  In this paper, we investigated the downlink transmission problem of a
cognitive radio network (CRN) equipped with a novel transmissive reconfigurable
intelligent surface (TRIS) transmitter. In order to achieve low power
consumption and high-rate multi-streams communication, time-modulated arrays
(TMA) is implemented and users access the network using rate splitting multiple
access (RSMA). With such a network framework, a multi-objective optimization
problem with joint design of the precoding matrix and the common stream rate is
constructed to achieve higher energy efficiency (EE) and spectral efficiency
(SE). Since the objective function is a non-convex fractional function, we
proposed a joint optimization algorithm based on difference-of-convex (DC)
programming and successive convex approximation (SCA). Numerical results show
that under this framework the proposed algorithm can considerably improve and
balance the EE and SE.
