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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 26 — Dec. 12, 2011
  • pp: B40–B46
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Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

Danish Rafique and Andrew D. Ellis  »View Author Affiliations


Optics Express, Vol. 19, Issue 26, pp. B40-B46 (2011)
http://dx.doi.org/10.1364/OE.19.000B40


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Abstract

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Qeff) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at ~2/3rd of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

© 2011 OSA

1. Introduction

With the ever increasing demand for high information rates and advances in bandwidth intense applications, the available transmission capacity for single mode optical fibre is rapidly approaching its limit [1

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

]. One of the main limitations is the nonlinear behavior of the optical fiber. It may be shown [2

2. A. R. Chraplyvy, “Limitations on lightwave communications imposed by optical-fiber nonlinearity,” J. Lightwave Technol. 8(10), 1548–1557 (1990). [CrossRef]

, 3

3. D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9(1), 121–128 (1991). [CrossRef]

] that the effects of four-wave mixing (FWM), self- and cross-phase modulation and other nonlinear effects approximately depend on the path averaged power, and become increasingly pronounced as power levels are increased.

The recent revival of coherent detection with the availability of high speed digital signal processing technologies has enabled electronic mitigation of these effects [4

4. X. Zhou, E. F. Mateo, and G. Li, “Fiber nonlinearity management – from carrier perspective,” Optical Fiber Communication Conference, OFC ‘11, NThB4, (2011).

, 5

5. C. Weber, C.-A. Bunge, and K. Petermann, “Fiber nonlinearities in systems using electronic predistortion of dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. 27(16), 3654–3661 (2009). [CrossRef]

]. In particular, electronic signal processing using digital back-propagation (DBP) has been applied to the compensation of channel nonlinearities [6

6. 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]

, 7

7. E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]

]. However the performance improvements by single-channel nonlinearity compensation are curtailed by inter-channel nonlinearities [7

7. E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]

] and multi-channel compensation is limited by signal-amplified spontaneous emission (ASE) four-wave mixing (SN-FWM) [8

8. D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011). [CrossRef] [PubMed]

]. A rather obvious way to minimize nonlinear impairments is by lowering the signal power, leading to a trade off with the optical signal-to-noise ratio (OSNR) at the receiver. This trade off has previously been studied for unequal amplifier spacing [9

9. A. Mecozzi, “On the optimization of the gain distribution of transmission lines with unequal amplifier spacing,” IEEE Photon. Technol. Lett. 10(7), 1033–1035 (1998). [CrossRef]

], distributed amplification [10

10. I. Nasieva, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinearity management in fibre links with distributed amplification,” Electron. Lett. 39(11), 856–857 (2003). [CrossRef]

], and phase modulated systems [11

11. A. P. T. Lau and J. M. Kahn, “Power profile optimization in phase-modulated systems in presence of nonlinear phase noise,” IEEE Photon. Technol. Lett. 18(23), 2514–2516 (2006). [CrossRef]

] where a longitudinal variation in launch power was found to be advantageous. However, to our knowledge there have been no reports on the impact of power profile optimization on the transmission performance of coherent systems, limited by SN-FWM, employing advanced multi-level modulation formats [12

12. 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]

, 13

13. S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDM-QAM16 transmission at 112 Gbit/s over 2400 km,” Optical Fiber Communication Conference, OFC ‘10, OMJ6, (2010).

] and mitigation of nonlinear fibre impairments via DBP. In context of increasing growth in capacity demands [1

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

], near-future transmission systems employing wide-band DBP would eventually be limited by SN-FWM effects [6

6. 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]

, 8

8. D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011). [CrossRef] [PubMed]

].

In this paper, we demonstrate that modifying the longitudinal power distribution by optimizing the gain of just one of the in-line amplifiers may improve the transmission performance for coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation (PM-mQAM, m=4, 16, 64, 256) transmission employing digital back-propagation. Our results suggest that if the gain of the in-line optical amplifiers is set to exactly compensate for uniform fibre loss, an increase (~4 dB) in the amplifier gain at ~2/3rd of the total reach improves the performance of the overall system, consistent with the theoretical predictions based on SN-FWM. In particular, for systems whose length is such that the bit error rate (BER) at the optimum uniform launch power would be ~1.5x10−3 (Qeff of ~9.5 dB), Qeff increases by 0.6 dB and enables over 1 dB reduction in transmitted power (power launched into the first fibre segment) for all formats studied. Furthermore, we report that with a fixed received OSNR, if a fault is encountered anywhere along the link, the transmission performance is always degraded.

3. Transmission model

After fiber transmission, the received signal was demultiplexed, pre-amplified and coherently-detected using a local oscillator to give baseband electrical signal, and down sampled to 2 samples per symbol. Transmission impairments were compensated via digital back-propagation (DBP), which was numerically implemented by up-sampling the received signal to 16 samples per symbol and reconstructing the optical field from the inphase and quadrature components, followed by a split-step Fourier method based solution of nonlinear Schrödinger equation. Although various simplifications of DBP algorithm have been proposed lately [15

15. L. B. Du and A. J. Lowery, “Experimental demonstration of XPM compensation for CO-OFDM systems with periodic dispersion maps,” Optical Fiber Communication Conference, OFC’11, OWW2, (2011).

