Optimization control of amplify‐and‐forward relay under Markov packet loss

Abstract This article investigates the optimal control of an amplify‐and‐forward relay in a dual‐hop remote state estimation system, where communication channels exhibit usage‐dependent packet loss characteristics. The sensor‐to‐relay and relay‐to‐estimator channels are modeled as Markov chains, with state transitions governed by the relay's actions, thereby explicitly capturing their influence on the overall network reliability. The relay control policy is designed to balance estimation accuracy and energy efficiency. To this end, the problem is formulated as a Markov decision process, and the existence of an optimal stationary deterministic policy with a threshold structure is established. This policy efficiently determines relay actions based on channel state and consecutive packet drop count. Simulation examples are provided to illustrate the results.