  Intelligent reflecting surface (IRS), composed of a large number of
hardware-efficient passive elements, is deemed as a potential technique for
future wireless communications since it can adaptively enhance the propagation
environment. In order to effectively utilize IRS to achieve promising
beamforming gains, the problem of channel state information (CSI) acquisition
needs to be carefully considered. However, most recent works assume to employ
an ideal IRS, i.e., each reflecting element has constant amplitude, variable
phase shifts, as well as the same response for the signals with different
frequencies, which will cause severe estimation error due to the mismatch
between the ideal IRS and the practical one. In this paper, we study channel
estimation in practical IRS-aided orthogonal frequency division multiplexing
(OFDM) systems with discrete phase shifts. Different from the prior works which
assume that IRS has an ideal reflection model, we perform channel estimation by
considering amplitude-phase shift-frequency relationship for the response of
practical IRS. Aiming at minimizing normalized-mean-square-error (NMSE) of the
estimated channel, a novel IRS time-varying reflection pattern is designed by
leveraging the alternating optimization (AO) algorithm for the case of using
low-resolution phase shifters. Moreover, for the high-resolution IRS cases, we
provide another practical reflection pattern scheme to further reduce the
complexity. Simulation results demonstrate the necessity of considering
practical IRS model for channel estimation and the effectiveness of our
proposed channel estimation methods.
