Abstract

We have analytically derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems. The phase and amplitude noises are correlated with each other for binary phase-shift keying (PSK) systems but uncorrelated for $M$-ary PSK systems with $M>2$. We have also derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems. Furthermore, we have studied the performance of an optimal linear phase-noise predictor derived from the IFWM-induced phase-noise autocorrelation function. This yields a performance improvement of 1.8dB when IFWM-induced phase noise is the dominant impairment, and an improvement of 0.8 to 1.2 dB in the presence of amplified spontaneous emission noise and nonlinear phase noise in typical terrestrial links.

© 2008 IEEE

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  1. K. P. Ho, H. C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005).
  2. F. Zhang, C. A. Bunge, K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038-1040 (2006).
  3. I. Shake, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).
  4. R.-J. Essiambre, B. Mikkelsen, G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1577 (1999).
  5. A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
  6. A. Mecozzi, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445-447 (2001).
  7. A. G. Striegler, B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. Lightw. Technol. 22, 1877-1882 (2004).
  8. H. Wei, D. V. Plant, "Intra-channel nonlinearity compensation with scaled translational symmetry," Opt. Express 12, 4282-4296 (2004).
  9. R. I. Killey, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).
  10. X. Liu, C. Xu, X. Wei, "Performance analysis of time-polarization multiplexed 40-Gb /s RZ-DPSK DWDM transmission," IEEE Photon. Technol. Lett. 16, 302-304 (2004).
  11. C. Xie, "Suppression of intrachannel nonlinear effects with alternate-polarization formats," J. Lightw. Technol. 22, 806-812 (2004).
  12. S. Appathurai, "Investigation of the optimum alternate-phase RZ modulation format and its effectiveness in the suppression of intrachannel nonlinear distortion in 40-Gbit/s transmission over standard single-mode fiber," IEEE J. Sel. Topics Quantum Electron. 10, 239-249 (2004).
  13. N. Alic, Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212-1214 (2004).
  14. M. Zou, "Suppression of ghost pulses in 40 Gbps optical transmission systems with fixed-pattern phase modulation," Opt. Express 13, 2251-2255 (2005).
  15. X. Liu, "Suppression of intrachannel four-wave-mixing-induced ghost pulses in high-speed transmissions by phase inversion between adjacent marker blocks," Opt. Lett. 27, 1177-1179 (2002).
  16. V. Pechenkin, F. R. Kschischang, "Constrained coding for quasi-linear optical data transmission systems," J. Lightw. Technol. 24, 4895-4902 (2006).
  17. I. B. Djordjevic, B. Vasic, "Constrained coding techniques for the suppression of intrachannel nonlinear effects in high-speed optical transmission," J. Lightw. Technol. 24, 411-419 (2006).
  18. I. B. Djordjevic, S. K. Chilappagari, B. Vasic, "Suppression of intrachannel nonlinear effects using pseudoternary constrained codes," J. Lightw. Technol. 24, 769-774 (2006).
  19. A. Chowdhury, "Compensation of intrachannel nonlinearities in 40-Gb/s pseudolinear systems using optical-phse conjugation," J. Lightw. Technol. 23, 172-177 (2005).
  20. X. Wei, X. Liu, "Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion," Opt. Lett. 28, 2300-2302 (2003).
  21. K. P. Ho, "Error probability of DPSK signals with intrachannel four-wave mixing in Highly Dispersive Transmission Systems," IEEE Photon. Technol. Lett. 17, 789-791 (2005).
  22. K. P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, (2004).
  23. G. Bellotti, S. Bigo, "Cross-phase modulation suppressor for multispan dispersion-managed WDM transmissions," IEEE Photon. Technol. Lett. 12, 726-728 (2000).
  24. G. Bellotti, "10 $\times$ 10 Gb/s cross-phase modulation suppressor for multispan transmissions using WDM narrow-band fiber Bragg gratings," IEEE Photon. Technol. Lett. 12, 1403-1405 (2000).
  25. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2002).
  26. K. P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).
  27. K.-P. Ho, J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightw. Technol. 22, 779-783 (2004).
  28. X. Wei, "Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map," Opt. Lett. 31, 29-31 (2006).
  29. X. Zhu, S. Kumar, X. Li, "Analysis and comparison of impairments in differential phase-shift keying and on-off keying transmission systems based on the error probability," Appl. Opt. 45, (2006).

