for a practical system setup[16]. The gain of each EDFA stage is set to compensate for thetotal loss per span and impose a power level at DCF input of
6 dBm in order to reduce the nonlinear effects in the DCF.The average power at the SSMF input is set to 5 dBm. This
PAVLOVIC AND CARTAXO: INFLUENCE OF TOF ON LH TRANSMISSION PERFORMANCE OF SEVERAL ADVANCED SIGNALING FORMATS 1341
Fig. 2. Schematic diagram of the 43-Gb/s single-channel system over � � 80 km SSMF with pre-, inline, and postcompensation of dispersion.
TABLE ISSMF AND DCF PARAMETERS
power level is approximately the optimum power level for theODM of all investigated formats, as will be seen later, and ischosen to consider a realistic situation in which the nonlinearfiber effects are present. Fiber parameter values are shownin Table I. The precompensation dispersion amount at thetransmitter side is chosen to mitigate dispersive and nonlineardistortions in the LH system. Each of the first nine spans hasthe same DCF length, which is appropriately chosen to setthe inline dispersion compensation (IDC) level, whereas theDCF length of the last span sets the postcompensation level or,equivalently, the total residual dispersion.
Transmission along the SSMF and DCF is modeled by thegeneralized nonlinear Schrödinger equation (NLSE) [17]. Inorder to determine rigorously the joint impact of group velocitydispersion (GVD) and fiber nonlinearity on the single-channelsystem performance, the total field approach is adopted in thesimulation. The NLSE is solved using the symmetrized split-step Fourier method. Each 43-Gb/s receiver is modeled by apositive–intrinsic–negative (PIN) photodiode with responsivityof 1 A/W, a third-order Bessel electrical filter with a 3-dB band-width of 0.7 ( is the bit rate), and a decision circuit. Thistype of filter with similar bandwidth is usually considered inUDWDM systems [18]. The average power at the PIN input isset to 0 dBm.
To evaluate the system performance, the Gaussian approachpresented in [19], based on the noise-free distorted signal andthe calculated noise variance taking into account the accumu-lated ASE noise of all optical amplifiers, is used to computethe -factor as further described in [8]. A deBruijn binary se-quence of bits is considered to assess the -factor in LHtransmission of the single-channel system. This sequence lengthallows assessing rigorously the single-channel system perfor-mance. This was confirmed by checking that almost the sameperformance is computed with a larger number of bits.
III. FILTERS OPTIMIZATION AND DISCUSSION
In order to assess only the impact of the TOF on the transmis-sion performance, the same system parameters, including pa-rameters of the generation scheme, are considered for the for-
TABLE IIOPTIMAL BANDWIDTH �� � AND DETUNING ����� OF TRANSMITTER (TX)
AND RECEIVER (RX) TOF NORMALIZED TO THE BIT RATE �� � FOR
BL-DUOBINARY, SSB-DCS-RZ, AND BL-CS-RZ SIGNALING
FORMATS, OBTAINED FOR BACK-TO-BACK OPERATION OF
43 Gb/s PER CHANNEL UDWDM SYSTEM
WITH 50 GHz OF CHANNEL SPACING
mats with and without TOF, except for the optical filters thatrealize the TOF. Furthermore, the generation schemes of sig-naling formats optimized for UDWDM systems (where TOF isused) are considered. In UDWDM systems, it is important tooptimize the electrical and optical filters at the transmitter andreceiver side [1]. The electrical filter of the generation schemeof the duobinary and DCS-RZ formats was optimized togetherwith optical filters at the transmitter and the receiver sides forUDWDM systems in a back-to-back configuration [8]. This op-timization was performed by varying randomly the phase andtime shifts within 64 blocks of bits between two interferingchannels and the center channel within 500 realizations. Thiswas proposed in [18] to evaluate correctly the influence of linearcrosstalk. The optimized 3-dB electrical transmitter bandwidthsof the duobinary and DCS-RZ signals of are assumed[6], [8]. The optimum bandwidths and detunings of transmitter(Tx) and receiver (Rx) optical filters for each signaling formatare shown in Table II. The optimized bandwidths of the trans-mitter and receiver filters depend mostly on the signal spectrumcharacteristics. Table II shows that BL-duobinary format hasthe narrowest optical filter bandwidth at the receiver side. Thisleads to further performance improvement of the BL-duobinaryformat due to the higher noise power reduction.
