Summary: Bounds on Space-Time-Frequency Dimensionality
Leif W. Hanlen and Thushara D. Abhayapala
National ICT Australia and Australian National University
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.
The concept of "rich multipath" as a positive communi-
cation medium is widely established in antenna  sig-
nal processing [4, 5] and communication  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].