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In this paper, we propose a robust secure transmission scheme for an activereconfigurable intelligent surface (RIS) enabled symbiotic radio (SR) system inthe presence of multiple eavesdroppers (Eves). In the considered system, theactive RIS is adopted to enable the secure transmission of primary signals fromthe primary transmitter to multiple primary users in a multicasting manner, andsimultaneously achieve its own information delivery to the secondary user byriding over the primary signals. Taking into account the imperfect channelstate information (CSI) related with Eves, we formulate the system powerconsumption minimization problem by optimizing the transmit beamforming andreflection beamforming for the bounded and statistical CSI error models, takingthe worst-case SNR constraints and the SNR outage probability constraints atthe Eves into considerations, respectively. Specifically, the S-Procedure andthe Bernstein-Type Inequality are implemented to approximately transform theworst-case SNR and the SNR outage probability constraints into tractable forms,respectively. After that, the formulated problems can be solved by the proposedalternating optimization (AO) algorithm with the semi-definite relaxation andsequential rank-one constraint relaxation techniques. Numerical results showthat the proposed active RIS scheme can reduce up to 27.0% system powerconsumption compared to the passive RIS.

Robust Secure Transmission for Active RIS Enabled Symbiotic Radio Multicast Communications