Abstract

In this paper, as an attractive alternative to the conventional discrete Fourier transform (DFT) based orthogonal frequency division multiplexing (OFDM), discrete cosine transform (DCT) based OFDM which has certain advantages over its counterpart is studied for optical fiber communications. As is known, laser phase noise is a major impairment to the performance of coherent optical OFDM (CO-OFDM) systems. However, to our knowledge, detailed analysis of phase noise and the corresponding mitigation methods for DCT-based CO-OFDM systems have not been reported yet. To address these issues, we analyze the laser phase noise in the DCT-based CO-OFDM systems, and propose phase noise estimation and mitigation schemes. Numerical results show that the proposal is very effective in suppressing phase noise and could significantly improve the performance of DCT-based CO-OFDM systems.

© 2009 Optical Society of America

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References

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  1. I. B. Djordjevic and B. Vasic, "Orthogonal frequency division multiplexing for high-speed optical transmission," Opt. Express 14, 3767-3775 (2006).
    [CrossRef] [PubMed]
  2. W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt. Express 16, 841-859 (2008).
    [CrossRef] [PubMed]
  3. J. Armstrong, "OFDM for optical communications," J. Lightwave Technol. 27, 189-204 (2009).
    [CrossRef]
  4. Q. Yang, S. Chen, Y. Ma, and W. Shieh, "Real-time reception of multi-gigabit coherent optical OFDM signals," Opt. Express 17, 7985-7992 (2009).
    [CrossRef] [PubMed]
  5. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, "Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF," J. Lightwave Technol. 26, 6-15 (2008).
    [CrossRef]
  6. N. Al-Dhahir, H. Minn, and S. Satish, "Optimum DCT-based multicarrier transceivers for frequency-selective channels," IEEE Trans. Commun. 54, 911-921 (2006).
    [CrossRef]
  7. F. Gao, T. Cui, A. Nallanathan, and C. Tellambura, "Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons," IEEE Trans. Commun. 56, 1425-1429 (2008).
    [CrossRef]
  8. W. H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun. 25, 1004-1009 (1977).
    [CrossRef]
  9. Z. D. Wang, "Fast algorithm for the discrete W transform and for the discrete Fourier transform," IEEE Trans. Acoust., Speech, Signal Processing 32, 803-816 (1984).
    [CrossRef]
  10. C. Yang, F. Yang, and Z. Wang, "Iterative minimum mean square error equalization for optical fiber communication systems," IEEE Photon. Technol. Lett. 19, 1571-1573 (2007).
    [CrossRef]
  11. N. Al-Dhahir, and J. M. Cioffi, "Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach," IEEE Trans. Inf. Theory 42, 903-915 (1996).
    [CrossRef]
  12. L. Tomba, "On the effect of Wiener phase noise in OFDM systems," IEEE Trans. Commun. 46, 580-583 (1998).
    [CrossRef]
  13. S. M. Kay, Fundamentals of Statistical Signal Processing V. 1. Estimation Theory, (Englewood Cliffs, NJ: Prentice-Hall PTR, 1993).

2009 (2)

2008 (3)

W. Shieh, H. Bao, and Y. Tang, "Coherent optical OFDM: theory and design," Opt. Express 16, 841-859 (2008).
[CrossRef] [PubMed]

S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, "Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF," J. Lightwave Technol. 26, 6-15 (2008).
[CrossRef]

F. Gao, T. Cui, A. Nallanathan, and C. Tellambura, "Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons," IEEE Trans. Commun. 56, 1425-1429 (2008).
[CrossRef]

2007 (1)

C. Yang, F. Yang, and Z. Wang, "Iterative minimum mean square error equalization for optical fiber communication systems," IEEE Photon. Technol. Lett. 19, 1571-1573 (2007).
[CrossRef]

2006 (2)

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

N. Al-Dhahir, H. Minn, and S. Satish, "Optimum DCT-based multicarrier transceivers for frequency-selective channels," IEEE Trans. Commun. 54, 911-921 (2006).
[CrossRef]

1998 (1)

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

1996 (1)

N. Al-Dhahir, and J. M. Cioffi, "Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach," IEEE Trans. Inf. Theory 42, 903-915 (1996).
[CrossRef]

1984 (1)

Z. D. Wang, "Fast algorithm for the discrete W transform and for the discrete Fourier transform," IEEE Trans. Acoust., Speech, Signal Processing 32, 803-816 (1984).
[CrossRef]

1977 (1)

W. H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun. 25, 1004-1009 (1977).
[CrossRef]

Al-Dhahir, N.

