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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2992–3004
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Semi-empirical system scaling rules for DWDM system design

Brian DeMuth, Michael Y. Frankel, and Vladimir Pelekhaty  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 2992-3004 (2012)
http://dx.doi.org/10.1364/OE.20.002992


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Abstract

Recently, several theoretical papers have derived relationships for fiber-optic transmission system performance in terms of associated physical layer parameters. At the same time, a large number of detailed experiments have been and continue being performed that demonstrate increasing capacities and unregenerated reach. We use this wealth of experimental data to validate the aforementioned relationships, and to propose a set of simple scaling rules for performance. We find that, despite substantial differences in experimental configurations, overall performance in terms of spectral efficiency and unregenerated reach is well explained by scaling rules. These scaling rules will be useful to carriers seeking to understand what they should expect to see in terms of network performance using deployed or easily accessible technology, which may be radically different from hero experiment results. These rules will also be useful to design engineers seeking cost effective tradeoffs to achieving higher performance using realistic upgrade strategies, and what might be encountered as a fundamental limit.

© 2012 OSA

1. Introduction

A survey of recent optical communications publications reveals a wealth of experiments, demonstrating extreme achievements in fiber optic data transmission. Commonly referred to as hero experiments, they set records for transmission distance, total capacities, and/or spectral efficiencies. Some of the achievements reported in recent literature are listed in Table (1)

Table 1. Sample of optical transmission reach results from recent literature

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.

It can be seen that performance varies considerably. As expected, reach varies based on the choice of modulation format and spectral efficiency [1

1. R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]

,2

2. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010). [CrossRef]

], and there is significant variation even among experiments whose modulation formats and spectral efficiencies are the same, as for example [3

3. M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.7.C.3.

,4

4. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett. 22(6), 371–373 (2010). [CrossRef]

] or [5

5. M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett. 22(15), 1150–1152 (2010). [CrossRef]

,6

6. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally Efficient Long-Haul Optical Networking Using 112-Gb/s Polarization-Multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010). [CrossRef]

]. Fiber types, span loss, amplification types, among other factors, are often different. In this work we apply the analytical results of [7

7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010). [CrossRef] [PubMed]

,8

8. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO7.

] to achieve the following. We use newly developed theoretical performance understanding to extract new and useful information from the wealth of experimental data. We allow engineers designing carrier networks a view of performance that can be expected in deployed implementations, which may not be able to leverage the advanced technologies deployed in experiments. Finally, we provide an indication of the most effective ways of improving performance.

We rely on supporting physical layer descriptions accompanying reported measured performance for information necessary to carry out the analysis of [7

7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010). [CrossRef] [PubMed]

,8

8. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO7.

]. We use transceiver characteristics such as modulation format and bit rate, Bit Error Rate (BER) or Q-factor vs. Optical Signal to Noise Ratio (OSNR), BER or Q and OSNR after fiber transmission, and details of optical, electrical, and/or digital signal processing. We also use line system characteristics such as span loss As (dB), span length Ls (km), number of spans Ns, type of amplification (i.e. EDFA, hybrid EDFA Ramam, Raman only), and amplifier noise figure Nf (dB). The following fiber characteristics also enter into analysis: attenuation α (dB/km), non-linearity coefficient γ (1/(W·km)), effective area of the optical mode Aeff (μm2), and chromatic dispersion D (ps/(nm·km)).

This information, when combined with analytic performance equations, provides a method for a fair comparison between experiments by normalizing results to a given baseline. Using these scaling rules, we transform the results of several diverse experiments into an expectation of how the approaches would work under a more conventional, commercially viable implementation. The fact that all experimental results to collapse to a single point (within experimental error) serves to confirm our analytic scaling equations.

1.1 Impact of the number of channels on unregenerated reach

The channel count varied considerably across the experiments we examine, from as low as 8, to as high as 198. Xia, et al [9

9. C. Xia and D. van den Borne, “Impact of the Channel Count on the Nonlinear Tolerance in Coherently-detected POLMUX-QPSK modulation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO1.

], have shown a relatively weak relationship between performance and the number of channels. Under conditions of optimal channel power, the difference in OSNR penalty is ~0.5 dB. This is generally below the experimental resolution and we neglect channel number differences. We do restrict our analysis to studies that have multiple channels.

1.2 A nominal network for normalization

What we refer to as a nominal network configuration represents a WDM fiber optic transmission system consistent with technology that is readily accessible for deployment by multiple worldwide vendors. This network has the following characteristics:

  • C-band EDFA only span amplification, with a Noise Figure of 5 dB
  • Span lengths of 80 km, with a loss per span of 20 dB to account for margin and aging
  • Fiber is standard single mode fiber (SSMF), γ = 1.31 1/(W·km), Aeff = 86 μm2, D = 16.7 ps/(nm·km), α = 0.22 dB/km
  • No inline optical dispersion compensation
  • FEC with a net effective coding gain (NECG) of 9.6 dB at 10−15 BER, allowing us to operate at a pre-corrected bit error rate of 4.3 10−3, or a Q2 of 8.4 dBQ.
  • A receiver operating at a back-to-back OSNR of 3 dB from ideal performance for PDM- QPSK, 5 dB from ideal for PDM-16QAM, and PDM-64QAM

2. Simple scaling rules

In order to scale network unregenerated reach, we transform performance results from an experimental network to those of a normalized equivalent, based on differences in the number of spans, span loss, noise figure, and fiber non-linearity coefficient between the two networks. An expression relating two networks, based on these characteristics can be written and evaluated, as discussed in the following.

