  This paper investigates a Stacked Intelligent Metasurfaces (SIM)-assisted
Integrated Sensing and Communications (ISAC) system. An extended target model
is considered, where the BS aims to estimate the complete target response
matrix relative to the SIM. Under the constraints of minimum
Signal-to-Interference-plus-Noise Ratio (SINR) for the communication users
(CUs) and maximum transmit power, we jointly optimize the transmit beamforming
at the base station (BS) and the end-to-end transmission matrix of the SIM, to
minimize the Cram\'er-Rao Bound (CRB) for target estimation. Effective
algorithms such as the alternating optimization (AO) and semidefinite
relaxation (SDR) are employed to solve the non-convex SINR-constrained CRB
minimization problem. Finally, we design and build an experimental platform for
SIM, and evaluate the performance of the proposed algorithms for communication
and sensing tasks.
