OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 2 — Jan. 27, 2014
  • pp: 1209–1219
« Show journal navigation

Reducing the complexity of perturbation based nonlinearity pre-compensation using symmetric EDC and pulse shaping

Ying Gao, John C. Cartledge, Abdullah S. Karar, Scott S.-H. Yam, Maurice O’Sullivan, Charles Laperle, Andrzej Borowiec, and Kim Roberts  »View Author Affiliations


Optics Express, Vol. 22, Issue 2, pp. 1209-1219 (2014)
http://dx.doi.org/10.1364/OE.22.001209


View Full Text Article

Acrobat PDF (1045 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Perturbation based nonlinearity pre-compensation has been performed for a 128 Gbit/s single-carrier dual-polarization 16-ary quadrature-amplitude-modulation (DP 16-QAM) signal. Without any performance degradation, a complexity reduction factor of 6.8 has been demonstrated for a transmission distance of 3600 km by combining symmetric electronic dispersion compensation and root-raised-cosine pulse shaping with a roll-off factor of 0.1. Transmission over 4200 km of standard single-mode fiber with EDFA amplification was achieved for the 128 Gbit/s DP 16-QAM signals with a forward error correction (FEC) threshold of 2 × 10−2.

© 2014 Optical Society of America

1. Introduction

2. SEDC and RRC pulse shaping

The perturbation-based pre-compensation of a DP 16-QAM signal includes self-phase modulation, intra-channel cross phase modulation (IXPM) and intra-channel four-wave-mixing (IFWM) [13

13. Y. Fan, L. Dou, Z. Tao, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Modulation format dependent phase noise caused by intra-channel nonlinearity,”, ” Proc. Eur. Conf. Opt. Commun., We.2.C.3. (2012). [CrossRef]

]. Without electronic pre-dispersion compensation, the optical field for the current symbol (at time 0) after nonlinear pre-compensation is:
A0,xout=(A0,xinA0,xIFWM)exp(Δψ0,x)(A0,xinA0,xIFWM)(1Δψ0,x)
(1)
A0,yout=(A0,yinA0,yIFWM)exp(Δψ0,y)(A0,yinA0,yIFWM)(1Δψ0,y)
(2)
where 1Δψ0,x/y is the first order Taylor approximation of exp(Δψ0,x/y), and
Δψ0,x=ψ0,xE{(ψ0,x)}
(3)
Δψ0,y=ψ0,yE{(ψ0,y)}
(4)
ψ0,x=P03/2[C0,0(|A0,x|2+|A0,y|2)+m0Cm,0(2|Am,x|2+|Am,y|2)]
(5)
ψ0,y=P03/2[C0,0(|A0,x|2+|A0,y|2)+m0Cm,0(2|Am,y|2+|Am,x|2)]
(6)
A0,xIFWM=P03/2[m0,n0Cm,n(An,xAm,xAm+n,x*+An,yAm,xAm+n,y*)+m0Cm,0(A0,yAm,xAm,y*)]
(7)
A0,yIFWM=P03/2[m0,n0Cm,n(An,yAm,yAm+n,y*+An,xAm,yAm+n,x*)+m0Cm,0(A0,xAm,yAm,x*)]
(8)
{Cm,n} is the nonlinear perturbation coefficient which depends on the pulse shape, fiber properties and fiber length L, P0 is the optical launch power, {An,x/y} is the sequence of complex transmitted symbols for the x- and y-polarization signals with zero dispersion, and E denotes expectation [8

8. Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightwave Technol. 29(17), 2570–2576 (2011). [CrossRef]

, 9

9. Y. Gao, J. C. Cartledge, A. S. Karar, and S. S.-H. Yam, “Reducing the complexity of nonlinearity pre-compensation using symmetric EDC and pulse shaping,” Proc. Eur. Conf. Opt. Commun., PD3.E.5 (2013). [CrossRef]

, 13

13. Y. Fan, L. Dou, Z. Tao, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Modulation format dependent phase noise caused by intra-channel nonlinearity,”, ” Proc. Eur. Conf. Opt. Commun., We.2.C.3. (2012). [CrossRef]

]. The coefficients Cm,0 are imaginary-valued. The complexity of the algorithm is primarily determined by the second terms in Eqs. (5) and (6) for IXPM and Eqs. (7) and (8) for IFWM. The summations are truncated in practice based on the values of |Cm,n| being larger than a specified criterion.

