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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 13 — Jun. 18, 2012
  • pp: 14362–14370
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Nonlinearity compensation using dispersion-folded digital backward propagation

Likai Zhu and Guifang Li  »View Author Affiliations


Optics Express, Vol. 20, Issue 13, pp. 14362-14370 (2012)
http://dx.doi.org/10.1364/OE.20.014362


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Abstract

A computationally efficient dispersion-folded (D-folded) digital backward propagation (DBP) method for nonlinearity compensation of dispersion-managed fiber links is proposed. At the optimum power level of long-haul fiber transmission, the optical waveform evolution along the fiber is dominated by the chromatic dispersion. The optical waveform and, consequently, the nonlinear behavior of the optical signal repeat at locations of identical accumulated dispersion. Hence the DBP steps can be folded according to the accumulated dispersion. Experimental results show that for 6,084 km single channel transmission, the D-folded DBP method reduces the computation by a factor of 43 with negligible penalty in performance. Simulation of inter-channel nonlinearity compensation for 13,000 km wavelength-division multiplexing (WDM) transmission shows that the D-folded DBP method can reduce the computation by a factor of 37.

© 2012 OSA

1. Introduction

Optical signal is distorted by noise, dispersion and nonlinearity in fiber transmission. The Kerr nonlinearity, an intensity dependence of the refractive index, induces impairments including self-phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM) [1

1. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Elsevier, 2001).

]. These nonlinear impairments increase with the optical signal power. As a tradeoff between high signal to noise ratio and low nonlinear impairment, there is an optimum power level for a fiber transmission system, corresponding to a maximal spectral efficiency [2

2. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]

].

In [13

13. L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise statistics monitoring,” in Proc. ECOC’09, Paper P3.16 (2009).

], an adaptive filtering carrier phase recovery method was proposed to suppress the nonlinear phase noise due to XPM. Lumped phase de-rotation proportional to the received single-channel or multi-channel optical intensity can also be used for SPM compensation [14

14. K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22(3), 779–783 (2004). [CrossRef]

] or XPM compensation [15

15. L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 22(5), 320–322 (2010). [CrossRef]

], respectively. However, the lump phase de-rotation method is based on the assumption that the intensity waveform remains unchanged throughout the fiber propagation. In long-haul broadband transmission where the chromatic dispersion causes significant pulse reshaping and inter-channel walk-off, a distributed nonlinearity compensation method, known as digital backward propagation (DBP), is necessary for the effective compensation of the joint effect of dispersion and nonlinearity [16

16. K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006). [CrossRef]

19

19. D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010). [CrossRef]

]. In order for DBP to be accurate, a small step size is usually required, resulting in a large number of steps and a heavy computational load [20

20. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21(1), 61–68 (2003). [CrossRef]

].

2. Dispersion-folded DBP method

The dispersion map of a typical dispersion-managed fiber transmission system is illustrated in Fig. 1
Fig. 1 Conventional DBP and D-folded DBP for a dispersion-managed coherent fiber link.
. After the dispersion-managed fiber transmission and coherent detection, conventional DBP can be performed in the backward direction of the fiber propagation. Multiple steps are required for each of the many fiber spans, resulting in a large number of steps.

At the optimum power level of fiber transmission, the total nonlinear phase shift is on the order of 1 radian [33

33. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15(23), 1351–1353 (1990). [CrossRef] [PubMed]

]. Therefore, in long-haul transmission, the nonlinear effect in each fiber span is weak, and the optical waveform evolution along the fiber is dominated by the chromatic dispersion. Under the weakly nonlinear assumption, the optical waveform repeats at locations where accumulated dispersions are identical. Since the Kerr nonlinear effects are determined by the instantaneous optical field, the nonlinear behavior of the optical signal also repeats at locations of identical accumulated dispersion. Hence we can fold the DBP according to the accumulated dispersion.

The propagation of the optical field,E(z,t), is governed by
E(z,t)z=[D+εN(|E(z,t)|2)]E(z,t),
(1)
whereDis the linear operator for dispersion, fiber loss and amplifier gain, N(|E(z,t)|2) is the nonlinear operator, ε(to be set to unity) is a parameter indicating that the nonlinear perturbation is small for the reasons given above.

