  This paper gives a replica analysis for the minimum mean square error (MSE)
of a massive multiple-input multiple-output (MIMO) system by using Bayesian
inference. The Bayes-optimal estimator is adopted to estimate the data symbols
and the channels from a block of received signals in the spatial-temporal
domain. We show that using the Bayes-optimal estimator, the interfering signals
from adjacent cells can be separated from the received signals without pilot
information. In addition, the MSEs with respect to the data symbols and the
channels of the desired users decrease with the number of receive antennas and
the number of data symbols, respectively. There are no residual interference
terms that remain bounded away from zero as the numbers of receive antennas and
data symbols approach infinity.
