Abstract

Recently, coherent-detection (CoD) polarization multiplexed (PM) transmission has attracted considerable interest, specifically as a possible solution for next-generation systems transmitting 100 Gb/s per channel and beyond. In this context, enabled by progress in ultra-fast digital signal processing (DSP) electronics, both multilevel phase/amplitude modulated formats (such as QAM) and orthogonal-frequency-division multiplexed (OFDM) formats have been proposed. One specific feature of DSP-supported CoD is the possibility of dealing with fiber chromatic dispersion (CD) electronically, either by post-filtering (PM-QAM) or by appropriately introducing symbol-duration redundancy (PM-OFDM). In both cases, ultra-long-haul fully uncompensated links seem to be possible. In this paper we estimate the computational effort required by CD compensation, when using the PM-QAM or PM-OFDM formats. Such effort, when expressed as number of operations per received bit, was found to be logarithmic with respect to link length, bit rate and fiber dispersion, for both classes of systems. We also found that PM-OFDM may have some advantage over PM-QAM, depending mostly on the over-sampling needed by the two systems. Asymptotically, for large channel memory and small over-sampling, the two systems tend to require the same CD-compensation computational effort. We also showed that the effort required by the mitigation of polarization-related effects can in principle be made small as compared to that of CD over long uncompensated links.