An expression for electrical signal to noise ratio (SNR) [8

8. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO7.

,10

10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011). [CrossRef]

] is given below in Eq. (1)
SNR=PchPASE+PNL
(1)
where Pch is the per channel power into a fiber span, PASE is the amplified spontaneous emission (ASE) noise power, and PNL is noise power due to nonlinear effects. Assuming that we measure powers in both optical polarizations, that ASE accumulates linearly, and that all fiber spans are generally identical (as is the case for most lab experiments), we write Eq. (2),
PASE=NsAsNfhfBn
(2)
where Ns is the number of spans, As is the span loss, Nf is the optical noise figure of the span amplifier, h is Planck’s constant, f is the channel optical frequency, and Bn is the equivalent channel bandwidth over which noise is measured (all in linear units). We now consider PNL, nonlinear noise power, and make use of the analysis in [7

7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010). [CrossRef] [PubMed]

,10

10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011). [CrossRef]

].

One aspect assumed in above referenced work is that channel spacing Δf is equal to the channel symbol rate. However, we are interested in a different aspect: the impact of channel spacing while keeping the symbol rate constant, which is more aligned with published experimental results. While most papers have considered ITU-based 50 GHz spacing of channels, several have pursued improved spectral efficiency through tighter channel spacing. Channel spacing can be reduced to the symbol rate without deleterious linear crosstalk effects, using either Nyquist WDM or OFDM type signal filtering. This moves overall system performance closer to the Shannon limit boundary, and should not be confused with moving along the Shannon boundary via increased constellation density.

Recent studies [14

14. V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance Evaluation of Long-Haul 111Gb/s PM-QPSK Transmission Over Different Fiber Types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010). [CrossRef]

] have suggested differences in fiber local dispersion can have significant effects on system performance, and we indeed see from Eq. (3) that the noise power is inversely proportional to D. Using Eq. (3), we express the nonlinear noise power in Eq. (1) as
PNL=κNLNsγ2LeffSE|D|(PchBn)3
(4)
where κNL is a nonlinear noise power proportionality constant, which depends only on modulation format. PNL’s dependence on baud rate is implicit in channel noise bandwidth, Bn. Substituting Eq. (2) and Eq. (4) into Eq. (1), one obtains for the SNR:

SNR=(PchBn)Ns(AsNfhf+κNLγ2LeffSE|D|(PchBn)3)
(5)

The experimental data are taken at the lowest bit error rate (BER) and optimal channel launch power levels. Similarly, our target normalized configuration operates under lowest BER conditions (i.e. highest SNR considering a balance of both PASE and PNL). The optimal launch power density is then [8

8. G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO7.

]:

Pch,optBn=[AsNfhfD2κNLγ2LeffSE]1/3
(6)

Substituting Eq. (6) into Eq. (5), we obtain

SNRopt=1Ns(AsNfhf)2/3(|D|2κNLγ2LeffSE)1/3
(7)

Similarly, we can include the effects of any difference in performance between the experimental transceiver, and that which is considered nominal. Transceiver performance is usually quantified experimentally via a back-to-back (B2B) measurement in which the BER is characterized vs. optical SNR (OSNR) in the absence of fiber spans, and then compared against ideal performance. The multiplicative factor derived above can thus be further scaled by taking the ratio of two back-to-back OSNR measurements made at the same BER: the experimental transceiver’s OSNR penalty relative to ideal performance (B2BE) and the nominal transceiver’s penalty relative to ideal performance (B2BN).

We use Eq. (7) and equate SNRE and SNRN, incorporating the adjustment factors defined above. We further note that κNL is assumed to be dependent on modulation format only, with other system factors being explicitly accounted for. Evaluating the difference in the number of spans between a nominal and experimental configuration, and casting the quantities into dB units, we obtain a single scaling rule with terms accounting for differences in BER, back-to-back transceiver performance, span loss, noise figure, dispersion, nonlinear coefficient, effective length, and spectral efficiency.

Ns,NNs,E=(SNRESNRN)(ΔB2BNΔB2BE)23(As,NAs,E)23(Nf,NNf,E)+13(DNDE)23(γNγE)13(Leff,NLeff,E)13(SENSEE)
(8)

The scaling rule term for dispersion D can be seen in evidence in the results of [7

7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010). [CrossRef] [PubMed]

,10

10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011). [CrossRef]

,14

14. V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance Evaluation of Long-Haul 111Gb/s PM-QPSK Transmission Over Different Fiber Types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010). [CrossRef]

]. Equation (8) implies that using low-dispersion fibers substantially penalizes span count relative to non dispersion shifted fiber (NDSF), but obtaining a substantial increase in span count above NDSF is difficult as one must increase dispersion significantly.

Recent numerical studies also confirm the gradual linear relationship between the number of spans and the spectral efficiency (i.e. inverse channel spacing) in cases with fixed symbol rate and modulation format [15

15. A. Carena, V. Curri, P. Poggiolini, G. Bosco, and F. Forghieri, “Maximum Reach Versus Transmission Capacity for Terabit Superchannels Based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM,” IEEE Photon. Technol. Lett. 22(11), 829–831 (2010). [CrossRef]

]. Channel spacing reduction only applies down to the limit imposed by linear cross-talk, which is given by baud rate, assuming Nyquist-type filtering. Referring to Eq. (8), we observe a very advantageous relationship between reducing Δf to improve spectral efficiency, and a reduction in span count, Ns (i.e. a 3 dB spectral efficiency improvement only results in a 1 dB reduction in reach). Span count reduction may be even smaller in practice due to single-channel SPM effect contributions.