2006 (6)

F. Zhang, C. A. Bunge, K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038-1040 (2006).

V. Pechenkin, F. R. Kschischang, "Constrained coding for quasi-linear optical data transmission systems," J. Lightw. Technol. 24, 4895-4902 (2006).

I. B. Djordjevic, B. Vasic, "Constrained coding techniques for the suppression of intrachannel nonlinear effects in high-speed optical transmission," J. Lightw. Technol. 24, 411-419 (2006).

I. B. Djordjevic, S. K. Chilappagari, B. Vasic, "Suppression of intrachannel nonlinear effects using pseudoternary constrained codes," J. Lightw. Technol. 24, 769-774 (2006).

X. Wei, "Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map," Opt. Lett. 31, 29-31 (2006).

X. Zhu, S. Kumar, X. Li, "Analysis and comparison of impairments in differential phase-shift keying and on-off keying transmission systems based on the error probability," Appl. Opt. 45, (2006).

2005 (4)

M. Zou, "Suppression of ghost pulses in 40 Gbps optical transmission systems with fixed-pattern phase modulation," Opt. Express 13, 2251-2255 (2005).

A. Chowdhury, "Compensation of intrachannel nonlinearities in 40-Gb/s pseudolinear systems using optical-phse conjugation," J. Lightw. Technol. 23, 172-177 (2005).

K. P. Ho, H. C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005).

K. P. Ho, "Error probability of DPSK signals with intrachannel four-wave mixing in Highly Dispersive Transmission Systems," IEEE Photon. Technol. Lett. 17, 789-791 (2005).

2004 (8)

K. P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, (2004).

A. G. Striegler, B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. Lightw. Technol. 22, 1877-1882 (2004).

K.-P. Ho, J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightw. Technol. 22, 779-783 (2004).

H. Wei, D. V. Plant, "Intra-channel nonlinearity compensation with scaled translational symmetry," Opt. Express 12, 4282-4296 (2004).

X. Liu, C. Xu, X. Wei, "Performance analysis of time-polarization multiplexed 40-Gb /s RZ-DPSK DWDM transmission," IEEE Photon. Technol. Lett. 16, 302-304 (2004).

C. Xie, "Suppression of intrachannel nonlinear effects with alternate-polarization formats," J. Lightw. Technol. 22, 806-812 (2004).

S. Appathurai, "Investigation of the optimum alternate-phase RZ modulation format and its effectiveness in the suppression of intrachannel nonlinear distortion in 40-Gbit/s transmission over standard single-mode fiber," IEEE J. Sel. Topics Quantum Electron. 10, 239-249 (2004).

N. Alic, Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212-1214 (2004).

2003 (1)

X. Wei, X. Liu, "Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion," Opt. Lett. 28, 2300-2302 (2003).

2002 (1)

2001 (1)

A. Mecozzi, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445-447 (2001).

2000 (4)

A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).

G. Bellotti, S. Bigo, "Cross-phase modulation suppressor for multispan dispersion-managed WDM transmissions," IEEE Photon. Technol. Lett. 12, 726-728 (2000).

G. Bellotti, "10 $\times$ 10 Gb/s cross-phase modulation suppressor for multispan transmissions using WDM narrow-band fiber Bragg gratings," IEEE Photon. Technol. Lett. 12, 1403-1405 (2000).

R. I. Killey, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).

1999 (1)

R.-J. Essiambre, B. Mikkelsen, G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1577 (1999).

1998 (1)

I. Shake, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).

Appl. Opt. (1)

X. Zhu, S. Kumar, X. Li, "Analysis and comparison of impairments in differential phase-shift keying and on-off keying transmission systems based on the error probability," Appl. Opt. 45, (2006).

Electron. Lett. (1)

R.-J. Essiambre, B. Mikkelsen, G. Raybon, "Intra-channel cross-phase modulation and four-wave mixing in high-speed TDM systems," Electron. Lett. 35, 1576-1577 (1999).