N. Al-Dhahir, H. Minn, and S. Satish, "Optimum DCT-based multicarrier transceivers for frequency-selective channels," IEEE Trans. Commun. 54, 911-921 (2006).
[CrossRef]

N. Al-Dhahir, and J. M. Cioffi, "Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach," IEEE Trans. Inf. Theory 42, 903-915 (1996).
[CrossRef]

Armstrong, J.

Bao, H.

Chen, S.

Chen, W. H.

W. H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun. 25, 1004-1009 (1977).
[CrossRef]

Cioffi, J. M.

N. Al-Dhahir, and J. M. Cioffi, "Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach," IEEE Trans. Inf. Theory 42, 903-915 (1996).
[CrossRef]

Cui, T.

F. Gao, T. Cui, A. Nallanathan, and C. Tellambura, "Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons," IEEE Trans. Commun. 56, 1425-1429 (2008).
[CrossRef]

Djordjevic, I. B.

Fralick, S. C.

W. H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun. 25, 1004-1009 (1977).
[CrossRef]

Gao, F.

F. Gao, T. Cui, A. Nallanathan, and C. Tellambura, "Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons," IEEE Trans. Commun. 56, 1425-1429 (2008).
[CrossRef]

Jansen, S. L.

Ma, Y.

Minn, H.

N. Al-Dhahir, H. Minn, and S. Satish, "Optimum DCT-based multicarrier transceivers for frequency-selective channels," IEEE Trans. Commun. 54, 911-921 (2006).
[CrossRef]

Morita, I.

Nallanathan, A.

F. Gao, T. Cui, A. Nallanathan, and C. Tellambura, "Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons," IEEE Trans. Commun. 56, 1425-1429 (2008).
[CrossRef]

Satish, S.

N. Al-Dhahir, H. Minn, and S. Satish, "Optimum DCT-based multicarrier transceivers for frequency-selective channels," IEEE Trans. Commun. 54, 911-921 (2006).
[CrossRef]

Schenk, T. C. W.

Shieh, W.

Smith, C. H.

W. H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun. 25, 1004-1009 (1977).
[CrossRef]

Takeda, N.

Tanaka, H.

Tang, Y.

Tellambura, C.

F. Gao, T. Cui, A. Nallanathan, and C. Tellambura, "Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons," IEEE Trans. Commun. 56, 1425-1429 (2008).
[CrossRef]

Tomba, L.

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

Vasic, B.

Wang, Z.

C. Yang, F. Yang, and Z. Wang, "Iterative minimum mean square error equalization for optical fiber communication systems," IEEE Photon. Technol. Lett. 19, 1571-1573 (2007).
[CrossRef]

Wang, Z. D.

Z. D. Wang, "Fast algorithm for the discrete W transform and for the discrete Fourier transform," IEEE Trans. Acoust., Speech, Signal Processing 32, 803-816 (1984).
[CrossRef]

Yang, C.

C. Yang, F. Yang, and Z. Wang, "Iterative minimum mean square error equalization for optical fiber communication systems," IEEE Photon. Technol. Lett. 19, 1571-1573 (2007).
[CrossRef]

Yang, F.

C. Yang, F. Yang, and Z. Wang, "Iterative minimum mean square error equalization for optical fiber communication systems," IEEE Photon. Technol. Lett. 19, 1571-1573 (2007).
[CrossRef]

Yang, Q.

