Robust Beamforming Design for Intelligent Omni-Surfaces Enabled Integrated Sensing and Communications With Imperfect CSI

Recent years have witnessed growing interest in leveraging the bidirectional wave control of intelligent omni-surfaces (IOS) for integrated sensing and communication (ISAC) systems. Nevertheless, acquiring precise channel state information (CSI) is particularly challenging due to the inherent interplay between the electromagnetic properties of IOS and the dual functions of ISAC. In this paper, we propose a robust beamforming design for IOS-enabled ISAC systems. We jointly optimize the transmit beamforming, sensing waveform and IOS phase shifts to minimize the Cram´er-Rao bound (CRB) for sensing while ensuring communication reliability under an outage probability constraint. The resulting mixed-integer non-convex problem is tackled via a dual-loop penalty dual decomposition (PDD) algorithm. This framework solves the augmented Lagrangian (AL) subproblem in the inner loop, while the outer loop adjusts dual variables and penalty parameters to enforce constraint satisfaction. Simulation results demonstrate that our design substantially enhances sensing accuracy and communication reliability in scenarios with large CSI errors or fluctuating service requirements. Furthermore, it is shown that an optimal ratio between sensing and passive IOS elements must be maintained to balance energy utilization and spatial sampling capability in ISAC systems.