A benefit of nonlinearity pre-compensation in the transmitter is that the symbol values An,x/y are known. For a QPSK signal, An,x/y and the multiplication results for three An,x/y values take the four values: 1, i, –1, –i. As a result, the multiplication An,xAm,xAm+n,x can be easily realized by logical operations [8

8. Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightwave Technol. 29(17), 2570–2576 (2011). [CrossRef]

]. For a 16-QAM signal, the An,x/y values can be formulated as a combination of two QPSK signals. The first QPSK signal is chosen from 2, 2i, –2, or –2i. The second QPSK signal is chosen from 1, i, –1, or –i. The multiplication of An,xAm,xAm+n,x can be realized by adding the eight QPSK signals with moduli of 8, 4, 2 and 1 from the distributive rule of multiplication. By taking advantage of the known symbol sequence at the transmitter, high resolution complex multipliers can be avoided.

The Cm,n coefficients are fixed for a given transmission spectrum and fiber length. For a RRC pulse shape with a roll-off factor of 0.1, the coefficients are calculated numerically as an analytical solution is not known [1

1. A. Mecozzi and R.-J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” J. Lightwave Technol. 30(12), 2011–2024 (2012). [CrossRef]

]. Cm,n for a RRC pulse shape with a roll-off factor of 0.1 and matched filtering was calculated as [9

9. Y. Gao, J. C. Cartledge, A. S. Karar, and S. S.-H. Yam, “Reducing the complexity of nonlinearity pre-compensation using symmetric EDC and pulse shaping,” Proc. Eur. Conf. Opt. Commun., PD3.E.5 (2013). [CrossRef]

]
Cm,n(z)=iγk[0Lspandz'fpd(z')/Lspan]0zdz'Im,n(z')
(15)
Im,n(z)=dtu0*(z,t)u0(z,tTn)u0(z,tTm)u0*(z,tTm+n)
(16)
where γ is the fiber nonlinear coefficient, k is a scaling factor, Lspan is the span length, fpd(z) is the power distribution profile along the link, T is the symbol period, Tm=mT, u0(0,t) is the pulse shape with zero accumulated dispersion (Z = 0), and u0(z,t) is the dispersed pulse shape corresponding to a fiber length z which is calculated according to u0(z,t)=ifft{fft[u0(0,t)]×exp[iβ2(2πf)2z/2]}, where (i)fft denotes the (inverse) Fourier transform, f is frequency, and β2 is the first order group velocity dispersion [1

1. A. Mecozzi and R.-J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” J. Lightwave Technol. 30(12), 2011–2024 (2012). [CrossRef]

].

In a practical implementation, the Cm,n values would be pre-calculated and stored in a look-up-table so the calculation requirements for Cm,n are not of significant consequence. The coefficients still satisfy Cm,n(L/2)=Cm,n(L/2) With the RRC pulse shape and SEDC, |Im[Cm,n(L/2)]| is plotted in Fig. 1(c). The RRC pulse shape with a roll-off factor of 0.1 has a smaller bandwidth than the Gaussian pulse shape and RRC pulse shapes with larger roll-off factors. This yields a smaller dispersion induced pulse spreading and hence a reduction in the number of terms in truncated approximations to Eqs. (13) and (14) that are based on the values of m and n for which 20log10|Cm,n/C0,0| is larger than a specified criterion. By combining SEDC and RRC pulse shaping, the number of summation terms is reduced from 8193 to 1201. The simplification using SEDC and a RRC pulse shape with a roll-off factor of 0.1 is denoted as RRC-SEDC.

