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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 25788–25795
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Flexible bandwidth DGD estimation for coherent optical OFDM system

Cuong C. Do, An V. Tran, Simin Chen, Trevor Anderson, Don Hewitt, and Efstratios Skafidas  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 25788-25795 (2013)
http://dx.doi.org/10.1364/OE.21.025788


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Abstract

A Stokes vector based non-data-aided (NDA) differential group delay (DGD) estimation scheme with flexible bandwidth requirements is investigated. The scheme is demonstrated in both experiments and simulations for 40-Gb/s polarization-multiplexed coherent optical OFDM systems with up to 1000-km long haul transmission with an estimation error of less than 2.5 ps after 1000-km standard single-mode fiber transmissions.

© 2013 Optical Society of America

1. Introduction

For optical transmission systems with bit rate of 40 Gb/s and beyond, polarization mode dispersion (PMD), normally characterized by the differential group delay (DGD), has become a detrimental impact on their speed and performance. Furthermore, modern optical networks have evolved from simple point-to-point networks to dynamically reconfigurable ones, which require accurate and up-to-date information of the impairments of each communication path. Therefore, a cost-effective estimation scheme to monitor these impairments to provide guaranteed service quality and fast reaction to performance degradation is in demand [1

1. D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. 22(1), 294–304 (2004). [CrossRef]

,2

2. Y. C. Chung, “Optical performance monitoring techniques; current status and future challenge,” in Proceedings of Eur. Conf. on Opt. Comm. (ECOC)2008 (Brussels, Belgium, 2008), pp. W.E.1.D.1.

]. Several DGD estimation techniques have been proposed for single-carrier systems, including schemes based on measurement of minimum degree of polarization (DOP) [3

3. H. Rosenfeldt, R. Ulrich, E. Brinkmeyer, U. Feiste, C. Schubert, J. Berger, R. Ludwig, H. G. Weber, and A. Ehrhardt, “Feedforward approach for automatic PMD compensation at 80 Gbit/s over 45 km installed single mode fiber,” in Proceedings of Eur. Conf. on Opt. Comm. (ECOC) 2001 (2001), pp. 68–69.

], eye diagram [4

4. F. Buchali, S. Lanne, J. P. Thiery, W. Baumert, and H. Bulow, “Fast eye monitoring for 10 Gbit/s and its application for optical PMD compensation,” in Proceedings of Opt. Fiber Conf. (OFC)2001(Anaheim, Calif., 2001), pp. TuP5. [CrossRef]

], equalizer filters algebraic manipulation [5

5. M. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairments monitoring from the equalizer in a digital coherent optical receiver,” Opt. Express 18, 26929–26936 (2010). [CrossRef]

7

7. F. Pittala, F. Hauske, Y. Ye, N. Gonzalez, and I. Monroy, “Fast and robust CD and DGD estimation based on data-aided channel estimation,” in Proceedings of Inter. Conf. on Transparent Opt. Networks ICTON 2011 (Stockholm, 2011), pp. 1–4. [CrossRef]

] and frequency-resolved state of polarization (SOP) rotation [8

8. G. W. Lu, C. Xie, Y. C. Ku, L. K. Chen, and C. K. Chan, “Enhanced PMD monitoring with frequency-resolved SOP rotation by self phase modulation,” IEEE Photon. Technol. Lett. 16(9), 2180–2182 (2004). [CrossRef]

]. On the other hand, research on DGD estimation for optical OFDM systems has not been widely studied, and furthermore all of the published schemes are executed at the receiver end as part of the digital signal processing procedure [9

9. X. Yi, W. Shieh, Y. Ma, Y. Tang, and G. J. Pendock, “Experimental demonstration of optical performance monitoring in coherent optical OFDM systems,” in Proceedings of Opt. Fiber Conf. (OFC)2008 (San Diego, Calif, 2008), pp. OThW3. [CrossRef]

11

11. M. Mayrock and H. Haunstein, “Monitoring of linear and nonlinear signal distortion in coherent optical OFDM transmission,” J. Lightwave Technol. 27(16), 3560–3566 (2009). [CrossRef]