© 2009 Optical Society of America

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References

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  1. R. Noé, "Phase Noise-Tolerant Synchronous QPSK/BPSK Baseband-Type Intradyne Receiver Concept with Feedforward Carrier Recovery," J. Lightwave Technol. 23, 802-808 (2005).
    [CrossRef]
  2. S. Tsukamoto, D. S. Ly-Gagnon, K. Katoh, K. Kikuchi, "Coherent Demodulation of 40-Gbit/s Polarization-Multiplexed QPSK Signals with 16-GHz Spacing after 200-km Transmission," in Proc. OFC 2005, PD paper 29, Anaheim (USA), March. 6-11, (2005).
  3. Y. Han and G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Express 13, 7527-7534 (2005).
    [CrossRef] [PubMed]
  4. D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation," J. Lightwave Technol. 24, 12-21 (2006).
    [CrossRef]
  5. S. J. Savory et al., "Digital Equalisation of 40 Gbit/s per Wavelength Transmission over 2480km of Standard Fibre without Optical Dispersion Compensation," in Proc. ECOC 2006, paper Th2.5.5, Cannes (FR), Sept. 24-28, (2006).
  6. C. R. S. Fludger, T. Duthel, T. Wuth, and C. Schulien, "Uncompensated Transmission of 86 Gbit/s Polarization Multiplexed RZ-QPSK over 100km of NDSF Employing Coherent Equalisation," in Proc. ECOC 2006, PD paper Th4.3.3, Cannes (FR), Sept. 24-28, (2006).
  7. K. Roberts, "Electronic Dispersion Compensation Beyond 10 Gb/s," in Proc. of IEEE LEOS Summer Topical Meetings, Portland (USA), paper MA2.3, Jul. 23-25, (2007).
  8. G. Charlet et al., "12.8 Tbit/s transmission of 160 PDM-QPSK (160X2X40 Gbit/s) channels with coherent detection over 2550 km," Proc. ECOC 2007, paper PD 1.6, Berlin (D), Sept. 16-20, (2007).
  9. C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, Han Sun, M. OSullivan, "WDM Performance and PMD Tolerance of a Coherent 40-Gbit/s Dual-Polarization QPSK Transceiver," J. Lightwave Technol. 26, 168-175 (2008).
    [CrossRef]
  10. C. R. S. Fludger,  et al., "Coherent Equalization and POLMUX-RZ-DQPSK for Robust 100-GE Transmission," J. Lightwave Technol. 26, 64-72 (2008).
    [CrossRef]
  11. J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, "Linear Fiber Impairments Mitigation of 40-Gbit/s Polarization-Multiplexed QPSK by Digital Processing in a Coherent Receiver," J. Lightwave Technol. 26, 36-42 (2008).
    [CrossRef]
  12. W. Shieh, H. Bao, and Y. Yang, "Coherent Optical OFDM: Theory and Design," Opt. Express 16, 841-859 (2008).
    [CrossRef] [PubMed]
  13. W. Shieh and C. Athaudage, "Coherent Optical Orthogonal Frequency Division Multiplexing," Electron. Lett. 42, 587-589 (2006).
    [CrossRef]
  14. W. Shieh, X. Yi, and Y. Tang, "Transmission Experiment of Multi-Gigabit Coherent Optical OFDM Systems over 1000 km SSMF Fibre," Electron. Lett. 43, 183184 (2007).
    [CrossRef]
  15. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, "20-Gb/s OFDM Transmission over 4160-km SSMF Enabled by RF-pilot Tone Phase Noise Compensation," Proc. OFC 2007, Anaheim (CA), paper PDP 15, March 25-29, (2007).
  16. S. L. Jansen, I. Morita, T. C. W. Schenck, N. Takeda, and H. Tanaka "Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF," J. Lightwave Technol. 26, 6-15 (2008).
    [CrossRef]
  17. B. Goebel, B. Fesl, L. D. Coelho and N. Hanik, "On the Effect of FWM in Coherent Optical OFDM Systems," in Proc. OFC 2008, Anaheim (CA), paper JWA58, San Diego (CA), Feb. 24-28, (2008).
  18. A. J. Lowery and J. Armstrong, "Orthogonal Frequency Division Multiplexing for Dispersion Compensation of Long-Haul Optical Systems," Opt. Express 14, 2079-2084 (2006).
    [CrossRef] [PubMed]
  19. A. J. Lowery, "Improving Sensitivity and Spectral Efficiency in Direct-Detection Optical OFDM Systems," in Proc. OFC 2008, paper OMM4, San Diego (CA), Feb. 24-28, (2008).
  20. S. L. Jansen, I. Morita and H. Tanaka, "16x52.5-Gb/s, 50-GHz Spaced, POLMUX-CO-OFDM Transmission over 4,160 km of SSMF Enabled by MIMO Processing," in Proc. ECOC 2007, paper PD 1.3, Berlin (D), Sept. 16-20, (2007).
  21. S. L. Jansen, I. Morita and H. Tanaka, "10x121.9-Gb/s PDM-ODFM Transmission with 2-b/s/Hz Spectral Efficiency over 1,000 km of SSMF," in Proc. OFC 2008, paper PDP2, San Diego (CA), Feb. 24-28, (2008).
  22. Y. Ma, W. Shieh, and Qi Yang, "Bandwidth-Efficient 21.4 Gb/s Coherent Optical 2x2 MIMO OFDM Transmission," in Proc. OFC 2008, paper JWA59, San Diego (CA), Feb. 24-28, (2008).
  23. E. Yamada,  et al., "Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1 Tb/s (50x88.8 Gb/s) DWDM Link over 800 km SMF Including 50-Ghz Spaced ROADM Nodes," in Proc. OFC 2008, paper PDP8, San Diego (CA), Feb. 24-28, (2008).
  24. W. Shieh, Q. Yang, and Y. Ma, "107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing," Opt. Express 16, 6378-6386 (2008).
    [CrossRef] [PubMed]
  25. H. Bulow, B. Franz, A. Klekkamp, and F. Buchali, "40 Gb/s Distortion Mitigation and DSP-Based Equalisation," in Proc. ECOC 2007, Berlin, Germany, Sept. (2007).
  26. A. V. Oppenheim and R. V. Schafer, Digital Signal Processing, (Prentice-Hall Inc., Englewood Cliffs, NJ, 1975), pp. 110-113.
  27. S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, San Diego, CA, 1997) Chap. 18.
  28. L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA, (John Wiley and Sons, Hoboken, NJ, 2003).
  29. X. Yi, W. Shieh, and Y . Tang, "Phase Estimation for Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 919-921 (2007).
    [CrossRef]
  30. J. H. Winters, "Equalization in Coherent Transmission Systems using a Fractionally Spaced Equalizer," J. Lightwave Technol. 8, 1487-1491 (1990).
    [CrossRef]
  31. M. G. Taylor, "Coherent Detection Method using DSP for Demodulation of Signal and Subsequent Equalization of Propagation Impairments," IEEE Photon. Technol. Lett. 16, 674676 (2004).
    [CrossRef]
  32. E. Ip and J. M. Kahn, "Digital Equalization of Chromatic Dispersion and Polarization Mode Dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
    [CrossRef]
  33. S. J. Savory, "Digital Filters for Coherent Optical Receivers," Opt. Express 16, 805-817 (2008).
    [CrossRef]
  34. G. Bosco, P. Poggiolini, and M. Visintin, "Performance Analysis of MLSE Receivers Based on the Square-Root Metric", J. Lightwave Technol. 26, 2098-2109 (2007).
    [CrossRef]
  35. P. Poggiolini, G. Bosco, and M. Visintin, "MLSE Receivers and Their Applications in Optical Transmission Systems", in Proc. of The 20th Annual Meeting of the IEEE LEOS, Lake Buena Vista, Florida (U.S.A.), 21-25 Oct., pp. 216-217, (2007).
  36. P. Poggiolini, G. Bosco, Y. Benlachtar, S. J. Savory, P. Bayvel, R. I. Killey, and J. Prat, "Long-Haul 10 Gbit/s Linear and Non-Linear IMDD Transmission over Uncompensated Standard Fiber Using a SQRT-Metric MLSE Receiver," Opt. Express 16, 12919-12936 (2008).
    [CrossRef] [PubMed]
  37. Xingwen Yi,W. Shieh, and Yiran Ma, "Phase Noise Effects on High Spectral Efficiency Coherent Optical OFDM Transmission," J. Lightwave Technol. 26, 1309-1316 (2008).
    [CrossRef]
  38. H. C. Bao and W. Shieh, "Transmission of Wavelength-Division-Multiplexed Channels With Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 922-924 (2007).
    [CrossRef]
  39. P. Duhamel and H. Hollmann, "Split-radix FFT algorithm," Electron. Lett. 20, 14-16 (1984).
    [CrossRef]

