  This paper investigates the use of the reconfigurable dual-functional surface
to guarantee the full-space secure transmission in non-orthogonal multiple
access (NOMA) networks. In the presence of eavesdroppers, the downlink
communication from the base station to the legitimate users is safeguarded by
the simultaneously transmitting and reflecting reconfigurable intelligent
surface (STAR-RIS), where three practical operating protocols, namely energy
splitting (ES), mode selection (MS), and time splitting (TS), are studied. The
joint optimization of power allocation, active and passive beamforming is
investigated to maximize the secrecy energy efficiency (SEE), taking into
account the imperfect channel state information (CSI) of all channels. For ES,
by approximating the semi-infinite constraints with the S-procedure and general
sign-definiteness, the problem is solved by an alternating optimization
framework. Besides, the proposed algorithm is extended to the MS protocol by
solving a mixed-integer non-convex problem. While for TS, a two-layer iterative
method is proposed. Simulation results show that: 1) The proposed STAR-RIS
assisted NOMA networks are able to provide up to 33.6\% higher SEE than
conventional RIS counterparts; 2) TS and ES protocols are generally preferable
for low and high power domain, respectively; 3) The accuracy of CSI estimation
and the bit resolution power consumption are crucial to reap the SEE benefits
offered by STAR-RIS.
