  In this paper, we investigate integrated sensing and communication (ISAC) in
high-mobility systems with the aid of an intelligent reflecting surface (IRS).
To exploit the benefits of Delay-Doppler (DD) spread caused by high mobility,
orthogonal time frequency space (OTFS)-based frame structure and transmission
framework are proposed. {In such a framework,} we first design a low-complexity
ratio-based sensing algorithm for estimating the velocity of mobile user. Then,
we analyze the performance of sensing and communication in terms of achievable
mean square error (MSE) and achievable rate, respectively, and reveal the
impact of key parameters. Next, with the derived performance expressions, we
jointly optimize the phase shift matrix of IRS and the receive combining vector
at the base station (BS) to improve the overall performance of integrated
sensing and communication. Finally, extensive simulation results confirm the
effectiveness of the proposed algorithms in high-mobility systems.
