—Path planning is an important component of autonomous mobile sensing systems. This paper studies upper and lower bounds of communication performance over Gaussian sensor 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 an...