 
Summary: SpaceTimeFrequency Degrees of Freedom:
Fundamental Limits for Spatial Information
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 [F  W, F + W]
a time interval [0, T] within a sphere of radius R. We show
that the such constrained signals may be represented by a
series expansion whose terms are bounded exponentially to zero
beyond a threshold. Our result implies there is a finite amount
of information which may be extracted from a region of space
via electromagnetic radiation.
I. INTRODUCTION
Wireless communication is fundamentally limited by the
physics of the medium. Electromagnetic wave propagation has
been given [1, 2] as a motivation for developing such limits:
information is ultimately carried on electromagnetic waves.
Narrowband degrees of freedom (dimensionality) results have
been given for dense multipath [35] and subsequently ex
