Power-Distortion Metrics for Path Planning over Gaussian Sensor Networks

TL;DR

This paper develops bounds on communication performance in Gaussian sensor networks to inform power-distortion metrics, which are then used to optimize path planning in autonomous sensing systems.

Contribution

It introduces a unified framework for deriving bounds on sensor power-distortion trade-offs and applies these metrics to optimize path planning algorithms.

Findings

Derived upper and lower bounds for sensor power-distortion curves.

Closed-form solutions for optimal power allocation under constraints.

Analyzed the impact of power-distortion metrics on path planning performance.

Abstract

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.