3. Experimental set-up and back to back measurement

The experimental setup is shown in Fig. 2
Fig. 2 Experimental setup.
. The laser was operated at a wavelength of 1557.36 nm. A 219 deBruijn bit sequence was mapped to symbols to generate a 128 Gbit/s DP 16-QAM signal. Each perturbation-based pre-compensation algorithm was implemented with one sample per symbol, RRC pulse shaping with a roll-off factor of 0.1, and SEDC as applicable. The generated waveforms were loaded into the programmable memory of a Ciena Wavelogic 3 transceiver which interfaced with 4 synchronized digital-to-analog converters (DACs) with a sampling rate of 39.4 GSa/s. The four synchronized DACs are used here since the nonlinear pre-compensations for the x-polarization and y-polarization signals both depend on the x- and y-polarization symbols. The output signals from the DACs were applied to a DP in-phase and quadrature (IQ) modulator. The pre-compensated signal was launched into a recirculating loop with four spans and a loop synchronous polarization scrambler (LSPS). Each span consisted of 75 km of standard single mode fiber (SSMF), an erbium doped fiber amplifier (EDFA), and a tunable optical band-pass filter (OBPF). The OBPFs were used in the loop to prevent the EDFAs from being saturated by ASE noise. The sample values obtained after coherent detection were recorded with two real-time sampling oscilloscopes operating at 80 GSa/s and processed off-line.

The off-line signal processing included (i) matched filtering for a RRC pulse shape with a roll-off factor of 0.1, (ii) quadrature imbalance compensation [17

17. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008). [CrossRef]

], (iii) re-sampling to two samples per symbol, (iv) fixed frequency domain equalization for estimated chromatic dispersion, (v) digital square and filter clock recovery [18

18. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communications Receivers (Wiley-Interscience, 1997), section 5.4.

], (vi) polarization recovery and residual distortion compensation using 11-tap adaptive equalizers in a butterfly configuration, (vii) carrier frequency offset recovery using a spectral domain algorithm [19

19. M. Selmi, Y. Jaouën, and P. Cibalt, “Accurate digital frequency offset estimator for coherent polmux QAM transmission systems,” Proc. Eur. Conf. Opt. Commun., P3.08 (2009).

], and (viii) carrier phase recovery using a sliding window two-stage simplified QPSK partitioning and QPSK constellation transformation algorithm [20

20. J. H. Ke, K. P. Zhong, Y. Gao, J. C. Cartledge, A. S. Karar, and M. A. Rezania, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation for dual-polarization 16-QAM coherent optical fiber communications,” J. Lightwave Technol. 30(24), 3987–3992 (2012). [CrossRef]

]. The adaptive equalizer used a constant modulus algorithm for pre-convergence followed by a radius directed algorithm [21

21. I. Fatadin, D. Ives, and S. J. Savory, “Blind equalization and carrier phase recovery in a 16-QAM optical coherent system,” J. Lightwave Technol. 27(15), 3042–3049 (2009). [CrossRef]

]. The BER was obtained by direct bit error counting using rectilinear decision boundaries.

The back-to-back signal generated with a RRC pulse shape with a roll-off factor of 0.1 was measured and analyzed. Without any dispersion compensation and amplified spontaneous emission (ASE) noise loading, the recovered constellation diagrams after the off-line signal processing are shown in Fig. 3
Fig. 3 Back-to-back constellation diagrams for a 128 Gbit/s DP 16-QAM signal with a RRC pulse shape (roll-off factor of 0.1).
for one recorded data file. The average EVM based on 5 data files is 6.74%. The measured optical spectrum with a resolution of 0.38 pm is shown in Fig. 4
Fig. 4 Measured optical spectrum for a 128 Gbit/s DP 16-QAM signal with a RRC pulse shape (roll-off factor of 0.1).
.

The measured back-to-back BER as a function of the optical signal to noise ratio (OSNR) is shown in Fig. 5
Fig. 5 Dependence of the BER on the OSNR for a 128 Gbit/s DP 16-QAM signal with a RRC pulse shape (roll-off factor of 0.1).
for the 128 Gbit/s DP 16-QAM signal. For a forward error correction (FEC) threshold BER of 2 × 10−2, the implementation penalty for the required OSNR is 1.8 dB relative to the theoretical performance. For a BER of 1 × 10−3, the implementation penalty is 2.3 dB.

