Abstract

This paper presents a novel method based on a parametric gain (PG) approach to study the impact of nonlinear phase noise in single-channel dispersion-managed differentially phase-modulated systems. This paper first shows through Monte Carlo simulations that the received amplified spontaneous emission (ASE) noise statistics, before photodetection, can be reasonably assumed to be Gaussian, provided a sufficiently large chromatic dispersion is present in the transmission fiber. This paper then evaluates in a closed form the ASE power spectral density by linearizing the interaction between a signal and a noise in the limit of a distributed system. Even if the received ASE is nonstationary in time due to pulse shape and modulation, this paper shows that it can be approximated by an equivalent stationary process, as if the signal were continuous wave (CW). This paper then applies the CW-equivalent ASE model to bit-error-rate evaluation by using an extension of a known Karhunen-Loéve method for quadratic detectors in colored Gaussian noise. Such a method avoids calculation of the nonlinear phase statistics and accounts for intersymbol interference due to a nonlinear waveform distortion and optical and electrical postdetection filtering. This paper compares binary and quaternary schemes with both nonreturn-and return-to-zero (RZ) pulses for various values of nonlinear phases and bit rates. The results confirm that PG deeply affects the system performance, especially with RZ pulses and with quaternary schemes. This paper also compares ON-OFF keying (OOK) differential phase-shifted keying (DPSK) systems, showing that the initial 3-dB advantage of DPSK is lost for increasing nonlinear phases because DPSK is less robust to PG than OOK.

© 2006 IEEE

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  2. O. Vassilieva, T. Hoshida, S. Choudhary and H. Kuwahara, "Nonlinear tolerant and spectrally efficient 86 Gb/s RZ-DQPSK format for a system upgrade", in Proc. OFC, Atlanta, GA, Mar. 2003,Paper ThE7,. pp. 22-24.
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  15. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York: McGraw-Hill, 1991.
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  24. M. J. Ablowitz, T. Hirooka and T. Inoue, "Higher-order analysis of dispersion-managed transmission systems: Solutions and their characteristics", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 12, pp. 2876-2885, Dec. 2002.
  25. A. M. Mathai and S. B. Provost, Quadratic Forms in Random Variables, New York: Marcel Dekker, 1992.
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  29. R. I. Killey, H. J. Thiele, V. Mikhailov and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber", IEEE Photon. Technol. Lett., vol. 12, no. 12, pp. 1624-1626, Dec. 2000.
  30. A. Bononi, P. Serena, J.-C. Antona and S. Bigo, "Implications of nonlinear interactions of signal and noise in low-OSNR transmission systems with FEC", presented at the Optical Fiber Communication (OFC), Anaheim, CA, Paper OTHW5, Mar. 2005.

Other (30)

A. Gnauck, "Phase shift keyed transmission", in Proc. OFC, Atlanta, GA, Mar. 2003,Paper ThE1,. pp. 14-15.

O. Vassilieva, T. Hoshida, S. Choudhary and H. Kuwahara, "Nonlinear tolerant and spectrally efficient 86 Gb/s RZ-DQPSK format for a system upgrade", in Proc. OFC, Atlanta, GA, Mar. 2003,Paper ThE7,. pp. 22-24.

A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission", J. Lightw. Technol., vol. 23, no. 1, pp. 115-130, Jan. 2005.

G. Charlet, E. Corbel, J. Lazaro, A. Klekamp, R. Dischler, P. Tran, W. Idler, H. Mardoyan, A. Konczykowska, F. Jorge and S. Bigo, "WDM transmission at 6-Tbit/s capacity over transatlantic distance, using 42.7-Gb/s differential phase-shift keying without pulse carver", J. Lightw. Technol., vol. 23, no. 1, pp. 104-107, Jan. 2005.

J.-P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers", Opt. Lett., vol. 15, no. 23, pp. 1351-1353, Dec. 1990.

K.-P. Ho, "Probability density of nonlinear phase noise", J. Opt. Soc. Amer. B, Opt. Phys., vol. 20, no. 9, pp. 1875-1879, Sep. 2003.

