  Reconfigurable Intelligent Surfaces (RISs) are recently attracting a wide
interest due to their capability of tuning wireless propagation environments in
order to increase the system performance of wireless networks. In this paper, a
multiuser single-cell wireless network assisted by a RIS is studied. First of
all, for the special case of a single-user system, three possible approaches
are shown in order to optimize the Signal-to-Noise Ratio with respect to the
beamformer used at the base station and to the RIS phase shifts. Then, for a
multiuser system, assuming channel-matched beamforming, the geometric mean of
the downlink Signal-to-Interference plus Noise Ratios across users is maximized
with respect to the base stations transmit powers and RIS phase shifts
configurations. Numerical results show that the proposed procedure are
effective and greatly improve the performance of the considered systems.
