  This paper investigates covert communications in an integrated sensing and
communications system, where a dual-functional base station (called Alice)
covertly transmits signals to a covert user (called Bob) while sensing multiple
targets, with one of them acting as a potential watcher (called Willie) and
maliciously eavesdropping on legitimate communications. To shelter the covert
communications, Alice transmits additional dual-functional artificial noise
(DFAN) with a varying power not only to create uncertainty at Willie's signal
reception to confuse Willie but also to sense the targets simultaneously. Based
on this framework, the weighted sum of the sensing beampattern means square
error (MSE) and cross correlation is minimized by jointly optimizing the covert
communication and DFAN signals subject to the minimum covert rate requirement.
The robust design considers both cases of imperfect Willie's CSI (WCSI) and
statistical WCSI. Under the worst-case assumption that Willie can adaptively
adjust the detection threshold to achieve the best detection performance, the
minimum detection error probability (DEP) at Willie is analytically derived in
the closed-form expression. The formulated covertness constrained optimization
problems are tackled by a feasibility-checking based difference-of-convex
relaxation (DC) algorithm utilizing the S-procedure, Bernstein-type inequality,
and the DC method. Simulation results validate the feasibility of the proposed
scheme and demonstrate the covertness performance gains achieved by our
proposed design over various benchmarks.
