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2012 | OriginalPaper | Chapter

4. Semianalytical Models for Network Performance Evaluation

Authors : Ronald Holzlöhner, Oleg V. Sinkin, Vladimir S. Grigoryan

Published in: WDM Systems and Networks

Publisher: Springer New York

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Abstract

We discuss the linearization and the momentum methods as two complementary approaches for analyzing signal statistics in optical communications systems governed by the nonlinear Schrödinger equation. Based on the linearization, we derive the covariance matrix method that allows us to accurately compute the bit error rates. The momentum method represents an alternative approach for computationally efficient analysis of the amplitude and timing jitter, as well as signal statistics.

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Note that by choosing this sign convention in the exponential functions, the optical frequency that corresponds to \(\omega_{n}\) lies at \(\omega_{\rm total}=\omega_{0}-\omega_{n},\) where \(\omega_{0}\) is the carrier frequency.

In the rest of this subsection, we will use a sans serif font to denote complex \(N\times N\) matrices like \({\mathsf B},\) a script font for real \(2N\times2N\) matrices like \({\fancyscript{R}},\) and a bold face font for real \(2N\)-vectors such as a. The only exception will be \(\alpha,\) which is a complex N-vector.

See Sect. 4.2.2.1 for a discussion of parametric gain.

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Title: Semianalytical Models for Network Performance Evaluation
Authors: Ronald Holzlöhner
Oleg V. Sinkin
Vladimir S. Grigoryan
Publisher: Springer New York
Book: WDM Systems and Networks
Print ISBN: 978-1-4614-1092-8

Electronic ISBN: 978-1-4614-1093-5

Copyright Year: 2012
DOI: https://doi.org/10.1007/978-1-4614-1093-5_4