4. Transmission results and discussion

For a fiber length of 3600 km, the dependence of the BER on the launch power is shown in Fig. 6
Fig. 6 Dependence of the BER on the optical launch power for a fiber length of 3600 km.
for five different algorithms: linear post-compensation for dispersion (LC); Gaussian; symmetric (pre and post) linear compensation for dispersion (LC-SEDC); Gaussian-SEDC; and RRC-SEDC. The number of terms used in the truncated summations was based on 20log10|Cm,n/C0,0|>-35 dB. In the nonlinear region, the RRC-SEDC algorithm has a slightly lower BER than the Gaussian and Gaussian-SEDC algorithms. This is attributed to the calculation of the Cm,n coefficients being based on the actual pulse shape. Without a degradation in the BER performance, the Gaussian-SEDC and RRC-SEDC algorithms reduced the number of summation terms by factors of 3.4 and 6.8, respectively.

The dependence of the BER at optimum launch power on fiber length for the five algorithms is shown in Fig. 7
Fig. 7 Dependence of the BER at optimum launch power on the fiber length.
and the corresponding complexity is shown in Fig. 8
Fig. 8 Dependence of the required number of summation terms on the fiber length.
. The performances of the three nonlinear pre-compensation algorithms for a selection criterion 20log10|Cm,n/C0,0|>-35 dB are similar. However, the RRC-SEDC algorithm reduces the number of summation terms by factors from 6.1 to 7.8 compared to the Gaussian algorithm as the fiber length decreases from 4800 km to 2700 km. For the FEC threshold BER of 2 × 10−2, transmission over 4200 km of fiber was achieved with a reduction in the number of summation terms by a factor of 6.4. Despite the near-linear dependence exhibited by the resultsin Fig. 8, since the number of terms is based on Eq. (15) and the selection criterion 20log10|Cm,n/C0,0|>-35 dB, an explicit formula for the complexity is not known.

The selection criterion for Cm,n may be relaxed at the expense of an increase in the BER. For a fiber length of 3600 km, the pre-compensation algorithms have similar performances for different selection criteria, as shown in Fig. 9
Fig. 9 Dependence of the BER and required number of summation terms on the Cm,n selection criterion for three different algorithms.
. For each Cm,n selection criterion, the BER is shown at the optimum launch power for each nonlinear pre-compensation algorithm. Compared to the Gaussian algorithm, the reduction in complexity offered by the Gaussian-SEDC algorithm decreases with an increase in the BER and ranges from 3.4 to 2.2 for selection criteria of 20log10|Cm,n/C0,0| from −35 to −10 dB. The corresponding reduction offered by the RRC-SEDC algorithm ranges from 6.8 to 2.2. The numbers of summation terms for a selection criterion of −10 dB, which are difficult to discern in Fig. 9, are 73 for the Gaussian algorithm and 33 for both the Gaussian-SEDC and RRC-SEDC algorithms.

For the RRC-SEDC algorithm, the dependence of the BER and required number of summation terms on the Cm,n selection criterion is shown in Fig. 10
Fig. 10 Dependence of the BER and required number of summation terms on the Cm,n selection criterion for three fiber lengths.
for fiber lengths of 3000 km, 3600 km and 4200 km. For each Cm,n selection criterion, the BER is shown at the optimum launch power for each fiber length. For a given Cm,n selection criterion, the BER increases with the fiber length, which is attributed to the accumulated linear noise and nonlinear impairments. For a given Cm,n selection criterion, the required number of summation terms increases with the fiber length, which is attributed to the increased dispersion. The numbers of summation terms for a selection criterion of −10 dB, which are difficult to discern in Fig. 10, are 33 for both 3000 km and 3600 km, and 37 for 4200 km.

5. Conclusion

Without degrading the BER performance, the complexity of the perturbation-based pre-compensation algorithm has been reduced by a factor of 6.8 for transmission of a 128 Gbit/s DP 16-QAM signal over 3600 km, which is realized by two relatively simple modifications (SEDC and RRC pulse shaping). For all the perturbation based nonlinearity pre-compensation algorithms with and without simplification, the transmission distance of a single channel 128 Gbit/s DP 16-QAM signal has been extended from 3300 km to 4200 km by applying nonlinearity pre-compensation at a FEC threshold of 2 × 10−2.

References

1.

A. Mecozzi and R.-J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” J. Lightwave Technol. 30(12), 2011–2024 (2012). [CrossRef]

2.

D. Rafique and A. D. Ellis, “Nonlinearity compensation in multi-rate 28 Gbaud WDM systems employing optical and digital techniques under diverse link configurations,” Opt. Express 19(18), 16919–16926 (2011). [CrossRef] [PubMed]

3.