2008 (9)

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, Han Sun, M. OSullivan, "WDM Performance and PMD Tolerance of a Coherent 40-Gbit/s Dual-Polarization QPSK Transceiver," J. Lightwave Technol. 26, 168-175 (2008).
[CrossRef]

C. R. S. Fludger,  et al., "Coherent Equalization and POLMUX-RZ-DQPSK for Robust 100-GE Transmission," J. Lightwave Technol. 26, 64-72 (2008).
[CrossRef]

J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, "Linear Fiber Impairments Mitigation of 40-Gbit/s Polarization-Multiplexed QPSK by Digital Processing in a Coherent Receiver," J. Lightwave Technol. 26, 36-42 (2008).
[CrossRef]

W. Shieh, H. Bao, and Y. Yang, "Coherent Optical OFDM: Theory and Design," Opt. Express 16, 841-859 (2008).
[CrossRef] [PubMed]

S. L. Jansen, I. Morita, T. C. W. Schenck, N. Takeda, and H. Tanaka "Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF," J. Lightwave Technol. 26, 6-15 (2008).
[CrossRef]

W. Shieh, Q. Yang, and Y. Ma, "107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing," Opt. Express 16, 6378-6386 (2008).
[CrossRef] [PubMed]

S. J. Savory, "Digital Filters for Coherent Optical Receivers," Opt. Express 16, 805-817 (2008).
[CrossRef]

P. Poggiolini, G. Bosco, Y. Benlachtar, S. J. Savory, P. Bayvel, R. I. Killey, and J. Prat, "Long-Haul 10 Gbit/s Linear and Non-Linear IMDD Transmission over Uncompensated Standard Fiber Using a SQRT-Metric MLSE Receiver," Opt. Express 16, 12919-12936 (2008).
[CrossRef] [PubMed]

