Polarization-Aware Rotatable Antennas for RIS-Empowered Symbiotic Radios

This paper investigates a dual-polarized reconfigurable intelligent surface (DP-RIS)-empowered symbiotic radio (SR) system with rotatable antennas (RAs). By reconfiguring antenna orientations, RAs can steer their radiation patterns toward desired directions, thereby effectively mitigating the double-fading effect in RIS-assisted cascaded links. However, antenna rotation not only changes the radiation direction but also alters the local polarization bases, which may result in polarization mismatch and degrade the achievable gain. This motivates a joint spatial-polarization design that simultaneously exploits directional radiation gain and polarization matching. Specifically, we formulate a transmit power minimization problem that jointly optimizes digital beamforming, RA rotations, transceiver polarization states, and DP-RIS phase shifts, subject to the primary and secondary rate requirements as well as interference temperature constraints for non-SR users. To solve this non-convex problem, we develop an alternating optimization algorithm that integrates semidefinite programming, difference-of-convex programming, and Riemannian conjugate gradient methods. Moreover, to reduce hardware and computational complexity for practical deployment, we propose two low-complexity RA designs, namely a subarray-wise shared rotation design and a discrete rotation codebook design. Simulation results show that the proposed polarization-aware RA design significantly reduces the required transmit power compared with fixed-orientation and polarization-unaware benchmark schemes. Moreover, both the proposed low-complexity RA designs achieve comparable performance with reduced rotation complexity.