Asymptotic Performance Analysis of Distributed Non-Bayesian Quickest Change Detection With Energy Harvesting Sensors

Abstract

This article focuses on the distributed non-Bayesian quickest change detection based on the cumulative sum (CUSUM) algorithm in an energy harvesting wireless sensor network, where the distributions before and after the change point are assumed to be known. Each sensor is powered by randomly available harvested energy from the surroundings. It samples the observation signal and computes the log-likelihood ratios (LLRs) of the aforementioned two distributions if enough energy is available in its battery for sensing and processing the sample ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$E_{s}$</tex-math></inline-formula> ). Otherwise, the sensor decides to abstain from the sensing process during that time slot and waits until it accumulates enough energy to perform the sensing and processing of a sample. This LLR is used for performing the CUSUM test to arrive at local decisions about the change point, which are then combined at the fusion center (FC) by a predecided fusion rule to arrive at a global decision. In this article, we derive the asymptotic expressions (as the average time to a false alarm goes to infinity) for the expected detection delay and the expected time to a false alarm at the FC for three common fusion rules, namely, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">or</small> , <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</small> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> out of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> majority rule, respectively, by considering the scenario, where the average harvested energy at each sensor is greater than the energy required for sensing and processing a sample <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$E_{s}$</tex-math></inline-formula> . To this end, we use the theory of order statistics and the asymptotic distribution of the first passage times of the local decisions. Numerical results are also provided to support the theoretical claims.