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INTRINSIC FINITE DIMENSIONALITY OF RANDOM MULTIPATH FIELDS Parastoo Sadeghi, Thushara D. Abhayapala, and Rodney A. Kennedy
 

Summary: INTRINSIC FINITE DIMENSIONALITY OF RANDOM MULTIPATH FIELDS
Parastoo Sadeghi, Thushara D. Abhayapala, and Rodney A. Kennedy
Research School of Information Science and Engineering (RSISE)
Australian National University
Canberra ACT 0200 Australia
Email: parastoo.sadeghi@rsise.anu.edu.au
ABSTRACT
We study the dimensions or degrees of freedom of random multipath
fields in wireless communications. Random multipath fields are pre-
sented as solutions to the wave equation in an infinite-dimensional
vector space. We prove a universal bound for the dimension of ran-
dom multipath field in the mean square error sense. The derived
maximum dimension is directly proportional to the radius of the
two-dimensional spatial region where the field is coupled to. Us-
ing the Karhunen-Loeve expansion of multipath fields, we prove
that, among all random multipath fields, isotropic random multipath
achieves the maximum dimension bound. These results mathemat-
ically quantify the imprecise notion of rich scattering that is often
used in multiple-antenna communication theory and show that even
the richest scatterer (isotropic) has a finite intrinsic dimension.

  

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

 

Collections: Computer Technologies and Information Sciences; Engineering