  We consider transmit beamforming and reflection pattern design in
reconfigurable intelligent surface (RIS)-assisted integrated sensing and
communication (ISAC) systems to jointly precode communication symbols and radar
waveforms. We treat two settings of multiple users and targets. In the first,
we use a single RIS to enhance the communication performance of the ISAC system
and design beams with good cross-correlation properties to match a desired beam
pattern while guaranteeing a desired signal-to-interference plus noise ratio
(SINR) for each user. In the second setting, we use two dedicated RISs to aid
the ISAC system, wherein the beams are designed to maximize the worst-case
target illumination power while guaranteeing a desired SINR for each user. We
propose solvers based on alternating optimization as the design problems in
both cases are non-convex optimization problems. Through a number of numerical
simulations, we demonstrate the advantages of RIS-assisted ISAC systems. In
particular, we show that the proposed single-RIS assisted ISAC system improves
the minimum user SINR while suffering from a moderate loss in radar target
illumination power. On the other hand, the dual-RIS assisted ISAC system
improves both minimum user SINR as well as worst-case target illumination power
at the targets, especially when the users and targets are not directly visible.
