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In this paper, we consider a status updating system where updates aregenerated at a constant rate at $K$ sources and sent to the correspondingrecipients through a noise-free broadcast channel. We assume that perfectchannel state information (CSI) is available at the transmitter before eachtransmission, and the transmitter is able to utilize the CSI information toprecode the updates. Our object is to design optimal precoding schemes tominimize the summed average \emph{age of information} (AoI) at the recipients.Under various assumptions on the size of each update $B$, the number oftransmit antennas $M$, and the number of receive antennas $N$ at each user,this paper identifies the corresponding age-optimal precoding and transmissionscheduling strategies. Specifically, for the case when $N=1$, a round-robinbased 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. Forother cases in the two-user systems, a framed alternating updating scheme isproven to be $2$-optimal.

Precoding and Scheduling for AoI Minimization in MIMO Broadcast Channels