Performance comparison of 40 Gb / s ULH transmissions using CSRZ-ASK or CSRZ-DPSK modulation formats on UltraWaveTM fiber

In this work we present extensive comparisons between numerical modelling and experimental measurements of the transmission performance of either CSRZ-ASK or CSRZ-DPSK modulation formats for 40-Gb/s WDM ULH systems on UltraWave fiber spans with all-Raman amplification. We numerically optimised the amplification and the signal format parameters for both CSRZ-DPSK and CSRZ-ASK formats. Numerical and experimental results show that, in a properly optimized transmission link, the DPSK format permits to double the transmission distance (for a given BER level) with respect to the ASK format, while keeping a substantial OSNR margin (on ASK modulation) after the propagation in the fiber line. Our comparison between numerical and experimental results permits to identify what is the most suitable BER estimator in assessing the transmission performance when using the DPSK format. © 2007 Optical Society of America OCIS codes: (060.4080) Modulation; (060.4510) Optical communications; (190.4370) Nonlinear optics, fibers. ___________________________________________________________________________ References and links 1. "Mintera achieves record ultra long haul transmission distance at 40 Gb/s", March 2002; "Migrating to 40Gbit/sec DWDM networks," FibreSystems Europe, September 2002, www.mintera.com. 2. "Lucent Technologies ships its new, industry-leading optical system LambdaXtremeTM transport to Deutsche Telekom," Lucent press release, March 2002, www.lucent.com 3. "LambdaxtremeTM Transport successfully completes field trial in Deutsche Telekom network," Lucent press release, July 2002, www.lucent.com. 4. 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Introduction
In spite of their availability since a few years as commercial products, 40 Gb/s optical transmission systems have not yet been extensively deployed in the field by carriers [1][2][3].The main reason for this delay was the competition from ultra long-haul (ULH) 10 Gb/s WDM transmission systems, whose mature technology enabled maximum transmission distances well beyond 2000 km, without electronic regeneration [4][5].At present however there is a renewed interest in the deployment of 40 Gb/s transport solutions, thanks to transponder technology advances and the associated cost reductions.As a consequence, it is expected that upgrading ULH transmission systems to a 40 Gb/s per channel granularity will enable further cost savings [6][7].A crucial issue for carriers intending to deploy 40 Gbit/s systems is to be able to perform a critical evaluation of the performances of ULH 40 Gb/s WDM transmission systems when introducing innovative fiber bases (such as the UltraWave TM fiber), which have been specially designed for enabling 40 Gb/s transmissions on more than 2000 km [8][9][10][11][12][13][14][15], when used in combination with advanced modulation formats [8][9][10][11][12][13][14][15][16][17][20][21][22].
In this work we present, we believe for the first time, a detailed numerical and experimental inter-comparison of ULH 40 Gbit/s WDM system performance, using either the CSRZ-ASK or the CSRZ-DPSK modulation format [8][9][10][11][12][13][14][15][16][17][20][21][22] over exactly the same link configuration of UltraWave TM fiber spans [8][9][10][11][12][13][14][15].In other words, in order to ensure a fair comparison of the system performance when using the two different modulation formats, we kept unchanged throughout the experiments both the fiber base (and the dispersion map), as well as the amplifier configuration.Moreover, we guided our experiments by means of extensive numerical simulations, in order to point out the contribution of the major sources of transmission penalty, and to determine the optimal signal and link configuration.For the DPSK format, we compared the experimental bit-error-rate (BER) with the predictions of different Q-factor estimators (such as the amplitude Q-factor [25][26], the differential-phase Qfactor [20], as well as the semi-stochastic BER estimation using moment generating functions and the saddle point approximation [27][28]).In this way, we could determine which BER estimator is best suited to predict the experimentally observed BER, as well as the optimal system configuration.Transmission losses were compensated by bi-directional all-Raman distributed amplification: the corresponding optimal amplifier configuration (i.e., the ratio between forward and backward Raman gain) was determined by means of the nonlinearity management approach [18].On the other hand, for each modulation format we independently optimized the span input power per channel, as well as the pre-and the post-compensation: as we shall see, the numerical and experimental optimization results are in good agreement.

