Abstract

Coherent optical OFDM (CO-OFDM) has recently been proposed and the proof-of-concept transmission experiments have shown its extreme robustness against chromatic dispersion and polarization mode dispersion. In this paper, we first review the theoretical fundamentals for CO-OFDM and its channel model in a 2×2 MIMO-OFDM representation. We then present various design choices for CO-OFDM systems and perform the nonlinearity analysis for RF-to-optical up-converter. We also show the receiver-based digital signal processing to mitigate self-phase-modulation (SPM) and Gordon-Mollenauer phase noise, which is equivalent to the mid-span phase conjugation.

© 2008 Optical Society of America

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2007 (7)

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

W. Shieh, X. Yi, Y. Ma, and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Opt. Express 15, 9936-9947 (2007).
[CrossRef] [PubMed]

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

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, "Electronic compensation of chromatic dispersion using a digital coherent receiver," Opt. Express 15, 2120-2126 (2007).
[CrossRef] [PubMed]

X. Yi, W. Shieh, and Y. Tang, "Phase estimation for coherent optical OFDM," IEEE Photon. Technol. Lett. 19, pp. 919 - 921 (2007).
[CrossRef]

H. Bao and W. Shieh, "Transmission simulation of coherent optical OFDM signals in WDM systems," Opt. Express 15, 4410-4418 (2007).
[CrossRef] [PubMed]

2006 (4)

D. S. Ly-Gagnon, S. Tsukarnoto, 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]

J. M. Tang, P. M. Lane, and K. A. Shore, "Transmission performance of adaptively modulated optical OFDM signals in multimode fiber links," IEEE Photon. Technol. Lett. 18, 205-207 (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]

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

2005 (4)

A. J. Lowery and J. Armstrong, "10 Gb/s multimode fiber link using power-efficient orthogonal-frequency-division multiplexing," Opt. Express 13, 10003-10009 (2005).
[CrossRef] [PubMed]

A. D. Ellis and F. C. G. Gunning, "Spectral density enhancement using coherent WDM," IEEE Photon. Technol. Lett. 17, 504-506 (2005).
[CrossRef]

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Y. Han and G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Express 13, 7527-7534 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (1)

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM-based WLANs," IEEE Commun. Lett. 6, 535-537 (2002).
[CrossRef]

1998 (2)

Y. Li, L. J. Cimini, and N. R. Sollenberger, "Robust channel estimation for OFDM systems with rapid dispersive fading channels," IEEE Trans. Commun. 46, 902-915 (1998).
[CrossRef]

L. Tomba, "The effect of Wiener phase noise in OFDM systems," IEEE Trans. Commun. 46, 580-583 (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]

1996 (1)

S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-248 (1996).
[CrossRef]

1987 (1)

1980 (1)

F. Auracher and R. Keil, "Method for measuring the RF modulation characteristics of Mach-Zehnder-type modulators," Appl. Phys. Lett. 36, 626-629 (1980).
[CrossRef]

1971 (1)

S. B. Weinsten and P. M. Ebert, "Data transmission by frequency-division multiplexing using the discrete frouer transform," IEEE Trans. Commun. 19, 628-634 (1971).
[CrossRef]

1967 (1)

B. R. Saltzberg, "Performance of an efficient parallel data transmission system," IEEE Trans. Commun. 15, 805-813 (1967).
[CrossRef]

1966 (1)

R. W. Chang, "Synthesis of band-limited orthogonal signals for multichannel data transmission," Bell Syst. Tech. J. 45, 1775-1796 (1966).

Armstrong, J.

Athaudage, C.

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

Auracher, F.

F. Auracher and R. Keil, "Method for measuring the RF modulation characteristics of Mach-Zehnder-type modulators," Appl. Phys. Lett. 36, 626-629 (1980).
[CrossRef]

Bao, H.

Bar-Ness, Y.

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM-based WLANs," IEEE Commun. Lett. 6, 535-537 (2002).
[CrossRef]

Bayvel, P.

Chang, R. W.

R. W. Chang, "Synthesis of band-limited orthogonal signals for multichannel data transmission," Bell Syst. Tech. J. 45, 1775-1796 (1966).

Cimini, L. J.

