Age-Energy Tradeoff Optimization for Packet Delivery in Fading Channels

Abstract

Power control policies that minimize the weighted combination of age of information (AoI) and total energy consumption are studied in this paper. It is assumed that the status update information is acquired at the transmitter through sensors and then sent in packets to the receiver at fixed rate over Rayleigh fading channels. Retransmission mechanism is introduced to guarantee the reliability of the received update packets, and a limit on the maximum number of transmission rounds is imposed. On the one hand, with the channel distribution information (CDI) available at the transmitter, the age-energy tradeoff is optimized by formulating the problem as a constrained Markov decision process (CMDP) which takes into account the sensing power consumption as well as the average transmission power constraint. Employing the Lagrangian relaxation, the CMDP problem is transformed into an unconstrained Markov decision process (MDP) problem. A threshold-based policy is also provided. Subsequently, a dynamic programming approach is proposed to obtain the optimal power allocation policy. On the other hand, when the environment is unknown, two probabilistic reinforcement learning algorithms are proposed to optimize the age-energy tradeoff. Through simulation results, it is shown that the age-energy tradeoffs can be improved by the proposed optimal policies compared with benchmark schemes.