We consider a multi-user multiple-input single-
output (MISO) communications system which is assisted by a
hybrid active-passive reconfigurable intelligent surface (RIS).
Unlike conventional passive RISs, hybrid RIS is equipped with a
few active elements with the ability to reflect and amplify incident
signals to significantly improve the system performance. Towards
a fairness design, we maximize the minimum rate among all users
through jointly optimizing the transmit beamforming vectors
and RIS reflecting/amplifying coefficients. Combining tools from
block coordinate ascend and successive convex approximation,
the challenging nonconvex problem is efficiently solved by a low-
complexity iterative algorithm. The numerical results show that
a hybrid RIS with 4 active elements out of a total of 50 elements
with a power budget of −1 dBm offers an improvement of up
to 80% to the considered system, while that achieved by a fully
passive RIS is only 27
