Optimal Relay Function in the Low-Power Regime for Distributed Estimation Over a MAC

A random parameter is estimated by a distributed network of sensors that communicate over a common multiple-access channel (MAC). A MAC implies an additive fusion rule, and the goal here is to design a power-constrained forwarding strategy and fusion center post-processing. 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.