17

17. L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation efficient nonlinear equalizer based on correlated digital backpropagation,” Optical Fiber Communication Conference, OFC ‘11, 2011, OWW3.

], in order to determine the maximum potential performance of the power-profile management, the step-size was chosen adaptively such that in each step the change in phase of the optical field was no more than 0.05 degrees. Note that transmission performance reported here may reduce given a coarse-step DBP is employed [13

13. S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDM-QAM16 transmission at 112 Gbit/s over 2400 km,” Optical Fiber Communication Conference, OFC ‘10, OMJ6, (2010).

, 18

18. F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010). [CrossRef]

].

Residual distortion and any bandwidth limitations were compensated with a receiver amplitude response implemented using FIR filters (fractionally-spaced taps), and polarization de-multiplexing was then performed using a butterfly structure, where filters were adapted using a least mean square algorithm. Note that no carrier phase recovery was required since laser linewidth was neglected in this study. Finally, the symbol decisions were made, and the performance assessed by direct error counting (converted into an effective Q-factor (Qeff)).

3. Results and discussions

We first consider the performance of PM-64QAM after transmission over 3,200 km (40 spans) with DBP. We fix the reference launch power at the optimum launch power for a uniform power profile, where we observe a Qeff of 9.5 dB (BER of 1.4x10−3) and a received OSNR of 24.4 dB. This configuration is referred to as conventional power profile. Figure 3(a)
Fig. 3 Performance of PM-64QAM at a transmission distance of 3,200 km (40 spans) after DBP. Contour curves represent a) Qeff and, b) FWM power, as a function of position and gain/loss of power profile shaping element. Received OSNR is fixed to 24.4 dB for all the configurations.
plots the calculated Qeff (contour curves) as a function of the position and gain/loss of the node containing the power step, for a fixed received OSNR. It can be seen that when positive-step is employed, the transmission performance may improve for any given position of the additional gain element. From the plot, one can clearly locate an optimum region from 20th span to 30th span with a positive step size of ~3-4 dB. In particular, the best map can be identified when the amplifier is placed after the 25th span and a gain of 4 dB is employed, enabling a 0.6 dB Qeff improvement. In general performance improvement is obtained for a wide range of power steps provided the step is located after the midpoint of the system. On the other hand, the figure also shows that given a negative-step profile is employed, emulating an amplification stage failure or an increase in fibre loss, the transmission performance is always degraded, even if the OSNR is restored by adjusting the transmitter launch power.

Figure 5(a)
Fig. 5 Performance of PM-64QAM at a transmission distance of 3,200 km (40 spans) after DBP. a) Contour curves represent launch power as a function of position and gain/loss of power profile shaping element; b) Qeff as a function of OSNR for the optimum profile with a gain of 4 dB after the 25th span.
plots the required transmitter launch power for various configurations in Fig. 3. It can be seen that for positive-step profile, the launch power is always lower than conventional power profile, and a 1.1 dB reduction in launch power can be seen for the optimum power profile. This system is limited by the overall signal to noise ratio, including the parametrically amplified noise (Eq. (1)). Consequently the optimum configuration may be understood from the relative impacts of the signal power and transmission length in Eq. (1). In the optimum configuration, the signal power is reduced for part of the transmission length, and is increased for the remainder. Where the signal power is reduced, the quadratic dependence of the parametric gain on signal power ensures that the contribution from this section is reduced. On the other hand, where the signal power is increased, fewer spans are included, thereby strongly mitigating the impact of the increased signal power, and resulting in an optimum step size for a given step location.

Figure 5(b) plots the Qeff as a function of received OSNR for the optimum profile with a gain of 4 dB and a fixed step after the 25th span for PM-64QAM. It can be seen that the Qeff curve follows the well-known optimum launch power phenomenon, where at lower launch powers, the system performance is limited by noise and the performance peaks at an optimum OSNR. The figure depicts an important design criterion and shows that even with the new optimum power profile, the optimum OSNR is consistent with that of conventional power profile.

4. Conclusion

Acknowledgments

This work was based upon work supported by Science Foundation Ireland under Grant numbers 06/IN/I969 and 10/CE/I1853.

References and links

1.

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

2.

A. R. Chraplyvy, “Limitations on lightwave communications imposed by optical-fiber nonlinearity,” J. Lightwave Technol. 8(10), 1548–1557 (1990). [CrossRef]

3.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9(1), 121–128 (1991). [CrossRef]

4.

X. Zhou, E. F. Mateo, and G. Li, “Fiber nonlinearity management – from carrier perspective,” Optical Fiber Communication Conference, OFC ‘11, NThB4, (2011).

5.