Xingwen Yi,W. Shieh, and Yiran Ma, "Phase Noise Effects on High Spectral Efficiency Coherent Optical OFDM Transmission," J. Lightwave Technol. 26, 1309-1316 (2008).
[CrossRef]

2007 (5)

H. C. Bao and W. Shieh, "Transmission of Wavelength-Division-Multiplexed Channels With Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 922-924 (2007).
[CrossRef]

G. Bosco, P. Poggiolini, and M. Visintin, "Performance Analysis of MLSE Receivers Based on the Square-Root Metric", J. Lightwave Technol. 26, 2098-2109 (2007).
[CrossRef]

E. Ip and J. M. Kahn, "Digital Equalization of Chromatic Dispersion and Polarization Mode Dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
[CrossRef]

X. Yi, W. Shieh, and Y . Tang, "Phase Estimation for Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 919-921 (2007).
[CrossRef]

W. Shieh, X. Yi, and Y. Tang, "Transmission Experiment of Multi-Gigabit Coherent Optical OFDM Systems over 1000 km SSMF Fibre," Electron. Lett. 43, 183184 (2007).
[CrossRef]

2006 (3)

2005 (2)

2004 (1)

M. G. Taylor, "Coherent Detection Method using DSP for Demodulation of Signal and Subsequent Equalization of Propagation Impairments," IEEE Photon. Technol. Lett. 16, 674676 (2004).
[CrossRef]

1990 (1)

J. H. Winters, "Equalization in Coherent Transmission Systems using a Fractionally Spaced Equalizer," J. Lightwave Technol. 8, 1487-1491 (1990).
[CrossRef]

1984 (1)

P. Duhamel and H. Hollmann, "Split-radix FFT algorithm," Electron. Lett. 20, 14-16 (1984).
[CrossRef]

Armstrong, J.

Athaudage, C.

W. Shieh and C. Athaudage, "Coherent Optical Orthogonal Frequency Division Multiplexing," Electron. Lett. 42, 587-589 (2006).
[CrossRef]

Bao, H.

Bao, H. C.

H. C. Bao and W. Shieh, "Transmission of Wavelength-Division-Multiplexed Channels With Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 922-924 (2007).
[CrossRef]

Bayvel, P.

Benlachtar, Y.

Bigo, S.

Bosco, G.

Charlet, G.

Duhamel, P.

P. Duhamel and H. Hollmann, "Split-radix FFT algorithm," Electron. Lett. 20, 14-16 (1984).
[CrossRef]

Fludger, C. R. S.

Han, Y.

Han Sun, D.

Hollmann, H.

P. Duhamel and H. Hollmann, "Split-radix FFT algorithm," Electron. Lett. 20, 14-16 (1984).
[CrossRef]

Ip, E.

Jansen, S. L.

Kahn, J. M.

Katoh, K.

Kikuchi, K.

Killey, R. I.

Laperle, C.

Li, G.

Lowery, A. J.

Ly-Gagnon, D. S.

Ma, Y.

Mardoyan, H.

McGhan, D.

Morita, I.

Noé, R.

Pardo, O. B.

Poggiolini, P.

Prat, J.

Renaudier, J.

Salsi, M.

Savory, S. J.

Schenck, T. C. W.

Shieh, W.

W. Shieh, Q. Yang, and Y. Ma, "107 Gb/s coherent optical OFDM transmission over 1000-km SSMF fiber using orthogonal band multiplexing," Opt. Express 16, 6378-6386 (2008).
[CrossRef] [PubMed]

W. Shieh, H. Bao, and Y. Yang, "Coherent Optical OFDM: Theory and Design," Opt. Express 16, 841-859 (2008).
[CrossRef] [PubMed]

W. Shieh, X. Yi, and Y. Tang, "Transmission Experiment of Multi-Gigabit Coherent Optical OFDM Systems over 1000 km SSMF Fibre," Electron. Lett. 43, 183184 (2007).
[CrossRef]

H. C. Bao and W. Shieh, "Transmission of Wavelength-Division-Multiplexed Channels With Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 922-924 (2007).
[CrossRef]

X. Yi, W. Shieh, and Y . Tang, "Phase Estimation for Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 919-921 (2007).
[CrossRef]

W. Shieh and C. Athaudage, "Coherent Optical Orthogonal Frequency Division Multiplexing," Electron. Lett. 42, 587-589 (2006).
[CrossRef]

Takeda, N.