K.-P. Ho, (2005, Sep. "Statistical Properties of Nonlinear Phase Noise",

Y. Yadin, M. Shtaif and M. Orenstein, "Nonlinear phase noise in phase modulated WDM fiber-optic communications", IEEE Photon. Technol. Lett., vol. 16, no. 5, pp. 1307-1309, May 2004.

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and post-detection filtering", J. Lightw. Technol., vol. 18, no. 11, pp. 1493-1503, Nov. 2000.

J. Wang and J. M. Kahn, "Impact of chromatic and polarization-mode dispersions on DPSK systems using interferometric demodulation and direct detection", J. Lightw. Technol., vol. 22, no. 2, pp. 362-371, Feb. 2004.

G. Bosco and P. Poggiolini, "The impact of receiver imperfections on the performance of optical direct-detection DPSK", J. Lightw. Technol., vol. 23, no. 2, pp. 842-848, Feb. 2005.

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk and W. L. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization", J. Lightw. Technol., vol. 20, no. 3, pp. 389-400, Mar. 2002.

H. Kim and A. H. Gnauck, "Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise", IEEE Photon. Technol. Lett., vol. 15, no. 2, pp. 320-322, Feb. 2003.

A. Carena, V. Curri, R. Gaudino, P. Poggiolini and S. Benedetto, "New analytical results on fiber parametric gain and its effects on ASE noise", IEEE Photon. Technol. Lett., vol. 9, no. 4, pp. 535-537, Apr. 1997.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York: McGraw-Hill, 1991.

P. Serena, A. Bononi, J. C. Antona and S. Bigo, "Parametric gain in the strongly nonlinear regime and its impact on 10 Gb/s NRZ systems with forward-error correction", J. Lightw. Technol., vol. 23, no. 8, pp. 2352-2363, Aug. 2005.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. San Diego, CA: Academic, 1995.

D. Zwillinger, Handbook of Differential Equations, 3rd ed. Orlando, FL: Academic, 1997.

M. J. Ablowitz and T. Hirooka, "Managing nonlinearity in strongly dispersion-managed optical pulse transmission", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 3, pp. 425-439, Mar. 2002.

H. A. Haus, "Quantum noise in a solitonlike repeater system", J. Opt. Soc. Amer. B, Opt. Phys., vol. 8, no. 5, pp. 1122-1126, May 1991.

A. Cauvin, Y. Frignac and S. Bigo, "Single-channel nonlinear impairments at various bit-rate in dispersion-managed systems", presented at the Eur. Conf. Optical Communication (ECOC), Rimini, Italy,Paper Mo 4.2.4, Sep. 2003.

P. Serena, A. Orlandini and A. Bononi, "A parametric gain approach to performance evaluation of DSPK/DQPSK systems with nonlinear phase noise," in Optical Communication Theory and Techniques, E. Forestieri, Eds. New York: Springer-Verlag, 2004, pp. 129-136.

M. Midrio, P. Franco and M. Romagnoli, "Noise statistics in transmission systems with gating dispersion compensation", J. Opt. Soc. Amer. B, Opt. Phys., vol. 15, no. 11, pp. 2748-2756, Nov. 1998.

M. J. Ablowitz, T. Hirooka and T. Inoue, "Higher-order analysis of dispersion-managed transmission systems: Solutions and their characteristics", J. Opt. Soc. Amer. B, Opt. Phys., vol. 19, no. 12, pp. 2876-2885, Dec. 2002.

A. M. Mathai and S. B. Provost, Quadratic Forms in Random Variables, New York: Marcel Dekker, 1992.

J. G. Proakis, Digital Communications, 4th ed. : Singapore: McGraw-Hill, 2001.

S. Benedetto and E. Biglieri, Principles of Digital Transmission, New York: Kluwer, 1999.

P. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon and Y. Achiam, "Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber", IEEE Photon. Technol. Lett., vol. 15, no. 3, pp. 473-475, Mar. 2003.

R. I. Killey, H. J. Thiele, V. Mikhailov and P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber", IEEE Photon. Technol. Lett., vol. 12, no. 12, pp. 1624-1626, Dec. 2000.

A. Bononi, P. Serena, J.-C. Antona and S. Bigo, "Implications of nonlinear interactions of signal and noise in low-OSNR transmission systems with FEC", presented at the Optical Fiber Communication (OFC), Anaheim, CA, Paper OTHW5, Mar. 2005.

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