## Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels |

Optics Express, Vol. 20, Issue 7, pp. 8155-8160 (2012)

http://dx.doi.org/10.1364/OE.20.008155

Acrobat PDF (1132 KB)

### Abstract

In this paper we numerically investigate nonlinear impairments in a WDM system with mixed PM (D)QPSK and OOK channels. First we analyze the dependence of XPM and XPolM on SOP and baud rate in absence of PMD. In this case we find that the nonlinear impairments are highly dependent on relative SOP between the PM (D)QPSK and neighbouring OOK channels. The dependence on relative SOP is more pronounced in differential detection than in coherent detection. However, with increasing values of PMD this dependence decreases, and non-linear tolerance improves.

© 2012 OSA

## 1. Introduction

1. J. Renaudier, O. Bertran-Pardo, G. Charlet, M. Salsi, M. Bertolini, P. Tran, H. Mardoyan, and S. Bigo, “Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks,” IEEE Photon. Technol. Lett. **21**(24), 1816–1818 (2009). [CrossRef]

2. A. Bononi, M. Bertolini, P. Serena, and G. Bellotti, “Cross-phase modulation induced by OOK channels on higher-rate DQPSK and coherent QPSK channels,” J. Lightwave Technol. **27**(18), 3974–3983 (2009). [CrossRef]

## 2. Simulation setup

*x*and

*y*polarization. Laser sources with 1 MHz linewidth at a wavelength of 1550 nm were used both in the transmitter and as local oscillator. The signal was pulse carved at 50% duty cycle by an extra MZM for generation of return-to-zero signals. The optical fiber link consisted of eight spans of 80 km standard single mode fiber (SSMF) with full inline dispersion compensation. Each span was amplified by ideal (noise free) amplifiers. The attenuation in SSMF was 0.2 dB/km, the dispersion was 17 ps/nm-km and the non-linear coefficient was 1.31 W

^{−1}km

^{−1}. For dispersion compensating fibers (DCFs) the attenuation coefficient was 0.5 dB/km, the dispersion was −85 ps/nm-km and the non-linear coefficient was 3.5 W

^{−1}km

^{−1}. Four NRZ OOK channels were driven by different (PRBS) sequences at 10 Gb/s. The separation between the central PM (D)QPSK channel and the NRZ OOK channels was 100 GHz. The NRZ OOK channels were separated by 50 GHz from each other.

^{−3}), before being demultiplexed using a Gaussian filter having a bandwidth of 70 GHz. For both coherent and differential detection, the detected signal was low pass filtered by a fourth order Bessel filter with 3-dB bandwidth equal to 70% of the baud rate. In the coherent detection case, the digital field was reconstructed using the inphase/quadrature components of each polarization (sampled at 2 samples per symbol) and digitally processed by constant modulus algorithm (CMA) based adaptive filters having 7 taps in a butterfly structure [7

7. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De, K. Man, Giok-Djan, and H. de Waardt, “Coherent equalization and PolmuxRZ- DQPSK for robust 100-G transmission,” J. Lightwave Technol. **26**, 64–72 (2008). [CrossRef]

8. A. Viterbi and A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory **29**(4), 543–551 (1983). [CrossRef]

*x*and

*y*polarization components.

## 3. Dependence of non-linear impairments on SOP and baud rate

*x*polarization of the PM (D)QPSK channel at 0°, referred to as case (a), and 45° referred to as case (b). The launched power was increased from linear to non-linear regime and the power into DCFs was 5 dB lower than into SSMFs. The resulting required OSNRs for a bit error rate (BER) of 10

^{−3}are shown in Fig. 2 . It can be observed that the back-to-back performance of coherent detection is only marginally better than differential detection (while one could expect a difference of 1 or 2 dB). This is due to the fact that in coherent detection differential coding was used to increase robustness against cycle slips at high power levels [9

9. M. Kuschnerov, S. Calabrò, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “Low complexity soft differential decoding of QPSK for forward error correction in coherent optic receivers,” in *2010 36th European Conference and Exhibition on Optical Communication (ECOC)* (IEEE, 2010), 1–3.

