Abstract

In this paper, we conduct theoretical and experimental study on the PMD-supported transmission with coherent optical orthogonal frequency-division multiplexing (CO-OFDM). We first present the model for the optical fiber communication channel in the presence of the polarization effects. It shows that the optical fiber channel model can be treated as a special kind of multiple-input multiple-output (MIMO) model, namely, a two-input two-output (TITO) model which is intrinsically represented by a two-element Jones vector familiar to the optical communications community. The detailed discussions on variations of such coherent optical MIMO-OFDM (CO-MIMO-OFDM) models are presented. Furthermore, we show the first experiment of polarization-diversity detection in CO-OFDM systems. In particular, a CO-OFDM signal at 10.7 Gb/s is successfully recovered after 900 ps differential-group-delay (DGD) and 1000-km transmission through SSMF fiber without optical dispersion compensation. The transmission experiment with higher-order PMD further confirms the resilience of the CO-OFDM signal to PMD in the transmission fiber. The nonlinearity performance of PMD-supported transmission is also reported. For the first time, nonlinear phase noise mitigation based on receiver digital signal processing is experimentally demonstrated for COOFDM transmission.

© 2007 Optical Society of America

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References

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  1. C. Poole, R. Tkach, A. Chraplyvy, and D. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
    [CrossRef]
  2. W. Shieh, and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587-589 (2006).
    [CrossRef]
  3. W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon.Technol. Lett. 19, 134-136 (2006).
    [CrossRef]
  4. N. Cvijetic, L. Xu, and T. Wang, "Adaptive PMD Compensation using OFDM in Long-Haul 10Gb/s DWDM Systems," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper OTuA5.
  5. I. B. Djordjevic, "PMD compensation in fiber-optic communication systems with direct detection using LDPC-coded OFDM," Opt. Express 15, 3692-3701 (2007).
    [CrossRef] [PubMed]
  6. C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, "Wavelength division multiplexing (WDM) and Polarization Mode Dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper PDP16.
  7. G. Charlet1, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, "Efficient mitigation of fiber impairments in an ultra-long haul transmission of 40Gbit/s Polarization-multiplexed data, by digital processing in a coherent receiver," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper PDP17.
  8. W. Shieh, X. Yi, and Y. Tang, "Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber," Electron. Lett.,  43, 183-185 (2007).
    [CrossRef]
  9. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka; "20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper PDP15.
  10. N. Gisin, and B. Huttner, "Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers," Opt. Commun. 142, 119-125 (1997).
    [CrossRef]
  11. H. Bolcskei, D. Gesbert, and A. J. Paulraj, "On the capacity of OFDM-based spatial multiplexing systems," IEEE Trans. Commun. 50 (2), 225-34 (2002).
    [CrossRef]
  12. Y. Tang, W. Shieh, X. Yi, R. Evans, "Optimum design for RF-to-optical up-converter in coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 483 - 485 (2007).
    [CrossRef]
  13. W. Shieh, "On the second-order approximation of PMD," IEEE Photon. Technol. Lett. 12, 290-292 (2000).
    [CrossRef]
  14. H. Bulow, "System outage probability due to first- and second-order PMD," IEEE Photon. Technol. Lett. 10 (5), 696-698 (1998).
    [CrossRef]
  15. W. Shieh, R. S. Tucker, W. Chen, X. Yi, and G. Pendock, "Optical performance monitoring in coherent optical OFDM systems," Opt. Express 15, 350-356 (2007).
    [CrossRef] [PubMed]
  16. K.P. Ho, and J.M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. of Lightwave Technol. 22, 779-783 (2004).
    [CrossRef]
  17. K. Kikuchi, M. Fukase, and S. Kim, "Electronic post-compensation for nonlinear phase noise in a 1000-km 20-Gbit/s optical QPSK transmission system using the homodyne receiver with digital signal processing," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), PaperOTuA2.

2007 (4)

W. Shieh, X. Yi, and Y. Tang, "Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber," Electron. Lett.,  43, 183-185 (2007).
[CrossRef]

Y. Tang, W. Shieh, X. Yi, R. Evans, "Optimum design for RF-to-optical up-converter in coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 483 - 485 (2007).
[CrossRef]

W. Shieh, R. S. Tucker, W. Chen, X. Yi, and G. Pendock, "Optical performance monitoring in coherent optical OFDM systems," Opt. Express 15, 350-356 (2007).
[CrossRef] [PubMed]

I. B. Djordjevic, "PMD compensation in fiber-optic communication systems with direct detection using LDPC-coded OFDM," Opt. Express 15, 3692-3701 (2007).
[CrossRef] [PubMed]

2006 (2)

W. Shieh, and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587-589 (2006).
[CrossRef]

W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon.Technol. Lett. 19, 134-136 (2006).
[CrossRef]

2004 (1)

K.P. Ho, and J.M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. of Lightwave Technol. 22, 779-783 (2004).
[CrossRef]

2002 (1)

H. Bolcskei, D. Gesbert, and A. J. Paulraj, "On the capacity of OFDM-based spatial multiplexing systems," IEEE Trans. Commun. 50 (2), 225-34 (2002).
[CrossRef]

2000 (1)

W. Shieh, "On the second-order approximation of PMD," IEEE Photon. Technol. Lett. 12, 290-292 (2000).
[CrossRef]

1998 (1)

