Influence of transmitter chirp on optimiseddispersion managed 10 Gbit/s NRZ installed links

N.B. Pavlovic and A.V.T. Cartaxo

Abstract: The impact of transmitter chirp on the performance of pre- and post-compensationnormalised sections for non-return-to-zero single channel systems was studied by computersimulation. An acceptable dispersion and power margins in typical 10 � 80 and 20 � 80 km-longterrestrial transmission systems were found at 10 Gbit/s. Positive transmitter chirp can remarkablyincrease the optimised Q-factor of a pre-compensated scheme, increase the acceptable range of thedispersion compensation ratio for a prescribed Q-factor, and shift the optimum power levels towardhigher values. However, no significant improvement results from using chirp for thepost-compensated scheme. By independently varying the power at the transmission andcompensating fibres inputs and the dispersion compensation ratio, the post-compensation schemeshows better performance than the pre-compensation scheme at the expense of stricter parametertolerance.

1 Introduction

The systematic numerical optimisation of dispersionmanaged non-return-to-zero (NRZ) single channel links at10Gbits=s using standard single-mode fibre (SMF) anddispersion compensating fibre (DCF) has receivedconsiderable attention in last years. Of particular interestare the pre- and post-compensation schemes where each linkis made of spans with the DCF located before or after theSMF, respectively [1]. The use of DCF, which has anegative dispersion coefficient at the signal wavelength, isan efficient way to upgrade installed links using SMF. Theaccumulated chromatic dispersion in SMF is so large thatdispersion compensation is necessary to reduce inter-symbol interference (ISI) and to achieve better transmissionperformance. DCF has been used to compensate for thechromatic dispersion for reasons of manufacturability,stability over temperature, and wide-band dispersioncompensating characteristics [2]. Spans using SMF andDCF are good candidates as their high local dispersionis known to reduce the phase matching giving rise tofour-wave mixing in wavelength division multiplexing(WDM) systems. Signal quality degradation in such systemsis due to the combined effects of group velocity dispersion,Kerr nonlinearity, and accumulation of amplified spon-taneous emission noise due to periodic amplification [1].

The design of future optical transparent networks couldbe facilitated by the use of so-called ‘normalised sections’[3, 4]. Any network would then consist of a cascade ofidentical normalised sections. Therefore, both networkscalability and management would rely on the knowledgeof the accumulated signal degradation after transmission

through a certain number of these sections [1]. Thesystematic optimisation of ‘normalised sections’ has beenachieved for both compensation schemes, and optimumSMF and DCF input powers and residual dispersion havebeen found. Because of the nonlinear nature of propa-gation, system performance depends on the power levelsat the input of the different types of fibres, on the positionof the DCF, and on the amount of residual dispersion.The amount of dispersion compensation is tailoredspecifically to achieve the widest range of optimumsystem performance regarding Q-parameter, and it isidentical in each repeater. It has been shown that betterperformance can be obtained for post-compensationsystems provided that suitable power levels are used atthe SMF and DCF inputs [1].

Several techniques have been proposed to combat thechromatic dispersion in the SMF namely using electronicmethods at the receiver or transmitter, high dispersionoptical elements such as high dispersion fibres, opticalequaliser filters (namely fibre gratings), and optical phaseconjugation [5]. In this work, we consider the combinationof pre-chirping in the transmitter [2], and dispersionmanagement using DCF. The influence of transmitterchirp on the system performance has been usually neglectedin the optimisation studies before, and a chirplesstransmitted signal has been assumed. Several papers haveanalysed the influence of the transmitter chirp on the systemperformance [2, 6–10] but, to our knowledge, the chirpedsystem optimisation with respect to the SMF and DCF inputpowers and residual dispersion still remains.

In this paper, earlier analyses are generalised byoptimising the normalised sections with respect to thepower levels and residual dispersion for three typical valuesof the transmitter chirp parameter: �1; zero, and þ1:

The analysis of the impact of the transmitter chirp onsystem performance allows assessment of the margin ofpower at fibre input and dispersion compensation ratiowithin a certain performance degradation. Furthermore, wecan gain more understanding of how the dispersive andnonlinear properties of the SMF and DCF spans togetherwith noise accumulation during the transmission affect thepropagating signal. Moreover, the analysis helps to

q IEE, 2004

IEE Proceedings online no. 20040144

doi: 10.1049/ip-opt:20040144

The authors are with the Optical Communications Group, Instituto deTelecomunicacoes, Department of Electrical and Computers Engineering,Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Paper first received 10th December 2002 and in revised form 7th August2003

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 2004 27

anticipate which transmitter features are desirable for longertransmission distances.

