On the Szegö-Asymptotics for Doubly-Dispersive Gaussian Channels

Details On the Szegö-Asymptotics for Doubly-Dispersive Gaussian Channels On the Szegö-Asymptotics for Doubly-Dispersive Gaussian Channels

2011-02-25

arxiv.org/abs/1102.5253v3

Computer Science

Information Theory

5 pages, to be presented at ISIT 2011, minor typos corrected, references updated

Scientific paper

We consider the time-continuous doubly-dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this result is a new Szeg\"o formula for certain pseudo-differential operators. The formula justifies the water-filling principle along time and frequency in terms of the time--continuous time-varying transfer function (the symbol).

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