H. Bulow, "System outage probability due to first- and second-order PMD," IEEE Photon. Technol. Lett. 10 (5), 696-698 (1998).
[CrossRef]

1997 (1)

N. Gisin, and B. Huttner, "Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers," Opt. Commun. 142, 119-125 (1997).
[CrossRef]

1991 (1)

C. Poole, R. Tkach, A. Chraplyvy, and D. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

Electron. Lett. (2)

W. Shieh, and C. Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett. 42, 587-589 (2006).
[CrossRef]

W. Shieh, X. Yi, and Y. Tang, "Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber," Electron. Lett.,  43, 183-185 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

C. Poole, R. Tkach, A. Chraplyvy, and D. Fishman, "Fading in lightwave systems due to polarization-mode dispersion," IEEE Photon. Technol. Lett. 3, 68-70 (1991).
[CrossRef]

Y. Tang, W. Shieh, X. Yi, R. Evans, "Optimum design for RF-to-optical up-converter in coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 483 - 485 (2007).
[CrossRef]

W. Shieh, "On the second-order approximation of PMD," IEEE Photon. Technol. Lett. 12, 290-292 (2000).
[CrossRef]

H. Bulow, "System outage probability due to first- and second-order PMD," IEEE Photon. Technol. Lett. 10 (5), 696-698 (1998).
[CrossRef]

IEEE Photon.Technol. Lett. (1)

W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon.Technol. Lett. 19, 134-136 (2006).
[CrossRef]

IEEE Trans. Commun. (1)

H. Bolcskei, D. Gesbert, and A. J. Paulraj, "On the capacity of OFDM-based spatial multiplexing systems," IEEE Trans. Commun. 50 (2), 225-34 (2002).
[CrossRef]

J. of Lightwave Technol. (1)

K.P. Ho, and J.M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. of Lightwave Technol. 22, 779-783 (2004).
[CrossRef]

Opt. Commun. (1)

N. Gisin, and B. Huttner, "Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers," Opt. Commun. 142, 119-125 (1997).
[CrossRef]

Opt. Express (2)

Other (5)

K. Kikuchi, M. Fukase, and S. Kim, "Electronic post-compensation for nonlinear phase noise in a 1000-km 20-Gbit/s optical QPSK transmission system using the homodyne receiver with digital signal processing," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), PaperOTuA2.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, "Wavelength division multiplexing (WDM) and Polarization Mode Dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper PDP16.

G. Charlet1, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, "Efficient mitigation of fiber impairments in an ultra-long haul transmission of 40Gbit/s Polarization-multiplexed data, by digital processing in a coherent receiver," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper PDP17.

N. Cvijetic, L. Xu, and T. Wang, "Adaptive PMD Compensation using OFDM in Long-Haul 10Gb/s DWDM Systems," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper OTuA5.

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka; "20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest, (Optical Society of America, Washington, DC, 2007), Paper PDP15.

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Figures (7)

Fig. 1.
Fig. 1.

Variations of coherent optical MIMO OFDM (CO-MIMO-OFDM) models: (a) single-input single-output (SISO), (b) single-input two-output (SITO), (c) two-input single-output (TISO), and (d) two-input two-output (TITO). The optical OFDM transmitter includes RF OFDM transmitter and OFDM RF-to-optical up-converter, and the optical OFDM receiver includes OFDM optical-to-RF down-converter and RF OFDM receiver. PBC/S: Polarization Beam Combiner/Splitter.

Fig. 2.
Fig. 2.

Experimental setup for PMD-supported CO-OFDM transmission

Fig. 3.
Fig. 3.

(a) and (b) The RF spectra for two polarization components, and (c) the overall RF spectra

Fig. 4.
Fig. 4.

BER performance of a CO-OFDM signal

Fig. 5.
Fig. 5.

BER variation as a function of PMD state

Fig. 6.
Fig. 6.

System performance as a function of launch power. The curve with square is for the monitored Q factor without nonlinearity mitigation. The curve with triangle is for the monitored Q improvement with nonlinearity mitigation.

Fig. 7.
Fig. 7.

System performance as a function of the nonlinear coefficient α used in the receiver-based digital signal processing. The data are shown for both monitored Q and calculated (actual) Q.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

S ( t ) = i = + k = 1 2 N sc + 1 1 2 N sc c ik ( t iT s ) exp ( j 2 π f k ( t iT s ) )
S ( t ) = ( S x S y ) , c ik = ( c ik x c ik y )
f k = k 1 t s
( t ) = { 1 , ( Δ G < t t s ) 0 , ( t Δ G , t > t s )
c f 2 D t · N SC · Δ f + DGD max Δ G
c ki = e j ϕ i · e j Φ D ( f k ) · T k · c ki + n ki
T k = l = 1 N exp { ( 1 2 j · β l · f k 1 2 α l ) · σ }
Φ D ( f k ) = π · c · D t · f k 2 f LD 1 2
c ( 2 i 1 ) k = a ik ( 0 1 )
c ( 2 i ) k = a ik ( 1 0 )
c ik = a ik T k ( 1 0 )
c ki p = H k c ki + n ki p
s ( t ) = ( s x s y ) = s 0 ( t ) exp ( j ϕ NL )
ϕ NL = NL eff γ s 2 = β I 0 s ˜ 2 = α s ˜ 2 , s 2 ( s x 2 + s y 2 )
s 0 ( t ) = s ( t ) exp ( j β s ( t ) 2 )

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