  In this paper, the problem of sum-rate maximization for an active
reconfigurable intelligent surface (RIS) assisted downlink rate-splitting
multiple access (RSMA) transmission system is studied. In the considered model,
the active RIS is deployed to overcome severe power attenuation, which is
caused by the cumulative product of RIS incidence path loss and the reflection
path loss. Since the active RIS can adjust both the phase and the amplitude of
the incident signal simultaneously, the RIS control scheme requires delicate
design to improve RSMA communication performance. To address this issue, a
sum-rate maximization problem is formulated to jointly optimize the beamforming
vectors, rate allocation vector, and RIS precoding matrix. To solve this
non-convex sum-rate maximization problem, an iterative algorithm based on
fractional programming (FP) and quadratic constraint quadratic programming
(QCQP) is proposed. In particular, the proposed algorithm firstly decomposes
the original problem into two subproblems, namely, 1) beamforming and rate
allocation optimization and 2) active RIS precoding optimization. The
corresponding variables of the two subproblems are optimized through sequential
convex approximation (SCA) and block coordinate descent (BCD), respectively.
Numerical results show that the proposed active RIS-aided RSMA system could
increase the sum-rate by up to 45% over the conventional passive RIS-aided RSMA
system with the same energy consumption.