It should be stressed that, in order to draw general conclu-sions, we are considering signaling formats with different typesof optimum TOF. For the DCS-RZ signal, the optimum TOF isachieved with SSB filters, differently from the BL consideredin [13]. For duobinary and CS-RZ signals, the optimum TOFis achieved with BL filters due to the signal spectrum charac-teristics. Note that, after optimum TOF, the duobinary signalmaintains the NRZ type, and the CS-RZ signal maintains theRZ type. However, the DCS-RZ signal changes from RZ typeto NRZ type after optimum SSB filtering. These features can beseen in Fig. 3. This figure shows the time waveforms of inten-sity and chirp (only in the case of SSB-DCS-RZ). After SSBfiltering, the intensity of SSB-DCS-RZ format becomes similar
1342 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Fig. 3. Time waveforms of normalized intensity of duobinary (dotted line),BL-duobinary (solid line) in top; DCS-RZ (dotted line), SSB-DCS-RZ (solidline) in the middle; CS-RZ (dotted line), and BL-CS-RZ (solid line) in thebottom. For the SSB-DCS-RZ signal, the time waveform of chirp is also shownwith bold solid line.
to the one of BL-duobinary format. However, while TOF causesno chirping on the BL-duobinary signal, it leads to large chirpfluctuation on the SSB-DCS-RZ signal. As a consequence ofthis, these two formats perform differently [8], [11]. The op-timum TOF causes large degradation of CS-RZ and DCS-RZsignals as a consequence of the significant reduction of theirspectra widths. However, the optimum TOF improves the eyeopening of duobinary signal since it decreases the fluctuationsof intensity in “0” bits and causes no significant spectrum widthreduction due to the narrow signal spectrum before TOF.
Analysis of TOF optimization considering LH transmissionUDWDM system with five channels at 43 Gb/s per channel wasrealized to check if the TOF optimized in back-to-back (shownin Table II) is substantially different. This was performed con-sidering the ODM presented in Section IV for each format. Thenumerical simulation used deBruijn binary sequences ofbits to assess correctly the crosstalk influence. The -factorwas calculated from the bit error ratio (BER), which was aver-aged over five realizations. From realization to realization, thephase and time shifts were randomly varied between the centraland the neighboring channels to rigorously assess the crosstalk.Optimal filters characteristics similar to those obtained in theback-to-back optimization are found with LH transmission forBL-duobinary format due to its spectral compactness and largertolerance to cross-phase modulation (XPM) [8]. However, forSSB-DCS-RZ and BL-CS-RZ formats, different optima MUXand DMUX bandwidths are found in back-to-back and in LHUDWDM system scenarios due to their smaller tolerance toXPM [8], [12]. Only a small variation between the optima MUXand DMUX detunings for back-to-back and LH UDWDM sys-
tems is found for SSB-DCS-RZ format due to its large toleranceto MUX and DMUX detuning variation. Considerably large tol-erance to optical filter bandwidth variation leads to -factordegradation (after LH transmission) not exceeding 1 dB whenfilters optimized in the back-to-back scenario are used relativeto the case of using optical filters optimized with multichannelLH transmission, for the three formats analyzed.
When the formats are used without TOF, the influence of thebandwidth of the optical filter at the receiver on the system per-formance was assessed. In order to consider the same receiverfor all formats without TOF, an optical filter at the receiver sidewith a 3-dB bandwidth of is assumed guaranteeing nosignal distortion, particularly, in the CS-RZ signal (for whichoptical bandwidths as large as lead to signal distortion),and reduced degradation of -factor for DCS-RZ and duobinaryformats in comparison with using an optical filter with band-width of .