Current transmission systems are constrained by the ITU specified channel spacing, data rates specified by ITU-T G.709 (Optical Transport Network, or OTN), and a need to tolerate reconfigurable optical add/drop multiplexor (ROADM) filtering. These produce a significant amount of wasted spectrum, as for example 44% of the channel is wasted when 28 Gbaud signals are placed on a 50 GHz channel spacing. Capacity-limited systems will benefit from eliminating wasted spectrum between channels via some combination of reduction in channel spacing and/or an increase in channel symbol rate, while requiring a deviation from current standards. At the same time, the utility of ROADMs for arbitrary reconfigurable channel steering is diminished: optical filters cannot separate add/drop/express channels with zero guard-band.

3. Example of normalization based on the described scaling rule

The best way to illustrate the normalization process is via an example. In [3

3. M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.7.C.3.

], Salsi et al, present results of a transmission experiment in which 80 x 100 Gb/s channels are transmitted via PDM-QPSK, using a channel spacing of 50 GHz, over a distance of 7200 km. They used EDFA only amplification, pure silica core fiber (α = 0.161 dB/km, D = 20.5 ps/nm·km, Aeff = 112 μm2), and no optical dispersion compensation. First, we verify that the experiment itself follows the expected trends. Equation (5) shows that increasing system reach, while keeping overall system configuration the same, should produce a corresponding 1:1 linear decrease in SNR. This is clearly observed in Fig. 4 of [3

3. M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.7.C.3.

] over the experimental range of 7200km to 10200km, confirming the basic validity of assumptions for this experiment.

The experimental setup differs from our nominal network primarily in terms of span loss, fiber type used, and BER tolerated. Table (2)

Table 2. Example experimental vs. nominal network parameters

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compares the relevant experimental and nominal metrics.

Taking values from the table, converting any linear units to dB, and applying Eq. (8), we compute the normalized achievable span count, providing an expectation of how this experiment would perform in a more nominal configuration. We find for this experiment,
Ns,NNs,E=6.7dB
(9)
which for Ns,E = 144, gives a normalized reach of 31 spans. The same paper reported additional system measurements at 180 spans, and 204 spans. All three configurations normalize to the same number of spans, i.e. 31. This conforms to the general result that for a given modulation format and spectral efficiency, all experiments will normalize to the same nominal span count, because the limiting factor is nonlinear noise power, which is determined by spectral efficiency, as opposed to bit or symbol rate [15

15. A. Carena, V. Curri, P. Poggiolini, G. Bosco, and F. Forghieri, “Maximum Reach Versus Transmission Capacity for Terabit Superchannels Based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM,” IEEE Photon. Technol. Lett. 22(11), 829–831 (2010). [CrossRef]

,16

16. C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Fibre Nonlinearities in WDM-Systems with Reduced Channel-Spacing and Symbol-Rate,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper P4.20.

].

If the modulation format or spectral efficiency is changed we would expect the results to normalize to a different nominal span count, but experiments sharing that same modulation format and spectral efficiency will cluster to the new normalized span count. Experiments which fall outside their expected cluster merit further attention to determine why not (i.e. there’s a factor, unaccounted for, that might offer novel insight).

4. Results and discussion of additional normalizations

The experimental and normalized reach results of 18 experiments taken from 16 papers reported in recent literature are presented in Figs. 1
Fig. 1 Reported reach results taken from 18 experiments utilizing a diverse range of network characteristics.
and 2
Fig. 2 Normalization results for the 18 experiments in Fig. 1, assuming 20 dB spans of 80 km SSMF, with 5 dB amplifier Nf. Ideal lines correspond to the expected performance achievable using ideal transceiver performance on the same optical line system.
. For each experiment, where information was available, we performed additional verifications.

  • Self-consistency of reported OSNR with launch power and optical amplifier chain characteristics
  • Measured back-back characteristics within expected range from ideal
  • Optimum nonlinear-limited Q deviation from a pure linear limit by ~1.76 dB [17

    17. E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express 19(13), 12781–12788 (2011). [CrossRef] [PubMed]

    ]

The results in Figs. 1 and 2 come from seven experiments employing PDM-QPSK [3

3. M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.7.C.3.

,4

4. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett. 22(6), 371–373 (2010). [CrossRef]

,18

18. J. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s Capacity Transmission Over 6,860 km,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB4.

21

21. G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72x100Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPB6.

], eight employing PDM-16QAM [5

5. M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett. 22(15), 1150–1152 (2010). [CrossRef]

,6

6. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally Efficient Long-Haul Optical Networking Using 112-Gb/s Polarization-Multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010). [CrossRef]

,22

22. C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express 19(14), 12879–12884 (2011). [CrossRef] [PubMed]

26

26. A. Gnauck and P. J. Winzer, “Ultra-High-Spectral-Efficiency Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWE4.

], one employing PDM-36QAM [27

27. J. Yu and X. Zhou, “16 x 107-Gb/s 12.5-GHz-Spaced PDM-36QAM Transmission Over 400 km of Standard Single-Mode Fiber,” IEEE Photon. Technol. Lett. 22(17), 1312–1314 (2010). [CrossRef]

], and two employing PDM-64QAM [28

28. A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizuguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM Transmission over 160 km Using Linewidth-Tolerant Pilotless Digital Coherent Detection,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper pd2_4.