C. Weber, C.-A. Bunge, and K. Petermann, “Fiber nonlinearities in systems using electronic predistortion of dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. 27(16), 3654–3661 (2009). [CrossRef]

6.

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]

7.

E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]

8.

D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011). [CrossRef] [PubMed]

9.

A. Mecozzi, “On the optimization of the gain distribution of transmission lines with unequal amplifier spacing,” IEEE Photon. Technol. Lett. 10(7), 1033–1035 (1998). [CrossRef]

10.

I. Nasieva, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinearity management in fibre links with distributed amplification,” Electron. Lett. 39(11), 856–857 (2003). [CrossRef]

11.

A. P. T. Lau and J. M. Kahn, “Power profile optimization in phase-modulated systems in presence of nonlinear phase noise,” IEEE Photon. Technol. Lett. 18(23), 2514–2516 (2006). [CrossRef]

12.

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]

13.

S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDM-QAM16 transmission at 112 Gbit/s over 2400 km,” Optical Fiber Communication Conference, OFC ‘10, OMJ6, (2010).

14.

T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]

15.

L. B. Du and A. J. Lowery, “Experimental demonstration of XPM compensation for CO-OFDM systems with periodic dispersion maps,” Optical Fiber Communication Conference, OFC’11, OWW2, (2011).

16.

D. Rafique, M. Mussolin, M. Forzati, J. Mårtensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express 19(10), 9453–9460 (2011). [CrossRef] [PubMed]

17.

L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation efficient nonlinear equalizer based on correlated digital backpropagation,” Optical Fiber Communication Conference, OFC ‘11, 2011, OWW3.

18.

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010). [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Subsystems for Optical Networks

History
Original Manuscript: September 13, 2011
Revised Manuscript: October 19, 2011
Manuscript Accepted: October 19, 2011
Published: November 16, 2011

Virtual Issues
European Conference on Optical Communication 2011 (2011) Optics Express

Citation
Danish Rafique and Andrew D. Ellis, "Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation," Opt. Express 19, B40-B46 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-26-B40


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References

  1. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. 28(4), 423–433 (2010). [CrossRef]
  2. A. R. Chraplyvy, “Limitations on lightwave communications imposed by optical-fiber nonlinearity,” J. Lightwave Technol. 8(10), 1548–1557 (1990). [CrossRef]
  3. D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9(1), 121–128 (1991). [CrossRef]
  4. X. Zhou, E. F. Mateo, and G. Li, “Fiber nonlinearity management – from carrier perspective,” Optical Fiber Communication Conference, OFC ‘11, NThB4, (2011).
  5. C. Weber, C.-A. Bunge, and K. Petermann, “Fiber nonlinearities in systems using electronic predistortion of dispersion at 10 and 40 Gbit/s,” J. Lightwave Technol. 27(16), 3654–3661 (2009). [CrossRef]
  6. 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]
  7. E. Ip, “Nonlinear compensation using backpropagation for polarization-multiplexed transmission,” J. Lightwave Technol. 28(6), 939–951 (2010). [CrossRef]
  8. D. Rafique and A. D. Ellis, “Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems,” Opt. Express 19(4), 3449–3454 (2011). [CrossRef] [PubMed]
  9. A. Mecozzi, “On the optimization of the gain distribution of transmission lines with unequal amplifier spacing,” IEEE Photon. Technol. Lett. 10(7), 1033–1035 (1998). [CrossRef]
  10. I. Nasieva, J. D. Ania-Castanon, and S. K. Turitsyn, “Nonlinearity management in fibre links with distributed amplification,” Electron. Lett. 39(11), 856–857 (2003). [CrossRef]
  11. A. P. T. Lau and J. M. Kahn, “Power profile optimization in phase-modulated systems in presence of nonlinear phase noise,” IEEE Photon. Technol. Lett. 18(23), 2514–2516 (2006). [CrossRef]
  12. 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]
  13. S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDM-QAM16 transmission at 112 Gbit/s over 2400 km,” Optical Fiber Communication Conference, OFC ‘10, OMJ6, (2010).
  14. T. Pfau, S. Hoffmann, and R. Noé, “Hardware-efficient coherent digital receiver concept with feedforward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]
  15. L. B. Du and A. J. Lowery, “Experimental demonstration of XPM compensation for CO-OFDM systems with periodic dispersion maps,” Optical Fiber Communication Conference, OFC’11, OWW2, (2011).
  16. D. Rafique, M. Mussolin, M. Forzati, J. Mårtensson, M. N. Chugtai, and A. D. Ellis, “Compensation of intra-channel nonlinear fibre impairments using simplified digital back-propagation algorithm,” Opt. Express 19(10), 9453–9460 (2011). [CrossRef] [PubMed]
  17. L. Li, Z. Tao, L. Dou, W. Yan, S. Oda, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “Implementation efficient nonlinear equalizer based on correlated digital backpropagation,” Optical Fiber Communication Conference, OFC ‘11, 2011, OWW3.
  18. F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2(5), 816–832 (2010). [CrossRef]

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