Abstract

Next-generation optical fiber systems will employ coherent detection to improve power and spectral efficiency, and to facilitate flexible impairment compensation using digital signal processors (DSPs). In a fully digital coherent system, the electric fields at the input and the output of the channel are available to DSPs at the transmitter and the receiver, enabling the use of arbitrary impairment precompensation and postcompensation algorithms. Linear time-invariant (LTI) impairments such as chromatic dispersion and polarization-mode dispersion can be compensated by adaptive linear equalizers. Non-LTI impairments, such as laser phase noise and Kerr nonlinearity, can be compensated by channel inversion. All existing impairment compensation techniques ultimately approximate channel inversion for a subset of the channel effects. We provide a unified multiblock nonlinear model for the joint compensation of the impairments in fiber transmission. We show that commonly used techniques for overcoming different impairments, despite their different appearance, are often based on the same principles such as feedback and feedforward control, and time-versus-frequency-domain representations. We highlight equivalences between techniques, and show that the choice of algorithm depends on making tradeoffs.

© 2010 IEEE

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J. Armstrong, "OFDM for optical communications," J. Lightw. Technol. 27, 189-204 (2009).

G. Goldfarb, G. Li, "Efficient backward-propagation using wavelet-based filtering for fiber backward-propagation," Opt. Exp. 17, 8815-8821 (2009).

2008 (8)

Q. Zhang, M. I. Hayee, "Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems," J. Lightw. Technol. 26, 302-316 (2008).

D. J. F. Barros, J. M. Kahn, "Optimized dispersion compensation using orthogonal frequency-division multiplexing," J. Lightw. Technol. 26, 2889-2898 (2008).

H. Sun, K.-T. Wu, K. Roberts, "Real-time measurement of a 40-Gb/s coherent system," Opt. Exp. 16, 873-879 (2008).

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

S. J. Savory, "Digital filters for coherent optical receivers," Opt. Exp. 16, 804-817 (2008).

W. Shieh, K.-P. Ho, "Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing," Opt. Exp. 16, 15718-15727 (2008).

E. Ip, J. M. Kahn, "Compensation of dispersion and nonlinear impairments using digital backpropagation," J. Lightw. Technol. 26, 3416-3425 (2008).

E. Mateo, L. Zhu, G. Li, "Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation," Opt. Exp. 16, 16124-16137 (2008).

2007 (6)

A. J. Lowery, "Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation," IEEE Photon. Technol. Lett. 19, 1556-1558 (2007).

W. Shieh, X. Yi, Y. Ma, Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Opt. Exp. 15, 9936-9947 (2007).

A. J. Lowery, "Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM," Opt. Exp. 15, 12965-12970 (2007).

E. Ip, J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightw. Technol. 25, 2675-2692 (2007).

E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).

E. Inuzuka, E. Yamazaki, K. Yonenaga, A. Takada, "Performance of nonlinear interchannel crosstalk pre-compensation at zero-dispersion wavelength using carrier phase-locked WDM," Electron. Lett. 43, 729-730 (2007).

2006 (5)

E. Ip, J. M. Kahn, "Power spectra of return-to-zero optical signals," J. Lightw. Technol. 24, 1610-1618 (2006).

S. Tsukamoto, K. Katoh, K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).

A. Tarighat, R. C. J. Hsu, A. H. Sayed, B. Jalali, "Digital adaptive phase noise reduction in coherent optical links," J. Lightw. Technol. 24, 1269-1276 (2006).

K. Roberts, C. Li, L. Strawczynski, M. O'Sullivan, I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).

R.-J. Essiambre, P. J. Winzer, X. Q. Qang, W. Lee, C. A. White, E. C. Burrows, "Electronic predistortion and fiber nonlinearity," IEEE Photon. Technol. Lett. 18, 1804-1806 (2006).

2005 (1)

E. Ip, J. M. Kahn, "Carrier synchronization for 3- and 4-bit-per-symbol optical transmission," J. Lightw. Technol. 23, 4110-4124 (2005).

2004 (6)

S. Wu, Y. Bar-Ness, "OFDM systems in the presence of phase noise: Consequences and solutions," IEEE Trans. Commun. 52, 1988-1996 (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).

