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.
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