Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization

Ronald Holzlöhner*, V. S. Grigoryan, C. R. Menyuk, W. L. Kath

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


We present a novel linearization method to calculate accurate eye diagrams and bit error rates (BERs) for arbitrary optical transmission systems and apply it to a dispersion-managed soliton (DMS) system. In this approach, we calculate the full nonlinear evolution using Monte Carlo methods. However, we analyze the data at the receiver assuming that the nonlinear interaction of the noise with itself in an appropriate basis set is negligible during transmission. Noise-noise beating due to the quadratic nonlinearity in the receiver is kept. We apply this approach to a highly nonlinear DMS system, which is a stringent test of our approach. In this case, we cannot simply use a Fourier basis to linearize, but we must first separate the phase and timing jitters. Once that is done, the remaining Fourier amplitudes of the noise obey a multivariate Gaussian distribution, the timing jitter is Gaussian distributed, and the phase jitter obeys a Jacobi-Θ distribution, which is the periodic analogue of a Gaussian distribution. We have carefully validated the linearization assumption through extensive Monte Carlo simulations. Once the effect of timing jitter is restored at the receiver, we calculate complete eye diagrams and the probability density functions for the marks and spaces. This new method is far more accurate than the currently accepted approach of simply fitting Gaussian curves to the distributions of the marks and spaces. In addition, we present a deterministic solution alternative to the Monte Carlo method.

Original languageEnglish (US)
Pages (from-to)389-400
Number of pages12
JournalJournal of Lightwave Technology
Issue number3
StatePublished - Mar 2002


  • Amplifier noise
  • Error analysis
  • Karhunen-Loève transforms
  • Linear approximation
  • Monte Carlo methods
  • Nonlinearities
  • Optical fiber dispersion
  • Optical fiber theory
  • Simulation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


Dive into the research topics of 'Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization'. Together they form a unique fingerprint.

Cite this