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In this paper, we investigate the robust resource allocation design forsecure 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 targetssimultaneously, where already identified targets are treated as potentialsingle-antenna eavesdroppers. The DFRC BS scans a sector with a sequence ofdedicated beams, and the ISAC system takes a snapshot of the environment duringthe transmission of each beam. Based on the sensing information, the DFRC BScan acquire the channel state information (CSI) of the potential eavesdroppers.Different from existing works that focused on the resource allocation designfor a single snapshot, in this paper, we propose a novel optimization frameworkthat jointly optimizes the communication and sensing resources over a sequenceof snapshots with adjustable durations. To this end, we jointly optimize theduration of each snapshot, the beamforming vector, and the covariance matrix ofthe AN for maximization of the system sum secrecy rate over a sequence ofsnapshots while guaranteeing a minimum required average achievable rate and amaximum information leakage constraint for each legitimate user. The resourceallocation algorithm design is formulated as a non-convex optimization problem,where we account for the imperfect CSI of both the legitimate users and thepotential eavesdroppers. To make the problem tractable, we derive a bound forthe uncertainty region of the potential eavesdroppers' small-scale fading basedon a safe approximation, which facilitates the development of a blockcoordinate descent-based iterative algorithm for obtaining an efficientsuboptimal solution.

Robust and Secure Resource Allocation for ISAC Systems: A Novel Optimization Framework for Variable-Length Snapshots