  Recently, intelligent reflecting surface (IRS)-assisted communication has
gained considerable attention due to its advantage in extending the coverage
and compensating the path loss with low-cost passive metasurface. This paper
considers the uplink channel estimation for IRS-aided multiuser massive MISO
communications with one-bit ADCs at the base station (BS). The use of one-bit
ADC is impelled by the low-cost and power efficient implementation of massive
antennas techniques. However, the passiveness of IRS and the lack of signal
level information after one-bit quantization make the IRS channel estimation
challenging. To tackle this problem, we exploit the structured sparsity of the
user-IRS-BS cascaded channels and develop three channel estimators, each of
which utilizes the structured sparsity at different levels. Specifically, the
first estimator exploits the elementwise sparsity of the cascaded channel and
employs the sparse Bayesian learning (SBL) to infer the channel responses via
the type-II maximum likelihood (ML) estimation. However, due to the one-bit
quantization, the type-II ML in general is intractable. As such, a variational
expectation-maximization (EM) algorithm is custom-derived to iteratively
compute an ML solution. The second estimator utilizes the common row-structured
sparsity induced by the IRS-to-BS channel shared among the users, and develops
another type-II ML solution via the block SBL (BSBL) and the variational EM. To
further improve the performance of BSBL, a third two-stage estimator is
proposed, which can utilize both the common row-structured sparsity and the
column-structured sparsity arising from the limited scattering around the
users. Simulation results show that the more diverse structured sparsity is
exploited, the better estimation performance is achieved, and that the proposed
estimators are superior to state-of-the-art one-bit estimators.
