From Torch to Projector: Fundamental Tradeoff of Integrated Sensing and Communications

Sensing and communications (S&C) have been historically developed in parallel. In recent decade, they have been evolving from separation to integration, giving rise to the integrated sensing and communications (ISAC) paradigm, that has been recognized as one of the six key 6G usage scenarios. Despite the plethora of research works dedicated to ISAC signal processing, the fundamental performance limits of S&C remain widely unexplored in an ISAC system. In this tutorial paper, we attempt to summarize the recent research findings in characterizing the performance boundary of ISAC systems and the resulting S&C tradeoff from an information-theoretical viewpoint. We begin with a folklore "torch metaphor" that depicts the resource competition mechanism of S&C. Then, we elaborate on the fundamental capacity-distortion (C-D) theory, indicating the incompleteness of this metaphor. Towards that end, we further elaborate on the S&C tradeoff by discussing a special case within the C-D framework, namely the Cramer-Rao bound (CRB)-rate region. In particular, S&C have preference discrepancies over both the subspace occupied by the transmitted signal and the adopted codebook, leading to a "projector metaphor" complementary to the ISAC torch analogy. We also present two practical design examples by leveraging the lessons learned from fundamental theories. Finally, we conclude the paper by identifying a number of open challenges.