Y. Li, L. J. Cimini, and N. R. Sollenberger, "Robust channel estimation for OFDM systems with rapid dispersive fading channels," IEEE Trans. Commun. 46, 902-915 (1998).
[CrossRef]

de Waardt, H.

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Diddams, S. A.

Djordjevic, I. B.

Dolfi, D. W.

Ebert, P. M.

S. B. Weinsten and P. M. Ebert, "Data transmission by frequency-division multiplexing using the discrete frouer transform," IEEE Trans. Commun. 19, 628-634 (1971).
[CrossRef]

Ellis, A. D.

A. D. Ellis and F. C. G. Gunning, "Spectral density enhancement using coherent WDM," IEEE Photon. Technol. Lett. 17, 504-506 (2005).
[CrossRef]

Evans, R.

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

Gavioli, G.

Gisin, N.

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]

Gunning, F. C. G.

A. D. Ellis and F. C. G. Gunning, "Spectral density enhancement using coherent WDM," IEEE Photon. Technol. Lett. 17, 504-506 (2005).
[CrossRef]

Han, Y.

Huttner, B.

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]

Jansen, S. L.

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Jorgensen, C. G.

Katoh, K.

Keil, R.

F. Auracher and R. Keil, "Method for measuring the RF modulation characteristics of Mach-Zehnder-type modulators," Appl. Phys. Lett. 36, 626-629 (1980).
[CrossRef]

Khoe, G. D.

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Kikuchi, K.

Killey, R. I.

Kolner, B. H.

Krummrich, P.M.

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Lane, P. M.

J. M. Tang, P. M. Lane, and K. A. Shore, "Transmission performance of adaptively modulated optical OFDM signals in multimode fiber links," IEEE Photon. Technol. Lett. 18, 205-207 (2006).
[CrossRef]

Li, G.

Li, Y.

Y. Li, L. J. Cimini, and N. R. Sollenberger, "Robust channel estimation for OFDM systems with rapid dispersive fading channels," IEEE Trans. Commun. 46, 902-915 (1998).
[CrossRef]

Lowery, A. J.

Ly-Gagnon, D. S.

Ma, Y.

Monsalve, C. C.

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Newbury, N. R.

Nicholson, J. W.

Saltzberg, B. R.

B. R. Saltzberg, "Performance of an efficient parallel data transmission system," IEEE Trans. Commun. 15, 805-813 (1967).
[CrossRef]

Savory, S. J.

Shieh, W.

H. Bao and W. Shieh, "Transmission simulation of coherent optical OFDM signals in WDM systems," Opt. Express 15, 4410-4418 (2007).
[CrossRef] [PubMed]

W. Shieh, X. Yi, Y. Ma, and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Opt. Express 15, 9936-9947 (2007).
[CrossRef] [PubMed]

Y. Tang, W. Shieh, X. Yi, and 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, "PMD-supported coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 134-136 (2007).
[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]

X. Yi, W. Shieh, and Y. Tang, "Phase estimation for coherent optical OFDM," IEEE Photon. Technol. Lett. 19, pp. 919 - 921 (2007).
[CrossRef]

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

Shirasaki, M.

S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-248 (1996).
[CrossRef]

Shore, K. A.

J. M. Tang, P. M. Lane, and K. A. Shore, "Transmission performance of adaptively modulated optical OFDM signals in multimode fiber links," IEEE Photon. Technol. Lett. 18, 205-207 (2006).
[CrossRef]

Sollenberger, N. R.

Y. Li, L. J. Cimini, and N. R. Sollenberger, "Robust channel estimation for OFDM systems with rapid dispersive fading channels," IEEE Trans. Commun. 46, 902-915 (1998).
[CrossRef]

Spalter, S.

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Tang, J. M.

J. M. Tang, P. M. Lane, and K. A. Shore, "Transmission performance of adaptively modulated optical OFDM signals in multimode fiber links," IEEE Photon. Technol. Lett. 18, 205-207 (2006).
[CrossRef]

Tang, Y.

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

X. Yi, W. Shieh, and Y. Tang, "Phase estimation for coherent optical OFDM," IEEE Photon. Technol. Lett. 19, pp. 919 - 921 (2007).
[CrossRef]

W. Shieh, X. Yi, Y. Ma, and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Opt. Express 15, 9936-9947 (2007).
[CrossRef] [PubMed]

Tomba, L.