IV. OPTIMUM DISPERSION MAP ANALYSIS
In order to improve the LH optical link performance, the dis-persion map must be carefully optimized [1]. In this section, theODM is presented and analyzed. It is obtained by varying theamount of pre- and inline dispersion compensations and totalresidual dispersion, and computing the -factor correspondingto each triplet. The amount of dispersion of precompensation isdenoted as . The amount of IDC expressed in percentage isdefined as
IDC(%) (1)
where and are, respectively, the lengths of theSSMF and DCF in each of the first nine spans, and and
are the dispersion parameters of the SSMF and DCF, re-spectively. The total residual dispersion (TRD) is the total cu-mulated dispersion of the link and is given by
TRDIDC(%)
(2)
where is the number of spans (ten), and is the amountof dispersion of postcompensation. More than 150 000 differentdispersion maps were analyzed for each signaling format. Thecomputation error of , IDC, and TRD optima and tolerancesis mostly due to the , IDC, and TRD steps used in simula-tions, which are 10 ps/nm, 1%, and 5 ps/nm, respectively.
The system performance is characterized by the -factorpenalty defined as , where is the -factorand is the maximum attainable -factor for each sig-naling format. Thus, the -factor penalty is calculated assumingdifferent reference situations for different signaling formatsto compare easily the , IDC, and TRD optimizations andtolerances for each signaling format.
Fig. 4 shows the -factor penalty as a function of IDC andfor all investigated formats, with the optimal TRD chosen
for each pair of IDC and . The ODM obtained by calcu-lating the eye-opening penalty is similar to the one obtainedusing the -factor, shown in Fig. 4, for all investigated for-mats. The difference is that the optimum IDC using the eye
PAVLOVIC AND CARTAXO: INFLUENCE OF TOF ON LH TRANSMISSION PERFORMANCE OF SEVERAL ADVANCED SIGNALING FORMATS 1343
Fig. 4. Contour plots of the �-factor penalty (in decibels) as a function of � and IDC for the duobinary (left-hand side), DCS-RZ (middle), and CS-RZ(right-hand side) formats without (top) and with TOF (bottom). The thick-dashed line corresponds to the � –IDC relation given by expression (3).
opening occurs for overcompensation (IDC 100%) and usingthe -factor, for undercompensation (IDC 100%) with a verysmall difference of -factor and eye-opening penalty betweenthe two cases (less than 0.2 dB). This is a consequence of smallerASE noise power accumulation with smaller IDC and of the
-factor and eye-opening penalty are quasi-symmetrical to theIDC 100% axis. Only for the BL-CS-RZ format, the over-compensation (IDC 105%) is found to lead to the best perfor-mance even using the -factor because the large eye-openingdegradation is the main cause of performance degradation forthis format. However, approximately the same -factor and eye-opening penalty are observed for the same amount of residualdispersion per span (RDPS) (over- or undercompensation).
The optimum and IDC of all investigated formats are inaccordance with the thick-dashed line presented in Fig. 4. Thisline corresponds to the relation between and IDC given by
IDC(%)(3)
where is the attenuation parameter of the SSMF. Thefirst term of the right-hand side (RHS) of expression (3) is theoptimum for the system with IDC 100%, and the secondterm describes the influence of IDC on . The first term of theRHS of expression (3) is the same as the first term of the RHS of
–IDC relation given by [10, eq. (3)], and the second term ofthe RHS of expression (3) is the same as the second term of the
–IDC expression presented in [20]. Our results show thatthe dependence of the slope of the –IDC relation on issmaller than the one described by [10, eq. (3)] (proportional to
), and it is closer to , as given by –IDC expres-sion presented in [20].
Results of Fig. 4 show that, for all formats, a large IDC rangeis under 1 dB of -factor penalty even with significant non-linear effects in the transmission system due to the considerably
high level of average power at the SSMF input (of 5 dBm) andlarge number of spans. Thus, the importance of the optimumIDC analysis seems irrelevant. However, with a higher numberof spans or average power at the transmission fiber input than theones considered in Fig. 4, the optimum IDC range is much de-creased and setting the optimum IDC becomes important. Thesefeatures can be seen in Fig. 5. This figure shows the -factorpenalty as a function of the IDC assuming the optimum TRDand precompensation given by expression (3). These results arepresented for different number of spans (8, 12, and 14) and thesame average power at the SSMF input of 5 dBm. In Fig. 5, itcan be clearly seen that the IDC range on which the -factorpenalty is smaller than 1 dB decreases with the increase of thenumber of spans due to the increase of nonlinear effects in trans-mission system.
