Multi-User Joint Beamforming Optimization in Active RIS-Assisted Symbiotic Radio for Energy Efficient and Secure Communications

This paper investigates secure and energy-efficient multi-user symbiotic radio (SR) communication assisted by an active reconfigurable intelligent surface (ARIS). We consider a downlink multi-user unicast scenario where a multi-antenna primary transmitter (PTx) serves multiple primary users (PUs), while the ARIS embeds a secondary BPSK symbol into the reflected waveform to deliver sensitive information to a secondary user (SU). Two classes of eavesdroppers are present: EVs-I attempt to intercept the PU messages, whereas EVs-II aim to decode the ARIS-SU link and are typically located in the vicinity of the SU. Our goal is to minimize the total network power consumption, including the PTx transmit power and the ARIS circuit and amplification power, under QoS and secrecy constraints for both primary and secondary transmissions. To account for the lack of reliable instantaneous CSI for the eavesdroppers, we adopt a statistical CSI error model and formulate probabilistic secrecy constraints, which are then converted into tractable convex forms using Bernstein-type inequalities. The resulting non-convex optimization problem is solved via an alternating optimization framework that iteratively updates the PTx beamformers and the ARIS reflection vector, employing a sequential rank-one constraint relaxation (SROCR) to recover feasible rank-one solutions. Numerical results show that the proposed robust ARIS-assisted SR design significantly reduces the total system power consumption compared with PRIS and the considered benchmarks, while meeting the QoS and secrecy-outage constraints under statistical eavesdropper CSI uncertainty.