## Electronic Post-compensation for Nonlinear Phase Fluctuations in a 1000-km 20-Gbit/s Optical Quadrature Phase-shift Keying Transmission System Using the Digital Coherent Receiver

Optics Express, Vol. 16, Issue 2, pp. 889-896 (2008)

http://dx.doi.org/10.1364/OE.16.000889

Acrobat PDF (531 KB)

### Abstract

We demonstrate electronic post-compensation for nonlinear phase fluctuation in a 1000-km 20-Gbit/s optical quadrature phase-shift keying (QPSK) transmission system, where group-velocity dispersion is well managed. The inter-symbol interference (ISI) at the transmitter induces the nonlinear phase fluctuation through self-phase modulation (SPM) of the signal transmitted through a fiber. However, when the optimized phase shift proportional to the intensity fluctuation is given to the complex amplitude of the signal electric field by using a digital coherent receiver, the nonlinear phase fluctuation can be reduced effectively.

© 2008 Optical Society of America

## 1. Introduction

9. D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phaseshift keying signals with carrier phase estimation,” J. Lightwave Technol. **24**, 12–21 (2006). [CrossRef]

## 2. Compensation for nonlinear phase fluctuation due to inter-symbol interference

*z*direction is generally described by the nonlinear Schrödinger equation [10] as

*A*(

*z*,

*T*) represents the complex amplitude of the signal electric field on exp(

*jω*), where

_{c}T*ω*is the angular frequency of the carrier,

_{c}*α*the loss coefficient,

_{p}*β*the group-velocity dispersion (GVD) parameter, and

_{2}*γ*the nonlinearity coefficient. The time

*T*in the moving frame is defined as

*T*=

*t*-

*z*/ν

*, where ν*

_{g}*is the group velocity. At the receiving end, the digital coherent receiver can measure*

_{g}*A*(

*L*,

*T*), where

*L*denotes the transmission distance. The measured complex amplitude will be distorted due to fiber dispersion and nonlinearity.

*α*is reversed. The back-propagating signal is the phase-conjugated replica of the forward-propagating signal at every point along the fiber. This fact means that if we virtually let the measured output complex amplitude

_{p}*A*(

*L*,

*T*) propagate backwardly through the fiber where the sign of

*α*is reversed, we can compensate for dispersive and nonlinear effects and restore the input complex amplitude

_{p}*A*(0,

*T*) by numerical calculations at the receiver. This principle of operation is the same as that of the midway optical phase conjugation (OPC) scheme [11

11. C. Lorattanasane and K. Kikuchi, “Design theory of long-distance optical transmission systems using midway optical phase conjugation,” IEEE J. Lightwave Technol. **15**, 948–955 (1997). [CrossRef]

*m*is the number of spans and (

*γ*ℓ)

*the effective phase rotation in a span length ℓ defined as*

_{eff}*t*instead of

*T*at the receiver, ignoring the delay time

*L*/ν

_{g}, and we assume that an EDFA in front of the receiver restores the received power to the power launched on each span.

*z*=0) using a MZM. Equation (3) means that the initial ISI generates the nonlinear phase shift while traveling through the link, but that such nonlinear phase shift is cancelled at

*z*=

*L*by knowing the output power fluctuation. Therefore, Eq.(3) is valid as far as the intensity waveform is almost maintained along the link. However, this condition is not always satisfied because the local GVD generates ISI along the path, which in turn interacts with fiber nonlinearity. In such a case, the correlation between the intensity and phase fluctuations is not necessarily perfect, and Eq.(3) should be modified as

*α*shows the correlation degree ranging from 0 to 1, which is dependent on the dispersion map of the link. In the experiment shown in Sec.5,

*α*is used as an adjustable parameter, and the optimized value is confirmed by extensive computer simulations.

