Real-time Sampling and Estimation on Random Access Channels: Age of Information and Beyond

Real-time sampling and estimation of autoregressive Markov processes is considered in random access channels. Two classes of policies are studied: (i) oblivious policies in which decision making is independent of the source realizations, and (ii) non-oblivious policies in which sources are observed causally for decision making. In the first class, minimizing the expected time-average estimation error is equivalent to minimizing the expected age of information (AoI). Lower and upper bounds are provided for the achievable estimation error in this class and age-based threshold policies are shown to provide a two-fold improvement compared to the state-of-the-art. In the second class, an error-based threshold policy is proposed: a transmitter becomes active when its error exceeds a threshold in which case it transmits probabilistically following slotted ALOHA. A closed-form expression is derived for the estimation error as a function of the peak age, the transmission delay, a term which we call the silence delay, as well as the source realization. It is analyzed approximately by considering the underlying source as a discretized Wiener process. The proposed threshold policy provides a three-fold improvement compared to oblivious policies and its performance is close to that of centralized greedy scheduling.