Abstract

Unlike conventional CO-OFDM systems, we show in this paper that reduced-guard-interval (RGI) CO-OFDM systems experience subcarrier-dependent phase noise (PN) from the local oscillator laser. This phenomenon manifests in RGI-CO-COFM systems because the chromatic dispersion (CD) induced walk-off becomes comparable to the OFDM symbol length. We term this phenomenon the dispersion enhanced PN (DEPN). In this work an analytical study of the impact of DEPN on CO-OFDM transmission is conducted. We develop a system-level analytical model and calculate the variance of the dispersion-induced subcarrier-dependent phase rotation term (PRT) using two different distribution patterns of pilot subcarriers (PS). Moreover, we present a bit error rate (BER) estimator to quantify the system performance degradation due to PRT. Numerical simulations are then performed to verify the analytical model. Finally, we propose a grouped maximum-likelihood (GML) phase estimation approach to mitigate the DEPN impairment, and demonstrate a 0.7-1.7 dB SNR improvement at BER = 10−3 for typical 100 Gb/s RGI CO-OFDM systems.

© 2011 OSA

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References

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  1. Q. Yang, Y. Tang, Y. Ma, and W. Shieh, “Experimental Demonstration and Numerical Simulation of 107-Gb/s High Spectral Efficiency Coherent Optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009).
    [CrossRef]
  2. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM Transmission with 2-b/s/Hz Spectral Efficiency Over 1000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009).
    [CrossRef]
  3. H. Takahashi, K. Takeshima, I. Morita, and H. Tanaka, “400-Gbit/s Optical OFDM Transmission over 80 km in 50-GHz Frequency Grid,” ECOC’10, paper Tu.3.C.1.
  4. A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus Single-Carrier Transmission for 100 Gbps Optical Communication,” J. Lightwave Technol. 28(17), 2537–2551 (2010).
    [CrossRef]
  5. X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s reduced-guard-interval CO-OFDM signal with a 60-GHz optical bandwidth over 2000 km of ULAF and five 80-GHz-Grid ROADMs,” OFC2010, San Diego, USA, paper PDPC2.
  6. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” 29(4), J. Lightwave Technol. 483–490 (2011).
    [CrossRef]
  7. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, and D. W. Peckham, “7 x 224-Gb/s WDM Transmission of Reduced-Guard-Interval CO-OFDM with 16-QAM Subcarrier Modulation on a 50-GHz Grid over 2000 km of ULAF and Five ROADM Passes,” ECOC’10, paper Tu.3.C.2.
  8. X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single Coherent Detection of a 606-Gb/s CO-OFDM Signal with 32-QAM Subcarrier Modulation Using 4x 80-Gsamples/s ADCs,” ECOC’10, post-deadline paper PD2.6.
  9. Q. Zhuge, C. Chen and D. V. Plant, “Impact of Intra-Channel Fiber Nonlinearity on Reduced-Guard-Interval CO-OFDM Transmission,” OFC2011, paper OWO3.
  10. C. Chen, Q. Zhuge and D. V. Plant, “Coherent Optical OFDM with Zero Cyclic Prefix Using Overlapped Frequency-Domain CD and PMD Equalization,” OFC2011, paper OWE7.
  11. B. Spinnler, “Equalizer Design and Complexity for Digital Coherent Receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010).
    [CrossRef]
  12. W. Shieh and K.-P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008).
    [CrossRef] [PubMed]
  13. C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express 17(6), 4815–4823 (2009).
    [CrossRef] [PubMed]
  14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express 18(16), 17239–17251 (2010).
    [CrossRef] [PubMed]
  15. W.-R. Peng, “Analysis of Laser Phase Noise Effect in Direct-Detection Optical OFDM Transmission,” J. Lightwave Technol. 28(17), 2526–2536 (2010).
    [CrossRef]
  16. C. C. Wei and J. J. Chen, “Study on dispersion-induced phase noise in an optical OFDM radio-over-fiber system at 60-GHz band,” Opt. Express 18(20), 20774–20785 (2010).
    [CrossRef] [PubMed]
  17. X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919 (2007).
    [CrossRef]
  18. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent Optical Single Carrier Transmission Using Overlap Frequency Domain Equalization for Long-Haul Optical Systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
    [CrossRef]
  19. X. Liu, F. Buchali, and R. W. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
    [CrossRef]
  20. S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
    [CrossRef]
  21. L. Pan, and Y. Bar-Ness, “Closed-Form Expressions for BER Performance in OFDM Systems with Phase Noise,” in Communications,2006. ICC '06. IEEE International Conference on, 2006, pp. 5366–5370.
  22. W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 20(8), 605–607 (2008).
    [CrossRef]
  23. X. Zhou, “An Improved Feed-Forward Carrier Recovery Algorithm for Coherent Receivers With M-QAM Modulation Format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
    [CrossRef]

2011 (1)

2010 (6)

2009 (5)

2008 (2)

W. Shieh and K.-P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008).
[CrossRef] [PubMed]

W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 20(8), 605–607 (2008).
[CrossRef]

2007 (1)

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919 (2007).
[CrossRef]

2004 (1)

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[CrossRef]

Barbieri, A.

