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

Sensing and communications (S&C) were historically developed in parallel. In the last decade, they have been evolving from separation to integration, giving rise to the integrated sensing and communication (ISAC) paradigm, that has been recognized as one of 6G key usage scenarios. Despite the plethora of research works dedicated to ISAC signal processing, the fundamental performance limits of S&C remain widely unexplored in ISAC systems. 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 folkloric “torch metaphor” that depicts the subspace tradeoff between 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 Cramér-Rao bound (CRB)-rate region. In particular, S&C have preference discrepancies over both the signal subspace and the adopted codebook, leading to a “projector metaphor” complementary to the 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.