L. Zhu and G. Li, “Nonlinearity compensation using dispersion-folded digital backward propagation,” Opt. Express 20(13), 14362–14370 (2012). [CrossRef] [PubMed]

4.

Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, and S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual-polarization 16-QAM Transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013). [CrossRef]

5.

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

6.

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]

7.

Y. Gao, J. H. Ke, K. P. Zhong, J. C. Cartledge, and S. S.-H. Yam, “Assessment of intrachannel nonlinear compensation for 112 Gb/s dual-polarization 16QAM systems,” J. Lightwave Technol. 30(24), 3902–3910 (2012). [CrossRef]

8.

Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightwave Technol. 29(17), 2570–2576 (2011). [CrossRef]

9.

Y. Gao, J. C. Cartledge, A. S. Karar, and S. S.-H. Yam, “Reducing the complexity of nonlinearity pre-compensation using symmetric EDC and pulse shaping,” Proc. Eur. Conf. Opt. Commun., PD3.E.5 (2013). [CrossRef]

10.

X. Liu, S. Chandrasekhar, P. J. Winzer, R. W. Tkach, and A. R. Chraplyvy, “406.6-Gb/s PDM-BPSK superchannel transmission over 12,800-km TWRS fiber via nonlinear noise squeezing,” Proc. Conf. Opt. Fiber Commun., PDP5B.10 (2013). [CrossRef]

11.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]

12.

H. Lu, Y. Mori, C. Han, and K. Kikuchi, “Novel polarization-diversity scheme based on mutual phase conjugation for fiber-nonlinearity mitigation in ultra-long coherent optical transmission systems,” Proc. Eur. Conf. Opt. Commun., We.3.C.3 (2013).

13.

Y. Fan, L. Dou, Z. Tao, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Modulation format dependent phase noise caused by intra-channel nonlinearity,”, ” Proc. Eur. Conf. Opt. Commun., We.2.C.3. (2012). [CrossRef]

14.

L. Dou, Z. Tao, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, ‘Pre-distortion method for intra-channel nonlinearity compensation with phase-rotated perturbation term’, Proc. Conf. Opt. Fiber Commun., OTh3C.2 (2012). [CrossRef]

15.

T. Oyama, H. Nakashima, T. Hoshida, Z. Tao, C. Ohshima, and J. C. Rasmussen, “Efficient transmitter-side nonlinear equalizer for 16QAM,” Proc. Eur. Conf. Opt. Commun., We.3.C.1 (2013).

16.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(4), 392–394 (2000). [CrossRef]

17.

I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008). [CrossRef]

18.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communications Receivers (Wiley-Interscience, 1997), section 5.4.

19.

M. Selmi, Y. Jaouën, and P. Cibalt, “Accurate digital frequency offset estimator for coherent polmux QAM transmission systems,” Proc. Eur. Conf. Opt. Commun., P3.08 (2009).

20.

J. H. Ke, K. P. Zhong, Y. Gao, J. C. Cartledge, A. S. Karar, and M. A. Rezania, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation for dual-polarization 16-QAM coherent optical fiber communications,” J. Lightwave Technol. 30(24), 3987–3992 (2012). [CrossRef]

21.

I. Fatadin, D. Ives, and S. J. Savory, “Blind equalization and carrier phase recovery in a 16-QAM optical coherent system,” J. Lightwave Technol. 27(15), 3042–3049 (2009). [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Subsystems for Optical Networks and Datacomms

History
Original Manuscript: November 7, 2013
Revised Manuscript: December 23, 2013
Manuscript Accepted: December 23, 2013
Published: January 13, 2014

Virtual Issues
European Conference and Exhibition on Optical Communication (2013) Optics Express

Citation
Ying Gao, John C. Cartledge, Abdullah S. Karar, Scott S.-H. Yam, Maurice O’Sullivan, Charles Laperle, Andrzej Borowiec, and Kim Roberts, "Reducing the complexity of perturbation based nonlinearity pre-compensation using symmetric EDC and pulse shaping," Opt. Express 22, 1209-1219 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1209


