## Power pre-emphasis for suppression of FWM in coherent optical OFDM transmission |

Optics Express, Vol. 22, Issue 6, pp. 7238-7248 (2014)

http://dx.doi.org/10.1364/OE.22.007238

Acrobat PDF (1161 KB)

### Abstract

Four-wave-mixing (FWM) due to the fiber nonlinearity is a major limiting factor in coherent optical OFDM transmission. We propose to apply power pre-emphasis, i.e. to allocate the transmitted power non-uniformly among subcarriers in order to suppress the FWM impairment. The proposed technique was numerically investigated for both single channel 15.6 Gbs CO-OFDM transmissions and 7-channel WDM transmissions, showing that up to 1 dB improvement in the system’s Q-factor can be achieved without considering sophisticated power loading algorithms developed for wireless communications.

© 2014 Optical Society of America

## 1. Introduction

1. A. Leke and J. M. Cioffi, “A maximum rate loading algorithm for discrete multitone modulation systems,” in *Global Telecommunications Conference**,**GLOBECOM '97., IEEE* (1997), pp. 1514–1518 vol.3. [CrossRef]

15. E. Ciaramella, L. Giorgi, A. D’Errico, F. Cavaliere, G. Gaimari, and G. Prati, “A highly effective technique for setting the power preemphasis in WDM optical systems,” J. Lightwave Technol. **24**(1), 342–356 (2006). [CrossRef]

1. A. Leke and J. M. Cioffi, “A maximum rate loading algorithm for discrete multitone modulation systems,” in *Global Telecommunications Conference**,**GLOBECOM '97., IEEE* (1997), pp. 1514–1518 vol.3. [CrossRef]

4. A. Lozano, A. M. Tulino, and S. Verdu, “Optimum power allocation for parallel Gaussian channels with arbitrary input distributions,” IEEE Trans. Inf. Theory **52**(7), 3033–3051 (2006). [CrossRef]

5. G. Miao, N. Himayat, and G. Li, “Energy-efficient link adaptation in frequency-selective channels,” IEEE Trans. Commun. **58**(2), 545–554 (2010). [CrossRef]

9. A. R. Chraplyvy, J. A. Nagel, and R. W. Tkach, “Equalization in amplified WDM lightwave transmission systems,” Photonics Technol. Lett. **4**(8), 920–922 (1992). [CrossRef]

15. E. Ciaramella, L. Giorgi, A. D’Errico, F. Cavaliere, G. Gaimari, and G. Prati, “A highly effective technique for setting the power preemphasis in WDM optical systems,” J. Lightwave Technol. **24**(1), 342–356 (2006). [CrossRef]

2. R. S. Prabhu and B. Daneshrad, “An Energy-Efficient Water-Filling Algorithm for OFDM Systems,” in *Communications (ICC),**IEEE International Conference on* (2010), pp. 1–5. [CrossRef]

4. A. Lozano, A. M. Tulino, and S. Verdu, “Optimum power allocation for parallel Gaussian channels with arbitrary input distributions,” IEEE Trans. Inf. Theory **52**(7), 3033–3051 (2006). [CrossRef]

2. R. S. Prabhu and B. Daneshrad, “An Energy-Efficient Water-Filling Algorithm for OFDM Systems,” in *Communications (ICC),**IEEE International Conference on* (2010), pp. 1–5. [CrossRef]

5. G. Miao, N. Himayat, and G. Li, “Energy-efficient link adaptation in frequency-selective channels,” IEEE Trans. Commun. **58**(2), 545–554 (2010). [CrossRef]

9. A. R. Chraplyvy, J. A. Nagel, and R. W. Tkach, “Equalization in amplified WDM lightwave transmission systems,” Photonics Technol. Lett. **4**(8), 920–922 (1992). [CrossRef]

11. P. Yan and L. Pavel, “OSNR optimization in optical networks: extension for capacity constraints,” in *American Control Conference*, *Proceedings of the* (2005), pp. 2379–2384 vol. 4. [CrossRef]

15. E. Ciaramella, L. Giorgi, A. D’Errico, F. Cavaliere, G. Gaimari, and G. Prati, “A highly effective technique for setting the power preemphasis in WDM optical systems,” J. Lightwave Technol. **24**(1), 342–356 (2006). [CrossRef]

