Abstract

In coherent optical systems employing electronic digital signal processing, the fiber chromatic dispersion can be gracefully compensated in electronic domain without resorting to optical techniques. Unlike optical dispersion compensator, the electronic equalizer enhances the impairments from the laser phase noise. This equalization-enhanced phase noise (EEPN) imposes a tighter constraint on the receive laser phase noise for transmission systems with high symbol rate and large electronically-compensated chromatic dispersion.

© 2008 Optical Society of America

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References

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  1. 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]
  2. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Express 16, 753-791 (2008).
    [CrossRef] [PubMed]
  3. R. Noé, "Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23, 802-808 (2005).
    [CrossRef]
  4. H. Sun, K. -T. Wu, and K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Express 16, 873-879 (2008).
    [CrossRef] [PubMed]
  5. 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]
  6. L. G. Kazovsky, "Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems," J. Lightwave Technol. 4, 415-425 (1986).
    [CrossRef]
  7. S. Norimatsu and K. Iwashita, "Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time," J. Lightwave Technol. 10, 341-349 (1992).
    [CrossRef]
  8. K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.
  9. H. Bulow, F. Buchali, and A. Klekamp, "Electronic dispersion compensation," J. Lightwave Technol. 26, 158 - 167 (2007).
    [CrossRef]
  10. M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon. Technol. Lett. 16, 674-676 (2004).
    [CrossRef]
  11. S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006).
    [CrossRef]
  12. X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007).
    [CrossRef]
  13. E. Ip and J. M. Kahn, "Compensation of dispersion and nonlinear effects using digital back-propagation," to be published in J. Lightwave Technol..
  14. F. M. Gardner, Phaselock Techniques, (2nd Ed., New York: John Wiley, 1979).
  15. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, (New York: John Wiley, 1997).
  16. A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000).
    [CrossRef]
  17. T. H. Lee and A. Hajimiri, "Oscillator phase noise: A tutorial," IEEE J. Solid-State Circuits 35, 326-336 (2000).
    [CrossRef]

2008

2007

2006

S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006).
[CrossRef]

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]

2005

2004

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon. Technol. Lett. 16, 674-676 (2004).
[CrossRef]

2000

A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000).
[CrossRef]

T. H. Lee and A. Hajimiri, "Oscillator phase noise: A tutorial," IEEE J. Solid-State Circuits 35, 326-336 (2000).
[CrossRef]

1992

S. Norimatsu and K. Iwashita, "Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time," J. Lightwave Technol. 10, 341-349 (1992).
[CrossRef]

1986

L. G. Kazovsky, "Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems," J. Lightwave Technol. 4, 415-425 (1986).
[CrossRef]

Barros, D. J. F.

Bayvel, P.

Buchali, F.

Bulow, H.

Chen, X.

X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007).
[CrossRef]

Demir, A.

A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000).
[CrossRef]

Gavioli, G.

Hajimiri, A.

T. H. Lee and A. Hajimiri, "Oscillator phase noise: A tutorial," IEEE J. Solid-State Circuits 35, 326-336 (2000).
[CrossRef]

Ip, E.

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Express 16, 753-791 (2008).
[CrossRef] [PubMed]

E. Ip and J. M. Kahn, "Compensation of dispersion and nonlinear effects using digital back-propagation," to be published in J. Lightwave Technol..

Iwashita, K.

S. Norimatsu and K. Iwashita, "Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time," J. Lightwave Technol. 10, 341-349 (1992).
[CrossRef]

Kahn, J. M.

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Express 16, 753-791 (2008).
[CrossRef] [PubMed]

E. Ip and J. M. Kahn, "Compensation of dispersion and nonlinear effects using digital back-propagation," to be published in J. Lightwave Technol..

Katoh, K.

S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006).
[CrossRef]

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]

Kazovsky, L. G.

L. G. Kazovsky, "Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems," J. Lightwave Technol. 4, 415-425 (1986).
[CrossRef]

Kikuchi, K.

