Estimation of the Distribution of Randomly Deployed Wireless Sensors

Merouane Debbah (1) , Babar Khan H. (2) , T.Y. Al-Naffouri (2) , Ryan Oyvind (3)

1 E3S - Supélec Sciences des Systèmes
2 King Fahd University of Petroleum & Minerals
3 UiO - University of Oslo

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.

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Merouane Debbah, Babar Khan H., T.Y. Al-Naffouri, Ryan Oyvind. Estimation of the Distribution of Randomly Deployed Wireless Sensors. IEEE International Symposium on Information Theory, Jun 2009, South Korea. 5 p. ⟨hal-00447065⟩