*x*and

*y*polarization shown in Fig. 3 . From the transmitter, the central channel has its SOP at either +45°, right hand circular (RHC), −45° or left hand circular (LHC). During transmission, the SOP of the central channel rotates around the total Stokes vector according to the Manakov model [10

10. M. Karlsson and H. Sunnerud, “Effects of nonlinearities on PMD-induced system impairments,” J. Lightwave Technol. **24**(11), 4127–4137 (2006). [CrossRef]

*x*and

*y*polarization components have equal amplitudes, but different relative phase. In case (a), it can be observed in Fig. 3 that the central channel signals rotate on that meridian (around the total Stokes vector at LHP). As a result, the

*x*and

*y*polarization components will accumulate a relative phase shift due to XPM. While the average polarization rotation can be reversed by the butterfly equalizer in coherent detection or an analog polarization controller in differential detection, a pattern-dependent spread along the magenta meridian remains (shown in Poincaré Sphere in 2nd row in Fig. 3). This spread we refer to as XPM induced phase noise and is the dominating effect in case (a). The same phenomenon can also be seen from a different viewpoint, using the constellation diagrams for the

*x*and

*y*polarization: the XPM-induced phase jitter in

*x*is higher than in

*y*polarization. The reason is that the XPM induced in

*x*polarization by NRZ OOK channels (co-polarized to

*x*polarization) is twice as large as XPM in

*y*polarization, which is orthogonal to NRZ OOK channels [10

10. M. Karlsson and H. Sunnerud, “Effects of nonlinearities on PMD-induced system impairments,” J. Lightwave Technol. **24**(11), 4127–4137 (2006). [CrossRef]

*x*and

*y*polarization components have a phase difference of 90° but different amplitudes. In case(b), it can be observed in Fig. 3, 3rd row, that the central channel signals rotate on that meridian (around the total Stokes vector at + 45°). The remaining spread along the green meridian after reversing the average polarization rotation (shown in Poincaré Sphere in 4th row in Fig. 3) leads to polarization crosstalk resulting in additional amplitude jitter. This effect is what we refer to as XPolM [11

11. E. Tipsuwannakul, M. N. Chughtai, M. Forzati, J. Mårtensson, P. Andrekson, and M. Karlsson, “Influence of self- and cross-phase modulation on 40 Gbaud dual polarization DQPSK/D8PSK signals in 10 Gbit/s OOK WDM systems,” Opt. Express **18**(23), 24178–24188 (2010). [CrossRef] [PubMed]

*x*and

*y*polarization have been impacted by XPM in equal amount, since the NRZ OOK channels are at 45° with respect to both

*x*and

*y*polarization. The signal in case(b) is therefore impacted by both XPM and XPolM.

*x*polarization of central channel to further investigate the dependence of XPM and XPolM on relative SOPs for coherent detection. Figure 4 shows the BER versus NRZ OOK SOPs at 18 dB OSNR for 10 Gbaud, at 19 dB OSNR for 28 Gbaud and at 21 dB OSNR for 56 Gbaud. From the analysis of Fig. 4(a) it is apparent that at 10 Gbaud, BER for

*x*and

*y*polarization are complimentary of each other and average BER remains fairly constant. Each polarization has maximum BER due to XPM when the NRZ OOK channel SOPs are parallel to it and minimum when SOPs are orthogonal to it. However for 28 Gbaud and 56 Gbaud the average BER as well as the BER of the individual polarizations is maximum at 45° SOP of NRZ OOK channels. This additional penalty is due to XPolM at 45° SOP (which we have discussed above).

^{−3}.