2 System description and method ofperformance assessment

The transmission system under investigation is shown inFig. 1. Continuous wavelight is externally modulated at10Gbits=s by a Mach–Zehnder modulator (MZM) driven byan NRZ de Bruijn binary sequence with 128 bits. The chirpintroduced by the MZM is modelled by the Koyama and Iga’smodel of chirp [11]. Three �-parameter values for chirp areconsidered: �1; 0 (chirpless signal), and þ1: The transmittersignal has 13 dB of extinction ratio and 25 ps rise and falltimes, before being launched in a link consisting of 10 or 20pre- or post-compensated ‘normalised sections’. Eachtransmission section consists of 80 km of SMF and a variablelength of DCF, which is adjusted for a given dispersioncompensation ratio (DCR). The DCR is defined as [1]:

DCR ¼jLDCF � DDCFj

LSMF � DSMF

where LDCF and LSMF are the length of the DCF and SMF,respectively, and DDCF and DSMF are the dispersionparameters of the DCF and SMF, respectively. So, for perfectdispersion compensation (PDC), DCR ¼ 100%: Two dis-persion compensation maps are investigated: the distributedpre- and post-compensation schemes, where pre- and post-compensation of SMF dispersion is, respectively, used. Inboth schemes, the amount of compensation needed tomaximise the system performance is equally distributedover all transmission sections. SMF and DCF parameters areshown in Table 1.

Inline erbium-doped fibre amplifiers (EDFA) with 5-dBnoise figure are used before the SMF and DCF to setindependently the power levels at the input to the fibres.

Optical filters with 320 GHz of bandwidth and modelled by20th order Bessel filters are placed after each inline amplifier.The signal at the optical pre-amplifier output is set to 0 dBmand then is filtered by a Bessel optical filter with �3 dBbandwidth of 25 GHz. The electrical receiving filter is a 5thorder Bessel filter with a �3 dB bandwidth of 10 GHz.

The simulations, reported in this work, were performedusing the standard split-step Fourier method includingdispersion terms up to the second order [12]. The Q-factoras a quality parameter is calculated from the Gaussianapproach described in [13], and takes into account thepreamplifier noise and the noise accumulation due to allinline amplifiers. The effect of nonlinear propagation on theamplified spontaneous emission (ASE) noise is assumednegligible by the reasons presented in [14–16]. Therefore,the semi-analytical computation of the Q-factor is based onthe noise free distorted signal and the calculated noisevariance. This method is widely used because of itssimplicity and short computation time, though withreasonable accurate results.

In the analysis of results presented throughout the paper,we consider a minimum required Q-factor of 10, resultingfrom a requirement of a maximum bit error probability of10�12; corresponding to Q ¼ 7; and some additional margin.Accordingly, the acceptable range of DCR is defined as therange of DCR for which the Q-factor is above 10.

3 Results and discussion

The impact of chirp parameter on system performance issystematically analysed for pre- and post-compensationschemes, and for different transmission length of10 � 80 km; and 20 � 80 km: A wide range of power levelsand DCR are investigated to assess the optimum powerlevels, DCR and the corresponding Q-factor and itssensitivity to the variation of those quantities.

Table 1: SMF and DCF parameters

SMF DCF

Attenuation parameter, dB=km 0.25 0.5

Dispersion parameter, ps=ðnm�kmÞ 16 �102

Dispersion slope, ps=ðnm2�kmÞ 0.06 �0:2

Nonlinear index, m2=W 2:6 � 10�20 2:6 � 10�20

Effective area, mm2 80 22

Fibre nonlinearity coefficient �; 1=ðW�kmÞ 1.3 4.8

Fig. 1 Post- and pre-compensation systems under investigation

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3.1 Transmission system with 10 � 80 kmlength

In this Section, the performance of the system with 10 spansof transmission fibre is investigated. The optimisation of thesystem performance is accomplished with respect to thepowers at the input of the SMF and DCF, and dispersioncompensation ratio, for both compensation schemes anddifferent chirp parameters.

