Abstract

Digital coherent superposition (DCS) provides an approach to combat fiber nonlinearities by trading off the spectrum efficiency. In analogy, we extend the concept of DCS to the optical OFDM subcarrier pairs with Hermitian symmetry to combat the linear and nonlinear phase noise. At the transmitter, we simply use a real-valued OFDM signal to drive a Mach-Zehnder (MZ) intensity modulator biased at the null point and the so-generated OFDM signal is Hermitian in the frequency domain. At receiver, after the conventional OFDM signal processing, we conduct DCS of the optical OFDM subcarrier pairs, which requires only conjugation and summation. We show that the inter-carrier-interference (ICI) due to phase noise can be reduced because of the Hermitain symmetry. In a simulation, this method improves the tolerance to the laser phase noise. In a nonlinear WDM transmission experiment, this method also achieves better performance under the influence of cross phase modulation (XPM).

© 2014 Optical Society of America

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References

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  1. W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007).
    [CrossRef]
  2. A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Commun. Conf., Anaheim, CA (2006), Paper PDP39.
    [CrossRef]
  3. S. L. Jansen, I. Morita, C. W. Schenk, N. Takeda, H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008).
    [CrossRef]
  4. D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Commun. Conf., USA (2011), paper PDPB5.
  5. S. Wu, Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004).
    [CrossRef]
  6. X. Yi, W. Shieh, Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008).
    [CrossRef]
  7. J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999).
    [CrossRef]
  8. X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express 20(17), 19088–19095 (2012).
    [CrossRef] [PubMed]
  9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
    [CrossRef]
  10. Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express 21(4), 5099–5106 (2013).
    [CrossRef] [PubMed]
  11. X. Yi, X. Chen, C. Li, M. Luo, Q. Yang, Z. Li, and K. Qiu, “Experimental demonstration of digital coherent superposition of optical OFDM subcarrier pairs for mitigation of linear and nonlinear phase noise,” in Optical Fiber Commun. Conf. (2014), Tu3G.6.
    [CrossRef]
  12. Y. Wu, J. Li, C. Zhao, Y. Zhao, F. Zhang, Z. Chen, “Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation,” Chin. Opt. Lett. 8, 634–638 (2010).
    [CrossRef]
  13. Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007).
    [CrossRef]
  14. X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
    [CrossRef]
  15. T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995).
    [CrossRef]
  16. Q. Yang, Y. Tang, Y. Ma, 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]

2013

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[CrossRef]

Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express 21(4), 5099–5106 (2013).
[CrossRef] [PubMed]

2012

2010

2009

2008

2007

W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007).
[CrossRef]

Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007).
[CrossRef]

X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

2004

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

1999

J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999).
[CrossRef]

1995

T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995).
[CrossRef]

Armstrong, J.

J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999).
[CrossRef]

Bar-Ness, Y.

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

Chandrasekhar, S.

Chen, Z.

Chraplyvy, A. R.

DiGiovanni, D. J.

Evans, R.

Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007).
[CrossRef]

Fishteyn, M.

Huang, Y. K.

Jansen, S. L.

Li, J.

Liu, X.

Ma, Y.

Moeneclaey, M.

T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995).
[CrossRef]

Morita, I.

Pollet, T.

T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995).
[CrossRef]

Prucnal, P. R.

Schenk, C. W.

Shieh, W.

Q. Yang, Y. Tang, Y. Ma, 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]

X. Yi, W. Shieh, Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008).
[CrossRef]

Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007).
[CrossRef]

W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007).
[CrossRef]

X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

Takeda, N.

Tanaka, H.

Tang, Y.

Q. Yang, Y. Tang, Y. Ma, 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]

W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007).
[CrossRef]

X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007).
[CrossRef]

Taunay, T. F.

Tian, Y.

Tkach, R. W.

Van Bladel, M.

T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995).
[CrossRef]

Wang, T.

Winzer, P. J.

Wu, S.

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

Wu, Y.

Yang, Q.

Yi, X.

X. Yi, W. Shieh, Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008).
[CrossRef]

Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007).
[CrossRef]

W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007).
[CrossRef]

X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

Zhang, F.

Zhang, S.

Zhao, C.

Zhao, Y.

Zhu, B.

Chin. Opt. Lett.

Electron. Lett.

W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007).
[CrossRef]

IEEE Photon. Technol. Lett.

Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007).
[CrossRef]

X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007).
[CrossRef]

IEEE Trans. Commun.

T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995).
[CrossRef]

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

J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013).
[CrossRef]

Opt. Express

Other

A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Commun. Conf., Anaheim, CA (2006), Paper PDP39.
[CrossRef]

D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Commun. Conf., USA (2011), paper PDPB5.

X. Yi, X. Chen, C. Li, M. Luo, Q. Yang, Z. Li, and K. Qiu, “Experimental demonstration of digital coherent superposition of optical OFDM subcarrier pairs for mitigation of linear and nonlinear phase noise,” in Optical Fiber Commun. Conf. (2014), Tu3G.6.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

BER comparison for three cases with 0-MHz laser linewdith (solid line) and 1-MHz (dash line). The insets on the left are the constellations at the indicated BER points.

Fig. 2
Fig. 2

Experimental setup of the emulated WDM transmission. The inset optical spectra are the optical signal before and after the data modulation. ECL: external cavity laser, PM: phase modulator, IM: intensity modulator, IQ: IQ modulator, WSS: wavelength selective switch, ATT: attenuator, BPF: bandpass filter.

Fig. 3
Fig. 3

Estimated SNR vs launch power in the nonlinear WDM transmission: (a) without electrical dispersion compensation, (b) with electrical dispersion compensation. The dash lines are the SNR difference between Case III and Case II. (c) Constellations before and after DCS at the maximum SNR improvement.

Equations (16)

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s(m)= 1 N k=0 N1 X(k)exp(j2πkm/N) , k,m=0,...,N1.
X(Nk)= X * (k),
y(m)=s(m)exp[jϕ(m)].
Y k = X k I(0)+ICI(k),
ICI(k)= l=0,lk N1 X(l)I(kl) ,
I(k)= 1 N n=0 N-1 exp[j2πkn/N+jϕ(n)] .
Y ^ k = X k | I(0) |+ICI(k)exp(jψ).
| ICI(k) | 2 = E s ( 1 | I(0) | 2 ) ,
( Y ^ k + Y ^ Nk * )/2= X k | I(0) |+ICI(k)exp(jψ)/2+IC I * (Nk)exp(jψ)/2.
IC I * (Nk)= l=0,lk N1 X(l) I * (lk) .
( Y ^ k + Y ^ Nk * )/2= X k | I(0) |+IC I DCS (k) ,
IC I DCS (k)= l=0,lk N1 X(l) I DCS (kl),
I DCS (k)= 1 N n=0 N-1 exp( j2πkn/N )cos[ ϕ(n)-ψ ] .
A= k=0 N1 | I DCS (k) | 2 = | cos[ϕ(n)-ψ] | 2 ,
| IC I DCS (k) | 2 = E s ( A | I DCS (0) | 2 ).
| I DCS (0) | 2 = | cos[ϕ(n)ψ] | 2 | exp[jϕ(n)jψ] | 2 = | exp[jϕ(n)] | 2 = | I(0) | 2 .

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