Robust Beamforming Design for Covert Integrated Sensing and Communication in the Presence of Multiple Wardens

The integrated sensing and communication (ISAC) plays an increasingly pivotal role in numerous emerging applications. In this article, we focus on the covert transmission of the confidential information within the ISAC system in the presence of multiple wardens, i.e., non-colluding and colluding scenarios. Specifically, we first develop the theoretical detection error probability (DEP) under the strategy of the separate detection and the maximal ratio combining (MRC) based cooperative detection, respectively. Secondly, we propose the robust beamforming optimization model comprised of the beampattern mean square error (MSE) based sensing metric and the Kullback-Leibler (KL) divergence based covertness measure under the sensing assisted imperfect channel state information (CSI) of wardens. In order to tackle the non-convexity of the proposed optimization problem, we propose the iterative algorithms comprised of the successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques to achieve the robust beamforming design for the covert ISAC system under the CSI uncertainty. Due to the significant large complexity of the robust beamforming design for colluding wardens, we further propose the low complexity optimization algorithm based on the monotonicity of the theoretical DEP for the MRC based detection instead of KL divergence. Simulation results demonstrate the superior performance of proposed algorithms in terms of the average covert rate and the DEP over other baseline schemes under various simulation settings.