Robust Transceiver Design for SIM-Assisted Integrated Sensing and Covert Communications
Stacked intelligent metasurfaces (SIMs) have emerged as a promising wave-domain processing technology for sixth-generation integrated sensing and communication networks, reducing reliance on complex radio-frequency hardware. Nevertheless, imperfect channel state information (CSI) can compromise sensing performance and communication reliability. Moreover, ensuring covert transmission introduces a further challenge, as the system must sense potential targets while concealing communication activity from unauthorized wardens. These challenges motivate the development of robust SIM-assisted integrated sensing and covert communication (ISACC) systems. In this paper, we investigate the robust transceiver design of a multi-user, multi-target ISACC system under imperfect CSI. We jointly optimize the transmit and receive beamformers, sensing covariance matrix, and SIM phase shifts to maximize the worst-case minimum sensing signal-to-interference-plus-noise ratio. The formulation enforces constraints on bounded channel uncertainties, user quality-of-service requirements, transmit-power budget, SIM phase shifts, and target detection probabilities. Since the formulated problem is highly non-convex, we develop an alternating optimization framework based on the S-procedure, successive convex approximation, and semidefinite relaxation. Furthermore, to reduce computational complexity, we derive exact lower-dimensional representations of the robust sensing linear matrix inequalities (LMIs) involved in transmit/receive-beamformer designs. We further develop a low-complexity phase-update method that avoids the large sensing LMIs. Numerical results demonstrate that the proposed design outperforms random phase shift and fully digital-beamforming benchmarks, while the low-complexity scheme achieves comparable performance to the LMI-based scheme at substantially lower computational cost.