3.1.1 Pre-compensation scheme: The Q-factoras a function of SMF and DCF input powers for the threetransmitter chirp parameters (�1; 0, and þ1), and a DCR of106% in the pre-compensation scheme is shown in Fig. 2.This DCR was chosen to illustrate the typical evolution ofoptimum powers at fibre input with transmitter chirp in theover-compensation range. These contour plots show that themaximum Q-factor is achieved for a certain pair of SMF andDCF input powers, which depends on the chirp parameter.Figure 2 shows that, for a given DCR, the performance ofthe pre-compensation scheme can be significantly improvedby using positive chirp. The increase of the chirp parametershifts the optimum power levels toward higher values.Higher power levels at the input of both fibres which aredesirable from a practical point of view, provide largenonlinear effects, but also provide large signal-to-noise ratio(SNR). This is important as it provides a higher Q-factor, ascan be seen in Fig. 2. The higher Q-factor results from the

combined effect of SNR increase and eye openingimprovement. To confirm this, Table 2 shows thenormalised eye-diagram opening and power spectral densityfor a DCR of 110%: With this DCR, when the transmitterchirp changes from negative to positive values, a remark-able increase of maximum attainable Q-factor (obtained bymaximisation of the Q-factor with respect to the SMF andDCF input powers) from 1.8 to 18.4 is observed due to asignificant increase of the normalised eye opening from 0.26to 0.68 and a significant decrease of the power spectraldensity from 1:9 � 10�16 to 4:5 � 10�17 W=Hz.

The influence of chirp parameter on the optimum powerlevels at the SMF and DCF input power against DCR for thepre-compensation scheme can be seen in Figs. 3a and 3b.The optimum levels of SMF and DCF input powers aretailored to achieve the maximum attainable Q-factor. Theoptimum DCF input power in the acceptable range of DCRincreases with changing the chirp parameter from negativeto positive value, as can be seen in Fig. 3. Optimum SMFinput powers have smaller variations with DCR thanoptimum DCF input powers, especially for DCR less than100%: This allows more uniform adjustment of theoptimum system performance.

To assess the impact of transmitter chirp on the maximumattainable Q-factor, the DCR has been varied between 90%and 110% (corresponding to residual dispersion of the linkbetween 1280 and �1280 ps=nm). The maximum attainable

Fig. 2 Q-factor for 10 spans as a function of SMF and DCF input powers for chirp � ¼ �1 (left), � ¼ 0 (middle), and � ¼ þ1 (right) forpre-compensated scheme and DCR of 106%

Table 2: Normalised eye-opening and power spectral density for pre-compensation scheme with DCR of 110% and forpost-compensation scheme with DCR of 91%

a-parameter Pre-compensation scheme (DCR ¼ 110%) Post-compensation scheme (DCR ¼ 91%)

PSD (W/Hz) Normalised eye-opening Q-factor PSD (W/Hz) Normalised eye-opening Q-factor

21 1:9 � 10�16 0.26 1.8 2:1 � 10�17 0.82 35.1

0 6:8 � 10�17 0.44 8.6 2 � 10�17 0.95 35.8

1 4:5 � 10�17 0.68 18.4 1:2 � 10�17 0.46 20.8

Optimum power levels are considered in each case. Ten spans are considered

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 2004 29

Q-factor has been extracted from contour plots similar to theones in Fig. 2. The results are summarised in Fig. 4, wherethe maximum attainable Q-factor is plotted for each DCR.Figure 4 shows that, for negative chirp parameter, thehighest Q-factor occurs for positive residual link dispersion,where maximum pulse compression is achieved, while forpositive chirp parameter the highest Q-factor occurs fornegative residual link dispersion. Chirpless signal has thehighest Q-factor for DCR of 102% what proofs the smallinfluence of self phase modulation (SPM). Moreover, theacceptable range of the DCR, as defined in Section 2, alsoincreases from negative to positive chirp parameter, as Fig. 4suggests. Our results reveal the optimum DCR for differentchirp parameters. The results show that, for the minimumrequired Q-factor of 10, we can in principle achieve anacceptable system performance using a wide range of DCRand chirp tolerance.

3.1.2 Post-compensation scheme: The Q-factor, as a function of SMF and DCF input powers forthe three transmitter chirp parameters (�1; 0, and þ1) and aDCR of 91%; in the post-compensation scheme is shown inFig. 5. This value of DCR leads to the optimum systemperformance. As can be seen in Fig. 5, the optimum powersdepend only slightly on chirp parameter, because of the

large influence of SPM. That can also be seen in Fig. 6,similar to Fig. 3 for the pre-compensation scheme, wherethe influence of chirp parameter on the optimum powerlevels at the SMF (top) and DCF (bottom) input powerversus DCR is presented. Figure 6 shows that when the DCRdecreases, optimum powers at SMF and DCF inputs need tobe increased to get the best performance. For a DCR of100%; the power levels at fibre input are mostly set by SNRrequirements and not by the need to counteract dispersionimbalance by SPM. On the other hand, when the DCRdecreases, some amount of SPM is required because SPM inthe anomalous dispersion regime leads to pulse compressionand, therefore, a higher power into the SMF is desirable.Figure 6b shows that some amount of SPM in the DCF canalso be helpful for an under-compensated system, which isin agreement with [1].

