Bayesian quickest change detection under energy constraints over wireless sensor networks with correlated fading channels

Abstract

In the existing approaches to Bayesian quickest change detection under energy constraints, the consumed energy is formulated as the number of observations and the communication channels between the sensors and the fusion center are assumed to be perfect, which are not quite realistic. We consider the correlated wireless fading channels and the associated packet loss probabilities depend on both time-varying channel gains and the power levels being used by the sensors. The channel gains are governed by a first-order stationary and homogeneous Markovian process and the power level can be adjusted by the fusion center. The optimal power control and stopping rules are studied to minimize the average detection delay as well as to satisfy certain energy constraints. This optimization problem is solved by formulating it as a partially observable Markov decision process (POMDP) and the optimal stopping rules are shown to have "weak" threshold structure. A numerical example is given to illustrate the main results. I. INTROCUTIONThe central Bayesian quickest change detection problem was proposed by Shiryaev [1], in which the change time is assumed to have the a priori geometric distribution, a sequence of observations are taken and the goal is to find the optimal stopping rule to minimize the average delay subject to certain false alarm rate. The decentralized counterpart is studied in [2], [3] and some useful results about quantization policy at the side of sensors are obtained.The above literature, however, did not consider energy constraints, which is of ultimate importance in applications using wireless sensor networks (WSNs). This is because the sensors are usually battery-powered and have limited energy. Recently, the problem of quickest change detection with energy constraints are studied in [4]-[7]. The energy consumed in these papers is formulated as the number of observations taken and the sensors are switched off when necessary to conserve energy. The optimal sleep/awake and stopping rules are studied.The limit of the above models, however, is that the authors assumed the communication channels between the sensors and the fusion center are perfect and each observation consumes equal energy, which is not quite realistic in WSNs.The authors are with the This work is supported by an HKUST Caltech Partnership FP004.Packet dropout is common in wireless communications due to many factors, such as fading channels, interference and low signal-to-noise ratio (SNR). In this paper, we consider the scenario where the data sent from the sensor nodes to the fusion center may get dropped over the fading channels. Packet dropout probabilities depend on both power levels of sensors and time-varying channel gains. The channel gains may be correlated with each other (see details in Section II-A). At each time slot, the fusion center makes a global decision based on available observations collected from the sensors and the state of communication channels to stop and declare the change or to continue. If continues, the center needs ...