Estimation Quality of High-dimensional Fields in Wireless Sensor Networks

In the fields of wireless communications, networking and signal processing, systems can be often modeled through a linear relationship involving a random Vandermonde matrix V, and their performance can be characterized through the eigenvalue distribution of the Gram matrix VV* . 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 VV* , as well as an excellent approx- imation 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 VV* 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.