IEEE Photon. Technol. Lett. (1)

C. Yang, F. Yang, and Z. Wang, "Iterative minimum mean square error equalization for optical fiber communication systems," IEEE Photon. Technol. Lett. 19, 1571-1573 (2007).
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Processing (1)

Z. D. Wang, "Fast algorithm for the discrete W transform and for the discrete Fourier transform," IEEE Trans. Acoust., Speech, Signal Processing 32, 803-816 (1984).
[CrossRef]

IEEE Trans. Commun. (4)

N. Al-Dhahir, H. Minn, and S. Satish, "Optimum DCT-based multicarrier transceivers for frequency-selective channels," IEEE Trans. Commun. 54, 911-921 (2006).
[CrossRef]

F. Gao, T. Cui, A. Nallanathan, and C. Tellambura, "Maximum likelihood based estimation of frequency and phase offset in DCT OFDM systems under non-circular transmissions: algorithms, analysis and comparisons," IEEE Trans. Commun. 56, 1425-1429 (2008).
[CrossRef]

W. H. Chen, C. H. Smith, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commun. 25, 1004-1009 (1977).
[CrossRef]

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

IEEE Trans. Inf. Theory (1)

N. Al-Dhahir, and J. M. Cioffi, "Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach," IEEE Trans. Inf. Theory 42, 903-915 (1996).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (3)

Other (1)

S. M. Kay, Fundamentals of Statistical Signal Processing V. 1. Estimation Theory, (Englewood Cliffs, NJ: Prentice-Hall PTR, 1993).

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Figures (5)

Fig. 1.
Fig. 1.

Baseband equivalent model of the DCT-based CO-OFDM system with the proposed signal processor. S/P: serial to parallel; P/S: parallel to serial.

Fig. 2.
Fig. 2.

Structure of the DCT-based OFDM symbol.

Fig. 3.
Fig. 3.

E(‖Θ(k)‖/‖Θ(0)‖) (dB) for different laser linewidths.

Fig. 4.
Fig. 4.

BER versus OSNR curves for different laser linewidths and residual CD=1600 ps/nm. Solid lines with circles: the case that phase noise is absent; solid lines with squares and diamonds: the case that the proposed phase noise compensation is employed; dashed lines with squres and diamonds: the case that phase noise compensation is absent.

Fig. 5.
Fig. 5.

BER versus OSNR curves for different laser linewidths and residual CD=2000 ps/nm. Solid lines with circles: the case that phase noise is absent; solid lines with squares and diamonds: the case that the proposed phase noise compensation is employed; dashed lines with squres and diamonds: the case that phase noise compensation is absent.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

ai=[ai(0)ai(1)ai(N1)]T,i=0,1,
xi=DTai ,
β(n)={1Nn=02Nn0.
x˜i=G xi ,
G=(Vν0ν×(Nν)IN0ν×(Nν)Vν) .
ri(m)=ejϕi(m) l=ννhi(l)x˜i(ml)+wi(m), m=0,1,,N1
hi(l)=hi(l),l=1,2,,ν .
MinimizeMSE=h˜iHI˜TRiI˜h˜i
I˜=(Iν+1Vν0ν×1) ,
ci=(Riyy)1Riyxhi
yi(k)=β (k) m=0N1ejϕi(m)cos(π(2m+1)k2N) n=0N1β(n)ai(n)Hi(n)
×cos(π(2m+1)n2n)+Wi(k),k=0,1,, N1 .
Wi(k)=β (k) m=0N1wi(m)cos(π(2m+1)k2N)
Θi(k)=m=0N1ejϕi(m)cos(π(2m+1)k2N) .
yi(k)=β2(k)2 (Θi(0)+Θi(2k)) Hi (k) ai (k)
+β(k)2[n=0,nkN1β(n)(Θi(n+k)+Θi(nk))Hi(n)ai(n)]+Wi(k) .
ξi(k)=β(k)2 [n=0,nkN1β(n)(Θi(n+k)+Θi(nk))Hi(n)ai(n)]
yi(k)β2(k)2Θi(0)Hi(k)ai(k)+ζi(k) .
yi=Γiai+ζi
Γi=diag {[β2(0)2Θi(0)Hi(0)β2(1)2Θi(0)Hi(1)β2(N1)2Θi(0)Hi(N1)]} .
Γ̂1(k,k)=y1(k)a1(k),k=0,1,,N1 .
ΔΘ̂i(0)=1M p=1Myi(kp)ai(kp)Γ̂1(kp,kp)
Γ̂i(k,k)=Δ Θ̂i (0) Γ̂1 (k,k) .
zi(k)=Γ̂i(k,k)*yi(k)Γ̂i(k,k)2

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