## 3. Compensation for nonlinear phase noise

3. T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, “A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise,” J. Lightwave Technol. **21**, 1933–1943 (2003). [CrossRef]

*m*-span configuration, the intensity fluctuation

*δI*(

*t*) at the receiver is the sum of all amplifiers’ contributions as

*A*

_{0}denotes the constant envelope and

*a*(

_{k}*t*) the in-phase ASE noise from the

*k*-th amplifier counting backwards from the receiver. The amount of the intensity noise is given as its variance as

*α*is an adjustable parameter. The variance of the compensated phase noise results in

*α*=1/2 when

*m*≫1 as

6. C. Xu and X. Liu, “Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. **27**, 1619–1621 (2002). [CrossRef]

*α*at 1/2.

## 4. Digital coherent receiver

9. D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phaseshift keying signals with carrier phase estimation,” J. Lightwave Technol. **24**, 12–21 (2006). [CrossRef]

*λ*/4 waveplate and the polarization beam splitter (PBS) creates the 90° optical hybrid necessary for phase diversity. The polarization of the local oscillator (LO) is aligned such that it becomes circular after passing through the

*λ*/4 waveplate. On the other hand, the signal is linearly polarized, and the polarization angle is 45° with respect to principle axes of PBS’s. The receiver is composed of free-space optical components packaged in a small metal case. All the input and output ports are fiber-pigtailed.

*A*(

*t*)∝

*A*

_{0}exp[

*j*(

*θ*(

_{s}*t*)+

*θ*(

_{n}*t*))], where

*A*

_{0}denotes the signal amplitude,

*θ*the

_{s}*M*-ary phase modulation(=2

*πm*/

*M*,

*m*=-

*M*/2+1,⋯,0,⋯,

*M*/2), and

*θ*the phase noise from both of the signal and LO. Balanced photodiodes PD1 and PD2 measure the real and imaginary parts of

_{n}*A*(

*t*), respectively. Next, analog-to-digital converters sample outputs from PD1 and PD2 simultaneously at a sample rate larger than 2/

*T*, where

*T*represents the symbol interval. The data are resampled to keep one sample/symbol according to the extracted clock. Thus, we have the digitized complex amplitude

*A*(

*iT*), where

*i*denotes the sample number.

*M*symbols are differentially precoded at the transmitter. To retrieve the phase modulation

*θ*(

_{s}*iT*), we must evaluate the carrier phase

*θ*(

_{n}*iT*). The procedure to estimate

*θ*(

_{n}*iT*) is shown in Fig.2. We take the

*M*-th power of

*A*(

*iT*), because the phase modulation is removed from

*A*(

*iT*)

*. Averaging*

^{M}*A*(

*iT*)

*over (2*

^{M}*k*+1) samples from

*t*=(-

*k*+

*i*)

*T*to (

*k*+1)

*T*constitutes a phase estimate at

*t*=

*iT*as

*θ*(

_{e}*iT*)=arg[∑

^{k}_{j=-k}

*A*(

*jT*)

*]/*

^{M}*M*. The phase modulation is first determined by subtracting the phase estimate from the measured phase of each symbol. The phase modulation is then discriminated among

*M*symbols. The restored symbols are finally differentially decoded.

## 5. Experimental setup for QPSK transmission system

_{3}IQ MZM [13

13. S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO_{3} integrated modulator consisting of four-phase modulator waveguides,” IEEE Photon. Technol. Lett. **13**, 364–366 (2001). [CrossRef]

^{7}-1 pseudo-random binary sequence (PRBS). 10-Gsymbol/s electrical signals were band-limited by 7.5-GHz electrical filters. A pulse carver converted the signal to the return-to-zero (RZ) format with a 50 % duty ratio. The 3-dB spectral width of the distributed feedback (DFB) semiconductor laser used as the transmitter was 150 kHz. The RZ QPSK signal was then transmitted through a 1074-km link in a 26 span configuration. Each span consisted of a 28-km-long large-core SMF and a 12-km-long inverse dispersion fiber (IDF). The GVD value, loss coefficient, and nonlinear coefficient of the SMF were 21 ps/nm/km, 0.2 dB/km, and 0.8/W/km, respectively. Those of the IDF were -50 ps/nm/km, 0.3 dB/km, and 3.0/W/km, respectively. A 0.98-µm forward-pumped erbium-doped fiber amplifier (EDFA) compensated for the span loss of 11dB including the splice loss of 1.8 dB. In the final span, a 74-km-long SMF was used for residual dispersion compensation.