,29

29. J. Yu, X. Zhou, Y. Huang, S. Gupta, M. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ-64QAM optical signal generation and transmission on a 12.5GHz WDM Grid,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OThM1.

]. Figure 1 illustrates number of spans taken directly from the literature to highlight the diversity of the data prior to analysis. Figure 2 illustrates the results after normalization. The normalization results illustrate the use of all terms in Eq. (8), except the spectral efficiency (SE) term. Also shown in Fig. 2 are lines representing span count corresponding to ideal transceiver performance for each basic approach considered (QPSK, 16QAM, 64QAM). Each line shows how we would expect the span count to vary with spectral efficiency, within that approach. They were obtained by normalizing the results of simulations [10

10. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011). [CrossRef]

,30

30. D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011). [CrossRef] [PubMed]

]. PM-QPSK modulation normalized to Ns ≅ 19 dB or 80 spans at an SE~3.7 b/s/Hz (corresponding to the Nyquist limit for a 50 GHz channel). We then use the SE term in Eq. (8) to compute the span count seen at the spectral efficiency at 50% of the Nyquist limit, essentially half filling that channel (90 spans, at 2.0 b/s/Hz). A trend line is drawn between those two points. The ideal span count values for 16QAM and 64QAM are computed in a similar fashion, resulting in a trend line for 16QAM drawn between 18 spans at 3b/s/Hz and 14 spans at 7.4b/s/Hz. A trend line for 64QAM is drawn between 5 spans at 4b/s/Hz and 3 spans at 11.1 b/s/Hz.

Six of seven PDM-QPSK experiments share a close spectral efficiency and cluster tightly into a range of 28-35 spans, with an average of 31 spans. Six of the eight PDM-16QAM experiments share the same SE, all of which cluster to four spans. Both the QPSK and 16QAM clusters have additional data points that share the same modulation format as the cluster, but not the same SE. The one PDM-36QAM experiment normalizes to two spans, and the two PDM-64QAM experiments, although differing in SE, normalize to 1 span.

4.1 Clusters having a common modulation format, and common SE

The cluster within the PDM-QPSK data sharing a common modulation format and SE has reach values that range from 28 spans to 35 spans. That difference represents −0.9 dB variation from the low to high span values. We assign these discrepancies to both experimental errors and data extraction inaccuracy and identify the range of 28-35 spans with a single cluster. The cluster within the PDM-16QAM data sharing a common modulation format and same SE all cluster to four spans, with no variation.

4.2 Data sharing a common modulation format, but having a different SE

Taking a closer look at all data sharing a PDM-QPSK modulation format, there is a result that normalizes to 28 spans, at an SE of 4, well outside the main cluster of 31 spans at a SE of 2. Using Eq. (8), we expect a −1 dB difference in spans between the cluster at SE of 2 and this study at SE of 4. This would imply the 28 span result should lie closer to 25 spans. While the difference between 28 and 25 spans is only ~0.5 dB, and could be attributed to the normalization process itself, it also lies to the right of the region indicated by our ideal line for the QPSK approach, indicating they’ve achieved a SE beyond what we would expect. A closer look at that study [18

18. J. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s Capacity Transmission Over 6,860 km,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB4.

] reveals the authors use offline receiver processing, including a combination of maximum likelihood sequence estimation (MLSE), and Viterbi-Viterbi to mitigate the effects of the inter-symbol interference (ISI) induced by narrowband filtering that has allowed them to achieve the SE of 4. They present results illustrating Q2 both pre and post MLSE processing, showing a 4 dB improvement in ISI tolerance at 6800 km.

Within the data sharing a PDM-16QAM modulation format, the main cluster occurs at 4 spans, with an SE of 4.2. There are two results using that same modulation format with different SE. They occur at 3 spans with 6.2 b/s/Hz [25

25. S. Yamanaka, T. Kobayashi, A. Sano, H. Masuda, E. Yoshida, Y. Miyamoto, T. Nakagawa, M. Nagatani, and H. Noaka, “11 x 171 Gb/s PDM 16-QAM Transmission over 1440 km with a Spectral Effiency of 6.4 b/s/Hz using High-Speed DAC,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.8.C.1.

] and 4 spans with 6.4 b/s/Hz [26

26. A. Gnauck and P. J. Winzer, “Ultra-High-Spectral-Efficiency Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWE4.

]. Using Eq. (8), the difference in SE of 4.2 and 6.2 should imply a −0.6 dB difference in spans, implying the reach at an SE of 6.2-6.4 should be between 3 and 4 spans, which is in agreement with our normalization.

The two studies using PDM-64QAM [28

28. A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizuguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM Transmission over 160 km Using Linewidth-Tolerant Pilotless Digital Coherent Detection,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper pd2_4.

,29

29. J. Yu, X. Zhou, Y. Huang, S. Gupta, M. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ-64QAM optical signal generation and transmission on a 12.5GHz WDM Grid,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OThM1.

] normalize to less than one span, and are rounded up to one span of 80km. They occur at an SE of 9 and 8. Using Eq. (8) the difference between the two results based on SE alone results in a scaling difference of −0.5 dB. This is below the accuracy of our approximate technique, and the two results are indistinguishable.

