Asymptotically optimal power-constrained distributed estimation

A random parameter is estimated by a distributed network of sensors that communicate over a common MAC. The channel implies an enforced additive fusion rule, and the goal here is to design a power-constrained forwarding strategy and the post-processing by the fusion center. To get an explicit solution we appeal to asymptotics, meaning that we design the locally optimal scheme for the limiting case that the received power goes to zero.