Integrated sensing and communication (ISAC) has been receiving a notable interest as an energy- and spectrum-efficient enabler for simultaneous communication and sensing. Notably, reconfigurable intelligent surfaces (RIS) is among the key technologies enabling robust communication and sensing, particularly in environments without a line-of-sight (LoS). Recently, a new type of RIS, called beyond-diagonal RIS (BD-RIS), has drawn attention, offering additional degrees of freedom in controlling the propagation medium. In this paper, a novel secure BD-RIS-aided ISAC scheme is proposed and evaluated. The scheme is applicable to a multi-user multi-target ISAC network, where a dual-functional radar-communication (DFRC) base station (BS) simultaneously serves multiple downlink users and senses various targets that aim to eavesdrop on the legitimate signal transmitted to the users. The presence of a BD-RIS enables circumventing the absence of the LoS link and ensures secure transmission and sensing. To this end, an optimization problem is formulated aiming at maximizing a weighted sum of per-target reflected powers, subject to secrecy and transmit power constraints. Thus, by virtue of an alternating optimization (AO)- and Riemannian conjugate gradient-based approach, local optima for the BD-RIS scattering matrix, transmit signal beamforming matrices, and artificial noise covariance matrix are obtained. Numerical results highlight (i) the notable sensing gains of the BD-RIS-aided design with respect to its diagonal RIS (D-RIS)-based baseline and (ii) the improved secrecy-sensing trade-off, whereby the BD-RIS can ensure an increasing system secrecy without degrading the per-target reflected power.

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