  In this paper, we investigate the downlink throughput performance of a
massive multiple-input multiple-output (MIMO) system that employs superimposed
pilots for channel estimation. The component of downlink (DL) interference that
results from transmitting data alongside pilots in the uplink (UL) is shown to
decrease at a rate proportional to the square root of the number of antennas at
the BS. The normalized mean-squared error (NMSE) of the channel estimate is
compared with the Bayesian Cram\'{e}r-Rao lower bound that is derived for the
system, and the former is also shown to diminish with increasing number of
antennas at the base station (BS). Furthermore, we show that staggered pilots
are a particular case of superimposed pilots and offer the downlink throughput
of superimposed pilots while retaining the UL spectral and energy efficiency of
regular pilots. We also extend the framework for designing a hybrid system,
consisting of users that transmit either regular or superimposed pilots, to
minimize both the UL and DL interference. The improved NMSE and DL rates of the
channel estimator based on superimposed pilots are demonstrated by means of
simulations.
