Channel Estimation for Intelligent Reflecting Surface Assisted Multiuser Communications: Framework, Algorithms, and Analysis

In intelligent reflecting surface (IRS) assisted communication systems, the acquisition of channel state information is a crucial impediment for achieving the beamforming gain of IRS because of the considerable overhead required for channel estimation. Specifically, under the current beamforming design for IRS-assisted communications, in total
$KMN+KM$
channel coefficients should be estimated, where
$K$
,
$N$
and
$M$
denote the numbers of users, IRS reflecting elements, and antennas at the base station (BS), respectively. For the first time in the literature, this paper points out that despite the vast number of channel coefficients that should be estimated, significant redundancy exists in the user-IRS-BS reflected channels of different users arising from the fact that each IRS element reflects the signals from all the users to the BS via the same channel. To utilize this redundancy for reducing the channel estimation time, we propose a novel three-phase pilot-based channel estimation framework for IRS-assisted uplink multiuser communications, in which the user-BS direct channels and the user-IRS-BS reflected channels of a typical user are estimated in Phase I and Phase II, respectively, while the user-IRS-BS reflected channels of the other users are estimated with low overhead in Phase III via leveraging their strong correlation with those of the typical user. Under this framework, we analytically prove that a time duration consisting of
$K+N+\max (K-1,\lceil (K-1)N/M \rceil)$
pilot symbols is sufficient for perfectly recovering all the
$KMN+KM$
channel coefficients under the case without receiver noise at the BS. Further, under the case with receiver noise, the user pilot sequences, IRS reflecting coefficients, and BS linear minimum mean-squared error channel estimators are characterized in closed-form.