Y. Chen, T. Le-Ngoc, B. Champagne, C. Xu, "Recursive least squares constant modulus algorithm for blind adaptive array," IEEE Trans. Signal Process. 52, 1452-1456 (2004).

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

A. Chowdhury, R.-J. Essiambre, "Optical phase conjugation and pseudolinear transmission," Opt. Lett. 29, 1105-1107 (2004).

J. M. Kahn, K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Topics Quantum Electron. 10, 259-272 (2004).

2003 (2)

J. H. Lee, M. S. Kim, Y. C. Chung, "Statistical PMD emulator using variable DGD elements," IEEE Photon Technol. Lett. 15, 54-56 (2003).

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communication systems," J. Lightw. Technol. 21, 61-68 (2003).

2002 (1)

J. Yang, J.-J. Werner, G. A. Dumont, "The multimodulus blind equalization and its generalized algorithms," IEEE J. Sel. Areas Commun. 20, 997-1015 (2002).

2001 (2)

P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).

P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).

2000 (1)

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. Nat. Acad. Sci. 97, 4541-4550 (2000).

1992 (5)

J. J. Shynk, "Frequency-domain multirate adaptive filtering," IEEE Signal Process. Mag. 9, 14-37 (1992).

J. R. Barry, J. M. Kahn, "Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying," J. Lightw. Technol. 10, 1939-1951 (1992).

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

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, "Polarization multiplexing with solitons," J. Lightw. Technol. 10, 28-35 (1992).

J. M. Kahn, A. M. Porter, U. Padan, "Heterodyne detection of 310-Mb/s quadriphase-shift keying using fourth-power optical phase-locked loop," IEEE Photon. Technol. Lett. 4, 1397-1399 (1992).

1990 (3)

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, B. L. Kasper, "4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers," IEEE Photon. Technol. Lett. 2, 285-287 (1990).

J. S. Soo, K. K. Pang, "Multidelay block frequency domain adaptive filter," IEEE Trans. Acoust. Speech Signal Process. 38, 373-376 (1990).

J. P. Gordon, L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett. 15, 1351-1353 (1990).

1985 (1)

S. U. H. Qureshi, "Adaptive equalization," Proc. IEEE 73, 1349-1387 (1985).

1983 (1)

A. J. Viterbi, A. M. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).

1982 (1)

D. Mansour, A. H. Gray, "Unconstrained frequency-domain adaptive filter," IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 726-734 (1982).

1981 (1)

R. D. Gitlin, S. B. Weinstein, "Fractionally spaced equalization: An improved digital transversal equalizer," Bell Syst. Tech. J. 60, 275-296 (1981).

1980 (1)

D. N. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. COM-28, 1867-1875 (1980).

Bell Syst. Tech. J. (1)

R. D. Gitlin, S. B. Weinstein, "Fractionally spaced equalization: An improved digital transversal equalizer," Bell Syst. Tech. J. 60, 275-296 (1981).

Electron. Lett. (1)

E. Inuzuka, E. Yamazaki, K. Yonenaga, A. Takada, "Performance of nonlinear interchannel crosstalk pre-compensation at zero-dispersion wavelength using carrier phase-locked WDM," Electron. Lett. 43, 729-730 (2007).

IEEE J. Sel. Areas Commun. (1)

J. Yang, J.-J. Werner, G. A. Dumont, "The multimodulus blind equalization and its generalized algorithms," IEEE J. Sel. Areas Commun. 20, 997-1015 (2002).

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

J. M. Kahn, K.-P. Ho, "Spectral efficiency limits and modulation/detection techniques for DWDM systems," IEEE J. Sel. Topics Quantum Electron. 10, 259-272 (2004).

IEEE Photon Technol. Lett. (1)

J. H. Lee, M. S. Kim, Y. C. Chung, "Statistical PMD emulator using variable DGD elements," IEEE Photon Technol. Lett. 15, 54-56 (2003).

IEEE Photon. Technol. Lett. (7)

J. M. Kahn, A. H. Gnauck, J. J. Veselka, S. K. Korotky, B. L. Kasper, "4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers," IEEE Photon. Technol. Lett. 2, 285-287 (1990).

