  In this letter, we consider an intelligent reflecting surface (IRS)-assisted
multiuser communication system, where an IRS is deployed to provide virtual
line-of-sight (LoS) links between an access point (AP) and multiple users. We
consider the practical codebook-based IRS passive beamforming and study
efficient design for IRS reflect beam training, which is challenging due to the
large number of IRS reflecting elements. In contrast to the conventional
single-beam training, we propose a new multi-beam training method by dividing
the IRS reflecting elements into multiple sub-arrays and designing their
simultaneous multi-beam steering over time. By simply comparing the received
signal power over time, each user can detect its optimal IRS beam direction
with a high probability, even without searching over all possible beam
directions as the single-beam training. Simulation results show that our
proposed multi-beam training significantly reduces the training time of
conventional single-beam training and yet achieves comparable IRS passive
beamforming performance for data transmission.
