Estimation of the distribution of randomly deployed wireless sensors

Authors:
Babar H. Khan;Mérouane Debbah;Øyvind Ryan;Tareq Y. AI-Naffouri
Affiliations:
Department of Electrical Engineering, King Fahd University of Petroleum & Minerals, Dhahran, K.S.A.;Supelec, Gif sur Yvette, France;Centre of Mathematics for Applications, University of Oslo, Blindern, Oslo, Norway;Department of Electrical Engineering, King Fahd University of Petroleum & Minerals, Dhahran, K.S.A.
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Year:
2009

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Abstract

The distribution of randomly deployed wireless sensors plays an important role in the quality of the methods used for data acquisition and signal reconstruction. Mathematically speaking, the estimation of the distribution of randomly deployed sensors can be related to computing the spectrum of Vandermonde matrices with non-uniform entries. In this paper, we use the recent free deconvolution framework to recover, in noisy environments, the asymptotic moments of the structured random Vandermonde matrices and relate these moments to the distribution of the randomly deployed sensors. Remarkably, the results are valid in the finite case using only a limited number of sensors and samples.