Abstract

In this paper, we show that the nonlinear parametric gain (PG) interaction between signal and noise is a nonnegligible factor in the design and analysis of long-haul dispersion-managed optical 10-Gb/s on-off keying nonreturn to zero transmission systems operated at small signal-to-noise ratios (OSNRs) such as those employing forward-error correction (FEC) coding. In such a regime, we show that the in-phase noise spectrum exhibits a large gain close to the carrier frequency, which is due to the higher order noise terms accounting for the noise-noise beating during propagation that is usually neglected in the nonlinear Schrödinger equation. With a novel stochastic analysis that keeps such higher order terms, we are able to analytically quantify the maximum tolerable signal power after which PG unacceptably degrades system performance. We verify such an analytical power threshold by both simulation and experiment. We finally quantify the needed extra OSNR, or equivalently FEC coding gain, required when taking PG into account.

© 2005 IEEE

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  2. J. Hansyrd, P. A. Andrekson, M. Westlund, J. Li and P. Hedekvist, "Fiber-based optical parametric amplifiers and their applications", IEEE J. Quantum Electron., vol. 8, no. 3, pp. 506-520, May/Jun. 2002.
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  14. D. Pennickx, G. Charlet, J.-C. Antona and L. Noirie, "Experimental validation of a transparent waveband-based optical backbone network", presented at the Eur. Conf. Optical Communication (ECOC), Copenhagen, Denmark,Paper 6.4.4, Sep. 2002.
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Other (21)

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

J. Hansyrd, P. A. Andrekson, M. Westlund, J. Li and P. Hedekvist, "Fiber-based optical parametric amplifiers and their applications", IEEE J. Quantum Electron., vol. 8, no. 3, pp. 506-520, May/Jun. 2002.

C. J. McKinstrie, S. Radic and A. R. Chraplyvy, "Parametric amplifiers driven by two pump waves", IEEE J. Quantum Electron., vol. 8, no. 3, pp. 538-547, May/Jun. 2002.

M. Karlsson, "Modulation instability in lossy optical fibers", J. Opt. Soc. Amer. B, vol. 12, no. 11, pp. 2071-2078, Nov. 1995.

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.

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini and S. Benedetto, "A novel approach to the evaluation of the impact of fiber parametric gain on the bit error rate", IEEE Trans. Commun., vol. 49, no. 12, pp. 2154-2163, Dec. 2001.

C. W. Helstrom, "Distribution of the filtered output of a quadratic rectifier computed by numerical contour integration", IEEE Trans. Inf. Theory, vol. IT-32, no. 7, pp. 450-463, Jul. 1986.

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.

D. Marcuse, "Single-channel operation in very long nonlinear fibers with optical amplifiers at zero dispersion", J. Lightw. Technol., vol. 9, no. 3, pp. 356-361, Mar. 1991.

P. Serena and A. Bononi, "Power threshold due to parametric gain in dispersion-mapped communication systems", IEEE Photon. Technol. Lett., vol. 14, no. 11, pp. 1521-1523, Nov. 2002.

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

P. Serena, "Studio dell'interazione tra segnale e rumore nella progettazione di sistemi ottici WDM in regime non lineare", Ph.D. thesis, Università degli Studi di Parma, Parma, Italy, Jan. 2003.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1999.

D. Pennickx, G. Charlet, J.-C. Antona and L. Noirie, "Experimental validation of a transparent waveband-based optical backbone network", presented at the Eur. Conf. Optical Communication (ECOC), Copenhagen, Denmark,Paper 6.4.4, Sep. 2002.

C. W. Helstroem, Elements of Signal Detection and Estimation, Englewood Cliffs, NJ: Prentice-Hall, 1995.

D. Zwillinger, Handbook of Differential Equations, Boston, MA: Academic, 1989.

A. Vannucci, P. Serena and A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schrödinger equation", J. Lightw. Technol., vol. 20, no. 7, pp. 1102-1112, Jul. 2002.

J.-C. Antona, S. Bigo and J.-P. Faure, "Nonlinear cumulated phase as a criteria to assess performance of terrestrial WDM systems", in Proc. Optical Fiber Communication (OFC), Anaheim, CA, Mar. 2002,paper WX5,. pp. 365-367.

D. J. Torrieri, "The information-bit error rate for block codes", IEEE Trans. Commun., vol. COM-32, no. 4, pp. 474-476, Apr. 1984.

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

W. A. Gardner, Introduction to Random Processes With Applications to Signals and Systems, 2nd ed. New York: McGraw-Hill, 1990, pp. 114-115.

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