Experimental set-up
Our experimental set-up is shown in Fig. 1.The transmitter involved sixteen DFB laser sources, ranging from 1544.53 nm to 1556.56 nm on a 100-GHz ITU-grid.Odd and even channels were separately multiplexed, independently modulated, combined and co-polarized through a polarization maintaining 3-dB coupler.Each transmitter was composed of two cascaded external LiNbO 3 Mach-Zehnder modulators.
The first modulator was used for either amplitude or phase modulation, when biased at the transmission mid or null-point, respectively.This modulator was driven by a 40-Gb/s pseudorandom bit sequence (PRBS) of 2 31 -1 bit length.The second modulator was biased at the transmission null-point, and it was driven by a 20 GHz clock for generating the 40-GHz RZ train with a 66% duty cycle.The different WDM channels were transmitted through a precompensation fiber, amplified by an Erbium-doped fiber amplifier (EDFA), and injected into the loop.In Fig. 2 we illustrate the temporal and spectral properties of our transmitter for each of the two modulation formats under test.In the left column of Fig. 2 we show the eye diagrams as measured by means of an oscilloscope equipped with a 65 GHz optical sampling module and a high-precision time base.In the right column of Fig. 2 we show the signal optical spectra from an optical spectrum analyser with 10 pm resolution bandwidth.The small residual carrier in the CSRZ-ASK spectrum of Fig. 2 is due to the imperfect modulator response.As shown in Fig. 1, the re-circulating loop contained four 100-km dispersion-managed fiber (DMF) spans of SLA-IDF-SLA UltraWave TM fiber [8][9][10][11][12][13][14][15].The SLA and IDF fibers at 1550 nm had a loss of 0.18 and 0.235 dB/km, a chromatic dispersion of 20 and -40 ps/nm/km, and an effective area of 107 and 31 µm², respectively [19].Each span involved a symmetrical fiber arrangement, namely: 34 km of SLA, 32 km of IDF, and 34 km of SLA. Figure 3 illustrates the details of the dispersion map over the two first circulations in the loop.The residual span cumulated dispersion was of about 40 ps/nm at 1550 nm.Therefore we inserted after the four transmission spans an additional 3.5 km of IDF, in order to bring back the loop cumulated dispersion to ~0 ps/nm.Note that the experimental loop cumulated dispersion was affected by contributions from the different devices.Therefore it was necessary to accurately measure the residual loop cumulated dispersion by means of a custom designed set-up [29], yielding the value of 40 ps/nm.The dispersion measurement set-up implemented the differential phase shift method, where a monochromatic tuneable light source is used as transmitter.The same measurement set-up (using this time the fixed analyser method) also permitted us to determine the net polarization mode dispersion (PMD) (or average differential group delay (DGD)) in the loop.We obtained a loop PMD value close to 1 ps, whereas the nominal span PMD was equal to 0.04 ps/km 1/2 .In order to minimize the loop-induced polarization effects, we used a polarisation scrambler, which was synchronously modulated with the loop circulation period.The cumulated loss of each fiber span of 22.5 dB (including splices, pump-signal WDM multiplexers and connectors) was fully compensated by means of bi-directional distributed Raman amplification.
As discussed in more details in the next section, the numerical optimization of the all-Raman amplification scheme [16] in the UltraWave TM spans suggested the forward and backward Raman gain values of 4.5 and 18 dB, respectively.Such gains were obtained by means of a forward pump at 1455 nm, and a backward pump at 1435 and 1455 nm, respectively.In addition, a dynamic gain equalizer (DGE) was used in order to achieve loop gain equalization, and to suppress amplified spontaneous emission noise outside the signal band.We further inserted in the loop two additional EDFAs.The first EDFA permitted us to adjust the input power level into the first span (and subsequent ones).Whereas the second EDFA was used in order to compensate for the losses of the IDF, of the various other devices in the loop, such as DGE, the loop acousto-optic switch, the 3-dB loop coupler and the polarization scrambler.After a pre-determined number of circulations, the channel under measurement was selected by means of a square flat-top optical filter with the 20-dB bandwidth of 0.7 nm.The optimization of the filter bandwidth was performed in back-to-back configuration, and led to the same results for both the CSRZ-ASK and the CSRZ-DPSK modulation formats.The value of post-compensation was also optimized by means of a tuneable dispersion compensation module (TDCM) for each configuration under test [19].Finally, the CSRZ-ASK signal was detected by a PIN photodiode and fed into a 40-Gb/s 1:4 electrical time division demultiplexer (ETDM).For the DPSK format, before detection, the optical signal was demodulated by a Mach-Zehnder 1-bit delayed fiber interferometer (MZDI).A balanced PIN photodiode circuit acted as the DPSK detector.After the ETDM, the average BER of the four 10-Gb/s tributaries was determined.Indeed, due to the loop operation, the BER was randomly measured on each of the four 10 Gb/s tributaries, for every signal burst that was sent to the BER tester.

