Age of Information Minimization with Power and Distortion Constraints in Multiple Access Channels

Emerging fifth generation and beyond networks are expected to deliver accurate information as fresh as possible. In this work, we consider a wireless fading multiple access channel, where M users communicate to a base station (BS) in a time-slotted system. Each user can sample an information packet in any slot of interest, compress it to a finite number of bits and then transmit the compressed packet to the BS. The compression and transmission result in distortion and power consumption, respectively. Using the age of information (AoI) metric for quantifying freshness of information, we consider minimization of a long-term weighted average AoI across the users, subject to average power and distortion constraints at each user, for obtaining the number of bits to be transmitted by a user in a given slot. We cast the problem as a constrained Markov decision process (CMDP) and solve it via Lagrange relaxation. We show that a threshold-type policy is optimal for the relaxed problem. We also propose a convex optimization problem to obtain a suboptimal but simpler stationary randomized policy, whose minimum achievable average AoI is within twice that of the optimal policy. Via numerical simulations, we illustrate the threshold structure of the CMDP based solution and study variation of the average AoIs achieved by the proposed policies when the bounds on the average power and distortion constraints are varied.