  Reconfigurable intelligent surface (RIS) have introduced unprecedented
flexibility and adaptability toward smart wireless channels. Recent research on
integrated sensing and communication (ISAC) systems has demonstrated that RIS
platforms enable enhanced signal quality, coverage, and link capacity. In this
paper, we explore the application of fully-connected beyond diagonal RIS
(BD-RIS) to ISAC systems. BD-RIS introduces additional degrees of freedom by
allowing non-zero off-diagonal elements for the scattering matrix, potentially
enabling further functionalities and performance enhancements. In particular,
we consider the joint design objective of maximizing the weighted sum of the
signal-to-noise ratio (SNR) at the radar receiver and communication users by
leveraging the extra degrees-of-freedom offered in the BD-RIS setting. These
degrees-of-freedom are unleashed by formulating an alternating optimization
process over known and auxiliary (latent) variables of such systems. Our
numerical results reveal the advantages of deploying BD-RIS in the context of
ISAC and the effectiveness of the proposed algorithm by improving the SNR
values for both radar and communication users by several orders of magnitude.
