  In this paper, we propose a robust secure transmission scheme for an active
reconfigurable intelligent surface (RIS) enabled symbiotic radio (SR) system in
the presence of multiple eavesdroppers (Eves). In the considered system, the
active RIS is adopted to enable the secure transmission of primary signals from
the primary transmitter to multiple primary users in a multicasting manner, and
simultaneously achieve its own information delivery to the secondary user by
riding over the primary signals. Taking into account the imperfect channel
state information (CSI) related with Eves, we formulate the system power
consumption minimization problem by optimizing the transmit beamforming and
reflection beamforming for the bounded and statistical CSI error models, taking
the worst-case SNR constraints and the SNR outage probability constraints at
the Eves into considerations, respectively. Specifically, the S-Procedure and
the Bernstein-Type Inequality are implemented to approximately transform the
worst-case SNR and the SNR outage probability constraints into tractable forms,
respectively. After that, the formulated problems can be solved by the proposed
alternating optimization (AO) algorithm with the semi-definite relaxation and
sequential rank-one constraint relaxation techniques. Numerical results show
that the proposed active RIS scheme can reduce up to 27.0% system power
consumption compared to the passive RIS.