Figs. 4 and 5 show that the TOF affects differently theoptimum IDC of these signaling formats. The TOF maintainsthe optimum large RDPS of duobinary format. However, itdecreases significantly the optimum RDPS of the DCS-RZformat. Besides, it increases the optimum RDPS of the CS-RZformat. Some amount of RDPS can improve the system perfor-mance due to its interplay with nonlinear fiber effects. Thus,the optimum IDC can be influenced by the signaling formattolerance to GVD and nonlinear fiber effects.
The optimum TRD decreases proportionally to the square ofthe bit rate, making it especially critical at high bit rates [21].Therefore, for 43-Gb/s systems, it is important to investigatethe optimum TRD and its tolerance for each signaling format[14]. Fig. 6 shows the -factor penalty as a function ofand TRD for each signaling format at the optimum IDC. For allformats, the same optimum TRD is found with the eye openingas with the -factor, thus, independently of the accumulatednoise power. Fig. 6 shows that, for duobinary format, the TOFdecreases the optimum TRD. For DCS-RZ format, a negativeoptimum TRD is found ( 35 ps/nm), which is not typical ei-ther for RZ-type formats, which is usually near zero [22], or forNRZ-type formats, which occurs usually for positive TRD [21].
1344 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Fig. 5. �-penalty (in decibels) as a function of inline dispersion compensation (in percent) for optimum TRD and precompensation calculated by expression(3) for the duobinary (left-hand side), DCS-RZ (middle), and CS-RZ (right-hand side) formats without (top) and with TOF (bottom) for “o”—8, “�”—12, and“�”—14 spans.
Fig. 6. Contour plots of the �-factor penalty (in decibels) as a function of � and TRD for the duobinary (left-hand side), DCS-RZ (middle), and CS-RZ(right-hand side) formats without (top) and with TOF (bottom).
Note that a different optimum TRD (around zero) for DCS-RZformat was found in [13] due to the combination of narrow BLfilters with the DCS-RZ format. With SSB filtering, the op-timum TRD of DCS-RZ format becomes positive (45 ps/nm)since the DCS-RZ format becomes an NRZ-type format. As in[12] and [23], the optimum TRD for the CS-RZ format is foundto be near zero. The optimum TRD of BL-CS-RZ format isfound to be the same as the one of the DCS-RZ format. This indi-cates that RZ-type formats with narrow signal spectrum widthscan achieve their optimum transmission performance at nega-tive TRD.
The optimum TRD was found to be proportional to the non-linear phase of the transmission path [21]. Besides, larger op-timum TRD was found for the formats with higher duty cyclethus, with smaller signal spectrum width [21], [23]. In [21], thisbehavior is attributed to the higher GVD tolerance of the sig-naling format. However, in [23], it is attributed to the smaller tol-erance to nonlinear fiber effects of the signaling format. Our re-sults are consistent with these explanations since the NRZ-type
formats (duobinary, BL-duobinary, and SSB-DCS-RZ formats)have larger optimum TRD than the RZ-type formats (CS-RZ,BL-CS-RZ, and DCS-RZ formats) due to their larger GVD tol-erance and smaller tolerance to nonlinear fiber effects. Furtheranalysis showed that figures of GVD optimum (computed withlinear transmission) are consistent with results shown in [23] forCS-RZ format and in [9] for duobinary format.
From the contour plots of the -factor penalty shown inFigs. 4 and 6, the ODM and the maximum -factor of eachsignaling format can be easily extracted. Table III summarizesthe optimum , IDC, and TRD, and presents the maximum
-factor for all investigated signaling formats obtained for tenspans. Additionally, the optimum , IDC, and TRD, andthe maximum -factor are also shown for 15 spans for allinvestigated signaling formats. In Table III, it can be seen thatall conclusions about the influence of the TOF on the optimum
, IDC, and TRD of all investigated formats maintain whenthe number of spans is increased. This makes us believe in thegenerality of those conclusions.