]. Although they are basically free of extra hardware cost, these schemes rely on full-bandwidth sampling so are not optimal solutions for distributed optical performance monitoring, which normally involves separate monitoring devices with low bandwidth components compared to the full bandwidth of the data signal. We previously proposed a DGD estimation scheme using low bandwidth coherent receiver in [12

12. S. Chen, T. Anderson, D. Hewitt, A. Tran, and E. Skafidas, “Non-data-aided PMD monitoring for optical OFDM systems using low bandwidth coherent receivers,” in Proceedings of Opt. Fiber Conf. (OFC)2013 (Anaheim, Calif., 2013), pp. JW2A.51. [CrossRef]

]. However, this scheme relies on the assumption that the arc traces are linear and thus could result in performance degradation in higher bandwidth receivers where the arc traces could have different shapes. Furthermore, a comparison between estimation performance and bandwidth requirement for the proposed estimation scheme has not been investigated.

In this paper we extend our initial investigation of DGD estimation using low bandwidth coherent receiver [12

12. S. Chen, T. Anderson, D. Hewitt, A. Tran, and E. Skafidas, “Non-data-aided PMD monitoring for optical OFDM systems using low bandwidth coherent receivers,” in Proceedings of Opt. Fiber Conf. (OFC)2013 (Anaheim, Calif., 2013), pp. JW2A.51. [CrossRef]

] and propose a complete solution for DGD estimation in coherent optical OFDM system with flexible bandwidth requirements. In addition to point-to-point estimation for low bandwidth receiver, a new interpolation estimation scheme is proposed which can estimate both linear and non-linear arc traces for high bandwidth coherent receivers. This non data-aided (NDA) DGD estimation scheme is based on subcarriers of individual OFDM signal block and thus can be adapted to different monitoring device bandwidths. The scheme is experimentally demonstrated through simulations and experiments to be able to accurately estimate DGD with estimation error of less than 2.5 ps in both back to back and after 1000-km standard single-mode fiber (SSMF) transmission.

2. Stokes vector based DGD estimation

DGD estimation based on Stokes vector does not measure DGD directly. Although it is possible in some cases to determine DGD directly from the intersection angle between the principal states of polarization (PSPs) and state of polarization (SOP), the results become very unreliable when the SOP is close to one of the PSPs. Therefore, instead of direct measurement this NDA scheme measures a slightly different quantity called DGD-induced SOP rotation. This value is the length of arc trace in Stokes space that is orthogonal to the SOP of the optical signal as shown in Fig. 1
Fig. 1 Representation of (a) the DGD vector and DGD-induced arc trace on the Poincaré sphere and (b) zoomed in arc trace generated by relative position of OFDM subcarriers.
.

The optical waveforms after a polarization beam splitter (PBS) can be written in the form of the Stokes vector S by the following set of Eq [13

13. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley & Sons, 1998), Chap. 4.

]:
S=(s1s2s3)=1s0(|ex|2|ey|22Re{ex*ey}2Im{ex*ey})
(1)
where ex and ey are the Jones vectors for the linear x and y polarization states and the Stokes vector component s0=|ex|2+|ey|2 represents the received signal power of two polarizations. Plotting the Stokes vector on the Poincaré sphere provides a convenient means of characterizing the DGD on subcarriers without the need for polarization de-multiplexing.

When low bandwidth coherent receiver is used, the arc traces in Fig. 1 are short and mostly linear thus DGD can be estimated by measuring the angle between the first and last subcarriers within the monitoring bandwidth (point-to-point estimation) [12

12. S. Chen, T. Anderson, D. Hewitt, A. Tran, and E. Skafidas, “Non-data-aided PMD monitoring for optical OFDM systems using low bandwidth coherent receivers,” in Proceedings of Opt. Fiber Conf. (OFC)2013 (Anaheim, Calif., 2013), pp. JW2A.51. [CrossRef]

]. For receiver with higher bandwidth, the number of subcarriers used is increased and it is possible to use interpolation to measure the arc length for more precise estimation. Interpolation is particularly more useful for higher bandwidth receivers since higher bandwidth receivers not only generate longer arces but also suffer from second-order PMD (SOPMD), which changes the shape of the DGD arc on the Stokes sphere. Figure 3
Fig. 3 (a) SOP traces with SOPMD = 1368 ps2 and (b) interpolation of longest trace in 2D plot.
shows the shape of the arc traces for SOPMD = 1368 ps2 and DGD = 30ps and it can be seen that while the longest arc length stays the same, the arc is no longer linear under SOPMD and thus cannot be measured using the angle between the first and last subcarriers. Due to the arc being on the surface of the sphere, we estimate the length of this arc using interpolation by first eliminating the sphere radius parameter to convert the arc into a 2-dimension plot. The data points are then interpolated using least square algorithm and the arc length is estimated by integration over the new arc.

