On the Szegö-Asymptotics for Doubly-Dispersive Gaussian Channels

Abstract

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 Szegö 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).

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