Downlink Performance of Superimposed Pilots in Massive MIMO systems
  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. 
Karthik Upadhya, Sergiy A. Vorobyov, Mikko Vehkapera
cs.IT math.IT