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Path planning is an important component of au- tonomous mobile sensingsystems. This paper studies upper and lower bounds of communication performanceover Gaussian sen- sor networks, to drive power-distortion metrics for pathplanning problems. The Gaussian multiple-access channel is employed as achannel model and two source models are considered. In the first setting, theunderlying source is estimated with minimum mean squared error, while in thesecond, reconstruction of a random spatial field is considered. For bothproblem settings, the upper and the lower bounds of sensor power-distortioncurve are derived. For both settings, the upper bounds follow from theamplify-and-forward scheme and the lower bounds admit a unified derivationbased on data processing inequality and tensorization property of the maximalcorrelation measure. Next, closed-form solutions of the optimal powerallocation problems are obtained under a weighted sum-power constraint. The gapbetween the upper and the lower bounds is analyzed for both weighted sum andindividual power constrained settings. Finally, these metrics are used to drivea path planning algorithm and the effects of power-distortion metrics, networkparameters, and power optimization on the optimized path selection areanalyzed.

Power-Distortion Metrics for Path Planning over Gaussian Sensor Networks