Figure 7 shows the maximum attainable Q-factor forDCR between 85% and 110% (corresponding to residualdispersion of the link between 1920 and �1280 ps=nm).Figure 7 shows that under-compensation is beneficial in thepost-compensated scheme, due to the interaction of the SPMeffect and positive residual dispersion per section, which isin agreement with [1] and [17]. A residual dispersion of1152 ps=nm (DCR of 91%) is found to lead to the highestQ-factor for both �1 and 0 chirp parameters. In the post-compensation scheme, the maximum attainable Q-factor isreached for higher optimum input powers that causes largerinfluence of SPM and negligible influence of negativetransmitter chirp, because a large negative chirp due to SPMis already present in the system. Both the eye opening andnoise accumulation are similar for �1 and zero �-parameterand this leads to similar Q-factor as can be seen in Fig. 7.However, the positive chirp degrades significantly theQ-factor for positive residual dispersion, due to theinteraction of chirp and SPM, which gives slightly smallernoise accumulation but a significant reduction of eyeopening. The normalised eye-openings and the powerspectral density for maximum attainable Q-factor (DCR of91%) are shown in Table 2.

The more uniform performance in the post-compensationscheme, with positive chirp can be explained by theexistence of two opposite effects on Q-factor: the increaseof noise accumulation and increase of eye opening with theDCR increase. In fact, the eye opening increase is largerthan the noise accumulation enhancement for DCR greaterthan 97%; which leads to a much flatter maximum attainable

Fig. 3 Optimum SMF and DCF input powers for 10 spansagainst DCR for pre-compensation scheme

a SMF input powerb DCF input powerThe small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

Fig. 4 Maximum attainable Q-factor for 10 spans for the pre-compensated scheme as a function of the DCR

The small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 200430

Q-factor. That is not the case with other chirp parameters.Normalised eye-openings and power spectral density forDCR values mentioned above are shown in Table 3.

To understand the weak dependence of optimum systemperformance on chirp parameter for under-compensationand negative chirp parameter, the Q-factor was obtained fordifferent chirp parameters between �4 and 4. Figure 8 showsthe results obtained assuming a DCR of 91% and DCF andSMF input powers of 2 dBm and 12 dBm, respectively.These values are very close to those leading to the optimumpowers at a DCR of 91% (for which the highest Q-factoris obtained) for the chirp parameters of �1; 0, and 1, seeFigs. 6 and 7. Figure 8 shows that chirped signals can onlydegrade system performance. For negative values of chirp,the Q-factor smoothly decreases with the decrease of thechirp parameter, as it is expected due to the large influence

Fig. 5 Q-factor for 10 spans as a function of SMF and DCF input powers for chirp � ¼ �1 (left), � ¼ 0 (middle), and � ¼ þ1 (right) forpost-compensated scheme and DCR of 91%

Fig. 6 Optimum SMF and DCF input powers for 10 spansagainst DCR for post-compensation scheme

a SMF input powerb DCF input powerThe small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

Fig. 7 Maximum attainable Q-factor for 10 spans for the post-compensated scheme as a function of the DCR

The small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 2004 31

of SPM. In this case, the eye opening decreases smoothlyalso and that explains the degradation of the systemperformance. However, for positive chirp parameter, Fig. 8shows a remarkable degradation of the system performancewith the increase of � up to 1.5, and then improvement till� ¼ 4: The reason why such a remarkable degradation isobserved for small positive chirp parameter is theappearance of ghost pulses for logical ‘0’ level. To showthese ghost pulses, we present, in Fig. 9, the eye-diagramsfor chirp parameter of 0, 1.5, and 4 in the same conditions asFig. 8. These pulses were not sent from transmitter, so they

result from the transmission. This effect is similar to theeffect called intrachannel four-wave mixing (FWM), whichhas been attributed to RZ systems [18, 19]. In our case,ghost pulses appear in NRZ system for particular levels oftransmitter chirp. They have been observed for positivechirp and in the post-compensation scheme for optimumsystem performance.

