  We propose a robust transceiver design for a covert integrated sensing and
communications (ISAC) system with imperfect channel state information (CSI).
Considering both bounded and probabilistic CSI error models, we formulate
worst-case and outage-constrained robust optimization problems of joint
trasceiver beamforming and radar waveform design to balance the radar
performance of multiple targets while ensuring communications performance and
covertness of the system. The optimization problems are challenging due to the
non-convexity arising from the semi-infinite constraints (SICs) and the coupled
transceiver variables. In an effort to tackle the former difficulty,
S-procedure and Bernstein-type inequality are introduced for converting the
SICs into finite convex linear matrix inequalities (LMIs) and second-order cone
constraints. A robust alternating optimization framework referred to
alternating double-checking is developed for decoupling the transceiver design
problem into feasibility-checking transmitter- and receiver-side subproblems,
transforming the rank-one constraints into a set of LMIs, and verifying the
feasibility of beamforming by invoking the matrix-lifting scheme. Numerical
results are provided to demonstrate the effectiveness and robustness of the
proposed algorithm in improving the performance of covert ISAC systems.
