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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 26 — Dec. 10, 2012
  • pp: B479–B484
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Experimental demonstration of PDL penalty reduction by wavelength-interleaving transmission

Kohki Shibahara and Kazushige Yonenaga  »View Author Affiliations


Optics Express, Vol. 20, Issue 26, pp. B479-B484 (2012)
http://dx.doi.org/10.1364/OE.20.00B479


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Abstract

Experiments and numerical simulation demonstrate the validity of wavelength-interleaving (WI) transmission for reducing the penalty induced by polarization dependent loss (PDL) through the method of extreme value statistics. It is confirmed that applying the WI technique across n (n>1) channels can effectively reduce PDL-induced Q-penalty or outage probability.

© 2012 OSA

1. Introduction

Digital equalization after coherent detection can effectively enhance tolerance to the impairments caused by PMD [2

2. S. Yamamoto, T. Inui, H. Kawakami, S. Yamanaka, T. Kawai, T. Ono, K. Mori, M. Suzuki, A. Iwaki, T. Kataoka, M. Fukutoku, T. Nakagawa, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Suzuki, K. Murata, T. Kotanigawa, and A. Maeda, “Hybrid 40-Gb/s and 100-Gb/s PDM-QPSK DWDM transmission using real-time DSP in field testbed,” Proc. OFC’12, JW2A.4 (2012).

]. On the other hand, PDL causes temporal power fluctuation in each optical PDM-channel, which cannot be equalized even with the digital signal processing technique. As a result, PDL degrades system performance significantly [3

3. O. Vassilieva, Inwoong Kim, and Takao Naito, “Systematic investigation of interplay between nonlinear and polarization dependent loss effects in coherent polarization multiplexed systems,” Proc. OFC’08, OThU6 (2008).

].

In this paper, we describe the first-ever experimental demonstration of using WI to improve the robustness to PDL-induced impairments via a statistical approach. In addition, through numerical simulation we reveal the mechanism by which WI reduces the PDL-induced penalty or the outage probability when the number of interleaving-channels n is increased.

2. n-wavelength-interleaving transmission

3. Experimental setup and results

We recorded the Q-factor sequence of both channels every minute for 5.7 hours (accordingly, the total number of data sets was 340). Figure 3
Fig. 3 (a) Temporal change in observed Q-factor of ch1 and ch2. (b) Scatter plots of Q-factors for the two channels. (c) Probability density of ch1, ch2, and interleaved channel as a function of Q-factor.
shows the statistical properties of the recorded Q-factors. As mentioned above, the Qint (Q-factor of the interleaved channels) is equivalently obtained by averaging BER1 and BER2. Figure 3(a) shows the temporal change in Q-factor for channels 1 and 2. Fluctuations in the Q-factor can be caused by changes of the PDL itself and the relative angle between the polarization states of optical signals and PDL-axes [2

2. S. Yamamoto, T. Inui, H. Kawakami, S. Yamanaka, T. Kawai, T. Ono, K. Mori, M. Suzuki, A. Iwaki, T. Kataoka, M. Fukutoku, T. Nakagawa, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Suzuki, K. Murata, T. Kotanigawa, and A. Maeda, “Hybrid 40-Gb/s and 100-Gb/s PDM-QPSK DWDM transmission using real-time DSP in field testbed,” Proc. OFC’12, JW2A.4 (2012).

]. The scatter plots of Q1 and Q2 for the two channels are shown in Fig. 3(b). They indicate that Q1 and Q2 are statistically uncorrelated: the calculated correlated coefficient was 0.102. Figure 3(c) represents the PDFs of Q1, Q2, and Qint. It is noteworthy that the calculated variance of Qint (0.052) is significantly smaller than that of Q1 (0.092) and Q2 (0.090).

4. Analysis by extreme value statistics

We here use the peaks over threshold (POT) analysis found in EVS literature [7

7. R. D. Reiss and M. Thomas, Statistical analysis of extreme values (Cambridge, 1997.)

]. Note that POT analysis is designed for estimating maxima given a large number of data points; our analysis should deal with -Q values (i.e., Q-factors multiplied by −1) as stochastic variables in order to estimate minimum Q-factors.