4.3 Broad relationships across the data

There are three basic data clusters visible in the results (Fig. 2), plus one 36QAM result. A key metric in validating this overall concept is whether or not the position of each cluster, relative to the ideal performance for that approach, is within the transceiver non-ideality used in the normalization for that approach (3 dB for QPSK, 5 dB for all others). This comparison is shown in Table (3)

Table 3. Comparison of idealized reach vs. normalized reach clusters

table-icon
View This Table
| View All Tables
.

The results show general agreement between the locations of the main data clusters and where we think they should lie based on differences in SE, modulation format, and performance.

Returning to the original three questions with respect to the results, for data sharing a common approach to modulation format and SE, we see consistent clustering with no significant or unexplainable variation. Data sharing a common modulation format but differing SE, conform to the predictions of our SE scaling rule within the expected accuracy of our normalization process. The overall position of the clusters themselves is consistent with theory with respect to modulation format performance and our SE scaling rule.

4.4 Possible sources of inaccuracy

While most reports of experiments used in this investigation provided enough detail to attempt normalization, the level of detail varied considerably and required varying levels of approximation. Care was taken to ensure estimations and approximations were applied consistently across experiments. For the purposes of normalization, the most useful experimental information to unambiguously include is BER or Q, average OSNR, both back-to-back and post transmission, average launch power, span loss, noise figure, α, γ, D, channel spacing, transmission rate, number of channels, and channel frequencies, along with any other known deviations from ideal performance. The developed scaling rules do not explicitly take into account BER flooring effects, and all experiments considered were well above possible BER floor for the relevant modulation format.

5. What are the limits to performance?

The results in Fig. 2 show that while there are a multitude of experimental conditions that can be varied and tested to achieve different reach results, when the conditions are normalized to that of our nominal network, they separate into clusters of roughly equivalent reach differentiated only by the approach taken to modulation format and spectral efficiency. Thus, for practical situations, using PM-QPSK with a spectral efficiency of ~2 b/s/Hz, one can expect an unregenerated reach of about 31 spans, or ~2500 km, at a capacity of about 8 Tb/s (assuming a nominal 80 channel configuration).

A corollary of the above statement is that performance of disparate system configurations and hero experiments can be predicted from a baseline configuration. The established and validated parameter dependencies are combined into a scaling equation that can be used by system designers and network architects to estimate expected WDM system performance. These apply only in the range where SE is small enough to avoid inter-channel linear interference, i.e. channel spacing is larger than baud rate, assuming Nyquist-type filtering.

For PDM-QPSK systems:

Ns,N=10log(62)+(NECG9.6)ΔB2BM23(As,N20)23(Nf,N5)+13(10log(DN16.7))2310log(γN1.31)1310log(Leff,N19.7)1310log(SE2)
(10)

For PDM-16QAM systems:

Ns,N=10log(13)+(NECG9.6)ΔB2BM23(As,N20)23(Nf,N5)+13(10log(DN16.7))2310log(γN1.31)1310log(Leff,N19.7)1310log(SE4)
(11)

For PDM-64QAM systems:
Ns,N=10log(3)+(NECG9.6)ΔB2BM23(As,N20)23(Nf,N5)+13(10log(DN16.7))2310log(γN1.31)1310log(Leff,N19.7)1310log(SE6)
(12)
where NECG is net effective coding gain of the applied FEC code, ΔB2B (dB) is transponder deviation from ideal QAM performance at relevant BER, and M (dB) is the allocation for field deployed margin (i.e. transponder aging, thermal effects, control loop errors, optical transients, etc…)

Equations (10), (11), and (12) also allow us to examine the limits of the nominal network, and what improvements can be made to (or within) the network itself. Below are several considerations.

5.1 Impact of forward error correction overhead

Forward error correction (FEC) requires some overhead in addition to the data payload. Prior work has explored possible optimal values for FEC overhead both experimentally [31

31. J.-X. Cai, M. Nissov, A. N. Pilipetskii, A. J. Lucero, C. R. Davidson, D. Foursa, H. Kidorf, M. A. Mills, R. Menges, P. C. Corbett, D. Sutton, and N. S. Bergano, “2.4 Tb/s (120 x 20 Gb/s) Transmission over Transoceanic Distance using Optimum FEC Overhead and 48% Spectral Efficiency,” in Optical Fiber Communication Conference, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper PD20.

] and numerically [32

32. A. Agata, K. Tanaka, and N. Edagawa, “Study on the Optimum Reed-Solomon-Based FEC Codes for 40-Gb/s-Based Ultralong-Distance WDM transmission,” J. Lightwave Technol. 20(12), 2189–2195 (2002). [CrossRef]

] for amplitude modulated signals, and found 10% overhead to be a good target. We may ask whether an optimal overhead may exist for achieving the highest data payload spectral efficiency in the context of QAM-based formats with coherent receivers and soft-decision processing.

Others [23

23. A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Packham, “10 x 224-Gb/s WDM Transmission of 28-Gbaud PDM 16-QAM on a 50-GHz Grid over 1,200 km of Fiber,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB8.

