Resource Allocation for STAR-RIS-Assisted MIMO Physical-Layer Key Generation

Due to the limited coverage of reflecting-only reconfigurable intelligent surfaces (RIS), the existing RIS-assisted physical-layer key generation (PKG) scheme limits its overall performance in the full space. This paper proposes a novel simultaneously transmitting and reflecting (STAR)-RIS-assisted PKG protocol for multiple-input multiple-output (MIMO) systems, where the closed-form sum secret key rate is derived in the presence of full-space eavesdroppers. Two optimization problems are formulated to maximize the sum secret key rate by designing the transmit beamforming (TBF) and transmitting and reflecting coefficients (TRCs) for energy splitting (ES) with coupled phase-shift and mode switching (MS) mode. For ES mode with coupled phase-shift, a penalty-based alternating optimization (AO) algorithm is proposed to address its non-convexity. For MS mode, the semidefinite relaxation-successive convex approximation-based AO algorithm is utilized to achieve continuous solutions and then quantize to binary value for the MS mode. Simulation results demonstrate that the coupled phase-shift STAR-RIS incurs a slight KGR loss in comparison to the independent phase-shift STAR-RIS. Additionally, the ES mode outperforms the MS mode in terms of KGR performance. Finally, STAR-RIS can achieve a higher sum secret key rate than traditional reflecting-only RIS.