Electron. Lett. (1)

I. Shake, "Influence of inter-bit four-wave mixing in optical TDM transmission," Electron. Lett. 34, 1600-1601 (1998).

IEEE Photon. Technol. Lett. (3)

K. P. Ho, "Error probability of DPSK signals with intrachannel four-wave mixing in Highly Dispersive Transmission Systems," IEEE Photon. Technol. Lett. 17, 789-791 (2005).

G. Bellotti, "10 $\times$ 10 Gb/s cross-phase modulation suppressor for multispan transmissions using WDM narrow-band fiber Bragg gratings," IEEE Photon. Technol. Lett. 12, 1403-1405 (2000).

A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 392-394 (2000).

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

K. P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise," IEEE J. Sel. Topics Quantum Electron. 10, (2004).

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

S. Appathurai, "Investigation of the optimum alternate-phase RZ modulation format and its effectiveness in the suppression of intrachannel nonlinear distortion in 40-Gbit/s transmission over standard single-mode fiber," IEEE J. Sel. Topics Quantum Electron. 10, 239-249 (2004).

IEEE Photon. Technol. Lett. (6)

N. Alic, Y. Fainman, "Data-dependent phase coding for suppression of ghost pulses in optical fibers," IEEE Photon. Technol. Lett. 16, 1212-1214 (2004).

A. Mecozzi, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445-447 (2001).

K. P. Ho, H. C. Wang, "Comparison of nonlinear phase noise and intrachannel four-wave mixing for RZ-DPSK signals in dispersive transmission systems," IEEE Photon. Technol. Lett. 17, 1426-1428 (2005).

R. I. Killey, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).

X. Liu, C. Xu, X. Wei, "Performance analysis of time-polarization multiplexed 40-Gb /s RZ-DPSK DWDM transmission," IEEE Photon. Technol. Lett. 16, 302-304 (2004).

G. Bellotti, S. Bigo, "Cross-phase modulation suppressor for multispan dispersion-managed WDM transmissions," IEEE Photon. Technol. Lett. 12, 726-728 (2000).

J. Lightw. Technol. (2)

A. G. Striegler, B. Schmauss, "Compensation of intrachannel effects in symmetric dispersion-managed transmission systems," J. Lightw. Technol. 22, 1877-1882 (2004).

I. B. Djordjevic, B. Vasic, "Constrained coding techniques for the suppression of intrachannel nonlinear effects in high-speed optical transmission," J. Lightw. Technol. 24, 411-419 (2006).

J. Lightw. Technol. (1)

C. Xie, "Suppression of intrachannel nonlinear effects with alternate-polarization formats," J. Lightw. Technol. 22, 806-812 (2004).

J. Lightw. Technol. (4)

I. B. Djordjevic, S. K. Chilappagari, B. Vasic, "Suppression of intrachannel nonlinear effects using pseudoternary constrained codes," J. Lightw. Technol. 24, 769-774 (2006).

A. Chowdhury, "Compensation of intrachannel nonlinearities in 40-Gb/s pseudolinear systems using optical-phse conjugation," J. Lightw. Technol. 23, 172-177 (2005).

V. Pechenkin, F. R. Kschischang, "Constrained coding for quasi-linear optical data transmission systems," J. Lightw. Technol. 24, 4895-4902 (2006).

K.-P. Ho, J. M. Kahn, "Electronic compensation technique to mitigate nonlinear phase noise," J. Lightw. Technol. 22, 779-783 (2004).

Opt. Lett. (3)

X. Wei, "Intrachannel four-wave mixing in highly dispersed return-to-zero differential-phase-shift-keyed transmission with a nonsymmetric dispersion map," Opt. Lett. 31, 29-31 (2006).

X. Wei, X. Liu, "Analysis of intrachannel four-wave mixing in differential phase-shift keying transmission with large dispersion," Opt. Lett. 28, 2300-2302 (2003).

F. Zhang, C. A. Bunge, K. Petermann, "Analysis of nonlinear phase noise in single-channel return-to-zero differential phase-shift keying transmission systems," Opt. Lett. 31, 1038-1040 (2006).

Opt. Express (2)

Opt. Lett. (1)

Other (2)

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2002).

K. P. Ho, Phase-Modulated Optical Communication Systems (Springer, 2005).

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