  This paper focuses on multi-user downlink signal transmission in a wireless
system aided by multiple reconfigurable intelligent surfaces (RISs). In such a
multi-RIS, multi-user, multi-antenna scenario, determining a set of RIS phase
shifts to maximize the sum throughput becomes intractable. Hence, we propose a
novel scheme that can substantially simplify the optimization of passive
beamforming. By opportunistically selecting a user with the best channel
condition as the only active transmitter in the system, it degrades to
single-user passive beamforming, where two methods, i.e., joint optimization
based on the semidefinite relaxation approach and alternating optimization, are
applicable. The superiority of the proposed scheme is demonstrated through
Monte-Carlo simulations.