Simulation results
In this section we describe an extensive set of numerical simulations, carried out with the purpose of supporting the experiments with design guidelines for the many independent link and signal parameters.Indeed, a careful optimization and fine tuning are required for both the Raman amplifier, as well as for the dispersion map configuration and the input signal power level.First of all, we identified the most appropriate ratio of forward to backward Raman gains.To this end, we applied a previously described general Raman amplifier optimization procedure, which is based on the mean-field approximation and the Raman power evolution equations [18].In this way, we could predict that the nonlinear transmission impairments can be minimized (for any desired level of the output optical signal-to-noise ratio) whenever the Raman pumping is such that the backward pump provides between 60% and 80% of the total Raman gain (see Fig. 3, right hand side).We could confirm this prediction by means of full (that is, without the mean-field approximation) numerical simulations involving the transmission of a comb of modulated WDM channels.More precisely, modulated signal transmission simulations show that the best system performance is obtained whenever 80% of the total gain is provided by the backward pump, and the remaining 20% by the forward pump.As a result, in our experiments we retained the 20% forward-80% backward pump ratio for both the CSRZ-ASK and the CSRZ-DPSK formats.
We performed a numerical optimisation of the dispersion map and of the input signal power level per channel.For each of the two modulation formats under study, we evaluated the dependence of Personick's Q factor, evaluated at a balanced receiver (for the central channel in a comb of 5 WDM channels with 100 GHz spacing), as a function of both the signal pre-compensation (or prechirp) and the net residual loop dispersion (as discussed in section 2). Figure 4 shows the various levels of constant output Q factor versus both pre and residual dispersion.The right plot in Fig. 4 was obtained after transmission through a 4000 km UltraWave TM fiber link with the CSRZ-DPSK format: as it can be seen, for residual loop dispersions higher than 20 ps/nm the pre-compensation should be reduced below -200 ps/nm.In particular, for the experimentally measured residual dispersion of 40 ps/nm (see section 2), Fig. 4 (right) predicts that the optimal pre-compensation should be equal to about -300 ps/nm.This value is very close to the actual optimal pre-compensation as it was determined in the experiments.The plots of Fig. 4 show that, with either ASK or DPSK modulation formats, precompensation should be a negative, linearly decreasing function of residual loop dispersion.Note that, although we used a nearly symmetrical dispersion map, the knowledge of the effective net residual dispersion per loop is a key element for determining the optimal precompensation value.