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]

S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006).
[CrossRef]

Killey, R. I.

Kim, C.

X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007).
[CrossRef]

Klekamp, A.

Lau, A. P. T.

Lee, T. H.

T. H. Lee and A. Hajimiri, "Oscillator phase noise: A tutorial," IEEE J. Solid-State Circuits 35, 326-336 (2000).
[CrossRef]

Li, G.

X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007).
[CrossRef]

Ly-Gagnon, D. S.

Mehrotra, A.

A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000).
[CrossRef]

Noé, R.

Norimatsu, S.

S. Norimatsu and K. Iwashita, "Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time," J. Lightwave Technol. 10, 341-349 (1992).
[CrossRef]

Roberts, K.

Roychowdhury, J.

A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000).
[CrossRef]

Savory, S. J.

Sun, H.

Taylor, M. G.

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon. Technol. Lett. 16, 674-676 (2004).
[CrossRef]

Tsukamoto, S.

S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006).
[CrossRef]

Tsukarnoto, S.

Wu, K. -T.

Zhou, B.

X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007).
[CrossRef]

IEEE J. Solid-State Circuits

T. H. Lee and A. Hajimiri, "Oscillator phase noise: A tutorial," IEEE J. Solid-State Circuits 35, 326-336 (2000).
[CrossRef]

IEEE Photon. Technol. Lett.

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon. Technol. Lett. 16, 674-676 (2004).
[CrossRef]

S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006).
[CrossRef]

X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007).
[CrossRef]

IEEE Trans. Circuits Syst. I

A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Other

E. Ip and J. M. Kahn, "Compensation of dispersion and nonlinear effects using digital back-propagation," to be published in J. Lightwave Technol..

F. M. Gardner, Phaselock Techniques, (2nd Ed., New York: John Wiley, 1979).

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, (New York: John Wiley, 1997).

K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.

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Figures (4)

Fig. 1.
Fig. 1.

The communication channel model including the phase noise at both transmit and receive ends. CPE/C stands for carrier phase estimation and compensation.

Fig. 2.
Fig. 2.

The structure of a coherent receiver. The receiver response functions are modeled as summation of finite number of taps.

Fig. 3.
Fig. 3.

The SNR penalty from EEPN interference as a function of the linewidth at various reaches when the symbol rate is (a) 10 Gbaud/s, and (b) 25 Gbaud/s, respectively. This corresponds to 40 Gb/s and 100 Gb/s systems with QPSK modulation and polarization multiplexing. Chromatic dispersion of 17 ps/(nm·km) and SNR (γ0) of 9.8 dB are assumed.

Fig. 4.
Fig. 4.

The required laser linewidth for 1 dB SNR penalty at a BER of 10-3 from EEPN interference for various reaches. The required laser linewidth at 1 dB SNR penalty from the feedback-forward carrier synchronizer (FFCS) is also shown as a comparison.

Equations (43)