Bar-Ness, Y.

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[CrossRef]

Buchali, F.

Chandrasekhar, S.

Chen, J. J.

Colavolpe, G.

Foggi, T.

Forestieri, E.

Gnauck, A. H.

Ho, K.-P.

Ishihara, K.

Jansen, S. L.

Kobayashi, T.

Kudo, R.

Lau, A. P. T.

Liu, X.

Ma, Y.

Miyamoto, Y.

Morita, I.

Peckham, D. W.

Peng, W.-R.

Prati, G.

Sano, A.

Schenk, T. C. W.

Shen, T. S. R.

Shieh, W.

Spinnler, B.

B. Spinnler, “Equalizer Design and Complexity for Digital Coherent Receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010).
[CrossRef]

Takatori, Y.

Tanaka, H.

Tang, Y.

Tkach, R. W.

Wei, C. C.

Winzer, P. J.

Wu, S.

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[CrossRef]

Xie, C.

Yang, Q.

Yi, X.

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919 (2007).
[CrossRef]

Zhou, X.

X. Zhou, “An Improved Feed-Forward Carrier Recovery Algorithm for Coherent Receivers With M-QAM Modulation Format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
[CrossRef]

Zhu, B.

IEEE J. Sel. Top. Quantum Electron. (1)

B. Spinnler, “Equalizer Design and Complexity for Digital Coherent Receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

W. Shieh, “Maximum-Likelihood Phase and Channel Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 20(8), 605–607 (2008).
[CrossRef]

X. Zhou, “An Improved Feed-Forward Carrier Recovery Algorithm for Coherent Receivers With M-QAM Modulation Format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010).
[CrossRef]

IEEE Trans. Commun. (1)

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
[CrossRef]

J. Lightwave Technol. (7)

Q. Yang, Y. Tang, Y. Ma, and W. Shieh, “Experimental Demonstration and Numerical Simulation of 107-Gb/s High Spectral Efficiency Coherent Optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009).
[CrossRef]

S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM Transmission with 2-b/s/Hz Spectral Efficiency Over 1000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009).
[CrossRef]

X. Liu, F. Buchali, and R. W. Tkach, “Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission,” J. Lightwave Technol. 27(16), 3632–3640 (2009).
[CrossRef]

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent Optical Single Carrier Transmission Using Overlap Frequency Domain Equalization for Long-Haul Optical Systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
[CrossRef]

W.-R. Peng, “Analysis of Laser Phase Noise Effect in Direct-Detection Optical OFDM Transmission,” J. Lightwave Technol. 28(17), 2526–2536 (2010).
[CrossRef]

A. Barbieri, G. Colavolpe, T. Foggi, E. Forestieri, and G. Prati, “OFDM versus Single-Carrier Transmission for 100 Gbps Optical Communication,” J. Lightwave Technol. 28(17), 2537–2551 (2010).
[CrossRef]

X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” 29(4), J. Lightwave Technol. 483–490 (2011).
[CrossRef]

Opt. Express (4)

Other (7)

L. Pan, and Y. Bar-Ness, “Closed-Form Expressions for BER Performance in OFDM Systems with Phase Noise,” in Communications,2006. ICC '06. IEEE International Conference on, 2006, pp. 5366–5370.

H. Takahashi, K. Takeshima, I. Morita, and H. Tanaka, “400-Gbit/s Optical OFDM Transmission over 80 km in 50-GHz Frequency Grid,” ECOC’10, paper Tu.3.C.1.

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “Transmission of a 448-Gb/s reduced-guard-interval CO-OFDM signal with a 60-GHz optical bandwidth over 2000 km of ULAF and five 80-GHz-Grid ROADMs,” OFC2010, San Diego, USA, paper PDPC2.

