Abstract

In wavelength-division-multiplexed (WDM) systems, performance is affected by the bit patterns on the various channels and, in order to account for this pattern dependence, one should perform a large number of simulations, each by using different patterns of suitable length in all channels and then average all results. However, since the number of patterns to be considered for averaging could be considerable, this approach would be very demanding from a computational point of view, even using multicanonical Monte Carlo (MMC) simulations. In single-channel systems, pattern dependence can be accounted for through the pattern perturbation method, a computationally efficient way for performing a random walk over an extended state space, which includes, in addition to noise components, also the transmitted bit pattern. In this way, not only the most relevant noise configurations but also the most relevant bit patterns (those having a major impact on the error events) are sampled more frequently by the MMC simulation, leading to enhanced efficiency in estimating the error probability. Here, the pattern perturbation method is extended to the WDM case, and simulations results are reported to show the effectiveness of the proposed approach.

© 2010 IEEE

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2009 (2)

M. Secondini, M. Frezzini, E. Forestieri, "Analytical performance evaluation of optical DQPSK systems with postdetection filtering ," IEEE Photon. Technol. Lett. 21, 908-910 (2009).

2009 (2)

P. Serena, N. Rossi, M. Bertolini, A. Bononi, "Stratified sampling Monte Carlo algorithm for efficient BER estimation in long-haul optical transmission systems," J. Lightw. Technol. 27, 2404-2411 (2009 ).

2009 (2)

E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706 -717 (2009).

2007 (1)

L. Gerardi, M. Secondini, E. Forestieri, "Pattern perturbation method for multicanonical monte carlo simulations in optical communications ," IEEE Photon. Technol. Lett. 19, 1934-1936 (2007).

2007 (1)

O. V. Sinkin, V. S. Grigoryan, C. R. Menyuk, "Accurate probabilistic treatment of bit-pattern-dependent nonlinear distortions in ber calculations for wdm rz systems," J. Lightw. Technol. 25, 2959-2967 (2007 ).

2005 (1)

W. Pellegrini, J. Zweck, C. R. Menyuk, R. Holzlohner, "Computation of bit error rates for a dense wdm system using the noise covariance matrix and multicanonical monte carlo methods," IEEE Photon. Techn. Lett. 17 , 1644-1646 (2005 ).

2005 (1)

R. S. Luís, A. V. T. Cartaxo, "Analytical characterization of spm impact on xpm-induced degradation in dispersion-compensated wdm systems," J. Lightw. Technol. 23, 1503-1513 (2005).

2005 (1)

P. Serena, A. Bononi, J.-C. Antona, 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. 23, 2352-2363 (2005 ).

2004 (1)

K.-P. Ho, "Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise ," IEEE J. Sel. Topics Quantum Electron. 10, 421-427 (2004).

2003 (2)

R. Holzlohner, C. R. Menyuk, W. L. Kath, V. S. Grigoryan, "A covariance matrix method to compute bit error rates in a highly nonlinear dispersion-managed soliton system," IEEE Photon. Technol. Lett. 15, 688-690 (2003 ).

2003 (2)

2001 (2)

G. O. Roberts, J. S. Rosenthal, "Optimal scaling for various Metropolis Hastings algorithms," Statist. Sci. 16, 351-367 (2001).

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A novel analytical approach to the evaluation of the impact of fiber parametric gain on the bit error rate," IEEE Trans. Commun. 49, 2154-2163 (2001).

1997 (1)

P. J. Smith, M. Shafi, H. Gao, "Quick simulation: A review of importance sampling techniques in communication systems ," IEEE J. Sel. Areas Commun. 15, 597-613 (1997).

1992 (1)

B. A. Berg, T. Neuhaus, "Multicanonical ensemble: A new approach to simulate first-order phase transitions," Phys. Rev. Lett. 68, 9-12 (1992).

1984 (1)

T. R. Taha, M. J. Ablowitz, "Analytical and numerical aspects of certain nonlinear evolution equation. II. numerical, nonlinear schrödinger equation," J. Comp. Phys. 55, 203-230 (1984).

1973 (1)

R. Hardin, F. D. Tappert, "Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations," SIAM Rev. Chronicle 15, 423 (1973).

1970 (1)

W. K. Hastings, "Monte Carlo sampling methods using Markov chains and their applications," Biometrika 57, 97-109 (1970).

1966 ()

L. A. Shepp, "Radon-Nikodym derivatives of Gaussian measures," Ann. Math. Statist. 37, 321-354 (1966 ).

1953 (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, "Equation of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).