3. Simulation results and discussion

4. Experimental setup and results

Figure 5
Fig. 5 Experimental setup.
shows the experimental setup for flexible bandwidth sampling NDA DGD estimation. The frequency-domain OFDM signal stream is mapped to 4-QAM symbols then converted to time-domain by the inverse fast Fourier transform operation. Guard intervals are inserted to resist CD. The length of the guard interval is chosen to match the delay of the polarization multiplexing emulator. The IFFT size is 256 and the guard interval is set to 16. The time-domain OFDM signal is uploaded onto an arbitrary waveform generator, which produces the analog signals at 10 Gsymbols/s. An optical I/Q modulator directly modulates the OFDM baseband electrical signals to the optical domain. The single-polarization optical OFDM signal from the modulator is evenly split into two polarization branches through a polarization-beam splitter (PBS) with one branch delayed by one OFDM frame period. A variable delay line is used in the delayed branch to finely tune the delay accurately equal to one OFDM frame period. The two polarization branches are subsequently combined by a polarization-beam combiner, emulating two independent transmitters on X and Y polarizations with a combined raw data rate of 40 Gb/s. The signal is then coupled into a recirculation loop to emulate 1000-km transmission or directly connected to the receiver to emulate back-to-back transmission.

At the receiver side, an amplified spontaneous emission (ASE) source consisting of two cascaded EDFAs and one optical band-pass filter is used to control the optical signal-to-noise ratio (OSNR) level. A Fiberpro PE4200 PMD emulator is used to add DGD to the OFDM signal and the control range is from 0 to 30 ps. Four balanced receivers are used to detect the in-phase and quadrature components of the received OFDM signal. The low-bandwidth receiver is emulated with four 0.8-GHz low-pass electrical filters while full bandwidth receiver uses four 3.3-GHz low-pass electrical filters attached to the outputs of 15-GHz balanced receivers. The signals are then captured by a 4-channel real-time oscilloscope running at 10 GSamples/s for full bandwidth and 2.5 GSamples/s for low bandwidth receiver and data are stored for offline processing. For OFDM signal, carrier frequency offset compensation is essential to eliminate the inter-subcarrier interference for FFT. As a non-data-aided DGD estimation scheme, this compensation is performed without training sequence assistance. The captured OFDM signal is converted to frequency-domain then the frequency offset between DC and signal carrier is measured and compensated. Timing synchronization is also performed in blind mode by minimizing the scatter of each subcarrier on the Stokes sphere [15

15. S. Chen, T. Anderson, D. Hewitt, A. V. Tran, C. Zhu, L. B. Du, A. J. Lowery, and E. Skafidas, “Optical performance monitoring for OFDM using low bandwidth coherent receivers,” Opt. Express 20(27), 28724–28733 (2012). [CrossRef] [PubMed]

].

Figure 6(a)
Fig. 6 Low bandwidth DGD estimation for (a) back-to-back and (b) after 1000-km transmission.
shows the estimated DGD versus actual DGD at back-to-back measurements in 22.5-dB and 12-dB OSNR for polarization-multiplexed OFDM signal with four 0.8GHz low-pass filters using point-to-point angle measurement method. The inset at the upper left corner of Fig. 6(a) is an example of 30-ps DGD-induced arc traces on the Poincaré sphere. It can be seen that the four arcs are short and noisy that direct estimation of DGD from the angle between PSPs and SOP is not reliable. Each point in Fig. 5 is an average of 30 captures of data blocks. Their maximum DGD estimation deviations are plotted as error bars. The two cases of NDA point-to-point estimation method coincide with the ideal values in the DGD region from 10 ps to 30 ps. The largest error is less than 2 ps in this span. The estimation deviation increases to nearly 4.8 ps when the system DGD is close to zero because of the background noise interference on the DGD estimation. When the DGD is set to zero, the average points of subcarriers cannot converge to one dot because of system noise. The angle between the first and last subcarriers is still measured and regarded as DGD-induced, which causes the relative higher deviation in small DGD region.