PAVLOVIC AND CARTAXO: INFLUENCE OF TOF ON LH TRANSMISSION PERFORMANCE OF SEVERAL ADVANCED SIGNALING FORMATS 1345
TABLE IIIOPTIMUM � , IDC, AND TRD, AND MAXIMUM �-FACTOR FOR DUOBINARY,
DCS-RZ, AND CS-RZ SIGNALING FORMATS WITH AND WITHOUT
TOF FOR TEN AND 15 SPANS
The influence of TOF on -factor can be also seen inTable III. These values of -factor show the different be-havior for the three signaling formats when TOF is used.With TOF, for duobinary format, the -factor increases due tothe eye-opening increase, as in [2], and due to the reductionof the noise bandwidth. For DCS-RZ format with TOF, theeye opening decreases, but the -factor increases due to thereduction of the noise bandwidth since the noise bandwidth issignificantly reduced with the use of SSB filters. These conclu-sions hold for both numbers of spans. For CS-RZ format andten spans, the -factor decreases due to the large eye-openingdegradation resulting from the TOF. However, for 15 spans, the
-factor increases with TOF. The signal degradation resultingfrom the nonlinear effects is more dominant than from theTOF for 15 spans. Thus, the format with higher tolerance tothe nonlinear effects shows improved performance for largernumber of spans. The higher nonlinearity tolerance of theBL-CS-RZ will be confirmed in Section V. For ten spans, thelargest -factor occurs for BL-duobinary format, and a verysimilar one occurs with SSB-DCS-RZ format. However, for15 spans, the largest -factor occurs for SSB-DCS-RZ formatdue to the presence of the chirp, which interacts constructivelywith increased nonlinear effects due to the increased numberof spans. The BL-CS-RZ format has a degradation of about3 dB in comparison with the BL-duobinary and SSB-DCS-RZformats for both numbers of spans due to a high degradationof the eye opening. Without TOF, for both numbers of spans,the DCS-RZ format has the highest -factor and the duobinaryhas the lowest, due to the highest and smallest eye opening,respectively. In Table III, it can be seen that, for all investigatedformats, the maximum -factor and the optimum absoluteRDPS decreases with the increase of the number of spans(except when it is already zero as for CS-RZ format) due tothe increase of the nonlinear effects in transmission system.Some further discussion about this feature can be found in [24].Moreover, the optimum TRD (the absolute value) increaseswith the increase of the nonlinear effects in the system as it isshown in [21] for NRZ and RZ formats due to the increase ofthe number of spans, except for the format with very large GVD
Fig. 7. �-factor (in decibels) calculated by “o”—Gaussian approach and“x”—exact method as a function of average power at the SSMF input for theduobinary (dashed line), BL-duobinary (solid line) in top; DCS-RZ (dashedline), SSB-DCS-RZ (solid line) at the middle; and CS-RZ (dashed line),BL-CS-RZ (solid line) in the bottom, for ODM given in Table III. Number ofspans is ten.
or fiber nonlinearity tolerance, as duobinary and BL-CS-RZformats have, respectively.
Fig. 7 shows the -factor as a function of the average power atthe SSMF input for each signaling format. For this analysis, foreach of the format, the amounts of pre-, inline and postcompen-sation of dispersion of the ODM shown in Table III (ten spans)are considered. Fig. 7 shows that the average power at the SSMFinput of 5 dBm is very close to the optimum power level thatmaximizes the -factor for all investigated signaling formats.Thus, the ODM shown in Table III has been obtained with sig-nificant impact of nonlinear fiber effects on the transmission per-formance for all investigated formats. Moreover, Fig. 7 showsthe -factor calculated by two different methods: Gaussian ap-proach and the exact method proposed in [25]. Results of Fig. 7show that the Gaussian approach provides usually excellent es-timates for these formats with LH transmission.
