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Electromagnetic wave propagation and inequalities for moments of chord lengths

Part of: Geometric probability and stochastic geometry Global differential geometry General convexity Optics, electromagnetic theory - General

Published online by Cambridge University Press:  01 July 2016

Jan Hansen  and
Matthias Reitzner
Jan Hansen*
Affiliation:
Stanford University
Matthias Reitzner*
Affiliation:
Technische Universität Wien
*
∗ Postal address: Communication Technology Laboratory, ETH Zürich, Sternwartstrasse 7, CH-8092 Zürich, Switzerland.
∗∗ Postal address: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria. Email address: mreitzne@mail.zserv.tuwien.ac.at
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Abstract

In a convex domain K in ℝd, a transmitter and a receiver are placed at random according to the uniform distribution. The statistics of the power received by the receiver is an important quantity for the design of wireless communication systems. Bounds for the moments of the received power are given, which depend only on the volume and the surface area of the convex domain.

Keywords

Convex bodyintegral geometrychord lengthinterpoint distancedual quermassintegral

MSC classification

Primary: 52A22: Random convex sets and integral geometry 60D05: Geometric probability and stochastic geometry 78A40: Waves and radiation
Secondary: 52A40: Inequalities and extremum problems 53C65: Integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 36 , Issue 4 , December 2004 , pp. 987 - 995
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Supported by the German Research Foundation HA3499/1-1.

Supported by Austrian Science Foundation J1940 MAT and J2193 MAT.

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