Flowing the Information from Shannon to Fisher: Towards the Fundamental Tradeoff in ISAC

—Integrated Sensing and Communication (ISAC) is recognized as a promising technology for the next-generation wireless networks. In this paper, we provide a general framework to reveal the fundamental tradeoff between sensing and communications (S&C), where a uniﬁed ISAC waveform is exploited to perform dual-functional tasks. In particular, we deﬁne the Cram´er-Rao bound (CRB)-rate region to characterize the S&C tradeoff, and propose a pentagon inner bound of the region. We show that the two corner points of the CRB-rate region can be achieved by the conventional Gaussian waveform and a novel strategy referred to as successive hypersphere coding, respectively. Moreover, we also offer our insights into transmission approaches achieving the boundary of the CRB-rate region, namely the Shannon-Fisher information ﬂow.