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Space-Time-Frequency Degrees of Freedom: Fundamental Limits for Spatial Information

Summary: Space-Time-Frequency Degrees of Freedom:
Fundamental Limits for Spatial Information
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 [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.
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-


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


Collections: Computer Technologies and Information Sciences