Next, Fig. 5 shows the dependence of the output Q factor (as in Fig. 4, the Q factor is evaluated for the central channel when propagating a comb of 5 WDM channels with 100 GHz spacing) as a function of pre-compensation and input channel power in the UltraWave TM fiber spans.In the simulations of Fig. 5, we fixed the value of the residual loop dispersion to 40 ps/nm, which again corresponds to the measured value in our experimental setup.The white dots in the plots of Fig. 5 indicate the experimental optimal working points.Figure 5 shows that, for both the ASK and the DPSK modulation formats, the simulations predict optimal pre-compensation and channel input powers which turn out to be in good quantitative agreement with the corresponding experimental optimal values.In the simulations leading to Fig. 4 and 5, the optimization of the dispersion map and of the CSRZ-DPSK signal power was based on the evaluation of Personick's signal quality Q factor as it is measured by a balanced detector.On the other hand, the experimental optimization of the CSRZ-DPSK transmissions was carried out by minimizing the bit-error-rate (BER) at the balanced receiver.As it is well known, with the DPSK format the simple relationship ( ) does not hold between the value of Q and the corresponding BER [27].Indeed, as we shall demonstrate in the remainder of this section, for the DPSK modulation format the BER value may only be correctly estimated by using moment generating functions and the saddle point approximation [27][28].Nevertheless, although it is known that the Q factor is invalid in predicting the observed BER value, a first approximation to the optimization of a transmission system parameters (namely, the optimal selection of the dispersion map or span input signal power level) may be performed by using a simple estimation of the Q factor as shown in Fig. 4 and 5. On the other hand, Fig. 6 shows that only the statistical direct calculation of the BER value properly predicts the experimentally observed optimum output signal OSNR (or, equivalently, span input channel power level).We show by empty circles (joined by a fitting red solid curve) the experimentally measured BER vs. the receiver OSNR (in 1 nm) after a 4000 km long UltraWave TM fiber link.The empty squares joined by a blue solid curve illustrate the numerically computed BER, obtained by the moment generating functions and the saddle point approximation, as discussed in reference [27] and implemented in the commercial software Virtual Photonics (VPI) Transmission Maker 7.0.In order to arrive at the direct numerical BER evaluation for signal transmission over a 4000 km long UltraWave TM fiber-based link using the DPSK format, we numerically computed with our proprietary simulation code the propagation of the optical field throughout the entire link.The resulting optical field emerging from the receiver's optical filter was fed into the VPI receiver module for the direct calculation of the corresponding BER.For simplicity, we did not include in all of our receiver modules any electrical receiver noise.: BER from semi-analytical approach; BER from differential phase Q. Insets: phasor diagrams (optical field) for input channel powers of either -6 dBm (left plot) or 0 dBm (right plot).
Next, we evaluated the Personick's amplitude Q factor at the output of a balanced receiver with both our own receiver module and with the corresponding VPI receiver module.In both cases, we obtained (via the Q factor and the hypothesis of a Gaussian pdf for the electrical current fluctuations) virtually the same BER estimate as a function of the output OSNR: this estimate is shown in Fig. 6 by the open triangles, joined by a violet solid curve.Finally, we also computed the differential phase Q factor, which is obtained as discussed in reference [20] from mean values and standard deviations of the phases of the optical pulses (see filled black circles joined by a black solid curve in Fig. 6).By comparing all curves in Fig. 6, it is clear that the direct BER calculation based on moment generating functions and the saddle point approximation compares much better with the measured BER (both in terms of the absolute BER values for all OSNRs, as well as in terms of the selection of the optimum output OSNR ~ 11.8 dB value) than the BER estimation based on the different Q factors.Indeed, the BER estimation based on the amplitude Q factor results in a minimum BER (or maximum Q value) for the output OSNR value of 12.5 dB, i.e., the Q factor estimation differs by 0.7 dB from the experimentally determined value.On the other hand, Fig. 6 shows that the differential phase Q factor leads to a significant under-estimation (by about 2 dB) of the optimal receiver OSNR.Note that in our numerical simulations we neglected, besides receiver electrical noise, the presence of both PMD and gain equalizers.We believe that neglecting these impairments explains the observed difference between numerical best fit (empty squares) and the experimental (empty circles) BER curves as shown in Fig. 6.Nevertheless, the results of Fig. 6 are important in that they show the excellent agreement between the experimental and numerical best-fit optimal OSNR value.Moreover, Fig. 6 also shows that a relatively good agreement exists between the predicted and the actual observed BER values when the semianalytical direct BER estimation is carried out at the receiver.As a final remark, the phasor plots which are shown in the insets of Fig. 6 reveal that, in the case of the CSRZ-DPSK modulation format, nonlinear phase noise is the main source of penalty for input powers above -1 dBm/ch, that is for OSNR values (1 nm calculated after 4000 km) larger than 13.5 dB.