3.1.3 Comparison of pre- and post-compen-sated system performance: The main reasonfor the comparison of the two compensation schemes isto find the better system performance. Optimum powersdepend differently on chirp parameter in these twocompensation schemes, which can be seen in Figs. 3and 6. In Fig. 3, a large chirp influence on the pre-compensation scheme can be seen, and in Fig. 6 a reducedchirp influence on the post-compensation scheme isobserved. That can be explained by the stronger effectof SPM on the post-compensation scheme. Moreover, inthe case of the post-compensation scheme, the optimumDCR does not vary much when the transmitter chirp isincreased. This allows for flexibility in network design, asthe power levels and optimum DCR can be setindependently of the chirp of the signal.

The results clearly show that the place of DCF in the span(if it is pre- or post-compensation) has great influence onsystem performance. Pre-compensation has smallereye-opening and larger spontaneous emission noiseaccumulation than post-compensation (see Table 2). Forthe post-compensation scheme, as can be seen in Figs. 4and 7, an improvement of the highest Q-factor is obtained.This is attained for higher power levels than for the pre-compensation scheme, as can be seen in Figs. 3 and 6.Moreover, the results show that pre- and post-compen-sations lead to opposite dependence on transmitter chirp.For the post-compensation scheme, the highest Q-factoroccurs for non-positive transmitter chirp and under-compensation, and for pre-compensation it occurs forpositive transmitter chirp and over-compensation.

Dispersion compensation should be set to optimisetransmission performance due to SPM [1, 7, 14, 17, 20,and 21]. In the post-compensation scheme, the Q-factorvaries significantly when the DCR is changed, which is notobserved in the pre-compensation showing poorer but moreuniform performance. For WDM systems, the DCR will

Table 3: Normalised eye-opening and power spectraldensity for post-compensation scheme and DCR of 98%and 105%

�-parameter PSD ½W=Hz Normalised eye-opening

DCR ¼ 98% DCR ¼ 105% DCR ¼ 98% DCR ¼ 105%

1 4:3 � 10�17 1 � 10�16 0.52 0.92

0 6:8 � 10�17 1:6 � 10�16 0.65 0.63

Optimum power levels are considered in each case. Ten spans are

considered

Fig. 8 Maximum Q-factor for 10 spans for the post-compen-sation scheme (DCR ¼ 91%) as a function of the chirp parameter

SMF input power ¼ 12 dBm; DCF input power ¼ 2 dBm: These are theoptimum input powers for the chirpless signal

Fig. 9 Noiseless eye-diagrams at the output of the receiving filter for the post-compensation scheme for � ¼ 0 (left), þ1.5 (middle),and þ4 (right)

Optimum SMF input power of 12 dBm, optimum DCF input power of 2 dBm, and optimum DCR of 91% for chirpless signal

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 200432

vary from one channel to another, resulting in unequalchannel performance, and using post-compensation schemedoes not allow for large DCR tolerance [1]. On the otherhand, the optimum system performance depends signifi-cantly on the transmitter chirp, especially for pre-compen-sation scheme. So, the choice of which compensationscheme should be used to have an optimised systemperformance is a compromise between better Q-factor andless dependence of the system performance on the DCRlevel and transmitter chirp.

3.2 Transmission system with 20 � 80 kmlength

In this Section, the transmission performance of 20 spans isinvestigated. In general, the same behaviour as for 10 spansis observed and only the main differences are described anddiscussed.

3.2.1 Pre-compensation scheme: Figure 10shows the Q-factor as a function of SMF and DCF inputpowers for the three transmitter chirp parameters (�1, 0, andþ1), and the specific DCR of 105% in the pre-compensationscheme. For 20 spans link as for 10 spans, the increase of thechirp parameter moves the optimum power levels towardhigh levels, and the Q-factor toward higher values.However, a lower Q-factor (of about a half the Q-factorfor 10 spans) than for 10 spans is observed around themaximum attainable Q-factor.

In Fig. 11, similar to Fig. 3, the influence of chirpparameter on the optimum power levels at the SMF andDCF input is shown. The optimum DCF input power in therange of DCR till 105% increases with changing the chirpparameter from negative to positive value, while thedependence of SMF input power on the chirp is muchweaker.