**24**(1), 342–356 (2006). [CrossRef]

9. A. R. Chraplyvy, J. A. Nagel, and R. W. Tkach, “Equalization in amplified WDM lightwave transmission systems,” Photonics Technol. Lett. **4**(8), 920–922 (1992). [CrossRef]

**4**(8), 920–922 (1992). [CrossRef]

**4**(8), 920–922 (1992). [CrossRef]

16. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. **42**(10), 587–589 (2006). [CrossRef]

17. A. J. Lowery, D. Liang, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Communication Conference, 2006 and the 2006 National Fiber Optic Engineers Conference. OFC 2006 (2006), pp. 1–3. [CrossRef]

18. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express **16**(2), 841–859 (2008). [CrossRef] [PubMed]

19. K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. **17**(11), 801–803 (1992). [CrossRef] [PubMed]

21. A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express **15**(20), 13282–13287 (2007). [CrossRef] [PubMed]

20. B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the Effect of FWM in Coherent Optical OFDM Systems,” in *Optical Fiber Communication/National Fiber Optic Engineers Conference, OFC/NFOEC 2008. Conference on* (2008), pp. 1–3. [CrossRef]

22. V. Pechenkin and I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. **29**(11), 1678–1691 (2011). [CrossRef]

1. A. Leke and J. M. Cioffi, “A maximum rate loading algorithm for discrete multitone modulation systems,” in *Global Telecommunications Conference**,**GLOBECOM '97., IEEE* (1997), pp. 1514–1518 vol.3. [CrossRef]

**24**(1), 342–356 (2006). [CrossRef]

23. F. Wäckerle, S. Stern, and R. Fischer, “Iterative bit and power loading for coherent optical OFDM to account for fiber nonlinearities,” in *Optical Communication (ECOC 2013), 39th European Conference and Exhibition on* (2013), pp. 1–3. [CrossRef]

## 2. Impact of FWM on CO-OFDM transmission

*f*) after N

_{g}= f_{i}+ f_{j}-f_{k}_{A}fiber spans can be calculated as [19

19. K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. **17**(11), 801–803 (1992). [CrossRef] [PubMed]

*D*for non-degenerate and

_{deg}= 6*D*for degenerate FWM products,

_{deg}= 3*L*–

_{eff}= (1*e*is the nonlinear effective length (

^{-αL})/α*P*) are the powers of subcarriers,

_{i}, P_{j}, P_{k}*η*is the FWM coefficient which strongly depends on the relative frequency spacing between the FWM components given by

*η = η*.

_{1}η_{2}*η*is responsible for intra-span FWM coefficient and

_{1}*η*is responsible for inter-span nonlinear interference. The expressions for

_{2}*η*and

_{1}*η*are given in [19

_{2}19. K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. **17**(11), 801–803 (1992). [CrossRef] [PubMed]

*η*and

_{1}*η*are independent of the OFDM subcarriers’ power.

_{2}*P*= constant, the power of this FWM product is strongest when the total power is distributed equally among these three subcarriers (

_{i}+ P_{j}+ P_{k}*P*=

_{i}= P_{j}= P_{k}*P/3*). As a result, equally allocating power among subcarriers, in fact, is not an optimum option in terms of mitigating the FWM impairments.

20. B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the Effect of FWM in Coherent Optical OFDM Systems,” in *Optical Fiber Communication/National Fiber Optic Engineers Conference, OFC/NFOEC 2008. Conference on* (2008), pp. 1–3. [CrossRef]

*N*is the number of OFDM subcarriers,

*i = 1…N*is the subcarrier index.

