  Intelligent reflecting surface (IRS) can be densely deployed in wireless
networks to significantly enhance the communication channels. In this letter,
we consider the downlink transmission from a multi-antenna base station (BS) to
a single-antenna user, by exploiting the cooperative passive beamforming (CPB)
and line-of-sight (LoS) path diversity gains of multi-IRS signal reflection.
Unlike existing works where only one single multi-IRS reflection path from the
BS to user is selected, we propose a new and more general multi-path beam
routing scheme. Specifically, the BS sends the user's information signal via
multiple orthogonal active beams (termed as active beam splitting), which point
towards different IRSs. Then, these beamed signals are subsequently reflected
by selected IRSs via their CPB in different paths, and finally coherently
combined at the user's receiver (thus named {\it \textbf{passive beam
combining}}). For this scheme, we formulate a new multi-path beam routing
design problem to jointly optimize the number of IRS reflection paths, the
selected IRSs for each of the reflection paths, the active/passive beamforming
at the BS/each selected IRS, as well as the BS's power allocation over
different active beams, so as to maximize the received signal power at the
user. To solve this challenging problem, we first derive the optimal BS/IRS
beamforming and BS power allocation for a given set of reflection paths. The
clique-based approach in graph theory is then applied to solve the remaining
multi-path selection problem efficiently. Simulation results show that our
proposed multi-path beam routing scheme significantly outperforms its
conventional single-path beam routing special case.
