  In connected vehicular networks, it is vital to have vehicular nodes that are
capable of sensing about surrounding environments and exchanging messages with
each other for automating and coordinating purpose. Towards this end,
integrated sensing and communication (ISAC), combining both sensing and
communication systems to jointly utilize their resources and to pursue mutual
benefits, emerges as a new cost-effective solution. In ISAC, the hardware and
spectrum co-sharing leads to a fundamental tradeoff between sensing and
communication performance, which is not well understood except for very simple
cases with the same sensing and channel states, and perfect channel state
information at the receiver (CSIR). In this paper, a general point-to-point
ISAC model is proposed to account for the scenarios that the sensing state is
different from but correlated with the channel state, and the CSIR is not
necessarily perfect. For the model considered, the optimal tradeoff is
characterized by a capacity-distortion function that quantifies the best
communication rate for a given sensing distortion constraint requirement. An
iterative algorithm is proposed to compute such tradeoff, and a few non-trivial
examples are constructed to demonstrate the benefits of ISAC as compared to the
separation-based approach.