The ODM was analyzed also for 5 43-Gb/s UDWDMsystems with LH transmission for each signaling format. Thisanalysis is performed as described in Section III, when theTOF optimization for LH UDWDM system is considered.Similar ODM for UDWDM system to the one of single-channelsystem is found, except for the SSB-DCS-RZ format, which hassmaller tolerance to XPM [8]. The ODM for UDWDM systemshas smaller or the same optimum TRD and higher IDC to re-duce the distortion caused by XPM. -factor degradations notexceeding 1.5 and 0.9 dB are obtained for the UDWDM systemconsidering the ODM obtained for the single-channel systemrelative to the case of considering the ODM optimized for the
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TABLE IVPRECOMPENSATION, IDC, AND TRD TOLERANCES FOR DUOBINARY, DCS-RZ,
AND CS-RZ SIGNALING FORMATS WITH AND WITHOUT TOF
UDWDM system, for BL-CS-RZ format, and BL-duobinaryand SSB-DCS-RZ formats, respectively.
V. TOLERANCE TO DISPERSION VARIATION
The tolerance of any signaling format to deviation from op-timum dispersion compensation map is of great importance inthe design of LH 40-Gb/s/channel terrestrial systems [14]. In thefollowing, the dispersion tolerances of each signaling format aredefined as the ranges of the dispersion compensation parameterswhere the -factor penalty remains within 1 dB of variationfrom the optimum performance. Its optimum performance foreach signaling format is shown in Table III. Table IV presentsthe precompensation, IDC, and TRD tolerances for the three in-vestigated signaling formats with and without TOF. These fig-ures were extracted from -factor contour plots presented inFigs. 4–6, for each signaling format.
We analyze the tolerance to precompensation to emphasizethe tolerance dependence on ODM. The optimum is di-rectly proportional to the optimum IDC, as shown by expression(3). Thus, it is expected that their tolerances vary in similar wayto the TOF, as shown for several signaling formats in Table IV.The precompensation imposes some prechirping on the signaland, through its optimization, the system performance is im-proved due to the interplay between the nonlinear fiber effectsand residual dispersion in the link [10]. Thus, the tolerances toprecompensation and IDC of a signaling format may depend onits tolerance to GVD and nonlinear fiber effects.
For the duobinary format, the TOF reduces the amount oflight in “0” bits, which is important for its large GVD toler-ance [2], [3], [6]. As a result, the TOF causes a reduction ofall dispersion tolerances of duobinary format. A signal witha wider spectrum is potentially more sensitive to pulse distor-tion at nonzero residual GVD than a signal with narrower spec-trum [21]. Thus, for DCS-RZ format with TOF, the TRD tol-erance is slightly improved due to the smaller signal spectrumwidth. However, the precompensation and IDC tolerances de-crease. The IDC tolerance of the BL-CS-RZ format is increasedcompared to the one of the CS-RZ format. Further investigationshowed that, for linear transmission and for nonlinear transmis-sion with zero residual dispersion per span, the TRD toleranceof CS-RZ format is improved with TOF due to the decrease ofthe signal spectrum width, as also reported in [12]. However, thetolerance to TRD variation of BL-CS-RZ format at the ODMis slightly decreased compared to the one of CS-RZ format.
TABLE VNLT FOR DUOBINARY, DCS-RZ, AND CS-RZ SIGNALING FORMATS
WITH AND WITHOUT TOF
Further analysis showed that figures on GVD tolerance (com-puted with linear transmission) are found consistent with resultsshown in [14] for CS-RZ and duobinary formats.
Among all formats, the largest precompensation and IDCtolerances are observed for the DCS-RZ format. Duobinaryformat has the largest tolerance to TRD among all investigatedformats, and the largest precompensation and IDC tolerancesamong all investigated NRZ-type formats. BL-duobinaryand SSB-DCS-RZ formats have similar dispersion tolerancesdue to the similar signal spectrum width. Different toleranceresults were shown in [8] for a dispersion compensationscheme without precompensation, where it was shown that theSSB-DCS-RZ format had much higher IDC tolerance than theBL-duobinary format. This difference results from the optimumprechirping of the signal caused by optimized precompensa-tion, which improves the tolerance of the BL-duobinary formatto nonlinear fiber effects and, thus, to IDC variation. Thehigher IDC tolerance of SSB-DCS-RZ signal compared tothe one of BL-duobinary signal happened due to the signalchirp originated from the SSB filtering [8], [11]. Thus, theadvantage of SSB-DCS-RZ format vanishes when optimizedprecompensation exists for both formats.
