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Summary: 1
Intrinsic Limits of Dimensionality and
Richness in Random Multipath Fields
Rodney A. Kennedy
, Parastoo Sadeghi
, Thushara D. Abhayapala
, and Haley M. Jones
Research School of Information Sciences and Engineering (RSISE)
The Australian National University
Canberra ACT 0200 Australia
Email: parastoo.sadeghi@rsise.anu.edu.au
Abstract
We study the dimensions or degrees of freedom of farfield multipath that is observed in a
limited, source-free region of space. The multipath fields are studied as solutions to the wave
equation in an infinite-dimensional vector space. We prove two universal upper bounds on the
truncation error of fixed and random multipath fields. A direct consequence of the derived bounds
is that both fixed and random multipath fields have an effective finite dimension. For circular
and spherical spatial regions, we show that this finite dimension is proportional to the radius and
area of the region, respectively. We use the Karhunen-Loeve (KL) expansion of random multipath
fields to quantify the notion of multipath richness. The multipath richness is defined as the number
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