*k*=10. Symbols were then discriminated among four phase states and the number of bit errors was counted.

## 6. Experimental results and discussion

*α*when the average power at the fiber input in each span is 0 dBm. The minimum BER is obtained by adjusting

*α*≃1/2.

*α*=1/2 between the received intensity fluctuation and the nonlinear phase fluctuation stems from ISI caused along the link in addition to the initial ISI.

## 7. Conclusion

## References and links

1. | C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Select. Topics Quantum Electron. |

2. | A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. |

3. | T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, “A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise,” J. Lightwave Technol. |

4. | J.P. Gordon and L.F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. |

5. | X. Liu, X Wei, R. Slusher, and C.J. McKinstrie, “Improving transmission performance in differential phase shift keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. |

6. | C. Xu and X. Liu, “Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. |

7. | K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Selected Topics on Quantum Electron. |

8. | K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol. |

9. | D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phaseshift keying signals with carrier phase estimation,” J. Lightwave Technol. |

10. | G. P. Agrawal, |

11. | C. Lorattanasane and K. Kikuchi, “Design theory of long-distance optical transmission systems using midway optical phase conjugation,” IEEE J. Lightwave Technol. |

12. | X. Wang, K. Kikuchi, and Y. Takushima, “Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion,” IEICE Trans. on Electron.E82-C, 1407–1413 (1999). |

13. | S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, “Single side-band modulation performance of a LiNbO |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

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

**ToC Category:**

Nonlinearity Compensation

**History**

Original Manuscript: August 27, 2007

Revised Manuscript: October 22, 2007

Manuscript Accepted: October 30, 2007

Published: January 9, 2008

**Virtual Issues**

Coherent Optical Communication (2008) *Optics Express*

**Citation**

Kazuro Kikuchi, "Electronic Post-compensation for Nonlinear Phase Fluctuations in a 1000-km 20-Gbit/s Optical Quadrature Phase-shift Keying Transmission System Using the Digital Coherent Receiver," Opt. Express **16**, 889-896 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-889

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### References

- C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Select. Topics Quantum Electron. 10, 281-293 (2004). [CrossRef]
- A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightwave Technol. 23,115-130 (2005). [CrossRef]
- T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, "A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise," J. Lightwave Technol. 21, 1933-1943 (2003). [CrossRef]
- J.P. Gordon and L.F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990). [CrossRef] [PubMed]
- X. Liu, X. Wei, R. Slusher, and C.J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27,1616-1618 (2002). [CrossRef]
- C. Xu and X. Liu, "Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission," Opt. Lett. 27, 1619-1621 (2002) [CrossRef]
- K. Kikuchi, "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation," IEEE J. Selected Topics on Quantum Electron. 12, 563-570 (2006). [CrossRef]
- K.-P. Ho and J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightwave Technol. 22, 779-783 (2004). [CrossRef]
- D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed. (Academic, New York, 2001).
- C. Lorattanasane and K. Kikuchi, "Design theory of long-distance optical transmission systems using midway optical phase conjugation," IEEE J. Lightwave Technol. 15, 948-955 (1997). [CrossRef]
- X. Wang, K. Kikuchi, and Y. Takushima, "Analysis of dispersion-managed optical fiber transmission system using non-return-to-zero pulse format and performance restriction from third-order dispersion," IEICE Trans. on Electron.E 82-C, 1407-1413 (1999).
- S. Shimotsu, S. Oikawa, T. Saitou, N. Mitsugi, K. Kubodera, T. Kawanishi, and M. Izutsu, "Single side-band modulation performance of a LiNbO3 integrated modulator consisting of four-phase modulator waveguides," IEEE Photon. Technol. Lett. 13, 364-366 (2001). [CrossRef]

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