Age-Optimal HARQ Design for Freshness-Critical Satellite-IoT Systems

In this article, we consider the satellite Internet of Things (IoT) system, in which the IoT device observes physical processes and transmits the status updates to the monitor node over an error-prone channel with nontrivial propagation delay. The freshness of status updates is characterized by Age of Information (AoI), a novel metric that is defined as the time that elapsed since the freshest received status update was generated. Channel coding is used to combat the burst channel errors and feedback is available through hybrid automatic repeat request (HARQ) protocols. By adopting both the simple-HARQ and incremental redundancy HARQ (IR-HARQ) transmission schemes, we study the age-optimal redundancy allocation problems under the constraint of reliability. As we put special interests on the satellite-IoT scenarios in which the propagation delays are nonnegligible, there exists a threshold of the propagation delay only below which using retransmissions is beneficial to AoI. However, the characterization of such a threshold has received little attention in the literature. By formulating and solving the age-optimal redundancy allocation problems for the adopted HARQ schemes, explicit expressions of the optimal codeword length for each transmission round are derived, and then the threshold of the propagation delay for beneficial retransmissions is obtained. Extensive numerical analysis is conducted to show the effects of propagation delay and channel state on the redundancy allocation results and the optimal AoI. The threshold is also demonstrated by numerical analysis. The results shed important light on the age-optimal HARQ design for freshness-critical satellite-IoT systems in the presence of nontrivial propagation delay.