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Mecozzi, R.-J. Essiambre, “Nonlinear Shannon limit in pseudolinear coherent systems,” J. Lightwave Technol. 30(12), 2011–2024 (2012). [CrossRef]
  2. D. Rafique, A. D. Ellis, “Nonlinearity compensation in multi-rate 28 Gbaud WDM systems employing optical and digital techniques under diverse link configurations,” Opt. Express 19(18), 16919–16926 (2011). [CrossRef] [PubMed]
  3. L. Zhu, G. Li, “Nonlinearity compensation using dispersion-folded digital backward propagation,” Opt. Express 20(13), 14362–14370 (2012). [CrossRef] [PubMed]
  4. Y. Gao, J. C. Cartledge, J. D. Downie, J. E. Hurley, D. Pikula, S. S.-H. Yam, “Nonlinearity compensation of 224 Gb/s dual-polarization 16-QAM Transmission over 2700 km,” IEEE Photon. Technol. Lett. 25(1), 14–17 (2013). [CrossRef]
  5. E. Ip, J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]
  6. L. B. Du, 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]
  7. Y. Gao, J. H. Ke, K. P. Zhong, J. C. Cartledge, S. S.-H. Yam, “Assessment of intrachannel nonlinear compensation for 112 Gb/s dual-polarization 16QAM systems,” J. Lightwave Technol. 30(24), 3902–3910 (2012). [CrossRef]
  8. Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, J. C. Rasmussen, “Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate,” J. Lightwave Technol. 29(17), 2570–2576 (2011). [CrossRef]
  9. Y. Gao, J. C. Cartledge, A. S. Karar, and S. S.-H. Yam, “Reducing the complexity of nonlinearity pre-compensation using symmetric EDC and pulse shaping,” Proc. Eur. Conf. Opt. Commun., PD3.E.5 (2013). [CrossRef]
  10. X. Liu, S. Chandrasekhar, P. J. Winzer, R. W. Tkach, and A. R. Chraplyvy, “406.6-Gb/s PDM-BPSK superchannel transmission over 12,800-km TWRS fiber via nonlinear noise squeezing,” Proc. Conf. Opt. Fiber Commun., PDP5B.10 (2013). [CrossRef]
  11. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]
  12. H. Lu, Y. Mori, C. Han, and K. Kikuchi, “Novel polarization-diversity scheme based on mutual phase conjugation for fiber-nonlinearity mitigation in ultra-long coherent optical transmission systems,” Proc. Eur. Conf. Opt. Commun., We.3.C.3 (2013).
  13. Y. Fan, L. Dou, Z. Tao, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Modulation format dependent phase noise caused by intra-channel nonlinearity,”, ” Proc. Eur. Conf. Opt. Commun., We.2.C.3. (2012). [CrossRef]
  14. L. Dou, Z. Tao, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, ‘Pre-distortion method for intra-channel nonlinearity compensation with phase-rotated perturbation term’, Proc. Conf. Opt. Fiber Commun., OTh3C.2 (2012). [CrossRef]
  15. T. Oyama, H. Nakashima, T. Hoshida, Z. Tao, C. Ohshima, and J. C. Rasmussen, “Efficient transmitter-side nonlinear equalizer for 16QAM,” Proc. Eur. Conf. Opt. Commun., We.3.C.1 (2013).
  16. A. Mecozzi, C. B. Clausen, M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photon. Technol. Lett. 12(4), 392–394 (2000). [CrossRef]
  17. I. Fatadin, S. J. Savory, D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008). [CrossRef]
  18. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communications Receivers (Wiley-Interscience, 1997), section 5.4.
  19. M. Selmi, Y. Jaouën, P. Cibalt, “Accurate digital frequency offset estimator for coherent polmux QAM transmission systems,” Proc. Eur. Conf. Opt. Commun., P3.08 (2009).
  20. J. H. Ke, K. P. Zhong, Y. Gao, J. C. Cartledge, A. S. Karar, M. A. Rezania, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation for dual-polarization 16-QAM coherent optical fiber communications,” J. Lightwave Technol. 30(24), 3987–3992 (2012). [CrossRef]
  21. I. Fatadin, D. Ives, S. J. Savory, “Blind equalization and carrier phase recovery in a 16-QAM optical coherent system,” J. Lightwave Technol. 27(15), 3042–3049 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited