Secure Transmission for Cell-Free Symbiotic Radio Communications With Movable Antenna: Continuous and Discrete Positioning Designs

In this paper, we study a movable antenna (MA) empowered secure transmission scheme for reconfigurable intelligent surface (RIS) aided cell-free symbiotic radio (SR) systems. Specifically, the MAs deployed at distributed access points (APs) work collaboratively with the RIS to establish high-quality propagation links for both primary and secondary transmissions, as well as suppressing the risk of eavesdropping on confidential primary information. We consider both continuous and discrete MA position cases and maximize the secrecy rate of primary transmission under the secondary transmission constraints, respectively. For the continuous position case, we propose a two-layer iterative optimization method based on differential evolution with one-in-one representation (DEO), to find a high-quality solution with relatively moderate computational complexity. For the discrete position case, we first extend the DEO based iterative framework by introducing the mapping and determination operations to handle the characteristic of discrete MA positions. To further reduce the computational complexity, we then design a single-layer iterative framework to solve all variables alternatively. In particular, we develop an efficient strategy to derive the sub-optimal solution for the discrete MA positions, superseding the DEO-based method. Numerical results validate the effectiveness of the proposed MA empowered secure transmission scheme along with its optimization algorithms.