  Intelligent reflecting surface (IRS) is an emerging technology to enhance the
spectral and energy efficiency of wireless communications cost-effectively.
This letter considers a new multi-IRS aided wireless network where a cascaded
line-of-sight (LoS) link is established between the base station (BS) and a
remote user by leveraging the multi-hop signal reflection of selected IRSs. As
compared to the conventional single-/double-hop IRS system, multi-hop IRS
system provides more pronounced path diversity and cooperative passive
beamforming gains, especially in the environment with dense obstacles. However,
a more challenging joint active/passive beamforming and multi-hop beam routing
problem also arises for maximizing the end-to-end channel gain. Furthermore,
the number of IRS-associated channel coefficients increases drastically with
the number of IRS hops. To tackle the above issues, in this letter we propose a
new and efficient beam training based solution by considering the use of
practical codebook-based BS/IRS active/passive beamforming without the need of
explicit channel estimation. Instead of exhaustively or sequentially searching
over all combinations of active and passive beam patterns for each beam route,
a distributed beam training scheme is proposed to reduce the complexity, by
exploiting the (nearly) time-invariant BS-IRS and inter-IRS channels and the
cooperative training among the BS and IRSs' controllers. Simulation results
show that our proposed design achieves the end-to-end channel gain close to
that of the sequential beam search, but at a much lower training overhead and
complexity.
