Abstract
This paper investigates the evolution of kurtosis of
the input Gaussian amplified spontaneous emission (ASE) noise in a nonlinear
fiber with negligible dispersion. The nonlinear Schrodinger equation (NLSE)
describing propagation in optical fibers is simplified such that the fiber
represents a zero memory nonlinear (ZMNL) system, and this approximation allows
the development of analytical formulas for the statistical moments of the
output noise. It is possible to calculate moments of all integer orders and
the explicit expressions for the first four moments are given. The investigations
show that the ASE noise does not preserve its Gaussian character when Kerr
nonlinearity is significant. This observation proves that the common assumption
of the Gaussian output ASE is not necessarily valid. Numerical simulations
are provided to support the derivation. Kurtosis deviating significantly from
the value typical for Gaussian noise is also an indicator that BER calculation
in the coherent systems based on the assumption that ASE is Gaussian is likely
to be inaccurate.
© 2008 IEEE
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