Age-Optimal Low-Power Status Update over Time-Correlated Fading Channel

In this paper, we consider transmission scheduling in a status update system, where updates are generated periodically and transmitted over a Gilbert-Elliott fading channel. The goal is to minimize the long-run average age of information (AoI) at the destination under an average energy constraint. The channel state is revealed by the feedback (Ack/Nack) of a transmission; while it remains unknown if there is no transmission. Thus, we have to design a scheduling policy that balances tradeoffs across energy, AoI, channel exploration, and channel exploitation. The problem is formulated as a constrained partially observable Markov decision process problem (POMDP). We show that the optimal policy is a randomized mixture of no more than two stationary deterministic policies each of which is of a threshold-type in the belief on the channel. We propose a finite-state approximation for our infinite-state belief MDP and show convergence. Based on the theoretical insights gained from studying this problem, we develop an optimal algorithm using the structure of the problem.