Abstract

We present an efficient channel estimation method for coherent optical OFDM (CO-OFDM) based on intra-symbol frequency-domain averaging (ISFA), and systematically study its robustness against transmission impairments such as optical noise, chromatic dispersion (CD), polarization-mode dispersion (PMD), polarization-dependent loss (PDL), and fiber nonlinearity. Numerical simulations are performed for a 112-Gb/s polarization-division multiplexed (PDM) CO-OFDM signal, and the ISFA-based channel estimation and the subsequent channel compensation are found to be highly robust against these transmission impairments in typical optical transport systems.

©2008 Optical Society of America

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References

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  1. See, for example, IEEE standards 802.11a, 802.11g, and 802.16.
  2. A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” OFC’06, post-deadline paper PDP39.
  3. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587–589 (2006).
    [Crossref]
  4. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14, 3767–3775 (2006).
    [Crossref] [PubMed]
  5. 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,” OFC’07, post-deadline paper PDP15.
  6. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16, 841–859 (2008).
    [Crossref] [PubMed]
  7. A. J. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express 16, 860–865 (2008).
    [Crossref] [PubMed]
  8. S. L. Jansen, I. Morita, T. C. Schenk, and H. Tanaka, “Long-haul transmission of 16×52.5 Gbits/s polarization-division- multiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. 7, 173–182 (2008).
    [Crossref]
  9. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come? [Invited],” J. Opt. Netw. 7, 234–255 (2008).
    [Crossref]
  10. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16, 753–791 (2008).
    [Crossref] [PubMed]
  11. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
    [Crossref] [PubMed]
  12. H. Sun, K. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16, 873–879 (2008)
    [Crossref] [PubMed]
  13. X. Liu and F. Buchali, “Improved nonlinear tolerance of 112-Gb/s PDM-OFDM in dispersionuncompensated transmission with efficient channel estimation,” ECOC’08, paper Mo.3.E.2.
  14. Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” OFC’09, paper OWM6.
  15. M. Shtaif, “Performance degradation in coherent polarization multiplexed systems as a result of polarization dependent loss,” Opt. Express 16, 13918–13932 (2008).
    [Crossref] [PubMed]
  16. A. Mecozzi and M. Shtaif, “Signal-to-noise-ratio degradation caused by polarization-dependent loss and the effect of dynamic gain equalization,” J. Lightwave Technol. 22, 1856–1871 (2004).
    [Crossref]
  17. W. Shieh, “PMD-supported coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19, 134–136 (2007).
    [Crossref]
  18. A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express 15, 13282–13287 (2007).
    [Crossref] [PubMed]
  19. M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.
  20. K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4.
  21. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15, 1351–1353 (1990).
    [Crossref] [PubMed]
  22. R.-J. Essiambre and P J Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” ECOC’05, paper Tu3.2.2.

2008 (8)

2007 (2)

2006 (2)

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587–589 (2006).
[Crossref]

I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14, 3767–3775 (2006).
[Crossref] [PubMed]

2004 (1)

1990 (1)

Armstrong, J.

A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” OFC’06, post-deadline paper PDP39.

Athaudage, C.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587–589 (2006).
[Crossref]

Bao, H.

Barros, D. J. F.

Buchali, F.

X. Liu and F. Buchali, “Improved nonlinear tolerance of 112-Gb/s PDM-OFDM in dispersionuncompensated transmission with efficient channel estimation,” ECOC’08, paper Mo.3.E.2.

Cho, P.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

Djordjevic, I. B.

Du, L.

A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” OFC’06, post-deadline paper PDP39.

Essiambre, R.-J.

R.-J. Essiambre and P J Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” ECOC’05, paper Tu3.2.2.

Forozesh, K.

K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4.

Gordon, J. P.

Ip, E.

Jansen, S. L.

S. L. Jansen, I. Morita, T. C. Schenk, and H. Tanaka, “Long-haul transmission of 16×52.5 Gbits/s polarization-division- multiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. 7, 173–182 (2008).
[Crossref]

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,” OFC’07, post-deadline paper PDP15.

K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4.

Kahn, J. M.

Kaneda, N.

Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” OFC’09, paper OWM6.

Khurgin, J.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

Lau, A. P. T.

Liu, X.

X. Liu and F. Buchali, “Improved nonlinear tolerance of 112-Gb/s PDM-OFDM in dispersionuncompensated transmission with efficient channel estimation,” ECOC’08, paper Mo.3.E.2.

Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” OFC’09, paper OWM6.

Lowery, A. J.

Ma, Y.

Mecozzi, A.