X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, and D. W. Peckham, “7 x 224-Gb/s WDM Transmission of Reduced-Guard-Interval CO-OFDM with 16-QAM Subcarrier Modulation on a 50-GHz Grid over 2000 km of ULAF and Five ROADM Passes,” ECOC’10, paper Tu.3.C.2.

X. Liu, S. Chandrasekhar, P. J. Winzer, S. Draving, J. Evangelista, N. Hoffman, B. Zhu, and D. W. Peckham, “Single Coherent Detection of a 606-Gb/s CO-OFDM Signal with 32-QAM Subcarrier Modulation Using 4x 80-Gsamples/s ADCs,” ECOC’10, post-deadline paper PD2.6.

Q. Zhuge, C. Chen and D. V. Plant, “Impact of Intra-Channel Fiber Nonlinearity on Reduced-Guard-Interval CO-OFDM Transmission,” OFC2011, paper OWO3.

C. Chen, Q. Zhuge and D. V. Plant, “Coherent Optical OFDM with Zero Cyclic Prefix Using Overlapped Frequency-Domain CD and PMD Equalization,” OFC2011, paper OWE7.

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Figures (10)

Fig. 1
Fig. 1

Block diagram of RGI CO-OFDM systems.

Fig. 2
Fig. 2

The communication channel model.

Fig. 3
Fig. 3

(a) The applied laser PN at the transmitter side; (b) the applied laser PN at the receiver side.

Fig. 4
Fig. 4

The normalized variance of PRT for each subcarrier obtained from both theory and simulation using either UD-PS’s or C-PS’s with no ASE noise (left) and with a SNR of 11 dB (right). L = 3200 km, β = 1 MHz and Nc = 80.

Fig. 5
Fig. 5

The constellation of the received symbols after phase estimation with UD-PS’s. L = 3200 km, β = 1 MHz and Nc = 80. (a): total subcarriers; (b): center subcarriers; (c): edge subcarriers.

Fig. 6
Fig. 6

The normalized average variance of PRT and ICI versus the number of subcarriers Nc . L = 3200 km, β = 1 MHz and SNR = 11 dB.

Fig. 7
Fig. 7

BER versus (a) SNR with L = 3200 km and (b) transmission distance with SNR = 11 dB. β = 1 MHz for both systems.

Fig. 8
Fig. 8

Required SNR at BER = 10−3 versus transmission distance L with (a) different numbers of subcarriers Nc with β = 1 MHz and (b) varying linewidths β and Nc = 80.

Fig. 9
Fig. 9

Required SNR at BER = 10−3 versus (a) the number of subcarriers in each group Ng with Np = 4 and (b) number of PS’s Np with Ng = 20.

Fig. 10
Fig. 10

Illustration of the effectiveness of GML phase estimation with (a) β = 1 MHz and (b) β = 2 MHz.

Equations (23)