In Fig. 12, the maximum attainable Q-factors are plottedfor DCR between 90% and 110%: A stricter range of DCRthan for 10 spans is observed around the highest Q-factor.The transmission performance of the pre-compensation

Fig. 10 Q-factor for 20 spans as a function of SMF and DCF input powers for chirp � ¼ 21 (left), � ¼ 0 (middle), and � ¼ þ1 (right) forpre-compensated scheme and DCR of 104%

Fig. 11 Optimum SMF and DCF input powers for 20 spansagainst DCR for pre-compensation scheme

a SMF input powerb DCF input powerThe small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 2004 33

scheme for a given DCR can be significantly improved byincreasing the chirp, as can be seen in Fig. 12. The sameeffect has been observed for 10 spans (Fig. 4). Figure 12shows that the minimum required Q-factor of 10 occurs onlyfor positive chirp parameter and DCR between 102% and105%: Comparison of Figs. 4 and 12 reveals that, when thenumber of spans increases from 10 to 20, the optimum DCRfor a certain chirp parameter is shifted to values where theresidual dispersion per section is nearly halved (for 10 spansand chirp parameter of 1, the optimal DCR is 107% andthe residual dispersion per section is 0:07 � 16 � 80 ¼89:6 ps=nm; while for 20 spans the optimal DCR is 104%and the residual dispersion per section is 0:04 � 16� 80 ¼ 51:2 ps=nm) to compensate for the twice longertransmission link. This result is in qualitative agreementwith the result presented in [21]. However, in [21] theeffect of amplifier noise was neglected, and only thepost-compensation scheme was considered.

3.2.2 Post-compensation scheme: Figure 13shows the Q-factor as a function of SMF and DCF inputpowers for the three transmitter chirp parameters (�1; 0, andþ1), for the specific DCR of 95%; and the post-compensa-tion scheme. Here, the optimum power levels depend onlyslightly on the chirp parameter, and the maximum attainableQ-factor occurs for higher power levels. These are basicallythe same effects as with 10 spans link.

The optimum power levels at the SMF and DCF inputsversus DCR are shown in Figs. 14a and 14b. Weakdependence of optimum power on chirp parameter isobserved. In Fig. 15, the maximum attainable Q-factorsare plotted for DCR between 85% and 110%: Figure 15shows that under-compensation is advantageous in the post-compensated scheme as for ten spans. Negative and zero�-parameter lead to similar Q-factor, and the positive�-parameter degrades significantly the Q-factor for positiveresidual dispersion, as for ten spans.

The main difference between the 20 spans and the tenspans links is that the highest Q-factor occurs for 95% ofDCR, that is, for residual dispersion of 1280 ps=nm: Thismeans that, with the increase of the number of spans, theoptimum system performance occurs for smaller residualdispersion per section. This is in agreement with the resultpresented in [21].

3.2.3 Comparison of pre- and post-compen-sated system performance: The increase of thetransmission link leads to a larger amount of fibre losses,noise accumulation, and fibre nonlinear effects and,consequently, to a degradation of the system performance.Larger optimum powers are expected for 20 spans than for10 to compensate for the system degradation due to theadditional fibre losses, and noise accumulation. However,the increase of the fiber nonlinear effects with the number ofspans restricts the increase of optimum powers. Therefore,the optimum powers for a certain DCR do not changesignificantly with the increase of the number of spans from10 to 20. This can be seen in Figs. 3 and 11 for pre-compensation, and Fig. 6 and 14 for post-compensation

Fig. 12 Maximum attainable Q-factor for 20 spans for the pre-compensated scheme as a function of the DCR

The small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

Fig. 13 Q-factor for 20 spans as a function of SMF and DCF input powers for chirp � ¼ �1 (left), � ¼ 0 (middle), and � ¼ þ1 (right) forpost-compensated scheme and DCR of 95%

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 200434

scheme. This is in very good agreement with the resultspresented in [1].

As for ten spans, Figs. 11 and 14 show that the influenceof chirp parameter on optimum powers is obvious only forpre-compensation scheme. Figures 12 and 15 demonstratethat higher optimum powers of post-compensation

scheme result in large Q-factors with this compensationscheme.

In general, optimum SMF powers are larger than DCFpowers for both compensation schemes and transmissiondistance. The main outcome of Fig. 12 is that thepre-compensation scheme has larger dependence on thetransmitter chirp than the post-compensation scheme,especially for negative chirp. Moreover, it can be observedthat, in the case of the post-compensation scheme, thehighest Q-factor is reached for the same DCR for differentchirp parameters but, for pre-compensation, the optimumDCR increases with the increase of the chirp parameter, asfor ten spans.

