AoI-Aware Multi-Level Dynamic Power Control with Sum-Power Constraint in Downlink Networks

Age of information (AoI), a metric for data freshness in status update systems, has received growing attention in various applications. This paper focuses on dynamic power control to minimize the average AoI of all users in a sum-power constrained downlink network, where each user has multi-level selectable powers in every slot. By relaxing instantaneous sum-power constraint to a time-averaged sum-power constraint, we decompose the Lagrangian minimization problem into multiple independent power allocation subproblems with each corresponding to a particular user. We show that the optimal policy of each subproblem under a given Lagrange multiplier holds a multi-threshold property, based on which the full indexability property can be possessed by every subproblem. By comparing the Whittle indices and the Lagrange multiplier, the full indexability allows us to obtain the Lagrange multiplier which can effectively utilize the power budget. Given this, a low-complexity power allocation approach is proposed to solve the problem. Moreover, we prove the proposed approach is asymptotic optimality when the number of selectable powers are three. Simulation results verify the analysis and show that our proposed approach outperforms benchmark policies.