Information-Theoretic Limits of Integrated Sensing and Communication with Correlated Sensing and Channel States for Vehicular Networks

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.