  Intelligent reflecting surface (IRS) is a promising new paradigm to achieve
high spectral and energy efficiency for future wireless networks by
reconfiguring the wireless signal propagation via passive reflection. To reap
the potential gains of IRS, channel state information (CSI) is essential,
whereas channel estimation errors are inevitable in practice due to limited
channel training resources. In this paper, in order to optimize the performance
of IRS-aided multiuser systems with imperfect CSI, we propose to jointly design
the active transmit precoding at the access point (AP) and passive reflection
coefficients of IRS, each consisting of not only the conventional phase shift
and also the newly exploited amplitude variation. First, the achievable rate of
each user is derived assuming a practical IRS channel estimation method, which
shows that the interference due to CSI errors is intricately related to the AP
transmit precoders, the channel training power and the IRS reflection
coefficients during both channel training and data transmission. Then, for the
single-user case, by combining the benefits of the penalty method, Dinkelbach
method and block successive upper-bound minimization (BSUM) method, a new
penalized Dinkelbach-BSUM algorithm is proposed to optimize the IRS reflection
coefficients for maximizing the achievable data transmission rate subjected to
CSI errors; while for the multiuser case, a new penalty dual decomposition
(PDD)-based algorithm is proposed to maximize the users' weighted sum-rate.
Simulation results are presented to validate the effectiveness of our proposed
algorithms as compared to benchmark schemes. In particular, useful insights are
drawn to characterize the effect of IRS reflection amplitude control
(with/without the conventional phase shift) on the system performance under
imperfect CSI.