*f*) we can accordingly find 3 FWM products, which are created with the contribution of this g’th subcarrier, namely (

_{g}= f_{i}+ f_{j}-f_{k}*f*), (

_{j}= f_{g}+ f_{k}-f_{i}*f*) and (

_{i}= f_{g}+ f_{k}-f_{j}*f*). Similary, for every degenerate FWM product falling on the g’th subcarrrier we can accordingly find 2 FWM products, which are created with the contribution of this subcarrier. Based on these arguments and taking into account the fact that the number of non-degenerate FWM products is much bigger than the number of degenerate FWM product [20

_{k}= f_{i}+ f_{j}-f_{g}20. B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the Effect of FWM in Coherent Optical OFDM Systems,” in *Optical Fiber Communication/National Fiber Optic Engineers Conference, OFC/NFOEC 2008. Conference on* (2008), pp. 1–3. [CrossRef]

*S(g,N)*on the subcarrier index is shown in the case of an OFDM system with 128 subcarriers. The result was obtained using both simulation with a MATLAB program and Eq. (3). In the simulation, we calculated the exact number of possible combinations of 3 subcarriers (

*f*), the interaction among which creates FWM products (

_{i}, f_{j}, f_{k}*f*) falling into the OFDM band. It can be seen in Fig. 1(a) that almost no mismatch between the analytical and numerical results is observed, which verifies that Eq. (3) provides very high accuracy, especially when the number of OFDM subcarriers is large. In the case considered with 128 subcarriers, the 68th subcarrier plays a role in around 18000 FWM combinations while the 1st and the 128th subcarriers have contribution to only approximately 12000 FWM combinations.

_{g}= f_{i}+ f_{j}-f_{k}## 3. System description and analysis

*A(k)*, and then the power distribution among subcarriers can be easily obtained by

*P(k) = A(k)*.

^{2}*A(k)*which has a “Super Gaussian hole” in the centre:where (

*a, b, x*) are the three parameters of the distribution function, which are required to be optimized in order to achieve the best performance. The distribution (4) is chosen for analysis because of its simplicity and possibility to use 3 free parameters to change the depth, width and roll-off of the power distribution curve in order to optimise the system’s performance.

*a, b, x*) the transmitted power can be allocated among subcarriers in various ways. Figure 2 shows some options of allocating power among subcarriers using the distribution function (4) for the case of 100 subcarriers (

*a = 0*) or (

*b = 0*) [Fig. 2(a)].

## 4. Single channel transmissions and optimization

^{0.5}. The fiber nonlinearity coefficient and dispersion are 1.22 W

^{−1}km

^{−1}and 16 ps/nm/km respectively. The fiber span loss is compensated by Erbium-doped optical amplifiers (EDFA) with 16 dB of gain and a noise figure of 6 dB. In the simulation the ASE noise is added inline after each fiber span. The transmitter and receiver lasers have the same linewidth of 100 kHz. The laser phase noise is modeled as a Wiener-Levy process with a variance

*σ*where

^{2}= 2πυt*υ*is the combined laser linewidth and

*t*is the time difference between two samples. The simulated time window contains 6000 OFDM symbols. The channel estimation and equalization is performed with the assistance of an initial training sequence using the zero forcing estimation method. The common phase error due to laser phase noises is estimated and compensated using a pilot-aided technique by inserting 8 pilot subcarriers in each OFDM symbol.

24. S. T. Le, K. J. Blow, V. K. Menzentsev, and S. K. Turitsyn, “Comparison of numerical bit error rate estimation methods in 112Gbs QPSK CO-OFDM transmission,” in *Optical Communication (ECOC 2013), 39th European Conference and Exhibition on* (2013), pp. 1–3. [CrossRef]

*a = 0.15, b = 0.002, x = 2*) are 0.91 dB and 1.56 dB when

*P =*–

*7 dBm*and

*P =*–

*4 dBm*respectively. For the second and the third power distributions shown in Fig. 2 the mean Q-factor improvements when

*P =*–

*4 dBm*are 0.63 dB and 0.62 dB respectively.

*x>2*) distributions does not improve the system’s performance in comparison with the second order (

*x = 2*) distribution. Therefore, we further consider only the second order case and present the optimization results for the two remaining parameters (

*a, b*).