The solution of Eq. (1) can be written as,
E(z,t)=El(z,t)+εEnl(z,t).
(2)
Substituting Eq. (2) into Eq. (1), expanding the equation in power series of ε, and equating to zero the successive terms of the series, we have
El(z,t)z=DEl(z,t),
(3)
Enl(z,t)z=DEnl(z,t)+N(|El(z,t)|2)El(z,t),
(4)
which describe the linear evolution and the nonlinear correction, respectively. It is noted that the nonlinear correction Enl(z,t)is governed by a linear partial differential equation with nonzero forcing which depends on the linear solution only.

It is shown in Fig. 1 that the dispersion map can be divided into m divisions as indicated by the horizontal dashed lines. The fiber segments within a division have the same accumulated dispersion. Based on the principle of superposition, the total nonlinear correction is the sum of nonlinear corrections due to nonzero forcing at each fiber segment.

In conventional DBP, the contribution from each fiber segment is computed separately. However, it is advantageous to calculate the total nonlinear correction as the sum of nonlinear corrections due to nonzero forcing at different accumulated dispersion divisions, each having multiple fiber segments. This is because, with the exception of different input power levels and effective lengths, the linear component El(z,t)that generates the nonlinear correction and the total dispersion for the generated nonlinear perturbation to reach the end of the transmission are identical for the fiber segments with the same accumulated dispersion. Therefore, the nonlinear corrections due to these multiple fiber segments with the same accumulated dispersion are identical except a constant and can be calculated all at once using a weighting factor as described below.

3. Experimental results

Without loss of generality, we solve the NLSE using the asymmetric Split-Step Fourier Method (SSMF) with one dispersion compensator per step [24

24. Q. Zhang and M. I. Hayee, “Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems,” J. Lightwave Technol. 26(2), 302–316 (2008). [CrossRef]

]. For long-haul transmission, the DBP step size is usually limited by dispersion [20

20. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21(1), 61–68 (2003). [CrossRef]

]. In this paper, we use DBP steps with equal dispersion per step for simplicity. The Q-value as a function of the number of steps is shown in Fig. 2(b). The required number of steps to approach the maximum Q-value can be reduced from 1,300 to 30 by using the D-folded DBP. The number of multiplications per sample (MPS) for DBP is reduced by a factor of 43 (see details in the Appendix). There is a trade-off between complexity and performance using either conventional DBP or D-folded DBP. A Q-value of 10.2 dB, corresponding to a 1.1 dB improvement in comparison with EDC, can be achieved using 130-step conventional DBP or 5-step D-folded DBP.

Figure 2(c) shows the Q-value as a function of the launching power. With only EDC for the accumulated residual dispersion, the maximum Q-value is 9.1 dB. With nonlinearity compensation using D-folded DBP, the maximum Q-value is increased to 10.7 dB. The performance after the 30-step D-folded DBP is almost the same as that after the 1,300-step conventional DBP. The Q-values and computational load are shown in Table 1

Table 1. Performance and complexity of conventional DBP and D-folded DBP for the single channel system

table-icon
View This Table
| View All Tables
.

4. Simulation results

In DBP for SPM + XPM compensation, coupled NLSE is solved with the asymmetric SSFM [35

35. L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46(16), 1140–1141 (2010). [CrossRef]

]. The inter-channel walk-off effects are considered in the nonlinearity compensation operators in order to increase the required step size [23

23. E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010). [CrossRef] [PubMed]

]. For each channel, the XPM from two neighboring channels and the SPM are compensated. Simulation results show that the XPM from the other channels is weak because of the walk-off effect.

