Robust and Secure Transmission for Movable-RIS Assisted ISAC with Imperfect Sense Estimation

Reconfigurable intelligent surfaces (RISs) have been extensively applied in integrated sensing and communication (ISAC) systems due to the capability of enhancing physical layer security (PLS). However, conventional static RIS architectures lack the flexibility required for adaptive beam control in multi-user and multifunctional scenarios. To address this issue without introducing additional hardware complexity and power consumption, in this paper, we exploit a movable RIS (MRIS) architecture, which consists of a large fixed sub-surface and a smaller movable sub-surface that slides on the fixed sub-surface to achieve dynamic beam reconfiguration with static phase shifts. This paper investigates an MRIS-assisted ISAC system under imperfect sensing estimation, where dedicated radar signals serve as artificial noise to enhance secure transmission against potential eavesdroppers (Eves). The transmit beamforming vectors, MRIS phase shifts, and relative positions of the two sub-surfaces are jointly optimized to maximize the minimum secrecy rate, ensuring robust secrecy performance for the weakest user under the uncertainty of the Eves' channels. To handle the non-convexity, a convex bound is derived for the Eve channel uncertainty, and the S-procedure is employed to reformulate semi-infinite constraints as linear matrix inequalities. An efficient alternating optimization and penalty dual decomposition-based algorithm is developed. Simulation results demonstrate that the proposed MRIS architecture substantially improves secrecy performance, especially when only a small number of elements are allocated to the movable sub-surface.