The estimation scheme is tested for 500-km and 1000-km transmission to further evaluate its performance in the presence of CD and large amount of ASE noise. An Adaptif A2000 optical component analyzer is used before the experiment to measure the DGD parameter of a single fiber loop and then compensate the background DGD. The fiber DGD parameter is 0.092 ps/km after 20 averagings. With this parameter the background DGD is 2.9 ps for the 1000-km recirculation loop and 2.1 ps for the 500-km loop. Figure 6(b) demonstrates the two estimated DGD curves after background DGD compensation. The curve for 500-km transmission coincides with the theoretical line if the emulated DGD is larger than 10 ps. The increased errors from 0~10-ps region are caused by the accumulated ASE noise as explained in the last paragraph. The estimated DGD values for 1000-km transmission are around 2.5-ps larger than the true values for the DGD between 5 ps and 30 ps. This is caused by the much more accumulated ASE noise and imperfections of the recirculation loop. The 5-ps offset at zero is due to the residual noise after averaging. For low bandwidth receivers, results for interpolation method are similar and have been omitted from the above plots for clarity purposes.

Figure 7(a)
Fig. 7 (a) Full bandwidth DGD estimation after 1000-km transmission and (b) estimation error as a function of receiver bandwidth.
shows the estimated DGD versus actual DGD at 1000-km transmission in 22.5-dB OSNR for full bandwidth receiver with their maximum error plotted as error bar. It can be seen that the average DGD estimated for full bandwidth receiver is around 1.7 ps higher compared to the DGD set by the emulator. This is caused by the ASE noise and imperfections of the recirculation loop similar to the low bandwidth case described above. Figure 7(b) shows the root mean squared (RMS) estimation error as a function of the receiver bandwidth emulated by selecting the amount of OFDM subcarriers used for estimation and it can be seen that there is an increase in performance of around 0.8 ps between the lowest receiver bandwidth of 0.8 GHz and full bandwidth at 3.3 GHz as expected since the SOP traces are longer in higher bandwidth receiver and enable more precise estimation. The accuracy when using interpolation is about 0.1 ps better compared to point-to-point estimation under full bandwidth receiver and both interpolation and point-to-point method achieve very similar performance under a wide range of receiver bandwidths. This is expected as the traces are linear and estimation accuracy is more likely limited by the system OSNR.

5. Conclusions

We have demonstrated an NDA Stokes vector based DGD estimation scheme using coherent OFDM receivers with flexible bandwidth requirement. The Stokes vector NDA approach does not require training sequences but employs the whole data block to estimate DGD based on the DGD induced traces in the Poincare sphere. Since this algorithm only relies on the DGD induced phase difference between the two polarizations signals and is independent to data contents, it is promising to be extended to any optical OFDM modulation formats, including constant and non-constant modulus formats. The scheme is demonstrated through experiments to be robust against CD and ASE distortion with a receiver bandwidth as low as 800 MHz. For DGD over 5 ps the estimation error is less than 2.5 ps in the presence of 12 dB OSNR and 1000-km single mode fiber transmission for both low bandwidth and full bandwidth receivers. Simulations also verify that by using interpolation, estimation is also robust against SOPMD impairments for full bandwidth receivers while under normal conditions both point-to-point and interpolation can be used for accurate estimation of system DGD. While higher modulation formats such as 16-QAM have not been considered, these formats should generate more traces on the sphere and with possibly higher trace complexities and thus modifications to the trace detection algorithm can be made in order to adapt the scheme for coherent OFDM optical systems with higher modulation formats.

Acknowledgments

NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications, the Digital Economy, and the Australian Research Council through the ICT Centre of Excellence program.

References and links

1.

D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol. 22(1), 294–304 (2004). [CrossRef]

2.