The average Q-value of all the WDM channels is calculated after 13,000 km transmission and DSP. The Q-values are calculated through variance estimation on the constellations under the assumption of Gaussian distribution. The Q-values presented here only provide a metric for comparison between different compensation schemes and are not reliable for the computation of bit error ratios because correlations exist in the nonlinear noise even after nonlinearity compensation. Figure 3(b) shows the Q-value as a function of the number of steps after DBP for SPM + XPM compensation using conventional DBP and D-folded DBP. With a RDPS of 20 ps/nm, the Q-values after 2,600-step conventional DBP and 80-step D-folded DBP are 11.5 dB and 11.3 dB, respectively. The minimum multiplications per sample for the 2,600-step conventional DBP and the 80-step D-folded DBP are 51,422 and 1,393, respectively. The computational load is reduced by a factor of 37 with a penalty of 0.2 dB in Q-value. With a RDPS of 80 ps/nm, the Q-values after 2,600-step conventional DBP and 200-step D-folded DBP are 11.9 dB and 11.7 dB, respectively. The step sizes of conventional DBP and D-folded DBP are usually limited by chromatic dispersion. As a result, with a larger RDPS, a larger number of steps for D-folded DBP are required to approach the maximum Q-value. Note that in realistic systems, exchanging information between channels for XPM compensation can increase the complexity of the DSP implementation.

Figure 3(c) shows the Q-value as a function of the number of steps after the DBP for SPM compensation. With a RDPS of 20 ps/nm, the Q-values after 1,040-step conventional DBP and 50-step D-folded DBP are 10.3 dB and 10.4 dB, respectively. The number of multiplications per sample is reduced from 10,400 to 408 with no penalty in Q-value. With a RDPS of 80 ps/nm, the Q-values after 1,040-step conventional DBP and 150-step D-folded DBP are 11.1 dB and 11.0 dB, respectively. The Q-values and computational loads are summarized in Table 2

Table 2. Performance and complexity of conventional DBP and D-folded DBP for the WDM system

table-icon
View This Table
| View All Tables
.

The Q-value obtained after DBP with sufficiently large number of steps as a function of the RDPS is shown in Fig. 3(d). For the dispersion-managed link, as the RDPS increases, the Q-value after EDC increases because the nonlinear effects and the span loss decrease. With DBP, the Q-value approaches the maximum value when the RDPS is larger than 20 ps/nm. In comparison with EDC, the DBP with XPM compensation can increase the Q-value by more than 3 dB when the RDPS is larger than 20 ps/nm. The performance using D-folded DBP is almost the same as that using conventional DBP.

5. Conclusion

In conclusion, we have proposed a dispersion-folded DBP method that can significantly reduce the computational load of DBP for fiber nonlinearity compensation. Experimental results show that the computation of DBP for 6,084 km single channel transmission can be reduced by a factor of 43. Simulation of a WDM system shows that the D-folded DBP method can reduce the computation for XPM compensation by a factor of 39.

Appendix: calculation of the computational load

The computational load can be associated to the number of complex multiplications per sample (MPS) involved in the operation. Either time-domain [using finite-impulse response (FIR) filters] or frequency-domain equalization can be used for the compensation of dispersion. In DBP, the frequency response of each dispersion compensator must be very accurate in order to minimize the error accumulation. When the amount of dispersion to be compensated and thus the theoretical minimum number of taps of the FIR filter are small, the number of taps required for the FIR filter can be much larger than the minimum number corresponding to the group delay [28

28. L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett. 21(5), 292–294 (2009). [CrossRef]

]. Therefore, frequency-domain overlap-add FFT method is assumed here for calculating the computational complexity of DBP in this paper [20

20. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21(1), 61–68 (2003). [CrossRef]

].

For an overhead length P, a signal block length M is chosen to minimize the computational load using the radix-2 Fast Fourier Transform (FFT) with an FFT block size of (M+P). For EDC, the overhead is approximately given byP=2π|β2|BhS whereβ2,B, handSare the dispersion, signal bandwidth per channel, fiber length and sampling rate, respectively. The MPS for the overlap-add filtering is given by[(M+P)log2(M+P)+(M+P)]/M. For the EDC of the 13,000 km dispersion-unmanaged link, we consider an FFT block size of 210 which is practical for the current electronic technology. By using 11 overlap-add filtering operators with M=548 andP=476, the minimum possible MPS is 245.