Experimental results and discussion
The experimental optimization of the transmission performance involved the determination of the best pre-compensation, span input power per channel and post-compensation for the two modulation formats under study.As suggested by the numerical simulations, the optimal percentage of total span gain from either forward or backward Raman gains was fixed in the experiments to 20%-80%, and it was kept unchanged when using either the CSRZ-ASK or the CSRZ-DPSK format.Figures 7 and 8 summarise the results of our experimental optimizations.In Fig. 7(a) we show the measured BER for the central channel at 1550 nm, versus precompensation.The measurements were taken at 2000 km for the CSRZ-ASK format and at 4000 km for the CSRZ-DPSK format.In Fig. 7(b) we display the central channel BER versus its residual chromatic dispersion for the two modulation formats, when measured at the same transmission distances as in Fig. 7(a).Note that in Fig. 7 we used a spline fit to join the experimental points as a guide to the eye.From the observations of Fig. 7(a), one may notice that the same optimal precompensation of -350 ps/nm holds for both the CSRZ-ASK and CSRZ-DPSK modulation formats.Note that in the measurements of Fig. 7(a) and (b) the span input power per channel was kept fixed to -5 dBm for the CSRZ-ASK format and to -3 dBm for the CSRZ-DPSK format.The results of Fig. 7(a) also show that the observed optimal negative values of precompensation are in good agreement with the simulation predictions of Fig. 4. On the other hand, Fig. 7(b) shows that it is necessary to accurately adjust the post-compensation in order to improve the transmission performance for the central channel by means of a proper control of the residual chromatic dispersion (with the pre-compensation fixed to -350 ps/nm).We achieved this optimal post-compensation by means of our TDCM.Figure 7(b) shows that the optimal residual dispersion for the central channel remains close to 0 ps/nm: in particular, the residual dispersion is slightly positive (+25 ps/nm) for the CSRZ-DPSK format, and it is slightly negative (-15 ps/nm) for the CSRZ-ASK format.In the following, we kept fixed the pre-compensation at its optimal value of -350 ps/nm for both modulation formats.
Figures 8(a) and (b) show the output BER as a function of the span input power per channel for the CSRZ-ASK and the CSRZ-DPSK formats.The BER was measured at various transmission distances (as indicated on the plots of Fig. 8(a) and (b)).As it can be seen in Fig. (8), at 4000 km with the CSRZ-DPSK format the optimal span input power is about 2 dB larger than at 2000 km with the CSRZ-ASK format (i.e., -3 dBm against -5 dBm); whereas the BER is nearly the same (~10 -7 ) in the two cases.We may also observe from Fig. 8(a) that the optimal span input signal power with the CSRZ-ASK format significantly changes with the transmission distance.Indeed, the optimal input power with the CSRZ-ASK decreases by about 1 dB per additional signal circulation through the loop.On the other hand, Fig. 8(b) shows that, when using the CSRZ-DPSK format, the transmission distance dependence of the optimal span input power per channel is significantly reduced.These measurements confirm that the CSRZ-ASK modulation format is largely more sensitive to the accumulation of nonlinear impairments than CSRZ-DPSK [20][21][22].Indeed, it is well known that the main sources of nonlinear degradation for pulse-overlapped 40 Gb/s optical transmissions are intra-channel cross-phase modulation (IXPM) and intra-channel four-wave mixing (IFWM).In ASK transmission, IXPM and IFWM lead to pulse timing and amplitude jitters for the marks, and to "ghost" pulse generation in the spaces [22].It is also established that a symmetric dispersion map (as the one which is implemented in the present experiments) significantly improves the performance of ASK-based transmissions [23], by limiting the impact of both IXPM and IFWM.Nonetheless, when using the DPSK format over the same symmetric dispersion map, one obtains a net reduction of the overall intra-channel nonlinear impairments as compared with the ASK format.First of all, it is clear that for a given level of the signal average power the pulse peak power with the DPSK format is twice lower than with the ASK format.Moreover, the Gordon-Mollenauer effect [24] which is responsible for a detrimental nonlinear phase noise with the DPSK format, may be highly reduced in a pulse-overlapped 40 Gb/s transmission owing to the strong impact of dispersive effects (as it is the case in the present transmission line owing to the high local dispersion of the SLA and IDF fibers).Finally, note that IFWM has only limited influence on DPSK transmissions: indeed the IFWM-induced nonlinear phase noise leads to a correlation between the nonlinear phase shifts that are experienced by any two adjacent bits [20][21].Clearly this does not affect the information which is contained, for the DPSK format, in the relative phase difference between bits [20][21].Figure 9(a) shows the measured dependence of the output OSNR (measured for the central channel in 1 nm) and BER versus the transmission distance for both the CSRZ-ASK and the CSRZ-DPSK formats.In