,26

26. A. Gnauck and P. J. Winzer, “Ultra-High-Spectral-Efficiency Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWE4.

] have already shown that raw performance is largely independent of the channel total raw symbol rate, assuming channel spacing is scaled proportionately. Thus, we may expect that for cases where channel spacing is determined by the ITU grid, it is beneficial to increase the overhead to fill in the available spectrum. For example, overhead in excess of 40% may be beneficial assuming 100 Gbps PM-QPSK channels on 50 GHz grid [33

33. M. O’Sullivan, “Expanding network application with coherent detection,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper NWC3.

,34

34. S. R. Desbruslais and S. J. Savory, “Relationship Between Electrical Bandwidth and FEC Overhead in a 100 GbE Digital Coherent Receiver,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper P3.19.

].

We assume an idealized Soft-Decision Net Effective Coding Gain dependence on overhead, and account for theoretical penalties expected for increased QAM constellation sizes at symbol rate channel spacing. Figure 3
Fig. 3 Relative distance to Shannon limit, vs spectral efficiency. Optimal reach vs. SE trade-off appears around 15% overhead.
shows that for a given reach, an optimal overhead is close to 15% across all the constellation sizes. Of course, within a given constellation defined by an oval, higher overhead produces better reach, but with a decreased spectral efficiency. Further, reducing overhead to 10% or even 7% may be beneficial for denser constellations as relative penalties decrease.

5.2 Use of high power Raman span amplification

High power Raman amplification was used alone, or in combination with EDFA’s, in 8 of the 18 experiments. The most typical configuration used backward Raman amplification with an on/off gain of 10-12 dB, in hybrid configuration with EDFA amplifiers. In this configuration, noise figures were improved by ~5 dB [36

36. J. Bromage, “Raman Amplification for Fiber Communications Systems,” J. Lightwave Technol. 22(1), 79–93 (2004). [CrossRef]

]. Based on the scaling rules from Eq. (8), that results in a ~3.3 dB improvement in span count. If our nominal configuration was changed to allow Raman amplification of this type it would more than double the span count performance (QPSK: 31 spans to 66 spans; 16QAM: 4 spans to 8 spans; 64QAM: 1 to 2 spans). The use of Raman amplification reduces line system noise figure, and degrades nonlinear accumulation, but the scaling conclusions hold. Optimal system performance is still achieved at the same relative balance of PASE and PNL. This is confirmed by our normalization results.

5.3 Impact of modulation format optimization

There have been several attempts to optimize system performance by manipulating transmitted signals. Some have looked at optimizing modulation constellations in both linear and nonlinear regimes [37

37. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical Links?” Opt. Express 17(13), 10814–10819 (2009). [CrossRef] [PubMed]

,38

38. H. Bülow and E. S. Masalkina, “Coded Modulation in Optical Communications,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America,2011), paper OThO1.

]. These have demonstrated sensitivity gains of ~1.8 dB for low density constellations relative to PM- QPSK, but at the expense of 1/3 reduction in achievable spectral efficiency. Higher density constellation optimizations have produced only marginal improvements compared to square-QAM constellations, even under conditions of high Self-Phase Modulation [39

39. L. Beygi, E. Agrell, and M. Karlsson, “Optimization of 16-point Ring Constellations in the Presence of Nonlinear Phase Noise,” in Optical Fiber communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO4.

].

Improved reach performance has been demonstrated using RZ pulse shaping [40

40. E. Torrengo, S. Makovejs, D. Millar, I. Fatadin, R. Killey, S. Savory, and P. Bayvel, “Influence of Pulse Shape in 112-Gb/s WDM PDM-QPSK Transmission,” IEEE Photon. Technol. Lett. 22(23), 1714–1716 (2010). [CrossRef]

], polarization modulation [41

41. I. Lyubomirsky, A. Nilsson, M. Mitchell, and D. Welch, “Signal Chirp Design for Supression of Nonlinear Polarization Scattering in DP-QPSK Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThF3.

], and optimized pulse shaping [42

42. B. Châtelain, C. Laperle, K. Roberts, X. Xu, M. Chagnon, A. Borowiec, F. Gagnon, J. Cartedge, and D. V. Plant, “Optimized Pulse Shaping for Intra-channel Nonlinearities Mitigation in a 10 Gbaud Dual-Polarization 16-QAM System,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO5.

], but all approaches show substantial spectral broadening and cannot scale down to symbol rate spacing. Such approaches are only worthwhile where absolute spectral efficiency is not relevant, and unused spectral regions can be filled with broadened signal content.

6. Conclusions

In this paper we analyzed 18 high capacity fiber optic transmission experiments taken from recent literature (i.e, hero experiments), and normalized their performance to a common baseline based on a small set of scaling rules.

We observe that experiments normalize to tight clusters sharing the same reach, based on shared approach to modulation format and spectral efficiency. The relationship between data having the same modulation format but differing SE, and between clusters differing in approach also conforms to expectations predicted by our scaling rules. This implies the novel result that despite wide differences in reported results and varying implementation details, these experiments all represent essentially the same performance if one were to restrict the experiments to parameters representative of commercially deployable systems. A further implication is that if a proposed hero experiment only alters experimental parameters consistent with those addressed by our scaling rules, the end results can be accurately inferred by simply applying the normalization process in reverse, and without the expense of experimental implementation.

Finally, we discussed what constitutes reasonably attainable performance in terms of reach and capacity, and some of the more promising ways in which that can be enhanced. Taking our nominal network as the baseline for expectations, one can reasonably expect to transmit 8Tb/s over 31 spans (~2500km). Some of the more promising possibilities for improvement include the incorporation of Raman amplification, soft decision FEC with higher NECG, and taking a considered look at possible tradeoffs between tighter channel spacing and reach. Also on the topic of FEC, we discussed tradeoffs between overhead and SE, and determined an optimum overhead to SE tradeoff at about 15%.