To ensure accuracy of the dispersion operator in DBP, we assume an overhead Pthat is 3 times the group delay2π|β2|BhS. In the nonlinearity operator of DBP, the calculations of the optical intensity and the nonlinear phase shift each costs one complex multiplication. The value of the nonlinear phase shift can be obtained using a lookup table. The MPS of DBP for SPM compensation is given bynst[(M+P)log2(M+P)+(M+P)+2M]/M, wherenstis the step number. For the 6,084 km single channel transmission, the minimum MPSs of the 1,300-step conventional DBP and the 30-step D-folded DBP are 13,385 and 314, respectively. For the SPM compensation of the 13,000 km WDM system, the minimum MPSs of the 1,040-step conventional DBP and the 50-step D-folded DBP are 12,222 and 500, respectively.

In the DBP with XPM compensation for the 13,000 km WDM transmission, the length of the inter-channel walk-off filter is given byP=2π|β2|ΔfhS where Δfis the channel spacing. The MPS for DBP is given bynst[2(M+P)log2(M+P)+3(M+P)+2M]/M. The minimum MPS for the 2,600-step conventional DBP is 51,422. For the 80-step D-folded DBP, the minimum MPS is 1,393.

References and links

1.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Elsevier, 2001).

2.

P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature 411(6841), 1027–1030 (2001). [CrossRef] [PubMed]

3.

B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. 5(10), 1250–1253 (1993). [CrossRef]

4.

K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep. 3(5), 292–339 (2006). [CrossRef]

5.

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(2), 753–791 (2008). [CrossRef] [PubMed]

6.

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]

7.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]

8.

E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Express 19(14), 13179–13184 (2011). [CrossRef] [PubMed]

9.

J. M. Kahn and K.-P. Ho, “A bottleneck for optical fibres,” Nature 411(6841), 1007–1010 (2001). [CrossRef] [PubMed]

10.

E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightwave Technol. 24(12), 4697–4710 (2006). [CrossRef]

11.

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

12.

R.-J. 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]

13.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise statistics monitoring,” in Proc. ECOC’09, Paper P3.16 (2009).

14.

K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. 22(3), 779–783 (2004). [CrossRef]

15.

L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 22(5), 320–322 (2010). [CrossRef]

16.

K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. 18(2), 403–405 (2006). [CrossRef]

17.

X. Li, X. Chen, G. Goldfarb, E. F. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008). [CrossRef] [PubMed]

18.

E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol. 28(4), 502–519 (2010). [CrossRef]

19.

D. S. Millar, S. Makovejs, C. Behrens, S. Hellerbrand, R. I. Killey, P. Bayvel, and S. J. Savory, “Mitigation of fiber nonlinearity using a digital coherent receiver,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1217–1226 (2010). [CrossRef]

20.

O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21(1), 61–68 (2003). [CrossRef]

21.

S. Oda, T. Tanimura, T. Hoshida, C. Ohshima, H. Nakashima, Z. Tao, and J. C. Rasmussen, “112 Gb/s DP-QPSK transmission using a novel nonlinear compensator in digital coherent receiver.” in Proc. OFC’09, Paper OThR6 (2009).

22.

E. F. Mateo, L. Zhu, and G. Li, “Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation,” Opt. Express 16(20), 16124–16137 (2008). [CrossRef] [PubMed]

23.

E. F. Mateo, F. Yaman, and G. Li, “Efficient compensation of inter-channel nonlinear effects via digital backward propagation in WDM optical transmission,” Opt. Express 18(14), 15144–15154 (2010). [CrossRef] [PubMed]

24.

Q. Zhang and M. I. Hayee, “Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems,” J. Lightwave Technol. 26(2), 302–316 (2008). [CrossRef]

25.

L. B. Du and A. J. Lowery, “Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems,” Opt. Express 18(16), 17075–17088 (2010). [CrossRef] [PubMed]

26.

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]

27.

L. Zhu and G. Li, “Folded digital backward propagation for dispersion-managed fiber-optic transmission,” Opt. Express 19(7), 5953–5959 (2011). [CrossRef] [PubMed]

28.

L. Zhu, X. Li, E. F. Mateo, and G. Li, “Complementary FIR filter pair for distributed impairment compensation of WDM fiber transmission,” IEEE Photon. Technol. Lett. 21(5), 292–294 (2009). [CrossRef]

29.

