Abstract

In this paper, the statistics of received signals in a single-channel dispersion-managed dual-polarization fiber-optical channel are derived in the limit of low dispersion. The joint probability density function (pdf) of the received amplitudes and phases of such a system is derived for both lumped and distributed amplification. The new pdf expressions are used to numerically evaluate the performance of modulation formats over channels with nonlinear phase noise. For example, a sensitivity gain of up to 2 dB is calculated for a specific system using polarization-multiplexed 8-ary phase-shift keying compared with a similar single-polarization system at the same spectral efficiency and a symbol error rate of 5 x 10<sup>-4</sup>. Moreover, the accuracy of the derived pdf is evaluated for some single-channel dispersion-managed fiber-optical links with different dispersion maps using the split-step Fourier transform method.

© 2011 IEEE

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2010

P. Winzer, "Beyond 100G ethernet," IEEE Commun. Mag. 48, 26-30 (2010).

L. E. Nelson, S. L. Woodward, S. Foo, M. Moyer, D. J. S. Beckett, M. O'Sullivan, P. D. Magill, "Detection of a single 40 Gb/s polarization-multiplexed QPSK channel with a real-time intradyne receiver in the presence of multiple coincident WDM channels," J. Lightw. Technol. 28, 2933-2943 (2010).

R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, "Capacity limits of optical fiber networks," J. Lightw. Technol. 28, 662-701 (2010).

A. D. Ellis, J. Zhao, D. Cotter, "Approaching the non-linear Shannon limit," J. Lightw. Technol. 28, 423-433 (2010).

A. Bononi, P. Serena, N. Rossi, "Modeling of signal-noise interactions in nonlinear fiber transmission with different modulation formats," Opt. Fiber Technol. 16, 73-85 (2010).

2009

M. Karlsson, E. Agrell, "Which is the most power-efficient modulation format in optical links?," Opt. Exp. 17, 10814-10819 (2009).

S. Kumar, "Analysis of nonlinear phase noise in coherent fiber-optic systems based on phase shift keying," J. Lightw. Technol. 27, 4722-4733 (2009).

E. Agrell, M. Karlsson, "Power-efficient modulation formats in coherent transmission systems," J. Lightw. Technol. 27, 5115-5126 (2009).

K. Roberts, M. O'Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. J. Krause, C. Laperle, "Performance of dual-polarization QPSK for optical transport systems," J. Lightw. Technol. 27, 3546-3559 (2009).

2008

T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, R. Noé, "Coherent optical communication: Towards realtime systems at 40 Gbit/s and beyond," Opt. Exp. 16, 866-872 (2008).

2007

A. Demir, "Nonlinear phase noise in optical-fiber-communication systems," J. Lightw. Technol. 25, 2002-2032 (2007).

A. P. T. Lau, J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightw. Technol. 25, 3008-3016 (2007).

2006

P. Serena, A. Orlandini, A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).

2004

Y. Yadin, M. Shtaif, M. Orenstein, "Nonlinear phase noise in phasemodulated WDM fiber-optic communications," IEEE Photon. Technol. Lett. 16, 1307-1309 (2004).

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

A. Mecozzi, "Probability density functions of the nonlinear phase noise," Opt. Lett. 29, 673-675 (2004).

2003

K.-P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Am. B 20, 1875-1879 (2003).

H. Kim, A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).

2002

1999

D. Wang, C. Menyuk, "Polarization evolution due to the Kerr nonlinearity and chromatic dispersion," J. Lightw. Technol. 17, 2520-2529 (1999).

1994

A. Mecozzi, "Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers," J. Lightw. Technol. 12, 1993-2000 (1994).

1990

IEEE Commun. Mag.

P. Winzer, "Beyond 100G ethernet," IEEE Commun. Mag. 48, 26-30 (2010).

IEEE Photon. Technol. Lett.

