Recently, reconfigurable intelligent surfaces (RISs) have attracted increasing attentions in the design of full-duplex (FD) systems due to their novel capability of propagation environment reconfiguration. However, in conventional RIS-assisted FD systems, the beamforming for self-interference cancellation (SIC) and sum rate maximization (SRM) are highly coupled during RIS optimization, which significantly degrades the system performance. To tackle this issue, we exploit a novel bilayer intelligent omni-surface (BIOS) structure in FD systems. Compared with the conventional RIS designs, the BIOS provides independent beams on both sides, thus enabling more flexible achievement of SRM and SIC. For the BIOS-assisted FD system, we first formulate an optimization problem to achieve SRM and efficient SIC simultaneously. Then, we exploit the relationship between the SRM and mean square error (MSE), and propose a weighted MSE minimization with SIC algorithm to solve the problem. Specifically, we jointly design the beamforming at the base station and the BIOS with manifold optimization while guaranteeing an SIC constraint. Furthermore, we theoretically derive a lower band for the BIOS size required for efficient SIC in FD systems. Simulation results indicate that the BIOS outperforms the conventional RIS designs in FD systems, and verify the accuracy of the derived lower bound for the BIOS size.
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