Different system performance is achieved regarding DCRinfluence, when the systems with ten and 20 spans arecompared. The Q-factor is approximately half smaller for atwofold increase of transmission length, due to twice largertransmission loss. This can be seen in Figs. 4 and 12 forthe pre-compensation scheme, or in Figs. 7 and 15 forpost-compensation scheme.

The comparison of Figs. 4 and 12 for the pre-compensation scheme, and Figs. 7 and 15 for thepost-compensation scheme reveals that no significantdifference of system performance, regarding the influenceof chirp parameter in the both compensation schemes, isfound between 20 spans and ten spans. The main differencebetween the systems with ten and 20 spans is that theoptimal DCR area is narrower for a larger number of spans,which can be seen in Figs. 4 and 12 for the pre-compensation scheme, and in Figs. 7 and 15 for thepost-compensation scheme. This means that, when thetransmission link is longer, the optimal system performanceoccurs in a smaller range of DCR. Therefore, a reduction ofthe system performance tolerance is observed with theincrease of the transmission length.

4 Conclusions

We have performed a systematic DCR and fibre input poweroptimisation of dispersion managed NRZ single channellinks at 10Gbits=s using distributed pre- and post-compensation of SMF dispersion by DCF dispersion.Numerical simulation has been used to compare the systemperformance for three different chirped signals (chirplesssignal, signal with positive chirp and signal with negativechirp), and for two different transmission lengths.

Numerical results have shown that, for the pre-compen-sated scheme, the positive transmitter chirp remarkablyincreases the maximum attainable Q-factor, the acceptablerange of the DCR, and shifts the optimum power levelstoward higher values. However, no significant improvementis observed from using chirp for the post-compensatedscheme and the optimum power levels are almost the samefor different chirp parameters. In the post-compensatedsystem, the positive transmitter chirp of 1 significantlydegrades system performance. Furthermore, the influence ofchirp on the system performance is similar for bothtransmission distances.

We have shown that optimal residual dispersion dependson the type of the compensation used in the link and opticalpower launched into it. It has been shown that post-compensation performs better at the expense of morestringent parameter tolerance. A DCR of 91% for 10 spans,and 95% for 20 spans has been found to be optimum forpost-compensation, which shows that, for longer trans-mission length, less residual dispersion per section is neededfor compensation of SPM effect and, on that way, optimisethe system. On the other hand, smaller influence of the

Fig. 15 Maximum attainable Q-factor for 20 spans for the post-compensated scheme as a function of the DCR

The small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

Fig. 14 Optimum SMF and DCF input powers for 20 spansagainst DCR for post-compensation scheme

a SMF input powerb DCF input powerThe small fluctuations are mostly due to the step size of 1 dB used in theoptimisation of the SMF and DCF input optical powers

IEE Proc.-Optoelectron., Vol. 151, No. 1, February 2004 35

DCR on the maximum attainable Q-factor and power levelsbut significant dependence on chirp parameter has beenobserved for the pre-compensation system. Longertransmission links narrow the range of acceptable DCRfor a prescribed system performance and lead to stricterparameter tolerance.

The results of this work provide understanding of theoperation of dispersion managed NRZ transmission systemsregarding chirp parameter, dispersion compensation, andoptical amplifiers noise. They also provide useful engineer-ing guidelines of designing such systems.

5 Acknowledgments

This work was supported by Fundacao para a Ciencia e aTecnologia (FCT) from Portugal and POSI under projectPOSI/CPS/35576/1999 - DWDM/ODC.

6 References

1 Peucheret, C., Hanik, N., Freund, R., Molle, L., and Jeppesen, P.:‘Optimization of pre- and post-dispersion compensation schemes for10-Gbits/s NRZ links using standard and dispersion compensatingfibers’, IEEE Photonics Technol. Lett., 2000, 12, (8), pp. 992–994

2 Nuyts, R.J., Park, Y.K., and Gallion, P.: ‘Dispersion equalization of a10 Gb/s repeatered transmission system using dispersion compensatingfibers’, J. Lightwave Technol., 1997, 15, (1), pp. 31–41

3 Bachus, E.J., Eiselt, M., Habel, K., Langer, K.D., Scheuing, E.U., andTischer, F.C.: ‘Photonic network design based on reference circuits’.Proc. Optical network design and modeling ONDM’97, 1997, pp. 56-69

