  In this paper, we investigate the robust resource allocation design for
secure communication in an integrated sensing and communication (ISAC) system.
A multi-antenna dual-functional radar-communication (DFRC) base station (BS)
serves multiple single-antenna legitimate users and senses for targets
simultaneously, where already identified targets are treated as potential
single-antenna eavesdroppers. The DFRC BS scans a sector with a sequence of
dedicated beams, and the ISAC system takes a snapshot of the environment during
the transmission of each beam. Based on the sensing information, the DFRC BS
can acquire the channel state information (CSI) of the potential eavesdroppers.
Different from existing works that focused on the resource allocation design
for a single snapshot, in this paper, we propose a novel optimization framework
that jointly optimizes the communication and sensing resources over a sequence
of snapshots with adjustable durations. To this end, we jointly optimize the
duration of each snapshot, the beamforming vector, and the covariance matrix of
the AN for maximization of the system sum secrecy rate over a sequence of
snapshots while guaranteeing a minimum required average achievable rate and a
maximum information leakage constraint for each legitimate user. The resource
allocation algorithm design is formulated as a non-convex optimization problem,
where we account for the imperfect CSI of both the legitimate users and the
potential eavesdroppers. To make the problem tractable, we derive a bound for
the uncertainty region of the potential eavesdroppers' small-scale fading based
on a safe approximation, which facilitates the development of a block
coordinate descent-based iterative algorithm for obtaining an efficient
suboptimal solution.