J. K. Fischer, C.-A. Bunge, and K. Petermann, “Equivalent single-span model for dispersion-managed fiber-optic transmission systems,” J. Lightwave Technol. 27(16), 3425–3432 (2009). [CrossRef]

30.

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express 17(6), 4815–4823 (2009). [CrossRef] [PubMed]

31.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of nonlinear effects in 111-Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008). [CrossRef]

32.

T. Yoshida, T. Sugihara, H. Goto, T. Tokura, K. Ishida, and T. Mizuochi, “A study on statistical equalization of intra-channel fiber nonlinearity for digital coherent optical systems,” in Proc. ECOC’11, Tu.3.A. (2011).

33.

J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15(23), 1351–1353 (1990). [CrossRef] [PubMed]

34.

T. Tanimura, T. Hoshida, T. Tanaka, L. Li, S. Oda, H. Nakashima, Z. Tao, and J. C. Rasmussen, “Semi-blind nonlinear equalization in coherent multi-span transmission system with inhomogeneous span parameters,” in Proc. OFC’10, OMR6 (2010).

35.

L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46(16), 1140–1141 (2010). [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 27, 2012
Revised Manuscript: May 18, 2012
Manuscript Accepted: May 25, 2012
Published: June 12, 2012

Citation
Likai Zhu and Guifang Li, "Nonlinearity compensation using dispersion-folded digital backward propagation," Opt. Express 20, 14362-14370 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14362


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References

  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Elsevier, 2001).
  2. P. P. Mitra and J. B. Stark, “Nonlinear limits to the information capacity of optical fibre communications,” Nature411(6841), 1027–1030 (2001). [CrossRef] [PubMed]
  3. B. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett.5(10), 1250–1253 (1993). [CrossRef]
  4. K. Mukasa, K. Imamura, I. Shimotakahara, T. Yagi, and K. Kokura, “Dispersion compensating fiber used as a transmission fiber: inverse/reverse dispersion fiber,” J. Opt. Fiber Commun. Rep.3(5), 292–339 (2006). [CrossRef]
  5. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16(2), 753–791 (2008). [CrossRef] [PubMed]
  6. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007). [CrossRef] [PubMed]
  7. H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express16(2), 873–879 (2008). [CrossRef] [PubMed]
  8. E. Yamazaki, S. Yamanaka, Y. Kisaka, T. Nakagawa, K. Murata, E. Yoshida, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Matsuoka, J. Matsui, A. Shibayama, J. Abe, Y. Nakamura, H. Noguchi, K. Fukuchi, H. Onaka, K. Fukumitsu, K. Komaki, O. Takeuchi, Y. Sakamoto, H. Nakashima, T. Mizuochi, K. Kubo, Y. Miyata, H. Nishimoto, S. Hirano, and K. Onohara, “Fast optical channel recovery in field demonstration of 100-Gbit/s Ethernet over OTN using real-time DSP,” Opt. Express19(14), 13179–13184 (2011). [CrossRef] [PubMed]
  9. J. M. Kahn and K.-P. Ho, “A bottleneck for optical fibres,” Nature411(6841), 1007–1010 (2001). [CrossRef] [PubMed]
  10. E. B. Desurvire, “Capacity demand and technology challenges for lightwave systems in the next two decades,” J. Lightwave Technol.24(12), 4697–4710 (2006). [CrossRef]
  11. A. D. Ellis, J. Zhao, and D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol.28(4), 423–433 (2010). [CrossRef]
  12. R.-J. 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]
  13. L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “XPM tolerant adaptive carrier phase recovery for coherent receiver based on phase noise statistics monitoring,” in Proc. ECOC’09, Paper P3.16 (2009).
  14. K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol.22(3), 779–783 (2004). [CrossRef]
  15. L. B. Du and A. J. Lowery, “Practical XPM compensation method for coherent optical OFDM systems,” IEEE Photon. Technol. Lett.22(5), 320–322 (2010). [CrossRef]
  16. K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(2), 403–405 (2006). [CrossRef]
  17. X. Li, X. Chen, G. Goldfarb, E. F. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express16(2), 880–888 (2008). [CrossRef] [PubMed]
  18. E. Ip and J. M. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” J. Lightwave Technol.28(4), 502–519 (2010). [CrossRef]
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