4 Hanik, N., Gladisch, A., and Lehr, G.: ‘An effective method to designtransparent optical WDM-networks’. Proc. Networks and opticalcommunications NOC’98, 1998, pp. 190-197

5 Agrawal, G.P.: ‘Fiber-optic communication systems’ (John Wiley &Sons, Inc., New York, USA, 1997, 2nd edn.), Chap. 9

6 Kim, S.K., Mizuhara, O., Park, Y.K., Tzeng, L.D., Kim, Y.S., andJeong, J.: ‘Theoretical and experimental study of 10 Gb/s transmissionperformance using 1.55mm LiNbO3-based transmitters with adjustableextinction ratio and chirp’, J. Lightwave Technol., 1999, 17, (8),pp. 1320–1325

7 Gnauck, A.H., Tkach, R.W., and Mazurczyk, M.: ‘Interplay of chirpand self phase modulation in dispersion-limited optical transmission

systems’. Proc. European Conf. on Optical communications ECOC’93,1993, paper TuC4.4, pp. 105-108

8 Cartledge, J.C., Debregeas, H., and Rolland, C.: ‘Dispersion compen-sation for 10 Gb/s lightwave systems based on a semiconductor Mach-Zehnder modulator’, IEEE Photonics Technol. Lett., 1995, 7, (2),pp. 224–226

9 Gnauck, A.H., Korotky, S.K., Veselka, J.J., Nagel, J., Kemmerer, C.T.,Minford, W.J., and Moser, D.T.: ‘Dispersion penalty reduction using anoptical modulator with adjustable chirp’, IEEE Photonics Technol.Lett., October 1991, 3, (10), pp. 916–918

10 Cartledge, J.C.: ‘Transmission performance a-parameter for semicon-ductor Mach-Zehnder modulators’. Proc. Optical Fibre CommunicationOFC’97, 1997, paper WL53, pp. 219-220

11 Koyama, F., and Iga, K.: ‘Frequency chirping in external modulators’,J. Lightwave Technol., 1988, 6, pp. 87–92

12 Agrawal, G.P.: ‘Nonlinear fiber optics’ (Academic Press, New York,USA, 1995, 2nd edn.), Chap. 2

13 Rebola, J.L., and Cartaxo, A.V.T.: ‘Gaussian approach for performanceevaluation of optically preamplified receivers with arbitrary optical andelectrical filters’, IEE Proc., Optoelectron., 2001, 148, (3), pp. 135–142

14 Bellotti, G., Bertaina, A., and Bigo, S.: ‘Dependence of self-phasemodulation impairments on residual dispersion in 10-Gb/s-basedterrestrial transmissions using standard fiber’, IEEE Photonics Technol.Lett., 1999, 11, (7), pp. 824–826

15 Bigo, S., Penninckx, D., and Chbat, M.W.: ‘Investigation of self-phasemodulation limitation on 10-Gbit/s transmission over different types offiber’. Proc. Optical Fibre Communication OFC’98, Feb. 1998,pp. 389–390

16 Farbert, A., Scheerer, C., Glingener, C., and Fischer, G.: ‘Optimaldispersion management for long-haul optical transmission systems’.Proc. European Conf. on Optical communications ECOC’99,Sept. 1999, pp. 154-155

17 Nuyts, R.J., Park, Y.K., and Gallion, P.: ‘Performance improvement of10 Gb/s standard fiber transmission systems by using the SPM effect inthe dispersion compensating fiber’, IEEE Photonics Technol. Lett.,1996, 8, (10), pp. 1406–1408

18 Kumar, S., ‘Intrachannel four-wave mixing in dispersion managed RZsystems’, IEEE Photonics Technol. Lett., 2001, 13, (8), pp. 800–802

19 Essiambre, R.J., Mikkelsen, B., and Raybon, G.: ‘Intrachannel crossphase modulation and four wave mixing in high speed TDM systems’,Electron. Lett., 1999, 35, pp. 1576–1578

20 Kikuchi, N., and Sasaki, S.: ‘Analytical evaluation technique of self-phase-modulation effect on the performance of cascaded opticalamplifier systems’, J. Lightwave Technol., 1995, 13, (5), pp. 868–878

21 Elbers, J., Farbert, A., Scheerer, C., Glingener, C., and Fischer, G.:‘Reduced model to describe SPM-limited fiber transmission indispersion-managed lightwave systems’, IEEE J. Sel. Top. QuantumElectron., 2000, 6, (2), pp. 276–281

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