Optimal Node Density for Two-Dimensional Sensor Arrays

TL;DR

This paper investigates the optimal density of sensor nodes in two-dimensional arrays for efficient inference of correlated random fields, balancing information gain and energy constraints.

Contribution

It introduces a model for analyzing the asymptotic information per node and derives the optimal node density considering energy limitations.

Findings

Optimal node density maximizes information under energy constraints

Asymptotic analysis characterizes information gain per node

Trade-offs among density, information, and energy are elucidated

Abstract

The problem of optimal node density for ad hoc sensor networks deployed for making inferences about two dimensional correlated random fields is considered. Using a symmetric first order conditional autoregressive Gauss-Markov random field model, large deviations results are used to characterize the asymptotic per-node information gained from the array. This result then allows an analysis of the node density that maximizes the information under an energy constraint, yielding insights into the trade-offs among the information, density and energy.