Abstract
In this paper, we consider a status updating system where updates are generated at a constant rate at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> sources and sent to the corresponding recipients through a noise-free broadcast channel. We assume that perfect channel state information (CSI) is available at the transmitter before each transmission, and the transmitter is able to utilize the CSI to precode the updates. Our object is to design optimal precoding schemes to minimize the summed average <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">age of information</i> (AoI) at the recipients. Under various assumptions on the size of each update <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$B$ </tex-math></inline-formula> , the number of transmit antennas <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> , and the number of receive antennas <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> at each user, this paper identifies the corresponding age-optimal precoding and transmission scheduling strategies. Specifically, for the case when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N=1$ </tex-math></inline-formula> , a round-robin based updating scheme is shown to be optimal. For the two-user systems with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N>B$ </tex-math></inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M\notin [N:2N]$ </tex-math></inline-formula> , 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
