  In this paper, we propose a simultaneously transmitting and reflecting
reconfigurable intelligent surface (STAR-RIS) empowered transmission scheme for
symbiotic radio (SR) systems to make more flexibility for network deployment
and enhance system performance. The STAR-RIS is utilized to not only beam the
primary signals from the base station (BS) towards multiple primary users on
the same side of the STAR-RIS, but also achieve the secondary transmission to
the secondary users on another side. We consider both the broadcasting signal
model and unicasting signal model at the BS. For each model, we aim for
minimizing the transmit power of the BS by designing the active beamforming and
simultaneous reflection and transmission coefficients under the practical phase
correlation constraint. To address the challenge of solving the formulated
problem, we propose a block coordinate descent based algorithm with the
semidefinite relaxation, penalty dual decomposition and successive convex
approximation methods, which decomposes the original problem into one
sub-problem about active beamforming and the other sub-problem about
simultaneous reflection and transmission coefficients, and iteratively solve
them until the convergence is achieved. Numerical results indicate that the
proposed scheme can reduce up to 150.6% transmit power compared to the
backscattering device enabled scheme.