*a, b*) for three values of the launch powers representing three transmission regimes, namely

*P =*–

*9 dBm*for the ASE noise limited regime [Fig. 6],

*P =*–

*7 dBm*for the optimum launch power point [Fig. 7] and

*P =*–

*4 dBm*for the nonlinear limited regime [Fig. 8]. One should notice that the conventional method of equally allocating power among subcarriers can be obtained by setting

*a = 0*or

*b = 0*. Therefore, in Figs. 6–8

*a = 0*or

*b = 0*can be considered as the reference points showing which values of

*P =*–

*9dBm*). When

*a<0.15*the system’s performance is almost independent of

*b*. However, when

*a>0.15*, the system performance starts to getting worse. This is because the SNR of the centre subcarriers decreases substantially due to the low power allocated in the middle of the OFDM band.

*P =*–

*7dBm*) the chosen power distribution function can improve the system’s performance in a wide range of (

*a, b*). In this case FWM noise due to the fiber nonlinearity is also an important limiting factor as well as ASE noise introduced by optical amplifiers. Therefore, the system’s performance will improve if the FWM noise is suppressed. The optimum values of (

*a, b*) are found to be (

*a = 0.15, b = 0.002*), which offer around 1dB advantage in the received signal quality. A larger improvement (around 1.6 dB) can be obtained in the nonlinear limited regime

*P =*–

*4dBm*as shown in Fig. 8. In this case, the dominant limiting factor is FWM noise. By applying the power distribution function with (

*a = 0.15, b = 0.002*) the system’s Q-factor can be improved to 12.2 dB in comparison with 10.6 dB for the conventional equal power distribution. This indicates that the modified power distribution is effective in mitigating the impact of FWM noise on the transmission performance. However, there is a trade-off in applying this technique. The power of FWM noise can be significantly reduced by using a large value of

*a*, however, in this case the transmitted power of the centre subcarriers becomes too small, thus increasing the number of errors falling on these subcarriers due to its low SNR. The optimum value of

*a*is found to be

*a = 0.15*, according to a power suppression ratio of 0.72 for the centre subcarrier.

*P(g) = S*, where

_{0}/S(g,N)*S*is a constant. If this power allocation method is applied the power suppression ratio of the centre subcarrier will be around 0.66 (when the number of subcarriers is large). However, in the presence of ASE noise (6 dB of noise figure) the optimum power suppression for the centre subcarrier in the investigated system was found to be 0.72, slightly higher than the value when ASE noise is not considered. This result indicates that for a particular application the optimum power allocation method should be defined flexibly in order to balance the impact of FWM and ASE noise.

_{0}## 5. WDM transmissions and discussions

## 6. Conclusion

25. A. Shafarenko, K. S. Turitsyn, and S. K. Turitsyn, “Information-theory analysis of skewed coding for suppression of pattern-dependent errors in digital communications,” IEEE Trans. Commun. **55**(2), 237–241 (2007). [CrossRef]

26. A. Shafarenko, A. Skidin, and S. K. Turitsyn, “Weakly-constrained codes for suppression of patterning effects in digital communications,” IEEE Trans. Commun. **58**(10), 2845–2854 (2010). [CrossRef]

## Acknowledgment

## References and links

1. | A. Leke and J. M. Cioffi, “A maximum rate loading algorithm for discrete multitone modulation systems,” in |

2. | R. S. Prabhu and B. Daneshrad, “An Energy-Efficient Water-Filling Algorithm for OFDM Systems,” in |

3. | R. F. H. Fischer and J. B. Huber, “A new loading algorithm for discrete multitone transmission,” in |

4. | A. Lozano, A. M. Tulino, and S. Verdu, “Optimum power allocation for parallel Gaussian channels with arbitrary input distributions,” IEEE Trans. Inf. Theory |

5. | G. Miao, N. Himayat, and G. Li, “Energy-efficient link adaptation in frequency-selective channels,” IEEE Trans. Commun. |

6. | S. Cui, A. J. Goldsmith, and A. Bahai, “Energy-constrained modulation optimization,” Wireless IEEE Trans. Commun. |

7. | F. Meshkati, H. V. Poor, S. C. Schwartz, and N. B. Mandayam, “An energy-efficient approach to power control and receiver design in wireless data networks,” IEEE Trans. Commun. |

8. | M. Guowang, N. Himayat, L. Ye, and D. Bormann, “Energy efficient design in wireless OFDMA,” in |

9. | A. R. Chraplyvy, J. A. Nagel, and R. W. Tkach, “Equalization in amplified WDM lightwave transmission systems,” Photonics Technol. Lett. |

