Power constrained distributed estimation with cluster-based sensor collaboration

We consider the problem of distributed estimation in a power constrained collaborative wireless sensor network (WSN), where the network is divided into a set of sensor clusters, with collaboration allowed among sensors within the same cluster but not across clusters. Specifically, each cluster forms one or multiple local messages via sensor collaboration (in particular, linear operation is considered) and transmits the messages over noisy channels to a fusion center (FC). The final estimate is constructed at the FC based on the noisy data received from all clusters. In this collaborative setup, we study the following fundamental problems. Given a total transmit power constraint, shall we transmit the raw data or some low-dimensional local messages for each cluster? What is the optimal collaboration scheme for each cluster? How to optimally allocate the power among different clusters? These questions are addressed in this paper. We will show that the optimum collaboration strategy is to compress the data into one local message which, depending on the channel characteristics, is transmitted using one or multiple available channels to the FC. The optimal power allocation among the clusters is also investigated, which yields a water- filling type of scheme.