Performance of Power-Constrained Estimation in Hierarchical Wireless Sensor Networks

In this paper we study estimation in a power-constrained wireless sensor network, where the network is divided into disjoint groups called clusters. The sensors in each cluster observe a random source that is correlated with the sources being observed by the other clusters. Each cluster has a designated cluster head (CH). Estimation of the sources is performed in two time slots: In the first slot, the sensors in each cluster amplify and forward their noisy measurements to the CH that forms a preliminary estimate of the underlying source; and in the second slot, the CHs send a scaled version of their partial estimates to a remote fusion center (FC) that forms the final estimate of the sources. The CHs and the FC use minimum mean square error estimation rule. To minimize the overall estimation distortion, we propose a power scheduling scheme which allocates power to the sensors and the CHs subject to constraints on the transmit powers of the individual clusters and the overall network. We show that when the sources are fully uncorrelated or fully correlated then the solution to the power allocation problem has a computationally favorable structure and is amenable for distributed implementation. However, the partial correlation between the sources leads to coupling of the optimization variables and the power allocation solution requires centralized computation, which may be computationally expensive. To this end, we propose an alternative formulation based on an upper-bound on the distortion function, which leads to a solution that shares characteristics of the fully uncorrelated and correlated cases. Simulation examples illustrate the effectiveness of the proposed power scheduling scheme.