On the impact of correlated sampling processes in WSNs with energy-neutral operation

In this paper, we consider a communication scenario where multiple EH sensor nodes collect correlated measurements of an underlying random field. The nodes operate in an energy-neutral manner (i.e. energy is used as soon as it is harvested) and, hence, the energy-harvesting and sampling processes at the sensor nodes become inter-twined, random and spatially correlated. Under some mild assumptions, we derive the multidimensional linear filter which minimizes the mean square error in the reconstructed measurements at the Fusion Center (FC). We also analyze the impact of correlated and random sampling processes in the resulting distortion and, in order to gain some insight, we particularize the analysis to the case of fully correlated spatial fields and with an asymptotically large number of sensor nodes.