Tanaka, H.

Tang, Y

X. Yi, W. Shieh, and Y . Tang, "Phase Estimation for Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 919-921 (2007).
[CrossRef]

Tang, Y.

W. Shieh, X. Yi, and Y. Tang, "Transmission Experiment of Multi-Gigabit Coherent Optical OFDM Systems over 1000 km SSMF Fibre," Electron. Lett. 43, 183184 (2007).
[CrossRef]

Taylor, M. G.

M. G. Taylor, "Coherent Detection Method using DSP for Demodulation of Signal and Subsequent Equalization of Propagation Impairments," IEEE Photon. Technol. Lett. 16, 674676 (2004).
[CrossRef]

Tran, P.

Tsukamoto, S.

Villeneuve, B.

Visintin, M.

Winters, J. H.

J. H. Winters, "Equalization in Coherent Transmission Systems using a Fractionally Spaced Equalizer," J. Lightwave Technol. 8, 1487-1491 (1990).
[CrossRef]

Xingwen Yi,

Yang, Q.

Yang, Y.

Yi, X.

W. Shieh, X. Yi, and Y. Tang, "Transmission Experiment of Multi-Gigabit Coherent Optical OFDM Systems over 1000 km SSMF Fibre," Electron. Lett. 43, 183184 (2007).
[CrossRef]

X. Yi, W. Shieh, and Y . Tang, "Phase Estimation for Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 919-921 (2007).
[CrossRef]

Zhang, Z.

Electron. Lett. (3)

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 Fibre," Electron. Lett. 43, 183184 (2007).
[CrossRef]

P. Duhamel and H. Hollmann, "Split-radix FFT algorithm," Electron. Lett. 20, 14-16 (1984).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

X. Yi, W. Shieh, and Y . Tang, "Phase Estimation for Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 919-921 (2007).
[CrossRef]

M. G. Taylor, "Coherent Detection Method using DSP for Demodulation of Signal and Subsequent Equalization of Propagation Impairments," IEEE Photon. Technol. Lett. 16, 674676 (2004).
[CrossRef]

H. C. Bao and W. Shieh, "Transmission of Wavelength-Division-Multiplexed Channels With Coherent Optical OFDM," IEEE Photon. Technol. Lett. 19, 922-924 (2007).
[CrossRef]

J. Lightwave Technol. (10)

Xingwen Yi,W. Shieh, and Yiran Ma, "Phase Noise Effects on High Spectral Efficiency Coherent Optical OFDM Transmission," J. Lightwave Technol. 26, 1309-1316 (2008).
[CrossRef]

E. Ip and J. M. Kahn, "Digital Equalization of Chromatic Dispersion and Polarization Mode Dispersion," J. Lightwave Technol. 25, 2033-2043 (2007).
[CrossRef]

G. Bosco, P. Poggiolini, and M. Visintin, "Performance Analysis of MLSE Receivers Based on the Square-Root Metric", J. Lightwave Technol. 26, 2098-2109 (2007).
[CrossRef]

J. H. Winters, "Equalization in Coherent Transmission Systems using a Fractionally Spaced Equalizer," J. Lightwave Technol. 8, 1487-1491 (1990).
[CrossRef]

S. L. Jansen, I. Morita, T. C. W. Schenck, N. Takeda, and H. Tanaka "Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF," J. Lightwave Technol. 26, 6-15 (2008).
[CrossRef]

R. Noé, "Phase Noise-Tolerant Synchronous QPSK/BPSK Baseband-Type Intradyne Receiver Concept with Feedforward Carrier Recovery," J. Lightwave Technol. 23, 802-808 (2005).
[CrossRef]

