  The extreme or maximum age of information (AoI) is analytically studied for
wireless communication systems. In particular, a wireless powered
single-antenna source node and a receiver (connected to the power grid)
equipped with multiple antennas are considered when operated under independent
Rayleigh-faded channels. Via the extreme value theory and its corresponding
statistical features, we demonstrate that the extreme AoI converges to the
Gumbel distribution whereas its corresponding parameters are obtained in
straightforward closed-form expressions. Capitalizing on this result, the risk
of the extreme AoI realization is analytically evaluated according to some
relevant performance metrics, while some useful engineering insights are
manifested.
