  We propose covert beamforming design frameworks for integrated radar sensing
and communication (IRSC) systems, where the radar can covertly communicate with
legitimate users under the cover of the probing waveforms without being
detected by the eavesdropper. Specifically, by jointly designing the target
detection beamformer and communication beamformer, we aim to maximize the radar
detection mutual information (MI) (or the communication rate) subject to the
covert constraint, the communication rate constraint (or the radar detection MI
constraint), and the total power constraint. For the perfect eavesdropper's
channel state information (CSI) scenario, we transform the covert beamforming
design problems into a series of convex subproblems, by exploiting semidefinite
relaxation, which can be solved via the bisection search method. Considering
the high complexity of iterative optimization, we further propose a
single-iterative covert beamformer design scheme based on the zero-forcing
criterion. For the imperfect eavesdropper's CSI scenario, we develop a
relaxation and restriction method to tackle the robust covert beamforming
design problems. Simulation results demonstrate the effectiveness of the
proposed covert beamforming schemes for perfect and imperfect CSI scenarios.