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation," J. Lightwave Technol. 24, 12-21 (2006).
[CrossRef]

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, Han Sun, M. OSullivan, "WDM Performance and PMD Tolerance of a Coherent 40-Gbit/s Dual-Polarization QPSK Transceiver," J. Lightwave Technol. 26, 168-175 (2008).
[CrossRef]

C. R. S. Fludger,  et al., "Coherent Equalization and POLMUX-RZ-DQPSK for Robust 100-GE Transmission," J. Lightwave Technol. 26, 64-72 (2008).
[CrossRef]

J. Renaudier, G. Charlet, M. Salsi, O. B. Pardo, H. Mardoyan, P. Tran, and S. Bigo, "Linear Fiber Impairments Mitigation of 40-Gbit/s Polarization-Multiplexed QPSK by Digital Processing in a Coherent Receiver," J. Lightwave Technol. 26, 36-42 (2008).
[CrossRef]

Opt. Express (6)

Other (17)

P. Poggiolini, G. Bosco, and M. Visintin, "MLSE Receivers and Their Applications in Optical Transmission Systems", in Proc. of The 20th Annual Meeting of the IEEE LEOS, Lake Buena Vista, Florida (U.S.A.), 21-25 Oct., pp. 216-217, (2007).

H. Bulow, B. Franz, A. Klekkamp, and F. Buchali, "40 Gb/s Distortion Mitigation and DSP-Based Equalisation," in Proc. ECOC 2007, Berlin, Germany, Sept. (2007).

A. V. Oppenheim and R. V. Schafer, Digital Signal Processing, (Prentice-Hall Inc., Englewood Cliffs, NJ, 1975), pp. 110-113.

S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, San Diego, CA, 1997) Chap. 18.

L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA, (John Wiley and Sons, Hoboken, NJ, 2003).

B. Goebel, B. Fesl, L. D. Coelho and N. Hanik, "On the Effect of FWM in Coherent Optical OFDM Systems," in Proc. OFC 2008, Anaheim (CA), paper JWA58, San Diego (CA), Feb. 24-28, (2008).

A. J. Lowery, "Improving Sensitivity and Spectral Efficiency in Direct-Detection Optical OFDM Systems," in Proc. OFC 2008, paper OMM4, San Diego (CA), Feb. 24-28, (2008).

S. L. Jansen, I. Morita and H. Tanaka, "16x52.5-Gb/s, 50-GHz Spaced, POLMUX-CO-OFDM Transmission over 4,160 km of SSMF Enabled by MIMO Processing," in Proc. ECOC 2007, paper PD 1.3, Berlin (D), Sept. 16-20, (2007).

S. L. Jansen, I. Morita and H. Tanaka, "10x121.9-Gb/s PDM-ODFM Transmission with 2-b/s/Hz Spectral Efficiency over 1,000 km of SSMF," in Proc. OFC 2008, paper PDP2, San Diego (CA), Feb. 24-28, (2008).

Y. Ma, W. Shieh, and Qi Yang, "Bandwidth-Efficient 21.4 Gb/s Coherent Optical 2x2 MIMO OFDM Transmission," in Proc. OFC 2008, paper JWA59, San Diego (CA), Feb. 24-28, (2008).

E. Yamada,  et al., "Novel No-Guard-Interval PDM CO-OFDM Transmission in 4.1 Tb/s (50x88.8 Gb/s) DWDM Link over 800 km SMF Including 50-Ghz Spaced ROADM Nodes," in Proc. OFC 2008, paper PDP8, San Diego (CA), Feb. 24-28, (2008).

S. Tsukamoto, D. S. Ly-Gagnon, K. Katoh, K. Kikuchi, "Coherent Demodulation of 40-Gbit/s Polarization-Multiplexed QPSK Signals with 16-GHz Spacing after 200-km Transmission," in Proc. OFC 2005, PD paper 29, Anaheim (USA), March. 6-11, (2005).