Let the obtained Q-factor sequence be one of identically and independently random variables. If we set X = -Q-u for a given threshold u, EVS gives the conditional probability H(x) = Pr{x>X | X>0}. H(x) is the probability that X does not exceed x under the condition of X>0, i.e. –Q>u, which is referred to as the generalized Pareto distribution. Cumulative probability H(x) has the explicit form of
H(x)=1(1+ξxσ)1/ξ,
(1)
where σ and ξ are the scale parameter and the shape parameter, respectively.

Parameters σ and ξ are estimated on the basis of the maxima likelihood method. Since there may still be uncertainty in setting appropriate threshold level u, we determine it by using the mean excess function, which is a familiar EVS technique (see [7

7. R. D. Reiss and M. Thomas, Statistical analysis of extreme values (Cambridge, 1997.)

] for more information). Fitted H(x) and the cumulative probabilities calculated from the experiment data are plotted in Fig. 4
Fig. 4 Cumulative probabilities from experimental data (symbols) and fitted H(x) obtained from Eq. (1) with estimated parameters (solid curves) for ch1 (a), ch2 (b), and interleaved channel (c).
; they show excellent agreement. The estimated parameters are summarized in Table 1

Table 1. Estimated parameters for ch1, ch2, and interleaved channel.

table-icon
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.

From this viewpoint of system design, we can draw the Q-limit curve as a function of outage probability (as in Fig. 5
Fig. 5 Estimated Q-limit from Eq. (2) as a function of outage probability for ch1, ch2 and interleaved channel. Note that error bars at outage probability of 10−2, 10−4, and 10−6 are estimated based on the 90% confidence intervals of σ and ξ.
). This reveals the reduction effect of WI transmission for PDL-induced Q-penalty or outage probability, as in the following two scenarios: (1) For a fixed outage probability of 10−6, the Q-limit can be mitigated from ~8.1 to ~8.6 dB, which can also be explained as the Q-penalty being improved by 0.5 dB. (2) For a fixed Q-limit of 8.5 dB, outage probability can be decreased from 10−3 to 10−6. It should be noted that the Q-limit generally depends on which FEC code is applied and what corrected BER is required for the system, and that outage probability generally depends on the required system reliability.

5. Numerical simulation

Figure 6(a)
Fig. 6 (a) Simulated probability densities of Q-factors for the channels without WI transmission (blue), with 4-WI transmission (magenta), and with 8-WI transmission (yellow). (b) The Q-penalty improvement in dB as a function of the number of interleaving wavelengths n for a fixed outage probability of 10−6.
depicts the PDFs of Q-factors for a single channel, a 4-WI channel, and a 8-WI channel. Compared to Fig. 3(c), it is obvious that the variance of the PDF for an n-WI channel is likely to become smaller as the number of interleaved channels n increases. Therefore, it is expected that the effect of WI transmission on reducing PDL-induced impairments may be enhanced when n becomes larger.

As in Section 4, here too we apply EVS analysis to the simulation results. The parameters for the generalized Pareto distribution are estimated in the same way as in Section 4. Figure 6(b) summarizes the improvement achieved in Q-penalty reduction for a fixed outage probability of 10−6 when n is increased from 2 to 8. It can be seen that the reduction effect enhances monotonically; in particular, the Q-penalty for the 8-WI channel improves by about 1.8 dB.

Furthermore, it is noteworthy that the reduction effect has a tendency to saturate as n increases. We give an explanation for this saturation phenomenon here. As n becomes closer to infinity, the PDF of the Q-factor for an n-WI channel approaches a delta-function-like shape, which has its mean around 9.5 dB in this case (one may be able to visualize this with an analogy of the central limit theorem). Accordingly, the upper bound of the PDF integrated area that gives the fixed outage probability of 10−6 becomes larger monotonically towards the mean Q-factor of 9.5 dB, which establishes the fact that the reduction effect has an upper limit.

