  A power constrained sensor network that consists of multiple sensor nodes and
a fusion center (FC) is considered, where the goal is to estimate a random
parameter of interest. In contrast to the distributed framework, the sensor
nodes may be partially connected, where individual nodes can update their
observations by (linearly) combining observations from other adjacent nodes.
The updated observations are communicated to the FC by transmitting through a
coherent multiple access channel. The optimal collaborative strategy is
obtained by minimizing the expected mean-square-error subject to power
constraints at the sensor nodes. Each sensor can utilize its available power
for both collaboration with other nodes and transmission to the FC. Two kinds
of constraints, namely the cumulative and individual power constraints are
considered. The effects due to imperfect information about observation and
channel gains are also investigated. The resulting performance improvement is
illustrated analytically through the example of a homogeneous network with
equicorrelated parameters. Assuming random geometric graph topology for
collaboration, numerical results demonstrate a significant reduction in
distortion even for a moderately connected network, particularly in the low
local-SNR regime.