10. | A. R. Chraplyvy, R. W. Tkach, K. C. Reichmann, P. D. Magill, and J. A. Nagel, “End-to-end equalization experiments in amplified WDM lightwave systems,” Photonics Technol. Lett. |

11. | P. Yan and L. Pavel, “OSNR optimization in optical networks: extension for capacity constraints,” in |

12. | O. K. Tonguz and F. A. Flood, “EDFA-based DWDM lightwave transmission systems with end-to-end power and SNR equalization,” IEEE Trans. Commun. |

13. | O. K. Tonguz and F. A. Flood, “Gain equalization of EDFA cascades,” J. Lightwave Technol. |

14. | A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, and T. Li, “High-capacity optical transmission systems,” J. Lightwave Technol. |

15. | E. Ciaramella, L. Giorgi, A. D’Errico, F. Cavaliere, G. Gaimari, and G. Prati, “A highly effective technique for setting the power preemphasis in WDM optical systems,” J. Lightwave Technol. |

16. | W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. |

17. | A. J. Lowery, D. Liang, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Communication Conference, 2006 and the 2006 National Fiber Optic Engineers Conference. OFC 2006 (2006), pp. 1–3. [CrossRef] |

18. | W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express |

19. | K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. |

20. | B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the Effect of FWM in Coherent Optical OFDM Systems,” in |

21. | A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express |

22. | V. Pechenkin and I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. |

23. | F. Wäckerle, S. Stern, and R. Fischer, “Iterative bit and power loading for coherent optical OFDM to account for fiber nonlinearities,” in |

24. | S. T. Le, K. J. Blow, V. K. Menzentsev, and S. K. Turitsyn, “Comparison of numerical bit error rate estimation methods in 112Gbs QPSK CO-OFDM transmission,” in |

25. | A. Shafarenko, K. S. Turitsyn, and S. K. Turitsyn, “Information-theory analysis of skewed coding for suppression of pattern-dependent errors in digital communications,” IEEE Trans. Commun. |

26. | A. Shafarenko, A. Skidin, and S. K. Turitsyn, “Weakly-constrained codes for suppression of patterning effects in digital communications,” IEEE Trans. Commun. |

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

**ToC Category:**

Optical Communications

**History**

Original Manuscript: January 30, 2014

Revised Manuscript: March 13, 2014

Manuscript Accepted: March 14, 2014

Published: March 20, 2014

**Citation**

Son Thai Le, Keith Blow, and Sergei Turitsyn, "Power pre-emphasis for suppression of FWM in coherent optical OFDM transmission," Opt. Express **22**, 7238-7248 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-7238

