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：传感与通信（S&C）在历史上一直并行发展。近十年来，它们从分离走向融合，催生了集成传感与通信（ISAC）范式，该范式已被公认为六大6G应用场景之一。尽管已有大量研究致力于ISAC信号处理，但ISAC系统中传感与通信的基本性能极限仍鲜有探索。在本教程论文中，我们尝试从信息论视角总结近期关于ISAC系统性能边界及由此产生的S&C权衡的研究成果。我们首先引入一个民间流传的“手电筒隐喻”来描述S&C的资源竞争机制。随后，我们阐述基本容量-失真（C-D）理论，指出这一隐喻的局限性。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在发射信号占据的子空间以及采用的码本上存在偏好差异，从而引出了一个“投影仪隐喻”，作为对ISAC手电筒类比的补充。我们还利用基础理论的经验教训，提出了两个实际设计示例。最后，我们通过指出若干开放挑战来总结全文。