Meiman, Y.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

Mollenauer, L. F.

Morita, I.

S. L. Jansen, I. Morita, T. C. Schenk, and H. Tanaka, “Long-haul transmission of 16×52.5 Gbits/s polarization-division- multiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. 7, 173–182 (2008).
[Crossref]

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,” OFC’07, post-deadline paper PDP15.

K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4.

Nazarathy, M.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

Noe, R.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

Premaratne, M.

Randel, S.

K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4.

Roberts, K.

Savory, S. J.

Schenk, T. C.

Shieh, W.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16, 841–859 (2008).
[Crossref] [PubMed]

W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come? [Invited],” J. Opt. Netw. 7, 234–255 (2008).
[Crossref]

W. Shieh, “PMD-supported coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19, 134–136 (2007).
[Crossref]

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587–589 (2006).
[Crossref]

Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” OFC’09, paper OWM6.

Shpantzer, I.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

Shtaif, M.

Sun, H.

Takeda, N.

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,” OFC’07, post-deadline paper PDP15.

Tanaka, H.

S. L. Jansen, I. Morita, T. C. Schenk, and H. Tanaka, “Long-haul transmission of 16×52.5 Gbits/s polarization-division- multiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. 7, 173–182 (2008).
[Crossref]

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,” OFC’07, post-deadline paper PDP15.

K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4.

Tang, Y.

Vasic, B.

Wang, S.

Weidenfeld, R.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

Winzer, P J

R.-J. Essiambre and P J Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” ECOC’05, paper Tu3.2.2.

Wu, K.

Yang, Q.

W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come? [Invited],” J. Opt. Netw. 7, 234–255 (2008).
[Crossref]

Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” OFC’09, paper OWM6.

Yi, X.

Electron. Lett. (1)

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587–589 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (1)

W. Shieh, “PMD-supported coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19, 134–136 (2007).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Netw. (2)

Opt. Express (8)

Opt. Lett. (1)

Other (8)

See, for example, IEEE standards 802.11a, 802.11g, and 802.16.

A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” OFC’06, post-deadline paper PDP39.

M. Nazarathy, J. Khurgin, R. Weidenfeld, Y. Meiman, P. Cho, R. Noe, and I. Shpantzer, “The FWM impairment in coherent OFDM compounds on a phased-array basis over dispersive multi-span links,” in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CWA4.

K. Forozesh, S. L. Jansen, S. Randel, I. Morita, and H. Tanaka, “The influence of the dispersion map in coherent optical OFDM transmission systems,” in Coherent Optical Communications Systems, (IEEE LEOS Summer Topic Meetings, 2008), paper WC2.4.

R.-J. Essiambre and P J Winzer, “Fibre nonlinearities in electronically pre-distorted transmission,” ECOC’05, paper Tu3.2.2.

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,” OFC’07, post-deadline paper PDP15.

X. Liu and F. Buchali, “Improved nonlinear tolerance of 112-Gb/s PDM-OFDM in dispersionuncompensated transmission with efficient channel estimation,” ECOC’08, paper Mo.3.E.2.

Q. Yang, N. Kaneda, X. Liu, and W. Shieh, “Demonstration of frequency-domain averaging based channel estimation for 40-Gb/s CO-OFDM with high PMD,” OFC’09, paper OWM6.

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Figures (17)

Fig. 1.
Fig. 1. Schematic of a 112-Gb/s PDM CO-OFDM system architecture. PMDC: PMD compensation. EDC: electronic dispersion compensation. PA-CPEC: pilot-assisted common phase error compensation. DAC: digital-to-analog converter. ADC: analog-to-digital converter, PBS: polarization beam splitter.

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Fig. 2.
Fig. 2. Allocations of the OFDM data subcarriers and pilot subcarriers.

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Fig. 3.
Fig. 3. Channel matrix coefficients as a function of the modulated subcarrier index without (left) and with (right) the ISFA process. <DGD>=100 ps. OSNR=15.5 dB.

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Fig. 4.
Fig. 4. Simulated BER of the 112-Gb/s PDM-OFDM signal vs. OSNR in the back-to-back case.

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Fig. 5.
Fig. 5. The phases of the subcarriers estimated by the ISFA-based channel estimation process using m=6 when the OFDM signal experiences 6800-ps/nm (upper) and 21,760-ps/nm (lower) dispersion. The dashed curves are based on the calculations from the theory.

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Fig. 6.
Fig. 6. Received signal Q factor as a function of the CD experienced by the signal prior to the ISFA process with m=6. OSNR=15.5 dB.