VI. TOLERANCE TO FIBER NONLINEARITY
In order to assess the impact of fiber nonlinearity on thesystem performance, the required OSNR for a BER ofis evaluated for different average power at the SSMF inputfor all formats considering one span only and optimizing thepre- and postcompensation of dispersion for each power level.The OSNR is measured at the receiver input with 0.1 nm ofbandwidth. The BER of is obtained by adjusting the lossof attenuators at the input and output of the SSMF and adjustingthe amplifier gain at the output of the SSMF to maintain thesame powers at the postcompensation ( 6 dBm) and receiver(0 dBm) inputs. The robustness of different signaling formatsto fiber nonlinearity is characterized by the nonlinear threshold(NLT) defined as the average power at the SSMF input thatleads to 1 dB of OSNR penalty with respect to the OSNRobtained in back-to-back operation, as in [26]. Table V showsthe NLT for all investigated signaling formats.
Comparison of figures shown in Table V indicates that theTOF of the duobinary format slightly increases the NLT dueto the eye-opening improvement. For the DCS-RZ format,the tight SSB-filtering decreases the NLT. This is due to theNRZ-shape of the SSB-DCS-RZ format. For the CS-RZ format,the TOF increases the NLT. This happens due to the systemperformance improvement through the interplay betweennonlinear fiber effects and residual dispersion, because the
PAVLOVIC AND CARTAXO: INFLUENCE OF TOF ON LH TRANSMISSION PERFORMANCE OF SEVERAL ADVANCED SIGNALING FORMATS 1347
optimum TRD of BL-CS-RZ format is much shifted from zerofor higher powers. The NLT found for the CS-RZ format is inagreement with the experimental results shown in [26].
The largest NLT among all formats occurs for the DCS-RZformat. Unexpectedly, a large NLT of duobinary format isfound due to its large GVD tolerance. Similar NLT occurs withBL-duobinary and SSB-DCS-RZ formats. Different NLT resultwas shown in [8] for the ODM without the precompensation,where it was shown that SSB-DCS-RZ format has much largerNLT than the BL-duobinary format due to the signal chirpimposed by the SSB filtering. However, as it was explained inthe previous section for the IDC tolerance, by optimizing theprecompensation for each power level, optimized prechirpingis imposed on both signals. Thus, better tolerance to nonlinearfiber effects of the SSB-DCS-RZ signal compared to the one ofthe BL-duobinary is decreased by precompensation.
VII. CONCLUSION
The influence of TOF on the performance of various ad-vanced signaling formats has been investigated numerically.This has been achieved through an extensive optimization ofpre- and inline compensations of dispersion and total residualdispersion of a 43-Gb/s LH dispersion-managed single-channelsystem for duobinary, DCS-RZ, and CS-RZ formats with andwithout TOF. The relation between the IDC and optimapresented in [10] and [20] has been shown to verify for allinvestigated formats.
The impact of TOF on the tolerances to precompensation,IDC, TRD, and nonlinear fiber effects has been analyzed andcompared for the investigated signaling formats. It has beenshown that the TOF affects differently the LH transmission per-formance of the three signaling formats. In general, the TOFreduces the eye opening of the investigated signaling formats,except for the duobinary for which the large fluctuations oflight in “0” bits are decreased with TOF. The TOF improvesthe -factor due to the reduction of noise power bandwidth, ex-cept for the CS-RZ format since a large eye-opening degrada-tion occurs. The TOF improves the dispersion tolerance due tosignal spectrum width reduction, except for duobinary format.The TOF increases the tolerance to fiber nonlinearity of all in-vestigated formats, except when the SSB filtering is used, whichleads to RZ-type to NRZ-type conversion.