## 4. Impact of polarization mode dispersion on non-linear impairments

^{−3}for different PMD values, at a fixed launched power of 2.2 dBm, for coherent detection. Again, 400 realizations of PMD and random initial SOPs were used. It is apparent that with increasing values of PMD, performance is improved, and the variance of PDFs of required OSNRs decreases, which is in agreement with what has been observed in previous studies [13]. This can be explained by the polarization walk-off effect [14, 15

15. P. Serena, N. Rossi, O. Bertran-Pardo, J. Renaudier, A. Vannucci, and A. Bononi, “Intra- versus Inter-channel PMD in linearly compensated coherent PDM-PSK nonlinear transmissions,” J. Lightwave Technol. **29**(11), 1691–1700 (2011). [CrossRef]

^{1/2}is needed for this process to become noticeable.

## 5. Summary and conclusion

## References and links

1. | J. Renaudier, O. Bertran-Pardo, G. Charlet, M. Salsi, M. Bertolini, P. Tran, H. Mardoyan, and S. Bigo, “Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks,” IEEE Photon. Technol. Lett. |

2. | A. Bononi, M. Bertolini, P. Serena, and G. Bellotti, “Cross-phase modulation induced by OOK channels on higher-rate DQPSK and coherent QPSK channels,” J. Lightwave Technol. |

3. | O. Vassilieva, T. Hoshida, J. C. Rasmussen, and T. Naito, “Symbol rate dependency of XPM-induced phase noise penalty on QPSK-based modulation formats,” in |

4. | A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in |

5. | E. Gabory, M. Arikawa, D. Ogasahara and K. Fukuchi, “Mixed bit rate DWDM transmission of 112Gb/s PM-QPSK signals over a dispersion managed link using teal-time DSP to assess nonlinear distortions,” in ECOC 2011, paper Tu 6 B 3. |

6. | H. Louchet, A. Richter, I. Koltchanov, S. Mingaleev, N. Karelin, and K. Kuzmin, “Comparison of XPM and XpolM-induced impairments in mixed 10G – 100G transmission,” in Proc. IEEE, 2011, 1–4. |

7. | C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De, K. Man, Giok-Djan, and H. de Waardt, “Coherent equalization and PolmuxRZ- DQPSK for robust 100-G transmission,” J. Lightwave Technol. |

8. | A. Viterbi and A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory |

9. | M. Kuschnerov, S. Calabrò, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “Low complexity soft differential decoding of QPSK for forward error correction in coherent optic receivers,” in |

10. | M. Karlsson and H. Sunnerud, “Effects of nonlinearities on PMD-induced system impairments,” J. Lightwave Technol. |

11. | E. Tipsuwannakul, M. N. Chughtai, M. Forzati, J. Mårtensson, P. Andrekson, and M. Karlsson, “Influence of self- and cross-phase modulation on 40 Gbaud dual polarization DQPSK/D8PSK signals in 10 Gbit/s OOK WDM systems,” Opt. Express |

12. | M. N. Chughtai, M. Forzati, J. Martensson, and D. Rafique, “Dependence of non-linear impairments on polarization state and baud rate in WDM systems with mixed DQPSK and OOK channels,” in (IEEE, 2011), 1–4 |

13. | C. Xie, “Impact of nonlinear and polarization effects on coherent systems,” in |

14. | P. Serena, N. Rossi, and A. Bononi, “Nonlinear penalty reduction induced by PMD in 112 Gbit/s WDM PDM-QPSK coherent systems,” in |

15. | P. Serena, N. Rossi, O. Bertran-Pardo, J. Renaudier, A. Vannucci, and A. Bononi, “Intra- versus Inter-channel PMD in linearly compensated coherent PDM-PSK nonlinear transmissions,” J. Lightwave Technol. |

**OCIS Codes**

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

(190.3270) Nonlinear optics : Kerr effect

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 13, 2012

Revised Manuscript: February 29, 2012

Manuscript Accepted: March 16, 2012

Published: March 23, 2012

**Citation**

Mohsan Niaz Chughtai, Marco Forzati, Jonas Mårtensson, and Danish Rafique, "Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels," Opt. Express **20**, 8155-8160 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-8155