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Fig. 7.
Fig. 7. Received signal Q factor as a function of the DGD experienced by the signal prior to the ISFA process with m=6. OSNR=15.5 dB.

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Fig. 8.
Fig. 8. Estimated channel coefficients |a(k)|2, |b(k)|2, |c(k)|2, and |d(k)|2 after the ISFA for 20 different PMD realizations with <DGD>=25 ps.

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Fig. 9.
Fig. 9. Contour plots of the estimated coefficients |a(k)|2 (left) and |b(k)|2 (right) after the ISFA for 50 different PMD realizations with <DGD>=25 ps.

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Fig. 10.
Fig. 10. Contour plots of the estimated coefficients |a(k)|2 (left) and |b(k)|2 (right) after the ISFA for 50 different PMD realizations with <DGD>=100 ps.

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Fig. 11.
Fig. 11. The distribution of received signal Q factors (derived from BER) after transmission over a fiber link with 50 different PMD realizations and <DGD>=25 ps (left) and 100 ps (right). OSNR=16.5 dB.

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Fig. 12.
Fig. 12. The distributions of the received signal Q factors after transmission over a fiber link with 10,000 different fiber realizations for <PDL>=0 dB (left column) and 4 dB (right column) and for <DGD>=0 ps (upper row), 25 ps (middle row), and 100 ps (lower row). OSNR=15.5(16.5) dB for <PDL>=0(4) dB.

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Fig. 13.
Fig. 13. Simulated signal Q factor after transmission over 16×80-km fiber spans vs. signal launch power Pin (a) and total nonlinear phase shift ΦNL (b). The received OSNR is fixed at 16.5 dB.

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Fig. 14.
Fig. 14. Simulated Q factor after single-channel transmission over 16×80-km SSMF spans vs. signal launch power Pin. The received OSNR increases proportionally with Pin and equals 15.5 dB at Pin=2 dBm.

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Fig. 15.
Fig. 15. Simulated Q factor vs. signal launch power for dispersion-managed transmission with different values of residual dispersion per span (RDPS). The results for dispersion-less (D=0) and dispersion-unmanaged transmission are plotted for comparison. The received OSNR is fixed at 16.5 dB.

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Fig. 16.
Fig. 16. Simulated optical spectrum of a 50-GHz spaced WDM system with 7×112-Gb/s PDM CO-OFDM wavelength channels.

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Fig. 17.
Fig. 17. Simulated Q factor of the center channel vs. Pin after the transmission over a 16×80-km SSMF link. Insets: the received x- and y- signal constellations at Pin=1 dBm.

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Tables (1)

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Table 1. OFDM design parameters used in this study.

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Equations (9)

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[ s ' x ( k ) s ' y ( k ) ] = [ a ( k ) b ( k ) c ( k ) d ( k ) ] [ s x ( k ) s y ( k ) ] ,
t 1 = [ t x 0 ] , t 2 = [ 0 t y ] ,
t ' 1 ( k ) = [ t ' 1 x ( k ) t ' 1 y ( k ) ] = [ a ( k ) t x ( k ) c ( k ) t x ( k ) ] , t ' 2 ( k ) = [ t ' 2 x ( k ) t ' 2 y ( k ) ] = [ b ( k ) t y ( k ) d ( k ) t y ( k ) ] .
[ a ( k ) b ( k ) c ( k ) d ( k ) ] = [ t ' 1 x ( k ) ⁄ t x ( k ) t ' 2 x ( k ) ⁄ t y ( k ) t ' 1 y ( k ) ⁄ t x ( k ) t ' 2 y ( k ) ⁄ t y ( k ) ] .
[ a ( k ' ) b ( k ' ) c ( k ' ) d ( k ' ) ] ISFA = 1 min ( k max , k ' + m ) − max ( k min , k ' − m ) + 1 ∑ k = k ' − m k ' + m [ a ( k ) b ( k ) c ( k ) d ( k ) ] ,
∣ D ISFA ( ps ⁄ nm ) ∣ < 10 6 8 π · Δ f OFDM ( GHz ) · Δ f ISFA ( GHz ) ,
DGD ( ps ) < 10 2 Δ f ISFA ( GHz ) ,
∣ a ( k ) ∣ 2 = 1 − ∣ b ( k ) ∣ 2 , ∣ c ( k ) ∣ 2 = 1 − ∣ d ( k ) ∣ 2 ,
∣ a ( k ) ∣ 2 = ∣ d ( k ) ∣ 2 , ∣ b ( k ) ∣ 2 = ∣ c ( k ) ∣ 2 .

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