these measurements, for each transmission distance we adjusted the span input power and the post-compensation to their optimal values.On the other hand, in Fig. 9(a) the pre-compensation was not changed with respect to the value that was previously obtained by optimising the transmission performance as in Fig. 7(a) (at 2000 km for the CSRZ-ASK and at 4000 km for the CSRZ-DPSK format).As it can be seen in Fig. 9 given level of the output BER, the DPSK format enables a dramatic increase of the transmission distance with respect to the ASK format.Namely, for a BER=10 -10 the transmission distance grows from 800 km (with the ASK) up to 2400 km (with the DPSK).For a BER=10 -9 one obtains 1200 km with the ASK format and 3200 km with the DPSK format.For a BER=10 -8 , Fig. 9(a) shows that one obtains 1600 km with the ASK and 3600 km with the DPSK.Finally, for a BER=10 -7 , we obtain a transmission distance of 2000 km with the ASK and of 4000 km with the DPSK format, respectively; that is, in this case the CSRZ-DPSK modulation format permits to double the transmission distance when compared with CSRZ-ASK.Figure 9(a) also shows that the output OSNR is equal to 13.8 dB at 2000 km (for the ASK format) and to 11.3 dB at 4000 km for the DPSK format, respectively.Although the output OSNR is 2.5 dB lower with the CSRZ-DPSK format at 4000 km when compared with the case of the ASK format at 2000 km, nevertheless one obtains the same BER performance (10 -7 ) in the two cases.The superior behaviour of the DPSK format can be mostly ascribed to its well-known 2.5-3 dB improvement in receiver sensitivity with respect to the ASK format (such improvement was clearly observed on the back-to-back sensitivity curves as shown in Fig. 9(b)).Additionally, as discussed above the resilience of the DPSK format to nonlinear impairments is higher than that of the ASK format [20][21].Let us point out that the results of the experimental optimization fit well the numerical results that we described in section 3: for both the ASK and the DPSK modulation formats, numerical predictions agree well with experimental optimal span input power per channel values.At last, note that the BER level (=10 -7 ) which is obtained at 2000 km and 4000 km (for the CSRZ-ASK and the CSRZ-DPSK formats, respectively) is well below the threshold for error-free operation of forward error correction codes (which is in the BER range of [1.10 -3 -4.10 -3 ], depending of the equipment supplier which is considered), proving that on UltraWave TM fiber both CSRZ-ASK and CSRZ-DPSK modulation formats respond to the requirement of carriers' core transport network for ULH transmissions reaching more than 2000 km.
In Fig. 9(b) we show the results of the comparison of the dependence of the output BER upon the received OSNR for both the ASK and the DPSK formats.The OSNR was measured in 1 nm for the central channel at 1550 nm, both in back-to-back and after transmission (over 4000 km for the CSRZ-DPSK and 2000 km for the CSRZ-ASK format, respectively).Clearly, the received OSNR is a monotonic increasing function of the span input power.Therefore, qualitatively similar plots to those in Fig. 9(b) result when one displays the output BER versus the span input power per channel.However, the advantage of showing the dependence of the ouput BER versus the received OSNR is that one may directly read from the plot of Fig. 9(b) the OSNR transmission penalty, by simply comparing the back-to-back OSNR value with that obtained after the transmission (for the same level of BER).The BER versus OSNR curves in Fig. 9(b) that are obtained after transmission clearly show that at low OSNRs (or, equivalently, low span input powers) the accumulated amplified spontaneous emission (ASE) noise sets the limit to the transmission performance.Whereas the same curves in Fig. 9(b) also show that at high OSNRs the transmission quality is mostly deteriorated by nonlinear impairments.Clearly, the optimal working point (and minimum BER level) is obtained when ASE and nonlinearities contribute to transmission penalties in equal manner.By comparing in Fig. 9(b) the back-toback BER curves with those obtained after transmission, one obtains that, at the above discussed optimal working point (i.e., OSNR value that yields minimum BER, which in the case of Fig. 9(b) is equal to 10 -7 for both modulation formats), the OSNR penalty is equal to 1 dB at 4000 km for the CSRZ-DPSK format, and to 2 dB at 2000 km for the CSRZ-ASK format.Namely, with the DPSK format we observed 1dB of transmission impairment reduction with respect to the ASK case, in spite of the doubled transmission distance.It is interesting to note that the well-known ~2.5 dB OSNR sensitivity difference between the CSRZ-ASK and the CSRZ-DPSK modulation formats that is obtained in back-to-back (at the BER level of 10 -7 ) is maintained nearly unchanged after signal transmission over either 2000 km or 4000 km, respectively.Note finally that we measured the BER of all the sixteen channels in both transmission configurations (i.e., CSRZ-ASK over 2000 km and CSRZ-DPSK over 4000 km).The resulting observed BER for all these channels was varying within 1 decade around the BER value that we obtained for the central channel.

