On the Minimum Average Age of Information in IRSA for Grant-Free mMTC

We consider the optimal design of the frame-based irregular repetition slotted ALOHA (IRSA) protocol for minimizing the average age of information (AAoI) in grant-free massive machine-type communications (mMTC). To this end, we first characterize the AAoI as a function of the number of user elements (UEs), the frame duration, and the repetition distribution of IRSA. We present this characterization for IRSA schemes with packet recovery at the end of frame and packet generation either at the beginning of the frame or just in time before first transmission in a frame. We also propose and characterize the AAoI of a novel early packet recovery method which further reduces the average age of information. In all cases, the analysis reveals that, as a function of normalized channel traffic (defined as the ratio of number of UEs to frame duration), the AAoI first decreases linearly due to more frequent updates received from the UEs, and increases sharply beyond a critical point due to packet recovery failures caused by collisions. We then consider the problem of minimizing AAoI by optimizing over the normalized channel traffic and repetition distribution for all the proposed sampling and recovery schemes. The optimization problem is challenging since the objective function is semi-analytical and can only be completely characterized using simulations. In an asymptotic regime where the number of UEs as well as the frame size is large, we characterize the AAoI using upper and lower bounds. We also obtain a locally optimal normalized channel traffic and repetition distribution using differential evolution. Based on the insights obtained from the asymptotic analysis, we also propose a pragmatic approach to obtain a normalized channel traffic and repetition distribution for AAoI reduction in the non-asymptotic case. Finally, we empirically show that our AAoI minimizing schemes outperform conventional throughput optimal schemes.