  Simultaneously reflecting and transmitting reconfigurable intelligent
surfaces (STAR-RIS) has recently emerged as prominent technology that exploits
the transmissive property of RIS to mitigate the half-space coverage limitation
of conventional RIS operating on millimeter-wave (mmWave). In this paper, we
study a downlink STAR-RIS-based multi-user multiple-input single-output
(MU-MISO) mmWave hybrid non-orthogonal multiple access (H-NOMA) wireless
network, where a sum-rate maximization problem has been formulated. The design
of active and passive beamforming vectors, time and power allocation for H-NOMA
is a highly coupled non-convex problem. To handle the problem, we propose an
optimization framework based on alternating optimization (AO) that iteratively
solves active and passive beamforming sub-problems. Channel correlations and
channel strength-based techniques have been proposed for a specific case of
two-user optimal clustering and decoding order assignment, respectively, for
which analytical solutions to joint power and time allocation for H-NOMA have
also been derived. Simulation results show that: 1) the proposed framework
leveraging H-NOMA outperforms conventional OMA and NOMA to maximize the
achievable sum-rate; 2) using the proposed framework, the supported number of
clusters for the given design constraints can be increased considerably; 3)
through STAR-RIS, the number of elements can be significantly reduced as
compared to conventional RIS to ensure a similar quality-of-service (QoS).
