Asymptotic Performance Analysis of Non-Bayesian Quickest Change Detection with an Energy Harvesting Sensor

TL;DR

This paper analyzes the asymptotic performance of a non-Bayesian CUSUM change detection algorithm used by an energy harvesting sensor, deriving delay and false alarm tail distributions under different energy harvesting conditions.

Contribution

It provides novel asymptotic expressions for detection delay and false alarm tail distribution considering the energy harvesting constraints, especially when energy is insufficient for sensing.

Findings

When average harvested energy exceeds sensing energy, standard CUSUM results apply.

For lower harvested energy, the energy level follows a Markov chain, affecting detection performance.

Numerical results validate the theoretical asymptotic expressions.

Abstract

In this paper, we consider a non-Bayesian sequential change detection based on the Cumulative Sum (CUSUM) algorithm employed by an energy harvesting sensor where the distributions before and after the change are assumed to be known. In a slotted discrete-time model, the sensor, exclusively powered by randomly available harvested energy, obtains a sample and computes the log-likelihood ratio of the two distributions if it has enough energy to sense and process a sample. If it does not have enough energy in a given slot, it waits until it harvests enough energy to perform the task in a future time slot. We derive asymptotic expressions for the expected detection delay (when a change actually occurs), and the asymptotic tail distribution of the run-length to a false alarm (when a change never happens). We show that when the average harvested energy ($\bar H$) is greater than or equal to the energy required to sense and process a sample ($E_s$), standard existing asymptotic results for the CUSUM test apply since the energy storage level at the sensor is greater than $E_s$ after a sufficiently long time. However, when the $\bar H < E_s$, the energy storage level can be modelled by a positive Harris recurrent Markov chain with a unique stationary distribution. Using asymptotic results from Markov random walk theory and associated nonlinear Markov renewal theory, we establish asymptotic expressions for the expected detection delay and asymptotic exponentiality of the tail distribution of the run-length to a false alarm in this non-trivial case. Numerical results are provided to support the theoretical results.