6. Conclusion

Subjecting experimental measured data to EVS analysis successfully demonstrated that WI transmission can decrease the Q-penalty or outage probability caused by PDL. Furthermore, numerical simulation revealed that this reduction effect tends to enhance as the number of interleaving channels n increases, and also that the amount of the reduction of PDL-induced impairments saturates towards an upper limit, which is explained by an analogy of the central limit theorem.

We believe that the use of WI may also be a valid approach to mitigating other impairments, such as signal degradation differing among different channels.

Acknowledgment

We would like to express our gratitude to K. Mori for his technical support in conducting our experiment.

References and links

1.

M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]

2.

S. Yamamoto, T. Inui, H. Kawakami, S. Yamanaka, T. Kawai, T. Ono, K. Mori, M. Suzuki, A. Iwaki, T. Kataoka, M. Fukutoku, T. Nakagawa, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Suzuki, K. Murata, T. Kotanigawa, and A. Maeda, “Hybrid 40-Gb/s and 100-Gb/s PDM-QPSK DWDM transmission using real-time DSP in field testbed,” Proc. OFC’12, JW2A.4 (2012).

3.

O. Vassilieva, Inwoong Kim, and Takao Naito, “Systematic investigation of interplay between nonlinear and polarization dependent loss effects in coherent polarization multiplexed systems,” Proc. OFC’08, OThU6 (2008).

4.

B. Xie, Y. Guan, Z. Li, and C. Lu, “FEC performance of optical communication systems with PMD and wavelength interleaving,” IEEE Photon. Technol. Lett. 16, 936–938 (2004). [CrossRef]

5.

S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, “PMD-PDL emulator designs for low interchannel correlation,” IEEE Photon. Technol. Lett. 18(22), 2362–2364 (2006). [CrossRef]

6.

S. Savory, F. Payne, and A. Hadjifotiou, “Estimating outages due to polarization mode dispersion using extreme value statistics,” J. Lightwave Technol. 24(11), 3907–3913 (2006). [CrossRef]

7.

R. D. Reiss and M. Thomas, Statistical analysis of extreme values (Cambridge, 1997.)

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications

ToC Category:
Transmission Systems and Network Elements

History
Original Manuscript: October 1, 2012
Revised Manuscript: November 14, 2012
Manuscript Accepted: November 14, 2012
Published: December 3, 2012

Virtual Issues
European Conference on Optical Communication 2012 (2012) Optics Express

Citation
Kohki Shibahara and Kazushige Yonenaga, "Experimental demonstration of PDL penalty reduction by wavelength-interleaving transmission," Opt. Express 20, B479-B484 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-26-B479


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References

  1. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16(18), 13918–13932 (2008). [CrossRef] [PubMed]
  2. S. Yamamoto, T. Inui, H. Kawakami, S. Yamanaka, T. Kawai, T. Ono, K. Mori, M. Suzuki, A. Iwaki, T. Kataoka, M. Fukutoku, T. Nakagawa, T. Sakano, M. Tomizawa, Y. Miyamoto, S. Suzuki, K. Murata, T. Kotanigawa, and A. Maeda, “Hybrid 40-Gb/s and 100-Gb/s PDM-QPSK DWDM transmission using real-time DSP in field testbed,” Proc. OFC’12, JW2A.4 (2012).
  3. O. Vassilieva, Inwoong Kim, and Takao Naito, “Systematic investigation of interplay between nonlinear and polarization dependent loss effects in coherent polarization multiplexed systems,” Proc. OFC’08, OThU6 (2008).
  4. B. Xie, Y. Guan, Z. Li, and C. Lu, “FEC performance of optical communication systems with PMD and wavelength interleaving,” IEEE Photon. Technol. Lett. 16, 936–938 (2004). [CrossRef]
  5. S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, “PMD-PDL emulator designs for low interchannel correlation,” IEEE Photon. Technol. Lett. 18(22), 2362–2364 (2006). [CrossRef]
  6. S. Savory, F. Payne, and A. Hadjifotiou, “Estimating outages due to polarization mode dispersion using extreme value statistics,” J. Lightwave Technol. 24(11), 3907–3913 (2006). [CrossRef]
  7. R. D. Reiss and M. Thomas, Statistical analysis of extreme values (Cambridge, 1997.)

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