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c ( t ) = [ r ( t ) e j ϕ r ( t ) ] h e h m + N ( t )
r ( t ) = k = ( c k e j ϕ t ( t ) h p s ( t k T s ) ) h f ( t )
N ( t ) = N ( t ) h e h m
c ( t ) = k = [ c k e j [ ϕ t ( t ) + ϕ r ( t ) ] h p s ( t k T s ) ] + N ( t )
c k = c k e j [ ϕ t ( k T s ) + ϕ r ( k T s ) ] + N ( k T s )
c ̂ k = c k e j ϕ ̂ ( k T s )
r ( t ) = [ ( e j ϕ t ( t ) h ps ( t ) ) h f ( t ) ] e j ϕ t ( t )
h f ( t ) = i = M M h i δ ( t i T s )
r ( t ) = i = M M ( e j ϕ t ( t i T s ) h ps ( t i T s ) h i ) e j ϕ r ( t )
= i = M M e j ϕ t ( t i T s ) + j ϕ r ( t i T s ) h ps ( t i T s ) h i ( t )
r ( t ) = i = M M ( e j ϕ t ( t i T s ) + j ϕ r ( t i T s ) h ps ( t i T s ) h i ( 1 + j Δ i ( t ) ) )
= ( e j ϕ t ( t ) + j ϕ r ( t ) h ps ) h f ( t ) + i = M M e j ϕ t ( t i T s ) + j ϕ t ( t i T s ; ) h ps ( t i T s ) h i · j Δ i ( t )
h e h m = i = M M h i δ ( t i T s )
c ̂ 0 = 1 + n E
n E = i = M M r ( i T ) h i ( e j Δ i ( 0 ) 1 )
c ( t ) = [ h ps ( t ) h f ( t ) ] e j ϕ r ( t ) [ h e ( t ) h m ( t ) ]
c ( t ) = c ( t ) e j ϕ r ( 0 ) = [ h ps ( t ) h f ( t ) ] e j ( ϕ r ( t ) ϕ r ( 0 ) ) [ h e ( t ) h m ( t ) ]
σ c 2 = E { c ( t ) 2 } E { c ( t ) } 2 .
h 1 ( t ) = h ps ( t ) h f ( t )
h 2 ( t ) = h e ( t ) h m ( t )
E { c ( t ) } = h 1 ( t t 1 ) E { e j ( ϕ r ( t t 1 ) ϕ r ( 0 ) ) } h 2 ( t 1 ) d t 1
υ ( t ) = e j ϕ ( t )
R υ υ = E { υ ( t 1 ) υ * ( t 2 ) } = E { e j ϕ ( t 1 ) j ϕ ( t 2 ) } = S ( f ) e j 2 π f ( t 1 t 2 ) df
S ( f ) = 1 2 π f 3 dB f 2 + ( f 3 dB 2 ) 2
E { c ( t ) } = S ( f ) H 2 ( f 1 ) H 1 ( f 1 f ) e i 2 π ft d f 1 df
E { | c ( t ) | 2 } = S ( f ) | H 2 ( f 1 ) H 1 ( f 1 f ) e i 2 π ft d f 1 | 2 df
E { c ( t ) } = k = E { c k } · ξ ( t k T s ) = ξ ( t )
E { c ( t ) 2 } = k = ρ k · ζ ( t k T s )
ξ ( t ) = S ( f ) H 2 ( f 1 ) H 1 ( f 1 f ) e i 2 π ft d f 1 d f
ζ ( t ) = S ( f ) H 2 ( f 1 ) H 1 ( f 1 f ) e i 2 π ft df 1 2 df
ρ k = E { | c k | 2 }
H ps ( f ) = H m ( f ) = { 1 , B 2 f B 2 0 , f > B 2 , f < B 2
H f ( f ) = e j π · c f 0 2 D t · f 2 , H e ( f ) = e j π · c f 0 2 D t · f 2
E { c ( 0 ) } = 1 α ( 1 e α )
E { c ( 0 ) 2 } = 1 2 α 2 ( e 2 α + 2 α 1 )
E { c ( 0 ) } = 1 α ( 1 e α ) 1 1 2 α
η E { c ( 0 ) } 2 1 α
E { c ( 0 ) 2 } = 1 2 α 2 ( e 2 α + 2 α 1 ) 1 2 3 α
σ c 2 = 1 3 α
σ T 2 = σ Intra 2 + σ Inter 2 = α , σ Intra 2 = 1 3 α , σ Inter 2 = 2 3 α
γ 0 = η P P σ T 2 + n 0 = η γ γ σ T 2 + 1
Δ P = γ γ 0 = γ σ T 2 + 1 η γ 0 σ T 2 + 1 η
Δ P ( dB ) = 10 log 10 ( γ 0 σ T 2 + 1 η ) 4 . 343 · α ( 1 + γ 0 )

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