  This paper studies the feasibility of deploying intelligent reflecting
surfaces (IRSs) in massive MIMO (multiple-input multiple-output) systems to
improve the performance of users in the service dead zone. To reduce the
channel training overhead, we advocate a novel protocol for the uplink
communication in the IRS-assisted massive MIMO systems. Under this protocol,
the IRS reflection coefficients are optimized based on the channel covariance
matrices, which are generally fixed for many coherence blocks, to boost the
long-term performance. Then, given the IRS reflecting coefficients, the BS
beamforming vectors are designed in each coherence block based on the effective
channel of each user, which is the superposition of its direct and reflected
user-IRS-BS channels, to improve the instantaneous performance. Since merely
the user effective channels are estimated in each coherence block, the training
overhead of this protocol is the same as that in the legacy wireless systems
without IRSs. Moreover, in the asymptotic regime that the numbers of IRS
elements and BS antennas both go to infinity with a fixed ratio, we manage to
first characterize the minimum mean-squared error (MMSE) estimators of the user
effective channels and then quantify the closed-form user achievable rates as
functions of channel covariance matrices with channel training overhead and
estimation error taken into account. Interestingly, it is shown that the
properties of channel hardening and favorable propagation still hold for the
user effective channels, and satisfactory user rates are thus achievable even
if simple BS beamforming solutions, e.g., maximal-ratio combining, are
employed. Finally, thanks to the rate characterization, we design a
low-complexity algorithm to optimize the IRS reflection coefficients based on
channel covariance matrices.
