  Active reconfigurable intelligent surface (RIS) is a new RIS architecture
that can reflect and amplify communication signals. It can provide enhanced
performance gain compared to the conventional passive RIS systems that can only
reflect the signals. On the other hand, the design problem of active RIS-aided
systems is more challenging than the passive RIS-aided systems and its
efficient algorithms are less studied. In this paper, we consider the sum rate
maximization problem in the multiuser massive multiple-input single-output
(MISO) downlink with the aid of a large-scale active RIS. Existing approaches
for handling this problem usually resort to general optimization solvers and
can be computationally prohibitive. We propose an efficient block successive
upper bound minimization (BSUM) method, of which each step has a (semi)
closed-form update. Thus, the proposed algorithm has an attractive low
per-iteration complexity. By simulation, our proposed algorithm consumes much
less computation than the existing approaches. In particular, when the MIMO
and/or RIS sizes are large, our proposed algorithm can be orders-of-magnitude
faster than existing approaches.
