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Estimation Quality of High-dimensional Fields in Wireless Sensor Networks

Authors:
Siyuan Zhou
Alessandro Nordio
Carla-Fabiana Chiasserini

Keywords: Sensor networks; Signal estimation; Vandermonde matrices

Abstract:
In the fields of wireless communications, networking and signal processing, systems can be often modeled through a linear relationship involving a random Vandermonde matrix $Vm$, and their performance can be characterized through the eigenvalue distribution of the Gram matrix $VmVmHerm$. In spite of its key role, little is known about the eigenvalue distribution of such a matrix and only few of its moments are known in closed form. In this work, we obtain a lower and an upper bound to the eigenvalue distribution of $VmVmHerm$, as well as an excellent approximation based on entropy maximization. As an application, we consider the case of a wireless sensor network sampling a physical phenomenon to be estimated. We characterize the quality of the estimate through the eigenvalue distribution of $VmVmHerm$ by adopting an asymptotic approach, which well suites medium-large scale networks. The proposed method is particularly efficient when dealing with physical phenomena defined over a $d$-dimensional support, with $d>2$.

Pages: 1 to 4

Copyright: Copyright (c) IARIA, 2014

Publication date: February 23, 2014

Published in: conference

ISSN: 2308-4480

ISBN: 978-1-61208-317-9

Location: Nice, France

Dates: from February 23, 2014 to February 27, 2014