Abstract

A pilot-based nonlinearity compensator (PB-NLC) is shown in this Letter to be an effective method for compensating cross-phase modulation (XPM) in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. An unmodulated pilot tone is transmitted at the center of each OFDM channel to detect phase errors caused by the Kerr effect, which converts intensity fluctuations from all channels to phase errors. The pilots are then used to cancel the XPM phase errors for each OFDM channel at the receiver after each channel’s self-phase modulation (SPM) has been compensated, using its intensity waveform to determine its SPM. Numerical simulations of a 58Gb/s single polarization 2375km system with inline dispersion compensation show that the signal quality, Q, at the optimal launch power is increased by 2.4dB if SPM compensation is used before the PB-NLC. This contrasts with only a 0.9dB improvement if the PB-NLC is used without an SPM compensator for the same link. This shows the PB-NLC can effectively mitigate XPM but not SPM.

© 2011 Optical Society of America

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References

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  1. C. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, G.-D. Khoe, and H. de Waardt, J. Lightwave Technol. 26, 64 (2008).
    [CrossRef]
  2. X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.
  3. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
  4. A. D. Ellis, Z. Jian, and D. Cotter, J. Lightwave Technol. 28, 423 (2010).
    [CrossRef]
  5. G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, 1989).
  6. R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol. 28, 662 (2010).
    [CrossRef]
  7. H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, J. Lightwave Technol. 28, 406 (2010).
    [CrossRef]
  8. L. B. Du and A. J. Lowery, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO1.
  9. S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.
  10. X. Liu and R. W. Tkach, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO5.
  11. W. Shieh, X. Yi, Y. Ma, and Y. Tang, Opt. Express 15, 9936(2007).
    [CrossRef] [PubMed]
  12. L. B. Du and A. J. Lowery, IEEE Photon. Technol. Lett. 22, 320 (2010).
    [CrossRef]
  13. B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.
  14. L. B. Du and A. J. Lowery, Opt. Express 16, 19920 (2008).
    [CrossRef] [PubMed]
  15. A. J. Lowery, Opt. Express 15, 12965 (2007).
    [CrossRef] [PubMed]
  16. L. B. Du and A. J. Lowery, Opt. Express 16, 6209 (2008).
    [CrossRef] [PubMed]
  17. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, J. Lightwave Technol. 26, 6 (2008).
    [CrossRef]
  18. T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, J. Lightwave Technol. 14, 249 (1996).
    [CrossRef]

2010 (4)

2008 (4)

2007 (2)

1996 (1)

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, J. Lightwave Technol. 14, 249 (1996).
[CrossRef]

1948 (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Adhikari, S.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, 1989).

Amin, A. Al

Benyuan, Z.

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.

Chandrasekhar, S.

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.

Chiang, T. K.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, J. Lightwave Technol. 14, 249 (1996).
[CrossRef]

Cotter, D.

De Man, E.

de Waardt, H.

Du, L. B.

L. B. Du and A. J. Lowery, IEEE Photon. Technol. Lett. 22, 320 (2010).
[CrossRef]

L. B. Du and A. J. Lowery, Opt. Express 16, 6209 (2008).
[CrossRef] [PubMed]

L. B. Du and A. J. Lowery, Opt. Express 16, 19920 (2008).
[CrossRef] [PubMed]

L. B. Du and A. J. Lowery, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO1.

Duthel, T.

Ellis, A. D.

Essiambre, R. J.

Fludger, C. S.

Forozesh, K.

S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.

Foschini, G. J.

Geyer, J.

Gnauck, A. H.

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.

Goebel, B.

Hanik, N.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.

Inan, B.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.

Jansen, S. L.

H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, J. Lightwave Technol. 28, 406 (2010).
[CrossRef]

S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, J. Lightwave Technol. 26, 6 (2008).
[CrossRef]

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.

S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.

Jian, Z.

Kagi, N.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, J. Lightwave Technol. 14, 249 (1996).
[CrossRef]

Kazovsky, L. G.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, J. Lightwave Technol. 14, 249 (1996).
[CrossRef]

Khoe, G.-D.

Kramer, G.

Liu, X.

X. Liu and R. W. Tkach, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO5.

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.

Lobato, A.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.

Lowery, A. J.

L. B. Du and A. J. Lowery, IEEE Photon. Technol. Lett. 22, 320 (2010).
[CrossRef]

L. B. Du and A. J. Lowery, Opt. Express 16, 6209 (2008).
[CrossRef] [PubMed]

L. B. Du and A. J. Lowery, Opt. Express 16, 19920 (2008).
[CrossRef] [PubMed]

A. J. Lowery, Opt. Express 15, 12965 (2007).
[CrossRef] [PubMed]

L. B. Du and A. J. Lowery, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO1.

Ma, Y.

Marhic, M. E.

T. K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, J. Lightwave Technol. 14, 249 (1996).
[CrossRef]

Morita, I.

H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, J. Lightwave Technol. 28, 406 (2010).
[CrossRef]

S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, J. Lightwave Technol. 26, 6 (2008).
[CrossRef]

S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.

Peckham, D. W.

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.

Randel, S.

S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.

Schenk, T. C. W.

Schmidt, E.-D.

Schulien, C.

Shannon, C. E.

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Shieh, W.

Takahashi, H.

Takeda, N.

Tanaka, H.

H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, J. Lightwave Technol. 28, 406 (2010).
[CrossRef]

S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, J. Lightwave Technol. 26, 6 (2008).
[CrossRef]

S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.

Tang, Y.

Tkach, R. W.

X. Liu and R. W. Tkach, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO5.

van den Borne, D.

C. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, G.-D. Khoe, and H. de Waardt, J. Lightwave Technol. 26, 64 (2008).
[CrossRef]

S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.

Winzer, P. J.

R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol. 28, 662 (2010).
[CrossRef]

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.

Wuth, T.

Yi, X.

Bell Syst. Tech. J. (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

IEEE Photon. Technol. Lett. (1)

L. B. Du and A. J. Lowery, IEEE Photon. Technol. Lett. 22, 320 (2010).
[CrossRef]

J. Lightwave Technol. (6)

Opt. Express (4)

Other (6)

B. Inan, S. Randel, S. L. Jansen, A. Lobato, S. Adhikari, and N. Hanik, in European Conference on Optical Communication (EUREL, 2010), paper Tu.4.A.6.

X. Liu, S. Chandrasekhar, Z. Benyuan, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, in Optical Fiber Communication Conference (Optical Society of America, 2010), paper PDPC2.

G. P. Agrawal, Nonlinear Fiber Optics, 1st ed. (Academic, 1989).

L. B. Du and A. J. Lowery, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO1.

S. L. Jansen, I. Morita, K. Forozesh, S. Randel, D. van den Borne, and H. Tanaka, in European Conference on Optical Communication (EUREL, 2008), paper Mo.3.E.3.

X. Liu and R. W. Tkach, in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OTuO5.

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Figures (3)

Fig. 1
Fig. 1

Illustration of the PB-NLC: (a) optical system and optical spectra, (b) received electrical spectra before and after the PB-NLC. X, signal before the PB-NLC; Y, signal after the PB-NLC; Pilot, pilot extracted by the LPF.

Fig. 2
Fig. 2

Block diagram of the receiver and DSP algorithms. ZF, zero-forcing.

Fig. 3
Fig. 3

Received Q against launch power after 2375 km of S-SMF.

Equations (1)

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η XPM = α 2 α 2 + ( ω . D . Δ λ ) 2 · [ 1 + 4 sin 2 ( ω . D . Δ λ . L 2 ) . e α L ( 1 e α L ) 2 ] ,

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