L. Tomba, "The effect of Wiener phase noise in OFDM systems," IEEE Trans. Commun. 46, 580-583 (1998).
[CrossRef]

Tsukarnoto, S.

van den Borne, D.

S. L. Jansen, D. van den Borne, C. C. Monsalve, S. Spalter, P.M. Krummrich, G. D. Khoe, and H. de Waardt, "Reduction of Gordon-Mollenauer phase noise by midlink spectral inversion," IEEE Photon. Technol. Lett. 17, 923-925 (2005).
[CrossRef]

Vasic, B.

Washburn, B. R.

Watanabe, S.

S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and kerr effect in a transmission fiber using optical phase conjugation," J. Lightwave Technol. 14, 243-248 (1996).
[CrossRef]

Weinsten, S. B.

S. B. Weinsten and P. M. Ebert, "Data transmission by frequency-division multiplexing using the discrete frouer transform," IEEE Trans. Commun. 19, 628-634 (1971).
[CrossRef]

Wu, S.

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM-based WLANs," IEEE Commun. Lett. 6, 535-537 (2002).
[CrossRef]

Yan, M. F.

Yi, X.

W. Shieh, X. Yi, Y. Ma, and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Opt. Express 15, 9936-9947 (2007).
[CrossRef] [PubMed]

X. Yi, W. Shieh, and Y. Tang, "Phase estimation for coherent optical OFDM," IEEE Photon. Technol. Lett. 19, pp. 919 - 921 (2007).
[CrossRef]

Y. Tang, W. Shieh, X. Yi, and 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, 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]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

F. Auracher and R. Keil, "Method for measuring the RF modulation characteristics of Mach-Zehnder-type modulators," Appl. Phys. Lett. 36, 626-629 (1980).
[CrossRef]

Bell Syst. Tech. J. (1)

R. W. Chang, "Synthesis of band-limited orthogonal signals for multichannel data transmission," Bell Syst. Tech. J. 45, 1775-1796 (1966).

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 Commun. Lett. (1)

S. Wu and Y. Bar-Ness, "A phase noise suppression algorithm for OFDM-based WLANs," IEEE Commun. Lett. 6, 535-537 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (6)

A. D. Ellis and F. C. G. Gunning, "Spectral density enhancement using coherent WDM," IEEE Photon. Technol. Lett. 17, 504-506 (2005).
[CrossRef]

W. Shieh, "PMD-supported coherent optical OFDM systems," IEEE Photon. Technol. Lett. 19, 134-136 (2007).
[CrossRef]

X. Yi, W. Shieh, and Y. Tang, "Phase estimation for coherent optical OFDM," IEEE Photon. Technol. Lett. 19, pp. 919 - 921 (2007).
[CrossRef]

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Figures (13)

Fig. 1.
Fig. 1.

Conceptual diagram for a generic multi-carrier modulation (MCM) system

Fig. 2.
Fig. 2.

Conceptual diagram for the OFDM transmitter and receiver

Fig. 3.
Fig. 3.

The OFDM signals (a) without cyclic prefix at the transmitter, (b) without cyclic prefix at the receiver, (c) with cyclic prefix at the transmitter, and (d) with cyclic prefix at the receiver.

Fig 4.
Fig 4.

The optical spectrum for (a) N wavelength-division-multiplexed COOFDM channels, (b) zoomed-in spectrum for one WDM channel, and (c) crosschannel OFDM (XC-OFDM) without guard band.

Fig. 5.
Fig. 5.

A complete CO-OFDM system including PMD, PDL and chromatic dispersion effects.

Fig. 6.
Fig. 6.

A CO-OFDM system in (a) direct up/down conversion architecture, and (b) intermediate frequency (IF) architecture.

Fig. 7.
Fig. 7.

The first-, second-, and third-order output powers as a function of modulation index M(dB)=20logM at the bias points of (a) π, and (b) π/2.

Fig. 8.
Fig. 8.

The transfer functions for the optical intensity and the optical field against the drive voltage.

Fig. 9.
Fig. 9.

A transmission system with mid-span phase conjugation

Fig. 10.
Fig. 10.

Abstraction of the split-step Fourier method for signal propagation in the fiber

Fig. 11.
Fig. 11.

