Large Deviations Analysis for the Detection of 2D Hidden Gauss-Markov Random Fields Using Sensor Networks

TL;DR

This paper analyzes the detection performance of 2D Gauss-Markov random fields in sensor networks using large deviations theory, revealing how correlation and SNR influence error exponents and energy efficiency.

Contribution

It provides explicit formulas for the error exponent under autoregressive models and explores the impact of correlation and sensor deployment on detection efficiency.

Findings

At high SNR, uncorrelated observations optimize detection error exponent.

At low SNR, a non-zero correlation maximizes the error exponent.

Energy efficiency decreases with increasing area but can be maintained with higher sensor density.

Abstract

The detection of hidden two-dimensional Gauss-Markov random fields using sensor networks is considered. Under a conditional autoregressive model, the error exponent for the Neyman-Pearson detector satisfying a fixed level constraint is obtained using the large deviations principle. For a symmetric first order autoregressive model, the error exponent is given explicitly in terms of the SNR and an edge dependence factor (field correlation). The behavior of the error exponent as a function of correlation strength is seen to divide into two regions depending on the value of the SNR. At high SNR, uncorrelated observations maximize the error exponent for a given SNR, whereas there is non-zero optimal correlation at low SNR. Based on the error exponent, the energy efficiency (defined as the ratio of the total information gathered to the total energy required) of ad hoc sensor network for detection is examined for two sensor deployment models: an infinite area model and and infinite density model. For a fixed sensor density, the energy efficiency diminishes to zero at rate O(area^{-1/2}) as the area is increased. On the other hand, non-zero efficiency is possible for increasing density depending on the behavior of the physical correlation as a function of the link length.