Power Allocation in Linear and Tree WSN Topologies

Estimation at a fusion center in a wireless sensor network is examined. The problem at hand is to perform power allocation subject to a total network power constraint while minimizing the mean-squared error of the estimate. In particular, amplify-and-forward and estimate-and-forward protocols are considered in linear and tree topologies. Analytical solutions for these cases appear to be intractable, and thus asymptotically optimal (for increasing measurement noise variance) solutions are derived. The optimal limiting power policy for the leaf nodes in branch and tree topologies is power equalization, whereas in linear networks, the optimal solution is weighted power equalization.