Acknowledgments

The authors wish to thank Joseph Berthold, Vladimir Grigoryan, and Maurice O’Sullivan for their comments and insight.

References and links

1.

R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]

2.

A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol. 28(4), 423–433 (2010). [CrossRef]

3.

M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.7.C.3.

4.

G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett. 22(6), 371–373 (2010). [CrossRef]

5.

M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett. 22(15), 1150–1152 (2010). [CrossRef]

6.

P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally Efficient Long-Haul Optical Networking Using 112-Gb/s Polarization-Multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010). [CrossRef]

7.

X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express 18(18), 19039–19054 (2010). [CrossRef] [PubMed]

8.

G. Bosco, A. Carena, R. Cigliutti, V. Curri, P. Poggiolini, and F. Forghieri, “Performance prediction for WDM PM-QPSK transmission over uncompensated links,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO7.

9.

C. Xia and D. van den Borne, “Impact of the Channel Count on the Nonlinear Tolerance in Coherently-detected POLMUX-QPSK modulation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO1.

10.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical Modeling of Nonlinear Propagation in Uncompensated Optical Transmission Links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011). [CrossRef]

11.

A. Bononi, N. Rossi, and P. Serena, “Transmission Limitations due to Fiber Nonlinearity,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO7.

12.

Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple Fiber Model for Determination of XPM Effects,” J. Lightwave Technol. 29(7), 974–986 (2011). [CrossRef]

13.

L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of coherent optical communications systems,” Opt. Express 19(9), 8079–8084 (2011). [CrossRef] [PubMed]

14.

V. Curri, P. Poggiolini, G. Bosco, A. Carena, and F. Forghieri, “Performance Evaluation of Long-Haul 111Gb/s PM-QPSK Transmission Over Different Fiber Types,” IEEE Photon. Technol. Lett. 22(19), 1446–1448 (2010). [CrossRef]

15.

A. Carena, V. Curri, P. Poggiolini, G. Bosco, and F. Forghieri, “Maximum Reach Versus Transmission Capacity for Terabit Superchannels Based on 27.75-GBaud PM-QPSK, PM-8QAM, or PM-16QAM,” IEEE Photon. Technol. Lett. 22(11), 829–831 (2010). [CrossRef]

16.

C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Fibre Nonlinearities in WDM-Systems with Reduced Channel-Spacing and Symbol-Rate,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper P4.20.

17.

E. Grellier and A. Bononi, “Quality parameter for coherent transmissions with Gaussian-distributed nonlinear noise,” Opt. Express 19(13), 12781–12788 (2011). [CrossRef] [PubMed]

18.

J. Cai, Y. Cai, C. R. Davidson, A. Lucero, H. Zhang, D. G. Foursa, O. V. Sinkin, W. W. Patterson, A. Pilipetskii, G. Mohs, and N. Bergano, “20 Tbit/s Capacity Transmission Over 6,860 km,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB4.

19.

J. Yu, X. Zhou, D. Qian, M. Huang, P. N. Ji, and G. Zhang, “20x112Gbit/s, 50GHz spaced, PolMux-RZ-QPSK straight-line transmission over 1540km of SSMF employing digital coherent detection and pure EDFA amplification,” in Proceedings ECOC 2008, Brussels, Belgium, 2008, Paper Th.2.A.2.

20.

J. Downie, J. E. Hurley, J. Cartledge, S. R. Bickham, and S. Mishra, “Transmission of 112 Gb/s PM-QPSK Signals over 7200 km of Optical Fiber with Very Large Effective Area and Ultra-Low Loss in 100 km Spans with EDFAs Only,” in Optical Fiber Communications Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMI6.

21.

G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72x100Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPB6.

22.

C. Behrens, S. Makovejs, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission,” Opt. Express 19(14), 12879–12884 (2011). [CrossRef] [PubMed]

23.

A. H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Packham, “10 x 224-Gb/s WDM Transmission of 28-Gbaud PDM 16-QAM on a 50-GHz Grid over 1,200 km of Fiber,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper PDPB8.

24.

M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “Transmission of 11 x 224-Gb/s POLMUX-RZ-16QAM over 1500 km of LongLine and pure-silica SMF,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.8.C.2.

25.

S. Yamanaka, T. Kobayashi, A. Sano, H. Masuda, E. Yoshida, Y. Miyamoto, T. Nakagawa, M. Nagatani, and H. Noaka, “11 x 171 Gb/s PDM 16-QAM Transmission over 1440 km with a Spectral Effiency of 6.4 b/s/Hz using High-Speed DAC,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.8.C.1.

26.

A. Gnauck and P. J. Winzer, “Ultra-High-Spectral-Efficiency Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OWE4.

27.

J. Yu and X. Zhou, “16 x 107-Gb/s 12.5-GHz-Spaced PDM-36QAM Transmission Over 400 km of Standard Single-Mode Fiber,” IEEE Photon. Technol. Lett. 22(17), 1312–1314 (2010). [CrossRef]

28.