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, "20-Gb/s OFDM Transmission over 4160-km SSMF Enabled by RF-pilot Tone Phase Noise Compensation," Proc. OFC 2007, Anaheim (CA), paper PDP 15, March 25-29, (2007).

S. J. Savory et al., "Digital Equalisation of 40 Gbit/s per Wavelength Transmission over 2480km of Standard Fibre without Optical Dispersion Compensation," in Proc. ECOC 2006, paper Th2.5.5, Cannes (FR), Sept. 24-28, (2006).

C. R. S. Fludger, T. Duthel, T. Wuth, and C. Schulien, "Uncompensated Transmission of 86 Gbit/s Polarization Multiplexed RZ-QPSK over 100km of NDSF Employing Coherent Equalisation," in Proc. ECOC 2006, PD paper Th4.3.3, Cannes (FR), Sept. 24-28, (2006).

K. Roberts, "Electronic Dispersion Compensation Beyond 10 Gb/s," in Proc. of IEEE LEOS Summer Topical Meetings, Portland (USA), paper MA2.3, Jul. 23-25, (2007).

G. Charlet et al., "12.8 Tbit/s transmission of 160 PDM-QPSK (160X2X40 Gbit/s) channels with coherent detection over 2550 km," Proc. ECOC 2007, paper PD 1.6, Berlin (D), Sept. 16-20, (2007).

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Figures (7)

Fig. 1.
Fig. 1.

Typical Tx structures for PM-QAM and PM-OFDM. Legend: ‘PBS’, polarizing beam splitter; ‘MOD’, electro-optical modulator (typically nested Mach-Zehnder); ‘DES’, data deserializer; ‘SER’, data serializer; ‘DAC’, digital-to-analog converter. Depending on specific implementations and, for PM-QAM, the size of the constellation, certain blocks/functions could be omitted or simplified.

Fig. 2.
Fig. 2.

Typical Rx structures for PM-QAM and PM-OFDM, with only CD-compensation post-processing shown. All other processing is omitted. Legend: ‘PBS’, polarizing beam splitter; ‘Bal’, dual balanced photo-detector; ‘LPF’, low-pass filter; ‘ADC’, analog-to-digital converter. The ‘CD FIR’ block for PM-QAM may contain an FFT and IFFT if implemented in frequency-domain. The ‘CD comp’ block for PM-OFDM multiplies each element of the FFT output array by a suitable complex number.

Fig. 3.
Fig. 3.

Necessary number of OFDM subcarriers N′sc vs. system OSNR penalty ∆OSNRdB, for uncompensated links of 1000, 2000 and 3000 km (dash-dotted, dashed and solid lines, respectively). The system parameters are shown in Table 1.

Fig. 4.
Fig. 4.

Operations per transmitted bit for PM-OFDM and PM-QPSK, vs. link length at 111 Gb/s (top) and vs. bit rate at 1000 km (bottom). D=16.7 ps/(nm·km). Other parameters: for PM-OFDM, k = 1.122 and n Tx = n Rx = 1.25; for PM-QPSK, p = 7.5 and n Rx = 1.5. The FFT parameter q was set to 5.

Fig. 5.
Fig. 5.

Single-stage compensation for combined CD and polarization-effects, using the ‘butterfly’ structure which mixes the ‘x’ and ‘y’ received polarizations. ‘POL’ stands for polarization effects, including birefringence, DGD and PDL. The ‘OAFD’ blocks for PM-QAM perform Overlap-and-Add Frequency-Domain FIR filtering, using 4 suitable complex transfer functions. The ‘COMP’ blocks for PM-OFDM perform an element-by-element complex multiplication between the FFT output arrays and suitable complex compensation arrays.

Fig. 6.
Fig. 6.

Dual-stage compensation for combined CD and polarization-effects, for PM-QAM. The first stage is implemented in frequency-domain. The second-stage ‘butterfly’ structure could be implemented either in time or frequency-domain.

Fig. 7.
Fig. 7.