J. M. Kahn, A. M. Porter, U. Padan, "Heterodyne detection of 310-Mb/s quadriphase-shift keying using fourth-power optical phase-locked loop," IEEE Photon. Technol. Lett. 4, 1397-1399 (1992).

S. Tsukamoto, K. Katoh, K. Kikuchi, "Coherent demodulation of optical multilevel phase-shift-keying signals using homodyne detection and digital signal processing," IEEE Photon. Technol. Lett. 18, 1131-1133 (2006).

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).

K. Roberts, C. Li, L. Strawczynski, M. O'Sullivan, I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006).

R.-J. Essiambre, P. J. Winzer, X. Q. Qang, W. Lee, C. A. White, E. C. Burrows, "Electronic predistortion and fiber nonlinearity," IEEE Photon. Technol. Lett. 18, 1804-1806 (2006).

A. J. Lowery, "Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation," IEEE Photon. Technol. Lett. 19, 1556-1558 (2007).

IEEE Signal Process. Mag. (1)

J. J. Shynk, "Frequency-domain multirate adaptive filtering," IEEE Signal Process. Mag. 9, 14-37 (1992).

IEEE Trans. Acoust. Speech Signal Process. (2)

D. Mansour, A. H. Gray, "Unconstrained frequency-domain adaptive filter," IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 726-734 (1982).

J. S. Soo, K. K. Pang, "Multidelay block frequency domain adaptive filter," IEEE Trans. Acoust. Speech Signal Process. 38, 373-376 (1990).

IEEE Trans. Commun. (2)

D. N. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. COM-28, 1867-1875 (1980).

S. Wu, Y. Bar-Ness, "OFDM systems in the presence of phase noise: Consequences and solutions," IEEE Trans. Commun. 52, 1988-1996 (2004).

IEEE Trans. Inf. Theory (1)

A. J. Viterbi, A. M. Viterbi, "Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission," IEEE Trans. Inf. Theory IT-29, 543-551 (1983).

IEEE Trans. Signal Process. (1)

Y. Chen, T. Le-Ngoc, B. Champagne, C. Xu, "Recursive least squares constant modulus algorithm for blind adaptive array," IEEE Trans. Signal Process. 52, 1452-1456 (2004).

J. Lightw. Technol. (15)

A. Tarighat, R. C. J. Hsu, A. H. Sayed, B. Jalali, "Digital adaptive phase noise reduction in coherent optical links," J. Lightw. Technol. 24, 1269-1276 (2006).

I. Fatadin, D. Ives, S. Savory, "Blind equalization and carrier phase recovery in 16-QAM optical coherent system," J. Lightw. Technol. .

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

E. Ip, J. M. Kahn, "Compensation of dispersion and nonlinear impairments using digital backpropagation," J. Lightw. Technol. 26, 3416-3425 (2008).

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communication systems," J. Lightw. Technol. 21, 61-68 (2003).

Q. Zhang, M. I. Hayee, "Symmetrized split-step Fourier scheme to control global simulation accuracy in fiber-optic communication systems," J. Lightw. Technol. 26, 302-316 (2008).

J. R. Barry, J. M. Kahn, "Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying," J. Lightw. Technol. 10, 1939-1951 (1992).

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

E. Ip, J. M. Kahn, "Carrier synchronization for 3- and 4-bit-per-symbol optical transmission," J. Lightw. Technol. 23, 4110-4124 (2005).

E. Ip, J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightw. Technol. 25, 2675-2692 (2007).

J. Armstrong, "OFDM for optical communications," J. Lightw. Technol. 27, 189-204 (2009).

D. J. F. Barros, J. M. Kahn, "Optimized dispersion compensation using orthogonal frequency-division multiplexing," J. Lightw. Technol. 26, 2889-2898 (2008).

E. Ip, J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion," J. Lightw. Technol. 25, 2033-2043 (2007).

E. Ip, J. M. Kahn, "Power spectra of return-to-zero optical signals," J. Lightw. Technol. 24, 1610-1618 (2006).

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, N. S. Bergano, "Polarization multiplexing with solitons," J. Lightw. Technol. 10, 28-35 (1992).

Nature (2)

P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).

P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fiber communications," Nature 411, 1027-1030 (2001).

Opt. Exp. (8)

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