  We consider a power-constrained sensor network, consisting of multiple sensor
nodes and a fusion center (FC), that is deployed for the purpose of estimating
a common random parameter of interest. In contrast to the distributed
framework, the sensor nodes are allowed to update their individual observations
by (linearly) combining observations from neighboring nodes. The updated
observations are communicated to the FC using an analog amplify-and-forward
modulation scheme and through a coherent multiple access channel. The optimal
collaborative strategy is obtained by minimizing the cumulative transmission
power subject to a maximum distortion constraint. For the distributed scenario
(i.e., with no observation sharing), the solution reduces to the
power-allocation problem considered by [Xiao, TSP08]. Collaboration among
neighbors significantly improves power efficiency of the network in the low
local-SNR regime, as demonstrated through an insightful example and numerical
simulations.