Y. Yadin, M. Shtaif, M. Orenstein, "Nonlinear phase noise in phasemodulated WDM fiber-optic communications," IEEE Photon. Technol. Lett. 16, 1307-1309 (2004).

H. Kim, A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 320-322 (2003).

J. Lightw. Technol.

A. Mecozzi, "Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers," J. Lightw. Technol. 12, 1993-2000 (1994).

P. Serena, A. Orlandini, A. Bononi, "Parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).

S. Kumar, "Analysis of nonlinear phase noise in coherent fiber-optic systems based on phase shift keying," J. Lightw. Technol. 27, 4722-4733 (2009).

A. Demir, "Nonlinear phase noise in optical-fiber-communication systems," J. Lightw. Technol. 25, 2002-2032 (2007).

A. P. T. Lau, J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightw. Technol. 25, 3008-3016 (2007).

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

D. Wang, C. Menyuk, "Polarization evolution due to the Kerr nonlinearity and chromatic dispersion," J. Lightw. Technol. 17, 2520-2529 (1999).

L. E. Nelson, S. L. Woodward, S. Foo, M. Moyer, D. J. S. Beckett, M. O'Sullivan, P. D. Magill, "Detection of a single 40 Gb/s polarization-multiplexed QPSK channel with a real-time intradyne receiver in the presence of multiple coincident WDM channels," J. Lightw. Technol. 28, 2933-2943 (2010).

R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, "Capacity limits of optical fiber networks," J. Lightw. Technol. 28, 662-701 (2010).

A. D. Ellis, J. Zhao, D. Cotter, "Approaching the non-linear Shannon limit," J. Lightw. Technol. 28, 423-433 (2010).

K. Roberts, M. O'Sullivan, K.-T. Wu, H. Sun, A. Awadalla, D. J. Krause, C. Laperle, "Performance of dual-polarization QPSK for optical transport systems," J. Lightw. Technol. 27, 3546-3559 (2009).

E. Agrell, M. Karlsson, "Power-efficient modulation formats in coherent transmission systems," J. Lightw. Technol. 27, 5115-5126 (2009).

J. Opt. Soc. Am. B

Opt. Exp.

M. Karlsson, E. Agrell, "Which is the most power-efficient modulation format in optical links?," Opt. Exp. 17, 10814-10819 (2009).

T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V. Herath, M. Porrmann, R. Noé, "Coherent optical communication: Towards realtime systems at 40 Gbit/s and beyond," Opt. Exp. 16, 866-872 (2008).

Opt. Fiber Technol.

A. Bononi, P. Serena, N. Rossi, "Modeling of signal-noise interactions in nonlinear fiber transmission with different modulation formats," Opt. Fiber Technol. 16, 73-85 (2010).

Opt. Lett.

Other

G. Charlet, J. Renaudier, O. B. Pardo, P. Tran, H. Mardoyan, S. Bigo, "Performance comparison of singly-polarized and polarization multiplexed at 10Gbaud under nonlinear impairments," presented at the Opt. Fiber Commun. Conf./Natl. Fiber Opt. Eng. Conf. San DiegoCA (2008) Paper OThU8.

T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley-Interscience, 2006).

G. Grimmett, D. Stirzaker, Probability and Random Processes (Oxford Univ. Press, 2001).

A. Bononi, P. Serena, N. Rossi, "Nonlinear limits in single- and dual-polarization transmission," Proc. LEOS Summer, Topicals (2010) pp. 38-39.

J. G. Proakis, M. Salehi, Digital Communications (McGraw-Hill, 2008).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

H. Bülow, "Polarization QAM modulation (POL-QAM) for coherent detection schemes," Proc. Opt. Fiber Commun. Conf. (2009) pp. 1-3.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, S. Bigo, "Transmission of 40 Gb/s QPSK with coherent detection over ultra-long distance improved by nonlinearity mitigation," Proc. Eur. Conf. Exhib. Opt. Commun. (2006).

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

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