Conclusion
We carried out a detailed experimental optimization and comparison of the performance of ULH WDM 40 Gb/s transmissions using either the CSRZ-ASK or the CSRZ-DPSK modulation format.We revealed that, for properly optimized systems, the error-free transmission distance with the CSRZ-DPSK format basically doubles the system reach with respect to the ASK format.Moreover, in our optimal configuration the well-known 2.5-dB receiver sensitivity advantage of DPSK which is observed in back-to-back is maintained unchanged after transmission.The observed results were closely reproduced by numerical fits of the experiments.In particular, we experimentally verified that in our system the semi-stochastic BER estimator using moment generating functions and the saddle point approximation [26] is better suited to predict both the BER level and the optimal working point when using the CSRZ-DPSK modulation format.Our study of the critical assessment and comparison of the performance of ULH WDM 40 Gb/s systems based on the UltraWave TM fiber represents a sort of reference case, to be extended in future work to links based on the G.652 standard single mode fiber (which is today's most deployed fiber worldwide) or on G.655 non-zero dispersion-shifted fibers.

Fig 1 .
Fig 1.Schematic of the experimental set-up.

Fig 3 .
Fig 3. Left: Dispersion map on the first two loop round-trips for the channel at 1550 nm.Right: Theoretical nonlinear phase shift versus the ratio of backward to total Raman gain.

Fig 4 .
Fig 4. Left: numerical estimation of the output Q factor [dB] as a function of the precompensation and of the residual loop dispersion for a transmission over 2000 km using the CSRZ-ASK format.Right: case of the CSRZ-DPSK format for a transmission over 4000 km.The input power per channel is equal to -3 dBm.

Fig 6 .
Fig 6.Comparisons of BER predictions (versus received OSNR in 1 nm after a 4000 km UltraWave TM link) and experiments for the CSRZ-DPSK format.: Numerical BER from the Q factor; : BER from experiments;: BER from semi-analytical approach; BER from differential phase Q. Insets: phasor diagrams (optical field) for input channel powers of either -6 dBm (left plot) or 0 dBm (right plot).

Fig 7 .
Fig 7. (a) BER versus pre-compensation at 2000 km for CSRZ-ASK and at 4000 km for CSRZ-DPSK for the central channel at 1550 nm, (b) BER versus residual chromatic dispersion of the central channel at 1550 nm at 2000 km for CSRZ-ASK and at 4000 km for CSRZ-DPSK.

Fig 8 .
Fig 8. (a) BER versus span input power of the central channel at 1550 nm at different transmission distances for CSRZ-ASK, (b) BER versus span input power of the central channel at 1550 nm at different transmission distances for CSRZ-DPSK.

Fig 9 .
Fig 9. (a) BER and OSNR of the central channel at 1550 nm versus transmission distance for CSRZ-ASK and CSRZ-DPSK, (b) BER versus OSNR of the central channel at 1550 nm after 2000 km for CSRZ-ASK (filled purple lozenges) and after 4000 km for CSRZ-DPSK (empty red triangles) and in back-to-back for the both modulation formats (filled purple circles for CSRZ-ASK and empty red circles for CSRZ-DPSK).