A. Sano, T. Kobayashi, A. Matsuura, S. Yamamoto, S. Yamanaka, E. Yoshida, Y. Miyamoto, M. Matsui, M. Mizuguchi, and T. Mizuno, “100 x 120-Gb/s PDM 64-QAM Transmission over 160 km Using Linewidth-Tolerant Pilotless Digital Coherent Detection,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper pd2_4.

29.

J. Yu, X. Zhou, Y. Huang, S. Gupta, M. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ-64QAM optical signal generation and transmission on a 12.5GHz WDM Grid,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OThM1.

30.

D. Rafique, J. Zhao, and A. D. Ellis, “Digital back-propagation for spectrally efficient WDM 112 Gbit/s PM m-ary QAM transmission,” Opt. Express 19(6), 5219–5224 (2011). [CrossRef] [PubMed]

31.

J.-X. Cai, M. Nissov, A. N. Pilipetskii, A. J. Lucero, C. R. Davidson, D. Foursa, H. Kidorf, M. A. Mills, R. Menges, P. C. Corbett, D. Sutton, and N. S. Bergano, “2.4 Tb/s (120 x 20 Gb/s) Transmission over Transoceanic Distance using Optimum FEC Overhead and 48% Spectral Efficiency,” in Optical Fiber Communication Conference, 2001 OSA Technical Digest Series (Optical Society of America, 2001), paper PD20.

32.

A. Agata, K. Tanaka, and N. Edagawa, “Study on the Optimum Reed-Solomon-Based FEC Codes for 40-Gb/s-Based Ultralong-Distance WDM transmission,” J. Lightwave Technol. 20(12), 2189–2195 (2002). [CrossRef]

33.

M. O’Sullivan, “Expanding network application with coherent detection,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper NWC3.

34.

S. R. Desbruslais and S. J. Savory, “Relationship Between Electrical Bandwidth and FEC Overhead in a 100 GbE Digital Coherent Receiver,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper P3.19.

35.

S. Dave, L. Esker, F. Mo, W. Thesling, J. Keszenheimer, and R. Fuerst, “Soft-decision Forward Error Correction in a 40-nm ASIC for 100-Gbps OTN Applications,” in National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JWA014.

36.

J. Bromage, “Raman Amplification for Fiber Communications Systems,” J. Lightwave Technol. 22(1), 79–93 (2004). [CrossRef]

37.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical Links?” Opt. Express 17(13), 10814–10819 (2009). [CrossRef] [PubMed]

38.

H. Bülow and E. S. Masalkina, “Coded Modulation in Optical Communications,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America,2011), paper OThO1.

39.

L. Beygi, E. Agrell, and M. Karlsson, “Optimization of 16-point Ring Constellations in the Presence of Nonlinear Phase Noise,” in Optical Fiber communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO4.

40.

E. Torrengo, S. Makovejs, D. Millar, I. Fatadin, R. Killey, S. Savory, and P. Bayvel, “Influence of Pulse Shape in 112-Gb/s WDM PDM-QPSK Transmission,” IEEE Photon. Technol. Lett. 22(23), 1714–1716 (2010). [CrossRef]

41.

I. Lyubomirsky, A. Nilsson, M. Mitchell, and D. Welch, “Signal Chirp Design for Supression of Nonlinear Polarization Scattering in DP-QPSK Transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThF3.

42.

B. Châtelain, C. Laperle, K. Roberts, X. Xu, M. Chagnon, A. Borowiec, F. Gagnon, J. Cartedge, and D. V. Plant, “Optimized Pulse Shaping for Intra-channel Nonlinearities Mitigation in a 10 Gbaud Dual-Polarization 16-QAM System,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWO5.

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 2, 2011
Revised Manuscript: January 16, 2012
Manuscript Accepted: January 17, 2012
Published: January 25, 2012

Citation
Brian DeMuth, Michael Y. Frankel, and Vladimir Pelekhaty, "Semi-empirical system scaling rules for DWDM system design," Opt. Express 20, 2992-3004 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2992


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References

  1. R. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity Limits of Optical Fiber Networks,” J. Lightwave Technol.28(4), 662–701 (2010). [CrossRef]
  2. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the Non-Linear Shannon Limit,” J. Lightwave Technol.28(4), 423–433 (2010). [CrossRef]
  3. M. Salsi, C. Koebele, P. Tran, H. Mardoyan, S. Bigo, and G. Charlet, “80x100Gbit/s transmission over 9000km using erbium-doped fibre repeaters only,” in Proceedings ECOC 2010, Torino, Italy, 2010, Paper We.7.C.3.
  4. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16 x 100Gb/s Transmission Over Installed Fiber With Different Dispersion Maps,” IEEE Photon. Technol. Lett.22(6), 371–373 (2010). [CrossRef]
  5. M. S. Alfiad, M. Kuschnerov, S. L. Jansen, T. Wuth, D. van den Borne, and H. de Waardt, “11 x 224 Gb/s POLMUX-RZ-16QAM Transmission Over 670 km of SSMF With 50-GHz Channel Spacing,” IEEE Photon. Technol. Lett.22(15), 1150–1152 (2010). [CrossRef]
  6. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally Efficient Long-Haul Optical Networking Using 112-Gb/s Polarization-Multiplexed 16-QAM,” J. Lightwave Technol.28(4), 547–556 (2010). [CrossRef]
  7. X. Chen and W. Shieh, “Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems,” Opt. Express18(18), 19039–19054 (2010). [CrossRef] [PubMed]
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