Summary: Bounds on Space-Time-Frequency Dimensionality
Leif W. Hanlen and Thushara D. Abhayapala
National ICT Australia and Australian National University
{Leif.Hanlen,Thushara.Abhayapala}@nicta.com.au
Abstract-- We bound the number of electromagnetic signals
which may be observed over a frequency range 2W for a time T
within a region of space enclosed by a radius R. Our result
implies that broadband fields in space cannot be arbitrarily
complex: there is a finite amount of information which may be
extracted from a region of space via electromagnetic radiation.
Three-dimensional space allows a trade-off between large
carrier frequency and bandwidth. We demonstrate applications
in super-resolution and broadband communication.
I. INTRODUCTION
The concept of "rich multipath" as a positive communi-
cation medium is widely established in antenna [1­3] sig-
nal processing [4, 5] and communication [6­8] literature. It
is well known that "rich" multipath allows multiplexing of
independent signals. Dimensionality has been offered as an
effective measure of richness in the narrow-band regime [4, 9].

Source: Abhayapala, Thushara D. - Department of Information Engineering, Australian National University

Collections: Computer Technologies and Information Sciences