On the Szeg\"o-Asymptotics for Doubly-Dispersive Gaussian Channels

TL;DR

This paper derives a capacity formula for doubly-dispersive Gaussian channels with periodic correlation operators, using a new Szeg"o formula for pseudo-differential operators, supporting the water-filling principle in time and frequency.

Contribution

It introduces a novel Szeg"o formula for pseudo-differential operators and applies it to establish a capacity formula for specific doubly-dispersive channels.

Findings

Capacity formula for channels with periodic correlation operators

Validation of water-filling principle in time and frequency domains

New Szeg"o formula for pseudo-differential operators

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 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).