  Low-complexity carrier frequency offset (CFO) estimation and compensation in
multi-user massive multiple-input multiple-output (MIMO) systems is a
challenging problem. The existing CFO estimation algorithms incur tremendous
increase in complexity with increasing number of base station (BS) antennas,
$M$ and number of user terminals (UTs) $K$ (i.e. massive MIMO regime). In this
paper, we address this problem by proposing a novel low-complexity algorithm
for CFO estimation which uses the pilot signal received at the BS during
special uplink slots. The total per-channel use complexity of the proposed
algorithm increases only linearly with increasing $M$ and is independent of
$K$. Analysis reveals that the CFO estimation accuracy can be considerably
improved by increasing $M$ and $K$ (i.e. massive MIMO regime). For example, for
a fixed $K$ and a fixed training length, the required per-user radiated power
during uplink training decreases as $\frac{1}{\sqrt{M}}$ with increasing $M$.