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### References

- A. Leke and J. M. Cioffi, “A maximum rate loading algorithm for discrete multitone modulation systems,” in Global Telecommunications Conference,GLOBECOM '97., IEEE (1997), pp. 1514–1518 vol.3. [CrossRef]
- R. S. Prabhu and B. Daneshrad, “An Energy-Efficient Water-Filling Algorithm for OFDM Systems,” in Communications (ICC),IEEE International Conference on (2010), pp. 1–5. [CrossRef]
- R. F. H. Fischer and J. B. Huber, “A new loading algorithm for discrete multitone transmission,” in Global Telecommunications Conference,GLOBECOM '96. 'Communications: The Key to Global Prosperity (1996), pp. 724–728 vol.1. [CrossRef]
- A. Lozano, A. M. Tulino, S. Verdu, “Optimum power allocation for parallel Gaussian channels with arbitrary input distributions,” IEEE Trans. Inf. Theory 52(7), 3033–3051 (2006). [CrossRef]
- G. Miao, N. Himayat, G. Li, “Energy-efficient link adaptation in frequency-selective channels,” IEEE Trans. Commun. 58(2), 545–554 (2010). [CrossRef]
- S. Cui, A. J. Goldsmith, A. Bahai, “Energy-constrained modulation optimization,” Wireless IEEE Trans. Commun. 4(5), 2349–2360 (2005). [CrossRef]
- F. Meshkati, H. V. Poor, S. C. Schwartz, N. B. Mandayam, “An energy-efficient approach to power control and receiver design in wireless data networks,” IEEE Trans. Commun. 53(11), 1885–1894 (2005). [CrossRef]
- M. Guowang, N. Himayat, L. Ye, and D. Bormann, “Energy efficient design in wireless OFDMA,” in Communications,ICC '08. IEEE International Conference on (2008), pp. 3307–3312.
- A. R. Chraplyvy, J. A. Nagel, R. W. Tkach, “Equalization in amplified WDM lightwave transmission systems,” Photonics Technol. Lett. 4(8), 920–922 (1992). [CrossRef]
- A. R. Chraplyvy, R. W. Tkach, K. C. Reichmann, P. D. Magill, J. A. Nagel, “End-to-end equalization experiments in amplified WDM lightwave systems,” Photonics Technol. Lett. 5(4), 428–429 (1993). [CrossRef]
- P. Yan and L. Pavel, “OSNR optimization in optical networks: extension for capacity constraints,” in American Control Conference, Proceedings of the (2005), pp. 2379–2384 vol. 4. [CrossRef]
- O. K. Tonguz, F. A. Flood, “EDFA-based DWDM lightwave transmission systems with end-to-end power and SNR equalization,” IEEE Trans. Commun. 50(8), 1282–1292 (2002). [CrossRef]
- O. K. Tonguz, F. A. Flood, “Gain equalization of EDFA cascades,” J. Lightwave Technol. 15(10), 1832–1841 (1997). [CrossRef]
- A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, T. Li, “High-capacity optical transmission systems,” J. Lightwave Technol. 26(9), 1032–1045 (2008). [CrossRef]
- E. Ciaramella, L. Giorgi, A. D’Errico, F. Cavaliere, G. Gaimari, G. Prati, “A highly effective technique for setting the power preemphasis in WDM optical systems,” J. Lightwave Technol. 24(1), 342–356 (2006). [CrossRef]
- W. Shieh, C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006). [CrossRef]
- A. J. Lowery, D. Liang, J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Communication Conference, 2006 and the 2006 National Fiber Optic Engineers Conference. OFC 2006 (2006), pp. 1–3. [CrossRef]
- W. Shieh, H. Bao, Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef] [PubMed]
- K. Inoue, “Phase-mismatching characteristic of four-wave mixing in fiber lines with multistage optical amplifiers,” Opt. Lett. 17(11), 801–803 (1992). [CrossRef] [PubMed]
- B. Goebel, B. Fesl, L. D. Coelho, and N. Hanik, “On the Effect of FWM in Coherent Optical OFDM Systems,” in Optical Fiber Communication/National Fiber Optic Engineers Conference, OFC/NFOEC 2008. Conference on (2008), pp. 1–3. [CrossRef]
- A. J. Lowery, S. Wang, M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express 15(20), 13282–13287 (2007). [CrossRef] [PubMed]
- V. Pechenkin, I. J. Fair, “On four-wave mixing suppression in dispersion-managed fiber-optic OFDM systems with an optical phase conjugation module,” J. Lightwave Technol. 29(11), 1678–1691 (2011). [CrossRef]
- F. Wäckerle, S. Stern, and R. Fischer, “Iterative bit and power loading for coherent optical OFDM to account for fiber nonlinearities,” in Optical Communication (ECOC 2013), 39th European Conference and Exhibition on (2013), pp. 1–3. [CrossRef]
- S. T. Le, K. J. Blow, V. K. Menzentsev, and S. K. Turitsyn, “Comparison of numerical bit error rate estimation methods in 112Gbs QPSK CO-OFDM transmission,” in Optical Communication (ECOC 2013), 39th European Conference and Exhibition on (2013), pp. 1–3. [CrossRef]
- A. Shafarenko, K. S. Turitsyn, S. K. Turitsyn, “Information-theory analysis of skewed coding for suppression of pattern-dependent errors in digital communications,” IEEE Trans. Commun. 55(2), 237–241 (2007). [CrossRef]
- A. Shafarenko, A. Skidin, S. K. Turitsyn, “Weakly-constrained codes for suppression of patterning effects in digital communications,” IEEE Trans. Commun. 58(10), 2845–2854 (2010). [CrossRef]

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