  Intelligent reflecting surface (IRS) has emerged as a competitive solution to
address blockage issues in millimeter wave (mmWave) and Terahertz (THz)
communications due to its capability of reshaping wireless transmission
environments. Nevertheless, obtaining the channel state information of
IRS-assisted systems is quite challenging because of the passive
characteristics of the IRS. In this paper, we consider the problem of beam
training/alignment for IRS-assisted downlink mmWave/THz systems, where a
multi-antenna base station (BS) with a hybrid structure serves a single-antenna
user aided by IRS. By exploiting the inherent sparse structure of the
BS-IRS-user cascade channel, the beam training problem is formulated as a joint
sparse sensing and phaseless estimation problem, which involves devising a
sparse sensing matrix and developing an efficient estimation algorithm to
identify the best beam alignment from compressive phaseless measurements.
Theoretical analysis reveals that the proposed method can identify the best
alignment with only a modest amount of training overhead. Simulation results
show that, for both line-of-sight (LOS) and NLOS scenarios, the proposed method
obtains a significant performance improvement over existing state-of-art
methods. Notably, it can achieve performance close to that of the exhaustive
beam search scheme, while reducing the training overhead by 95%.