Y. C. Chung, “Optical performance monitoring techniques; current status and future challenge,” in Proceedings of Eur. Conf. on Opt. Comm. (ECOC)2008 (Brussels, Belgium, 2008), pp. W.E.1.D.1.

3.

H. Rosenfeldt, R. Ulrich, E. Brinkmeyer, U. Feiste, C. Schubert, J. Berger, R. Ludwig, H. G. Weber, and A. Ehrhardt, “Feedforward approach for automatic PMD compensation at 80 Gbit/s over 45 km installed single mode fiber,” in Proceedings of Eur. Conf. on Opt. Comm. (ECOC) 2001 (2001), pp. 68–69.

4.

F. Buchali, S. Lanne, J. P. Thiery, W. Baumert, and H. Bulow, “Fast eye monitoring for 10 Gbit/s and its application for optical PMD compensation,” in Proceedings of Opt. Fiber Conf. (OFC)2001(Anaheim, Calif., 2001), pp. TuP5. [CrossRef]

5.

M. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairments monitoring from the equalizer in a digital coherent optical receiver,” Opt. Express 18, 26929–26936 (2010). [CrossRef]

6.

C. C. Do, A. V. Tran, C. Zhu, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, ” PMD monitoring in 16-QAM coherent optical system using Golay sequences,” in Proceedings of Opto-Elec. and Comm. Conf. (OECC)2012 (Busan, 2012), pp. 6B3–5. [CrossRef]

7.

F. Pittala, F. Hauske, Y. Ye, N. Gonzalez, and I. Monroy, “Fast and robust CD and DGD estimation based on data-aided channel estimation,” in Proceedings of Inter. Conf. on Transparent Opt. Networks ICTON 2011 (Stockholm, 2011), pp. 1–4. [CrossRef]

8.

G. W. Lu, C. Xie, Y. C. Ku, L. K. Chen, and C. K. Chan, “Enhanced PMD monitoring with frequency-resolved SOP rotation by self phase modulation,” IEEE Photon. Technol. Lett. 16(9), 2180–2182 (2004). [CrossRef]

9.

X. Yi, W. Shieh, Y. Ma, Y. Tang, and G. J. Pendock, “Experimental demonstration of optical performance monitoring in coherent optical OFDM systems,” in Proceedings of Opt. Fiber Conf. (OFC)2008 (San Diego, Calif, 2008), pp. OThW3. [CrossRef]

10.

F. Hauske, J. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. Fludger, D. van den Borne, E. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefficients in coherent receivers,” in Proceedings of Opt. Fiber Conf. (OFC)2008 (San Diego, Calif, 2008), pp. OThW2. [CrossRef]

11.

M. Mayrock and H. Haunstein, “Monitoring of linear and nonlinear signal distortion in coherent optical OFDM transmission,” J. Lightwave Technol. 27(16), 3560–3566 (2009). [CrossRef]

12.

S. Chen, T. Anderson, D. Hewitt, A. Tran, and E. Skafidas, “Non-data-aided PMD monitoring for optical OFDM systems using low bandwidth coherent receivers,” in Proceedings of Opt. Fiber Conf. (OFC)2013 (Anaheim, Calif., 2013), pp. JW2A.51. [CrossRef]

13.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley & Sons, 1998), Chap. 4.

14.

B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express 18(17), 17928–17939 (2010). [CrossRef] [PubMed]

15.

S. Chen, T. Anderson, D. Hewitt, A. V. Tran, C. Zhu, L. B. Du, A. J. Lowery, and E. Skafidas, “Optical performance monitoring for OFDM using low bandwidth coherent receivers,” Opt. Express 20(27), 28724–28733 (2012). [CrossRef] [PubMed]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4510) Fiber optics and optical communications : Optical communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 11, 2013
Revised Manuscript: September 5, 2013
Manuscript Accepted: October 2, 2013
Published: October 22, 2013

Citation
Cuong C. Do, An V. Tran, Simin Chen, Trevor Anderson, Don Hewitt, and Efstratios Skafidas, "Flexible bandwidth DGD estimation for coherent optical OFDM system," Opt. Express 21, 25788-25795 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-25788


