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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 8155–8160
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Influence of polarization state, baud rate and PMD on non-linear impairments in WDM systems with mixed PM (D)QPSK and OOK channels

Mohsan Niaz Chughtai, Marco Forzati, Jonas Mårtensson, and Danish Rafique  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 8155-8160 (2012)
http://dx.doi.org/10.1364/OE.20.008155


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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

2. Simulation setup

At the receiver white Gaussian optical noise is added to the signal (in order to vary the OSNR; performance was then evaluated by calculating the required OSNR to obtain BER = 10−3), 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]

]. Carrier phase recovery was done by employing “Viterbi-Viterbi” carrier phase estimation [8

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]

]. The number of taps for moving average filter in the carrier phase estimation was optimized for every power level and OSNR, by minimizing the average BER for the x and y polarization components.

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

Simulations were first performed at three baud rates of 10 Gbaud, 28 Gbaud and 56 Gbaud of the PM (D)QPSK channel and two states of polarization of the NRZ OOK channels relative to 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
Fig. 2 Required OSNR versus launch power per channel per polarization for differential detection (red curves) and coherent detection (blue curves) at 10 Gbaud (a), 28 Gbaud (b) and 56 Gbaud (c) with case(a) (triangle markers) and with case(b) (square markers).
. 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.

], which adds a penalty of 0.5 dB to the performance of coherent QPSK transmisssion.

We analyze the results in Fig. 2 with the help of SOPs on the Poincaré Sphere and constellation diagrams of x and y polarization shown in Fig. 3
Fig. 3 SOP of PM DQPSK signal at 28 Gbaud (1st column) as red dots after transmission at 0.2 dBm launch power when the SOP of the NRZ OOK neighbours is LHP (case (a)) or +45° (case (b)); the blue dots are the vector sum of the Stokes vectors of all the wavelength channels at the transmitter. Signal constellation in x polarization (2nd Column), signal constellation in y polarization (3rd column).
. 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]

]. For illustration, the blue dots show the total Stokes vector of the DWDM signal before transmission when all the neighbouring NRZ OOK channels carry a 1 bit, which is the scenario giving maximum polarization rotation. The red dots show the SOP of the received optical signal after transmission.

Points along the meridian shown in magenta on the Poincaré Spheres in Fig. 3 represent signals where the 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]

].

Points along the green meridian on Poincaré Spheres in Fig. 3 represent signals where the 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]

, 12

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

].This amplitude jitter is also depicted in constellation diagrams (shown in 4th row in Fig. 3) which have a higher amplitude jitter in comparison to constellation diagrams in 2nd row in Fig. 3. From the analysis of constellation diagram in 4th row of Fig. 3 we can also observe that both constellations in 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.

To quantify the nonlinear tolerances we compare the non linear threshold (NLT), defined as the launch power for which the required OSNR is increased by 2 dB compared to back-to-back, for the three baud rates and two relative states of polarization in Table 1

Table 1. NLT for Coherent and Differential Detection for Case (a) and Case (b) of SOPs

table-icon
View This Table
.

We can draw several conclusions from the Table. 1. For case (a) the nonlinear threshold increases with baud rate both for differential and coherent detection. This is due to the fact that the nonlinear phase shift introduced by XPM from neighbouring NRZ OOK channels becomes constant over several symbols of the PM (D)QPSK channel when the symbol time becomes relatively shorter than the neighbouring NRZ OOK pulses. This is obviously beneficial in differential detection, because a constant phase shift is effectively canceled. Also for coherent detection, however, carrier phase estimation can mitigate XPM induced phase noise more effectively for higher baud rate, because more slowly varying phase is more easily tracked.

For case (b) and differential detection, the NLT decreases with baud rate, indicating both that XPolM dominates in this case and that the impact of XPolM increases with baud rate. A possible explanation is that the amplitude noise becomes correlated over more symbols with increasing baud rate for XPolM (in the same way as phase noise becomes correlated over more symbols for XPM). Since differential detection compares one noisy symbol to another noisy symbol it may be sensitive to such a correlated amplitude noise. With coherent detection the NLT increases with baud rate also in case (b), which indicates that reduction in XPM is strong enough to impact the system performance even in this case.

Next, the SOP of neighbouring NRZ OOK channels was swept from 0° to 90° with respect to the x polarization of central channel to further investigate the dependence of XPM and XPolM on relative SOPs for coherent detection. Figure 4
Fig. 4 BER versus NRZ OOK channel SOPs at 10 Gbaud @ 18 dB OSNR (a), 28 Gbaud @ 19 dB OSNR (b), and 56 Gbaud @ 21 dB OSNR (c).
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).

In practical DWDM systems the SOPs of the neighbouring NRZ OOK channels are typically random and different for each channel. To investigate how system performance may vary in this case we also performed simulations with 400 different realizations of NRZ OOK signals having random SOPs uniformly distributed over the Poincaré sphere. Statistics were gathered for a coherent PM QPSK system at 28 Gbaud and fixed launched power of 2.2 dBm, and plotted in Fig. 5(a)
Fig. 5 Probability density function of required OSNR for BER = 10−3 at 0 ps/sqrt(km) PMD (a) and Probability density functions of required OSNRs for BER = 10−3 for various PMD values (b).
, which shows the probability density function (PDF) of the required OSNR for BER of 10−3.

The lowest required OSNR in Fig. 5(a) is 18.4 dB which is the same required OSNR as for case (a) of Fig. 2(b) at 2.2 dBm and the highest required OSNR is 24.1 dB which is the same required OSNR as for case (b) of Fig. 2(b) at 2.2 dBm. The average required OSNR for all SOPs is around 20.1 dB which is closer to the lowest than to the highest required OSNR. The result in Fig. 5(a) indicates that the SOP of all channels need to be quite well aligned in order for the non-linear impact to be highest, and consequently the likelihood of required OSNR to be close to the highest value of 24.1 dB is very low.

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

5. Summary and conclusion

In this paper we numerically investigated the dependence of nonlinear impairments on baud rates and relative SOP between central PM (D)QPSK channel and NRZ OOK channels. We discovered that for systems with very low or no PMD the impact of XPM and XPolM strongly depends on the baud rate and relative SOP between central channel and NRZ OOK channels for both coherent and differential detection. The dependence on relative SOP is more pronounced in differential detection than coherent detection. Secondly we also observed that the dependence of nonlinear impairments on SOPs of neighbouring channels reduces with increasing PMD thus making the system more immune to outage due to high nonlinear penalties.

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. 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]

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 34th European Conference on Optical Communication (2008), 1–2

4.

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.

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. 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]

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.

10.

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

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]

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 2011 37th European Conference and Exhibition on Optical Communication (ECOC) (IEEE, 2011), 1–3.

14.

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.

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]

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

  1. 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]
  2. 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]
  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 34th European Conference on Optical Communication (2008), 1–2
  4. 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.
  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, H. de Waardt, “Coherent equalization and PolmuxRZ- DQPSK for robust 100-G transmission,” J. Lightwave Technol. 26, 64–72 (2008). [CrossRef]
  8. 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]
  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.
  10. M. Karlsson, H. Sunnerud, “Effects of nonlinearities on PMD-induced system impairments,” J. Lightwave Technol. 24(11), 4127–4137 (2006). [CrossRef]
  11. 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]
  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 2011 37th European Conference and Exhibition on Optical Communication (ECOC) (IEEE, 2011), 1–3.
  14. 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.
  15. 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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