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.

翻译：感知与通信（S&C）在历史上是并行发展的。近十年来，它们从分离走向融合，催生了集成感知与通信（ISAC）范式，该范式已被公认为六大6G应用场景之一。尽管已有大量专注于ISAC信号处理的研究工作，但在ISAC系统中，S&C的基本性能极限仍未被充分探索。在本教程论文中，我们尝试从信息论角度总结刻画ISAC系统性能边界及其导致的S&C权衡的最新研究成果。我们首先引入一个传统的"手电筒隐喻"来描述S&C的资源竞争机制，然后阐述基本的容量-畸变（C-D）理论，揭示该隐喻的不完备性。为此，我们进一步通过讨论C-D框架内的一个特例——即克拉美-罗界（CRB）-速率区域——来详细阐述S&C权衡。特别地，S&C对传输信号所占据的子空间以及所采用的码本存在偏好差异，从而提出与ISAC手电筒类比互补的"投影仪隐喻"。我们还利用基础理论的经验教训，给出了两个实际设计示例。最后，我们通过指出若干开放性挑战来总结本文。