## Experimental demonstration of PDL penalty reduction by wavelength-interleaving transmission |

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

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).

*n*-wavelength-interleaving (

*n*-WI) technique was originally proposed in [4

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]

*n*is increased.

## 2. *n*-wavelength-interleaving transmission

## 3. Experimental setup and results

^{11}-1 PRBS pattern with a 32 GHz clock to create 128 Gbps PDM-QPSK optical signals. Note that the two channels are separated by 300 GHz and modulated by the same optical modulator. Optical signals enter the DGD-PDL-emulated link nine sections, each of which has a 1-km single mode fiber (SMF), a PDL-emulator, and a polarization-maintaining fiber (which works as a DGD-emulator). Each DGD- and PDL-emulator has DGD of ~10 ps and PDL of ~1 dB, respectively. Under the assumption of the large number of emulators, the estimated link PMD was 27.6 ps and the link PDL was 2.8 dB. To increase the exploration speed of DGD and PDL, 1-km SMFs are set in an isothermal chamber whose temperature randomly fluctuates between 10 and 50 ◦C. Before entering the optical frontend, amplified spontaneous emission (ASE) noise is added to optical signals to decrease the OSNR to 17 dB. Optical signals are detected by balanced-PD at the same time for both channels. After analog-to-digital conversion, the signals are demodulated by an offline program to calculate the BER and Q-factor of channels 1 and 2. Here we assumed PMD-induced penalty was almost completely equalized by four butterfly 11-tap T/2-spaced adaptive finite impulse response (FIR) filter based on the constant modulus algorithm [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).

## 4. Analysis by extreme value statistics

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]

*-Q*values (i.e., Q-factors multiplied by −1) as stochastic variables in order to estimate minimum Q-factors.

*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 ofwhere

*σ*and

*ξ*are the scale parameter and the shape parameter, respectively.

*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] for more information). Fitted

*H(x)*and the cumulative probabilities calculated from the experiment data are plotted in Fig. 4 ; they show excellent agreement. The estimated parameters are summarized in Table 1 .

*m*-observations, which is expressed as

*Qm*below. From Eq. (1),

*Qm*is approximated with estimated parameters after simple algebraic transformation aswhere

*N*and

*k*are respectively the total number of experimental data elements and the number of data elements exceeding threshold

*u*. On the basis of Eq. (2) and the estimated parameters (

*u*, σ, and ξ), we can ascertain the expected minimum Q-factor

*Qm*for a given

*m*: for example, if we were to observe Q-factor

*m*= 10

^{8}times for ch1 in this system, we can expect that we would, on average, witness the minimum Q-factor

*Qm*of ~8.0 dB once. It can be also interpreted that this example corresponds to a link system in which the designed Q-limit is 8.0 dB and the outage probability is 10

^{−8}, because outage probability is given by 1/

*m*.

^{−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.

*n*(

*n*>2) will decrease PDL-induced impairments more effectively. In the next section, we perform a numerical simulation in which

*n*is increased to 3 or more for the purpose of revealing the mechanism by which WI mitigates the PDL-induced penalty or outage probability.

## 5. Numerical simulation

*n*from 2 to 8. As in the experiment (Section 3), the transmission line has nine sections, each of which has a 10ps-DGD- and a 1dB-PDL-emulator. However, instead of installing 1-km SMFs in an isothermal chamber, which changes the angles of the principal axes for both the DGD- and PDL-emulators between sections, we install DGD- and PDL-emulators with random angles in each section. We add ASE noises to the optical signals so that the Q-factor of the transmitted optical signal becomes 10.8 dB when the total PDL of the optical link is 0 dB, which was the case in the experiment. Note that BERs (i.e., Q-factors) of transmitted channels are statistically independent in the simulation, and that, as in the case of the experiment, we neglect the impact of PMD-induced penalty using four butterfly adaptive FIR equalizing filter. In each simulated case of different

*n*, the number of data sets for Q-factor sequence is 500.

*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.

^{−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.

*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

*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.

## Acknowledgment

## References and links

1. | M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express |

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. |

5. | S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, “PMD-PDL emulator designs for low interchannel correlation,” IEEE Photon. Technol. Lett. |

6. | S. Savory, F. Payne, and A. Hadjifotiou, “Estimating outages due to polarization mode dispersion using extreme value statistics,” J. Lightwave Technol. |

7. | R. D. Reiss and M. Thomas, |

**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

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

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