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

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.