(a). The Q factor as a function of the launch power with varying number of steps used in split-step Fourier method in nonlinear phase noise mitigation, and (b) the Q factor improvement as a result of nonlinear noise phase noise mitigation.

Fig. 12.
Fig. 12.

OSNR dynamic range as a function of number of steps.

Fig. 13.
Fig. 13.

The Q factor as the function of the nonlinear coefficient β for a step size of 4.

Equations (36)

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s ( t ) = i = + k = 1 N sc c ki s k ( t iT s )
S k ( t ) = ( t ) exp ( j 2 π f k t )
( t ) = { 1 , ( 0 < t T s ) 0 , ( t 0 , t > T s )
c ki = 0 T s r ( t i T s ) S * k dt = 0 T s r ( t i T s ) exp ( j 2 π f k t ) dt
δ kl = 1 T s 0 T s s k s * l dt = 1 T s 0 T s exp ( j 2 π ( f k f l ) t ) dt
= exp ( ( f k f l ) T s ) sin ( π ( f k f l ) T s ) π ( f k f l ) T s
f k f l = m 1 T s
t d < Δ G
R = N sc T s
B OFDM = 2 T s + Nsc 1 t s
η = 2 R B OFDM = 2 α , α = t s T s
r ( t ) = e j ϕ ( t ) s ( t ) h ( t ) + N ( t )
h ( t ) = h t ( t ) h l ( t ) h r ( t )
C k i = I i 0 · h ki · C ki + ε ki + n ki
ε ki = m = Nsc 2 , m k Nsc 2 1 C mi h mi I i ( m k )
I im = 1 N sc n = Nsc 2 Nsc 2 1 e j 2 π nm Nsc e j ϕ in
I i 0 = 1 N sc n = Nsc 2 Nsc 2 1 e j ϕ in 1 N sc e j ϕ i 0 n = Nsc 2 Nsc 2 1 ( 1 + j Δ ϕ in ) e j ϕ i
Δ ϕ in = ϕ in ϕ i 0 , ϕ i = 1 N sc n = Nsc 2 Nsc 2 1 ϕ in
h ki = h ki t · h ki l · h ki r
h ki l = e j Φ ki D p = 1 M exp { ( 1 2 j · β pi · f k + 1 2 α pi ) · σ }
Φ ki D = π · c · D t · f k 2 f LD 2
C ki = e i ϕ i h k C ki + ζ ki
E ( t ) = A · cos ( π 2 · V I + V DC V π ) · exp ( j ω LD 1 t + j ϕ LD 1 )
+ A · cos ( π 2 · V Q + V DC V π ) exp ( j ω L D 1 + π 2 + j ϕ L D 1 )
E ( t ) = exp ( j ω LD 1 t + j ϕ LD 1 ) · E B ( t )
E B ( t ) = cos [ M 2 ( cos ω 1 t + cos ω 2 t ) + ϕ 2 ] + j cos [ M 2 ( sin ω 1 t + sin ω 2 t ) + ϕ 2 ]
E ω 1 , 2 B ( t ) = 2 · sin ( ϕ 2 ) · J 0 ( M 2 ) · J 1 ( M 2 ) · e j ω 1 , 2 t
E ω 1 , 2 ω 2 , 1 B ( t ) = 2 · cos ( ϕ 2 ) · J 1 2 ( M 2 ) · e j ( ω 1 , 2 ω 2 , 1 ) t
E 2 ω 1 , 2 ω 2 , 1 B ( t ) = 2 · sin ( ϕ 2 ) · J 1 ( M 2 ) · J 2 ( M 2 ) · e j ( 2 ω 1 , 2 ω 2 , 1 ) t
IP 2 = 2 · sin 4 ( ϕ 2 ) cos 2 ( ϕ 2 )
IP 3 = 4 · sin 2 ( ϕ 2 )
M IP 2 = 2 · tan ( ϕ 2 )
M IP 3 = 4 2
r 0 ( t ) = ( i = 2 m exp ( N ̂ i ) exp ( D ̂ i ) ) exp ( N ̂ 1 ) r * ( t )
N ̂ i A ( t ) = j β A i ( t ) 2
D ̂ i A ( t ) = { F 1 exp ( j ϕ D ) F } A ( t )

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