  This paper investigates an integrated sensing and communication (ISAC) system
with reconfigurable intelligent surface (RIS). Our simultaneous beam training
and target sensing (SBTTS) scheme enables the base station to perform beam
training with the user terminals (UTs) and the RIS, and simultaneously to sense
the targets. Based on our findings, the energy of the echoes from the RIS is
accumulated in the angle-delay domain while that from the targets is
accumulated in the Doppler-delay domain. The SBTTS scheme can distinguish the
RIS from the targets with the mixed echoes from the RIS and the targets. Then
we propose a positioning and array orientation estimation (PAOE) scheme for
both the line-of-sight channels and the non-line-of-sight channels based on the
beam training results of SBTTS by developing a low-complexity two-dimensional
fast search algorithm. Based on the SBTTS and PAOE schemes, we further compute
the angle-of-arrival and angle-of-departure for the channels between the RIS
and the UTs by exploiting the geometry relationship to accomplish the beam
alignment of the ISAC system. Simulation results verify the effectiveness of
the proposed schemes.
