  Intelligent reflecting surface (IRS) has been deemed as a transformative
technology to achieve smart and reconfigurable environment for wireless
communication. This letter studies a new IRS-aided communication system, where
multiple IRSs assist in the communication between a multi-antenna base station
(BS) and a remote single-antenna user by multi-hop signal reflection.
Specifically, by exploiting the line-of-sight (LoS) link between nearby IRSs, a
multi-hop cascaded LoS link between the BS and user is established where a set
of IRSs are selected to successively reflect the BS's signal, so that the
received signal power at the user is maximized. To tackle this new problem, we
first present the closed-form solutions for the optimal active and cooperative
passive beamforming at the BS and selected IRSs, respectively, for a given beam
route. Then, we derive the end-to-end channel power, which unveils a
fundamental trade-off in the optimal beam routing design between maximizing the
multiplicative passive beamforming gain and minimizing the multi-reflection
path loss. To reconcile this trade-off, we recast the IRS selection and beam
routing problem as an equivalent shortest simple-path problem in graph theory
and solve it optimally. Numerical results show significant performance gains of
the proposed algorithm over benchmark schemes and also draw useful insights
into the optimal beam routing design.
