  Path planning is an important component of au- tonomous mobile sensing
systems. This paper studies upper and lower bounds of communication performance
over Gaussian sen- sor networks, to drive power-distortion metrics for path
planning problems. The Gaussian multiple-access channel is employed as a
channel model and two source models are considered. In the first setting, the
underlying source is estimated with minimum mean squared error, while in the
second, reconstruction of a random spatial field is considered. For both
problem settings, the upper and the lower bounds of sensor power-distortion
curve are derived. For both settings, the upper bounds follow from the
amplify-and-forward scheme and the lower bounds admit a unified derivation
based on data processing inequality and tensorization property of the maximal
correlation measure. Next, closed-form solutions of the optimal power
allocation problems are obtained under a weighted sum-power constraint. The gap
between the upper and the lower bounds is analyzed for both weighted sum and
individual power constrained settings. Finally, these metrics are used to drive
a path planning algorithm and the effects of power-distortion metrics, network
parameters, and power optimization on the optimized path selection are
analyzed.