Operations per transmitted bit for PM-OFDM and PM-QPSK, vs. link length at 111 Gb/s, with fixed DGD τDGD = 120 ps. D=16.7 ps/(nm·km). Other parameters: for PM-OFDM, k = 1.122 and n Tx = n Rx = 1.25; for PM-QPSK, p = 7.5 and n Rx = 1.5. The FFT parameter q was set to 5. Solid and dashed lines: ‘single-stage’ processing; dashed-dotted line: ‘dual-stage’ processing for PM-QPSK.

Tables (1)

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Table 1. Reference System Parameters

Equations (33)

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T s = R s 1 = N SC · M R b .
Δ τ g = λ 2 c D ( f N SC f 1 ) L .
T′ s = T s + Δ τ g .
R′ s = 1 T′ s = R s 1 + Δ τ g T s .
R′ b = R s 1 + Δ τ g T s .
R′ s = R b N′ S C · M
N′ S C = [ 1 8 D · L · R b 2 N S C · M 2 ] 1 · N S C
k = N′ S C N S C .
ρ′ B = ρ B · k 1 .
ΔOSNR dB = 10 log 10 ( k ) .
N′ S C = k 2 k 1 8 D · L · R b 2 M 2 .
O P b = O P s , Tx + O P s , Rx N′ S C · M
O P = q · N log 2 ( N ) .
O P s , Tx = 2 q · n Tx N′ S C · log 2 ( n Tx N′ S C ) .
O P b = 2 q M n Tx log 2 ( n Tx k 2 k 1 8 D · L · R b 2 M 2 ) + 2 q M n Rx log 2 ( n Rx k 2 k 1 8 D · L · R b 2 M 2 ) .
O P b , PM OFDM = 2 q M n Tx log 2 ( n Tx k 2 k 1 8 D · L · R b 2 M 2 ) + 2 q M n Rx log 2 ( n Rx k 2 k 1 8 D · L · R b 2 M 2 ) + 12 M .
τ F = 10 · λ 2 3 π · c D · L R s 2 .
μ = λ 2 c 1 D L · R s 2 .
N F = 8 n R x D L · R s 2 = 8 n R x D L · R b 2 M 2 = n R x · μ
N′ S C = k 2 k 1 μ .
O P b , PM OFDM = 2 q M n Tx log 2 ( n Tx k 2 k 1 μ ) + 2 q M n Rx log 2 ( n Rx k 2 k 1 μ ) + 12 M .
O P b , PM QAM / TD = 4 n R x 2 ( 4 μ 1 ) / M
O P i = 4 q · ( P + N F ) · log 2 ( P + N F ) + 12 P + 16 N F .
O P b = 4 n Rx M · P [ q · ( P + N F ) · log 2 ( P + N F ) + 3 P + 4 N F ] .
O P b , PM QAM = 4 n Rx p M [ q ( 1 + p ) log 2 ( [ 1 + P ] N F ) + 3 P + 4 ] =
= 4 n Rx p M [ q ( 1 + p ) p log 2 ( 8 n Rx [ 1 + p ] D L R b 2 M 2 ) + 3 + 4 p ] .
O P b , PM QAM = 4 n Rx p M [ q ( 1 + p ) p log 2 ( 8 n Rx [ 1 + p ] μ ) + 3 + 4 p ] .
O P b , PM QAM = 4 q M [ ( 1 + p ) p log 2 ( μ ) + ( 1 + p ) p log 2 ( 1 + p ) + 3 q + 4 p q ] ,
O P b , PM OFDM = 4 q M [ log 2 ( μ ) + log 2 ( k 2 k 1 ) + 3 q ] .
O P b , PM QAM = O P b , PM OFDM 4 q M log 2 ( μ ) .
μ μ C D + μ D G D
O P b , PM OFDM = 2 q M n Tx log 2 ( n Tx k 2 k 1 μ ) + 2 q M n Rx log 2 ( n Rx k 2 k 1 μ ) + 28 M .
O P b , PM QAM = 4 n Rx p M [ q ( 1 + p ) p log 2 ( n Rx [ 1 + p ] μ ) + 7 + 8 p ] .

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