  In this paper we consider a constant envelope pilot signal based carrier
frequency offset (CFO) estimation in massive multiple-input multiple-output
(MIMO) systems. The proposed algorithm performs spatial averaging on the
periodogram of the received pilots across the base station (BS) antennas. Our
study reveals that the proposed algorithm has complexity only linear in $M$
(the number of BS antennas). Further our analysis and numerical simulations
also reveal that with fixed number of users and a fixed pilot length, the
minimum required transmit pilot power decreases as $\frac{1}{\sqrt{M}}$ with
increasing $M$, while maintaining a fixed desired mean squared error (MSE) of
CFO estimation.
