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Power-Distortion Metrics for Path Planning over Gaussian Sensor Networks

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.