  In this work, we consider the downlink of a single-cell multi-user
multiple-input multiple-output system in which zero-forcing precoding is used
at the base station (BS) to serve a certain number of user equipments (UEs). A
fixed data rate is guaranteed at each UE. The UEs move around in the cell
according to a Brownian motion, thus the path losses change over time and the
energy consumption fluctuates accordingly. We aim at determining the
distribution of the energy consumption. To this end, we analyze the asymptotic
regime where the number of antennas at the BS and the number of UEs grow large
with a given ratio. It turns out that the energy consumption is asymptotically
a Gaussian random variable whose mean and variance are derived analytically.
These results can, for example, be used to approximate the probability that a
battery-powered BS runs out of energy within a certain time period.