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### References

- J. Renaudier, O. Bertran-Pardo, G. Charlet, M. Salsi, M. Bertolini, P. Tran, H. Mardoyan, S. Bigo, “Investigation on WDM nonlinear impairments arising from the insertion of 100-Gb/s coherent PDM-QPSK over legacy optical networks,” IEEE Photon. Technol. Lett. 21(24), 1816–1818 (2009). [CrossRef]
- A. Bononi, M. Bertolini, P. Serena, G. Bellotti, “Cross-phase modulation induced by OOK channels on higher-rate DQPSK and coherent QPSK channels,” J. Lightwave Technol. 27(18), 3974–3983 (2009). [CrossRef]
- O. Vassilieva, T. Hoshida, J. C. Rasmussen, and T. Naito, “Symbol rate dependency of XPM-induced phase noise penalty on QPSK-based modulation formats,” in 34th European Conference on Optical Communication (2008), 1–2
- A. Bononi, N. Rossi, and P. Serena, “Transmission limitations due to fiber nonlinearity,” in Optical Fiber Communication Conference (Optical Society of America, 2011), p. OWO7.
- E. Gabory, M. Arikawa, D. Ogasahara and K. Fukuchi, “Mixed bit rate DWDM transmission of 112Gb/s PM-QPSK signals over a dispersion managed link using teal-time DSP to assess nonlinear distortions,” in ECOC 2011, paper Tu 6 B 3.
- H. Louchet, A. Richter, I. Koltchanov, S. Mingaleev, N. Karelin, and K. Kuzmin, “Comparison of XPM and XpolM-induced impairments in mixed 10G – 100G transmission,” in Proc. IEEE, 2011, 1–4.
- C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De, K. Man, Giok-Djan, H. de Waardt, “Coherent equalization and PolmuxRZ- DQPSK for robust 100-G transmission,” J. Lightwave Technol. 26, 64–72 (2008). [CrossRef]
- A. Viterbi, A. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]
- M. Kuschnerov, S. Calabrò, K. Piyawanno, B. Spinnler, M. S. Alfiad, A. Napoli, and B. Lankl, “Low complexity soft differential decoding of QPSK for forward error correction in coherent optic receivers,” in 2010 36th European Conference and Exhibition on Optical Communication (ECOC) (IEEE, 2010), 1–3.
- M. Karlsson, H. Sunnerud, “Effects of nonlinearities on PMD-induced system impairments,” J. Lightwave Technol. 24(11), 4127–4137 (2006). [CrossRef]
- E. Tipsuwannakul, M. N. Chughtai, M. Forzati, J. Mårtensson, P. Andrekson, M. Karlsson, “Influence of self- and cross-phase modulation on 40 Gbaud dual polarization DQPSK/D8PSK signals in 10 Gbit/s OOK WDM systems,” Opt. Express 18(23), 24178–24188 (2010). [CrossRef] [PubMed]
- M. N. Chughtai, M. Forzati, J. Martensson, and D. Rafique, “Dependence of non-linear impairments on polarization state and baud rate in WDM systems with mixed DQPSK and OOK channels,” in (IEEE, 2011), 1–4
- C. Xie, “Impact of nonlinear and polarization effects on coherent systems,” in 2011 37th European Conference and Exhibition on Optical Communication (ECOC) (IEEE, 2011), 1–3.
- P. Serena, N. Rossi, and A. Bononi, “Nonlinear penalty reduction induced by PMD in 112 Gbit/s WDM PDM-QPSK coherent systems,” in 35th European Conference on Optical Communication,2009. ECOC ’09 (IEEE, 2009), 1–2.
- P. Serena, N. Rossi, O. Bertran-Pardo, J. Renaudier, A. Vannucci, A. Bononi, “Intra- versus Inter-channel PMD in linearly compensated coherent PDM-PSK nonlinear transmissions,” J. Lightwave Technol. 29(11), 1691–1700 (2011). [CrossRef]

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