Computer Science – Information Theory
Scientific paper
2012-04-03
Computer Science
Information Theory
Submitted to IEEE Trans. on Information Theory
Scientific paper
In this paper, numerical methods are suggested to compute the discrete and the continuous spectrum of a signal with respect to the Zakharov-Shabat system, a Lax operator underlying numerous integrable communication channels including the nonlinear Schr\"odinger channel, modelling pulse propagation in optical fibers. These methods are subsequently tested and their ability to estimate the spectrum are compared against each other. These methods are used to compute the spectrum of various pulses commonly used in the optical fiber communications. It is found that the layer-peeling and the spectral methods are suitable schemes to estimate the nonlinear spectra with good accuracy. To illustrate the structure of the spectrum, the locus of the eigenvalues is determined under amplitude and phase modulation in a number of examples. It is observed that in some cases, as signal parameters vary, eigenvalues collide and change their course of motion. The real axis is typically the place from which new eigenvalues originate or are absorbed into after travelling a trajectory in the complex plane.
Kschischang Frank R.
Yousefi Mansoor I.
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