Precoding and Scheduling for AoI Minimization in MIMO Broadcast Channels

In this paper, we consider a status updating system where updates are generated at a constant rate at $K$ sources and sent to the corresponding recipients through a broadcast channel. We assume that perfect channel state information (CSI) is available at the transmitter before each transmission, and the additive noise is negligible at the receivers. While the transmitter is able to utilize the CSI information to precode the updates, our object is to design optimal precoding schemes to minimize the summed average \emph{age of information} (AoI) at the recipients. Under various assumptions on the size of each update $B$, the number of transmit antennas $M$, and the number of receive antennas $N$ at each user, this paper identifies the corresponding age-optimal precoding and transmission scheduling strategies. Specifically, for the case when $N=1$, a round-robin based updating scheme is shown to be optimal. For the two-user systems with $N>B$ or $M\notin[N:2N]$, framed updating schemes are proven to be optimal. For other cases in the two-user systems, a framed alternating updating scheme is proven to be $2$-optimal.