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References

  1. D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical performance monitoring,” J. Lightwave Technol.22(1), 294–304 (2004). [CrossRef]
  2. Y. C. Chung, “Optical performance monitoring techniques; current status and future challenge,” in Proceedings of Eur. Conf. on Opt. Comm. (ECOC)2008 (Brussels, Belgium, 2008), pp. W.E.1.D.1.
  3. H. Rosenfeldt, R. Ulrich, E. Brinkmeyer, U. Feiste, C. Schubert, J. Berger, R. Ludwig, H. G. Weber, and A. Ehrhardt, “Feedforward approach for automatic PMD compensation at 80 Gbit/s over 45 km installed single mode fiber,” in Proceedings of Eur. Conf. on Opt. Comm. (ECOC) 2001 (2001), pp. 68–69.
  4. F. Buchali, S. Lanne, J. P. Thiery, W. Baumert, and H. Bulow, “Fast eye monitoring for 10 Gbit/s and its application for optical PMD compensation,” in Proceedings of Opt. Fiber Conf. (OFC)2001(Anaheim, Calif., 2001), pp. TuP5. [CrossRef]
  5. M. S. Faruk, Y. Mori, C. Zhang, K. Igarashi, and K. Kikuchi, “Multi-impairments monitoring from the equalizer in a digital coherent optical receiver,” Opt. Express18, 26929–26936 (2010). [CrossRef]
  6. C. C. Do, A. V. Tran, C. Zhu, S. Chen, L. B. Du, T. Anderson, A. J. Lowery, and E. Skafidas, ” PMD monitoring in 16-QAM coherent optical system using Golay sequences,” in Proceedings of Opto-Elec. and Comm. Conf. (OECC)2012 (Busan, 2012), pp. 6B3–5. [CrossRef]
  7. F. Pittala, F. Hauske, Y. Ye, N. Gonzalez, and I. Monroy, “Fast and robust CD and DGD estimation based on data-aided channel estimation,” in Proceedings of Inter. Conf. on Transparent Opt. Networks ICTON 2011 (Stockholm, 2011), pp. 1–4. [CrossRef]
  8. G. W. Lu, C. Xie, Y. C. Ku, L. K. Chen, and C. K. Chan, “Enhanced PMD monitoring with frequency-resolved SOP rotation by self phase modulation,” IEEE Photon. Technol. Lett.16(9), 2180–2182 (2004). [CrossRef]
  9. X. Yi, W. Shieh, Y. Ma, Y. Tang, and G. J. Pendock, “Experimental demonstration of optical performance monitoring in coherent optical OFDM systems,” in Proceedings of Opt. Fiber Conf. (OFC)2008 (San Diego, Calif, 2008), pp. OThW3. [CrossRef]
  10. F. Hauske, J. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. Fludger, D. van den Borne, E. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefficients in coherent receivers,” in Proceedings of Opt. Fiber Conf. (OFC)2008 (San Diego, Calif, 2008), pp. OThW2. [CrossRef]
  11. M. Mayrock and H. Haunstein, “Monitoring of linear and nonlinear signal distortion in coherent optical OFDM transmission,” J. Lightwave Technol.27(16), 3560–3566 (2009). [CrossRef]
  12. S. Chen, T. Anderson, D. Hewitt, A. Tran, and E. Skafidas, “Non-data-aided PMD monitoring for optical OFDM systems using low bandwidth coherent receivers,” in Proceedings of Opt. Fiber Conf. (OFC)2013 (Anaheim, Calif., 2013), pp. JW2A.51. [CrossRef]
  13. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley & Sons, 1998), Chap. 4.
  14. B. Szafraniec, B. Nebendahl, and T. Marshall, “Polarization demultiplexing in Stokes space,” Opt. Express18(17), 17928–17939 (2010). [CrossRef] [PubMed]
  15. S. Chen, T. Anderson, D. Hewitt, A. V. Tran, C. Zhu, L. B. Du, A. J. Lowery, and E. Skafidas, “Optical performance monitoring for OFDM using low bandwidth coherent receivers,” Opt. Express20(27), 28724–28733 (2012). [CrossRef] [PubMed]

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