Integrated sensing and communication (ISAC) emerges as a new design paradigm that combines both sensing and communication systems to jointly utilize their resources and to pursue mutual benefits for future B5G and 6G networks. 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 more 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.Index Terms-Integrated sensing and communication, correlated sensing and channel states, imperfect channel state information at the receiver, capacity-distortion tradeoff.
I. INTRODUCTIONWith the integration of massive MIMO and millimeter-wave communications into mobile networks, communication signals tend to have high resolution in both time and angular domain, which provides an unprecedented opportunity to employ mobile network for high-accuracy sensing. Integrated sensing and communication (ISAC) through co-sharing the same hardware and spectrum for both sensing and communication systems, is envisioned as an important new cost-efficient technology in future B5G and 6G networks [1], [2].Substantial studies have been conducted to investigate the key techniques for ISAC in different scenarios and system architectures, such as the state-of-art in the levels of coexistence, collaboration, and co-design [3], the representative methodologies in vehicular networks [4], the framework for large-scale mobile networks [5], joint waveform design [6], and spatial signal processing [7]. While these studies demonstrate the advantages of joint design of sensing and communication, it is unclear whether these schemes have reached the optimal performance for the resources given. This motivates one to investigate the fundamental performance limits of ISAC and to quantify the optimal tradeoff between sensing accuracy and communication rate for a given ISAC scenario.