Ann. Math. Statist. (1)

L. A. Shepp, "Radon-Nikodym derivatives of Gaussian measures," Ann. Math. Statist. 37, 321-354 (1966 ).

Biometrika (1)

W. K. Hastings, "Monte Carlo sampling methods using Markov chains and their applications," Biometrika 57, 97-109 (1970).

IEEE Contr. Syst. Mag. (1)

J. C. Spall, "Estimation via Markov chain Monte Carlo," IEEE Contr. Syst. Mag. 23, 34-45 (2003).

IEEE J. Sel. Areas Commun. (1)

P. J. Smith, M. Shafi, H. Gao, "Quick simulation: A review of importance sampling techniques in communication systems ," IEEE J. Sel. Areas Commun. 15, 597-613 (1997).

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, 421-427 (2004).

IEEE Photon. Techn. Lett. (1)

W. Pellegrini, J. Zweck, C. R. Menyuk, R. Holzlohner, "Computation of bit error rates for a dense wdm system using the noise covariance matrix and multicanonical monte carlo methods," IEEE Photon. Techn. Lett. 17 , 1644-1646 (2005 ).

IEEE Photon. Technol. Lett. (3)

M. Secondini, M. Frezzini, E. Forestieri, "Analytical performance evaluation of optical DQPSK systems with postdetection filtering ," IEEE Photon. Technol. Lett. 21, 908-910 (2009).

R. Holzlohner, C. R. Menyuk, W. L. Kath, V. S. Grigoryan, "A covariance matrix method to compute bit error rates in a highly nonlinear dispersion-managed soliton system," IEEE Photon. Technol. Lett. 15, 688-690 (2003 ).

L. Gerardi, M. Secondini, E. Forestieri, "Pattern perturbation method for multicanonical monte carlo simulations in optical communications ," IEEE Photon. Technol. Lett. 19, 1934-1936 (2007).

IEEE Trans. Commun. (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A novel analytical approach to the evaluation of the impact of fiber parametric gain on the bit error rate," IEEE Trans. Commun. 49, 2154-2163 (2001).

J. Lightw. Technol. (1)

E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706 -717 (2009).

J. Chem. Phys. (1)

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, "Equation of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).

J. Comp. Phys. (1)

T. R. Taha, M. J. Ablowitz, "Analytical and numerical aspects of certain nonlinear evolution equation. II. numerical, nonlinear schrödinger equation," J. Comp. Phys. 55, 203-230 (1984).

J. Lightw Technol. (1)

P. Serena, A. Bononi, J.-C. Antona, 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. 23, 2352-2363 (2005 ).

J. Lightw. Technol. (3)

P. Serena, N. Rossi, M. Bertolini, A. Bononi, "Stratified sampling Monte Carlo algorithm for efficient BER estimation in long-haul optical transmission systems," J. Lightw. Technol. 27, 2404-2411 (2009 ).

R. S. Luís, A. V. T. Cartaxo, "Analytical characterization of spm impact on xpm-induced degradation in dispersion-compensated wdm systems," J. Lightw. Technol. 23, 1503-1513 (2005).

O. V. Sinkin, V. S. Grigoryan, C. R. Menyuk, "Accurate probabilistic treatment of bit-pattern-dependent nonlinear distortions in ber calculations for wdm rz systems," J. Lightw. Technol. 25, 2959-2967 (2007 ).

Opt. Lett. (1)

Phys. Rev. Lett. (1)

B. A. Berg, T. Neuhaus, "Multicanonical ensemble: A new approach to simulate first-order phase transitions," Phys. Rev. Lett. 68, 9-12 (1992).

SIAM Rev. Chronicle (1)

R. Hardin, F. D. Tappert, "Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations," SIAM Rev. Chronicle 15, 423 (1973).

Statist. Sci. (1)

G. O. Roberts, J. S. Rosenthal, "Optimal scaling for various Metropolis Hastings algorithms," Statist. Sci. 16, 351-367 (2001).

Other (2)

J. F. C. Kingman, S. J. Taylor, Introduction to Measure and Probability (Cambridge Univ. Press, 1966).

M. Secondini, D. Fertonani, G. Colavolpe, E. Forestieri, "Performance evaluation of viterbi decoders by multicanonical monte carlo simulations ," Proc. IEEE Int. Symp. Inf. Theory (2009) pp. 1363-1367.

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