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s ( t ) = k = 1 N c c k e j 2 π k Δ f t
r ( t ) = { [ s ( t ) e j ϕ t ( t ) ] h ( t ) } e j ϕ r ( t ) + z ( t ) = [ k = 1 N c c k e j 2 π k Δ f t + j ϕ t ( t ) δ ( t T k ) ] e j ϕ r ( t ) + z ( t ) = k = 1 N c c k e j 2 π k Δ f ( t T k ) + j ϕ t ( t T k ) + j ϕ r ( t ) + z ( t )
r d c ( n ) = r ( n ) h d c ( n ) = k = 1 N c c k e j 2 π k Δ f ( n D k ) + j ϕ t ( n D k ) + j ϕ r ( n ) δ ( n + D k ) + z ( n ) = k = 1 N c c k e j 2 π k Δ f n + j ϕ t ( n ) + j ϕ r ( n + D k ) + z ( n )
R ( k ) = c k I k ( 0 ) + I C I ( k ) + Z ( k )
I ( p ) = 1 N n = 0 N 1 e j [ 2 π p n N + ϕ t ( n ) + ϕ r ( n + D k ) ]
I k ( 0 ) = 1 N n = 0 N 1 e j ϕ t ( n ) + ϕ r ( n + D k ) 1 + j [ 1 N n = 0 N 1 ϕ t ( n ) + 1 N n = 0 N 1 ϕ r ( n + D k ) ]
Φ ( k ) = 1 N n = 0 N 1 ϕ r ( n + D k ) ϕ e s t ϕ n
ϕ e s t = 1 N c l = 1 N c ( 1 N n = 0 N 1 ϕ r ( n + D l ) )
σ P R T , k 2 = E { | Φ ( k ) | 2 } = E { | 1 N n = 0 N 1 ϕ r ( n + D k ) 1 N c l = 1 N c ( 1 N n = 0 N 1 ϕ r ( n + D l ) ) ϕ n | 2 } = σ 2 { i = 0 D k [ 1 1 N c N A ( i ) ] 2 + i = D k + 1 N 1 + D k { [ N ( i D k ) ] 1 N c N A ( i ) } 2 + i = N + D k N 1 + D N c ( 1 N c N A ( i ) ) 2 } + ( σ I C I 2 + σ A S E 2 ) 2 N p
A ( i ) = 1 N c N n = 0 N 1 max ( 0 , min ( N c , D N c i + n + 1 Δ D ) )
ϕ e s t = 1 N n = 0 N 1 ϕ r ( n + D ( N c + 1 ) / 2 )
σ P R T , k 2 = E { | Φ ( k ) | 2 } = E { | 1 N n = 0 N 1 ϕ r ( n + D k ) 1 N n = 0 N 1 ϕ r ( n + D ( N c + 1 ) / 2 ) ϕ n | 2 } = σ 2 N 2 [ 1 3 M a 3 + M b M a 2 + M a 3 ] + ( σ I C I 2 + σ A S E 2 ) 2 N p
f k ( θ ) = 1 2 π σ P R T , k e θ 2 σ P R T , k 2
α k = E [ | I ( 0 ) | 2 ] 1 π β o T 3
σ I C I , k 2 = E [ | I C I ( k ) | 2 ] π β o T 3
S I N R k = α k σ I C I , k 2 + 1 γ k
B E R ( k ) = 1 2 { e r f c ( S I N R k cos 2 ( π 4 + θ ) ) + e r f c ( S I N R k sin 2 ( π 4 + θ ) ) } f k ( θ ) d θ
H m = k = ( m 1 ) N g + 1 m N g R ( k ) [ R ^ ( k ) ] *
ϕ m = tan 1 ( Im [ H m ] / Re [ H m ] )
ϕ k ( n ) = i = 0 n + D k v ( i )
σ P R T , k 2 = E { | Φ ( k ) | 2 } = E { | 1 N n = 0 N 1 ϕ r ( n + D k ) 1 N c l = 1 N c ( 1 N n = 0 N 1 ϕ r ( n + D l ) ) ϕ n | 2 } = E { | 1 N n = 0 N 1 i = 0 n + D k v ( i ) 1 N c l = 1 N c ( 1 N n = 0 N 1 i = 0 n + D l v ( i ) ) ϕ n | 2 } = E { | i = 0 D k v ( i ) + 1 N i = D k + 1 N 1 + D k [ N ( i D k ) ] v ( i ) 1 N c N i = 0 N 1 + D N c A ( i ) v ( i ) ϕ n | 2 } = E { | i = 0 D k [ 1 1 N c N A ( i ) ] v ( i ) + i = D k + 1 N 1 + D k { 1 N [ N ( i D k ) ] 1 N c N A ( i ) } v ( i ) 1 N c N i = N + D k N 1 + D N c A ( i ) v ( i ) ϕ n | 2 }
σ P R T , k 2 = σ 2 { i = 0 D k [ 1 1 N c N A ( i ) ] 2 + i = D k + 1 N 1 + D k { [ N ( i D k ) ] 1 N c N A ( i ) } 2 + i = N + D k N 1 + D N c ( 1 N c N A ( i ) ) 2 } + ( σ I C I 2 + σ A S E 2 ) 2 N p
σ P R T , k 2 = E { | Φ ( k ) | 2 } = E { | 1 N n = 0 N 1 ϕ r ( n + D k ) 1 N n = 0 N 1 ϕ r ( n + D ( N c + 1 ) / 2 ) ϕ n | 2 } = E { | 1 N n = 0 N 1 i = 0 n + D k v ( i ) 1 N n = 0 N 1 i = 0 n + D ( N c + 1 ) / 2 v ( i ) ϕ n | 2 } = E { | 1 N n = 0 N 1 i = n + 1 n + D k v ( i ) ϕ n | 2 } = E { | 1 N q = 1 M a 1 q [ v ( q ) + v ( N + D k q ) ] + M a N p = M a M b v ( p ) ϕ n | 2 } = σ 2 N 2 [ 2 ( M a 1 ) M a ( 2 M a 1 ) 6 + M a 2 ( M b M a + 1 ) ] + ( σ I C I 2 + σ A S E 2 ) 2 N p = σ 2 N 2 [ 1 3 M a 3 + M b M a 2 + M a 3 ] + ( σ I C I 2 + σ A S E 2 ) 2 N p

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