Taking into account the maximum achieved value for the-factor and the largest tolerance to dispersion and nonlinear
fiber effects, the most recommended signaling format for LHsingle-channel and UDWDM systems can be indicated. Withoutthe TOF, the most recommended format for LH single-channeltransmission is DCS-RZ format due to the highest maximum
-factor and NLT, and high dispersion tolerances. With TOF, themost recommended signaling format (among all the investigatedones) for LH UDWDM transmission systems with optimizedprecompensation is the BL-duobinary format because the trans-mitter has less complexity than the SSB-DCS-RZ format.
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Natasa B. Pavlovic was born in Belgrade, Serbia,on December 26, 1977. She received the gradua-tion degree in electrotechnical engineering (majorin telecommunications) and the M.Sc. degree intelecommunications from Faculty of Electro-Tech-nical Engineering, Belgrade University, Belgrade,Serbia, in 2001 and 2003, respectively. Currently,she is working towards the Ph.D. degree in opticalcommunications at Instituto Superior Técnico,Lisbon, Portugal. Her doctoral thesis is in the fieldof advanced modulation formats for high spectral
efficient optical communication systems.She spent one year in the dense wavelength division multiplexing/optical
dispersion compensation (DWDM/ODC) project as a beginning researcherworking on the performance assessment of optical dispersion compensationschemes in conventional intensity modulation direct detection systems. Hermain research interests are new modulation formats for ultradense wavelengthdivision multiplexing systems.
Adolfo V. T. Cartaxo (S’89–M’98–SM’02) wasborn in Montemor-o-Novo, Portugal, on January10, 1962. He received the degree of “Licenciatura”in electrical and computer engineering, the M.Sc.degree in telecommunications and computers, thePh.D. degree in electrical and computer engineering,and the “Agregação” degree in electrical and com-puter engineering, in 1985, 1989, 1992, and 2005,respectively, from Instituto Superior Técnico (IST),Faculty of Engineering, Lisbon Technical University,Lisbon, Portugal. His Ph.D. work focused on clock
recovery circuit optimization in direct detection optical communications.In 1985, he joined the Department of Electrical and Computer Engineering,
IST. In 1992, he became an Assistant Professor and in January 2002, he waspromoted to Associate Professor. Over those years, he has lectured severalcourses on telecommunications. He has been the scientific advisor of eightM.Sc. theses and two Ph.D. dissertations. Currently, he is a scientific advisorof four M.Sc. theses and four Ph.D. dissertations. He joined the OpticalCommunications Group of Lisbon Pole of Instituto de Telecomunicações (IT)as a Researcher in 1993. He is now a Senior Researcher conducting research ondense wavelength division multiplexed systems and networks. Since January2002, he has been a member of the National Coordination Commission onOptical Communications of IT. He has been the Leader of the IST participationand the Lisbon site of IT in six projects of the European Union programs onR&D in the optical communications area. He has been the Leader of severalnational projects in the optical communications area. He is the Leader ofIST–IT participation in the cooperation project with Brazil in the area ofoptical networks. In the past few years, he has acted as a Technical Auditor andEvaluator for projects included in “Advanced Communications Technologiesand Services: European RTD” (ACTS) and “Information Society Technolo-gies” (IST) European Union R&D Programs. He has authored or coauthoredmore than 50 journal publications (15 as first author) as well as more than 80international conference papers. He is coauthor of two international patents.His main research interests include fiber optic communication systems andnetworks.
Dr. Cartaxo has served as a Reviewer for the following internationalpublications in the area of optical communications and networks: theIEEE/OSA JOURNAL OF LIGHTWAVE TECHNOLOGY, the IEEE PHOTONICS
TECHNOLOGY LETTERS, the IEE Electronics Letters, the IEE PROCEEDINGS
PART J—OPTOELECTRONICS, OPTICS LETTERS, OPTICS EXPRESS, OPTICS
COMMUNICATIONS, and the IEEE TRANSACTIONS ON COMMUNICATIONS.
