ISAC is recognized as a promising technology for the next-generation wireless networks, which provides significant performance gains over individual S&C systems via the shared use of wireless resources. The characterization of the S&C performance tradeoff is at the core of the theoretical foundation of ISAC. In this paper, we consider a point-to-point ISAC model under vector Gaussian channels, and propose to use the CRB-rate region as a basic tool for depicting the fundamental S&C tradeoff. In particular, we consider the scenario where a unified ISAC waveform is emitted from a dual-functional ISAC Tx, which simultaneously performs S&C tasks with a communication Rx and a sensing Rx. In order to perform both S&C tasks, the ISAC waveform is required to be random to convey communication information, with realizations being perfectly known at both the ISAC Tx and the sensing Rx as a reference sensing signal as in typical radar systems. As the main contribution of this paper, we characterize the S&C performance at the two corner points of the CRB-rate region, namely, $P_{SC}$ indicating the max. achievable rate constrained by the min. CRB, and $P_{CS}$ indicating the min. achievable CRB constrained by the max. rate. In particular, we derive the high-SNR capacity at $P_{SC}$, and provide lower and upper bounds for the sensing CRB at $P_{CS}$. We show that these two points can be achieved by the conventional Gaussian signaling and a novel strategy relying on the uniform distribution over the Stiefel manifold, respectively. Based on the above-mentioned analysis, we provide an outer bound and various inner bounds for the achievable CRB-rate regions. Our main results reveal a two-fold tradeoff in ISAC systems, consisting of the subspace tradeoff (ST) and the deterministic-random tradeoff (DRT) that depend on the resource allocation and data modulation schemes employed for S&C, respectively.

翻译：通感一体化（ISAC）被认为是下一代无线网络中的一项有前景技术，通过共享无线资源，相较于独立的通信与感知系统，可提供显著的性能增益。刻画通信与感知的性能权衡是ISAC理论基础的核⼼。本文考虑矢量高斯信道下的点对点ISAC模型，提出以模糊克拉美-罗界（CRB）与可达速率区域作为描述基本感知与通信权衡的基本工具。特别地，我们关注一个双功能ISAC发射机发射统一ISAC波形，同时与通信接收机和感知接收机执行感知与通信任务的场景。为同时完成这两项任务，ISAC波形需要具备随机性以传输通信信息，而其具体实现需被ISAC发射机和感知接收机（作为典型雷达系统中的参考感知信号）精确已知。本文的主要贡献在于刻画CRB-速率区域两个角点处的感知与通信性能：$P_{SC}$（受最小CRB约束的最大可达速率）与$P_{CS}$（受最大速率约束的最小可达CRB）。具体而言，我们推导了$P_{SC}$处的高信噪比容量，并给出了$P_{CS}$处感知CRB的下界与上界。研究表明，这两点可分别通过传统高斯信令和基于斯蒂弗尔流形上均匀分布的新策略实现。基于上述分析，我们提供了可达CRB-速率区域的外界和各内界。主要结果揭示了ISAC系统中的双重权衡，包括依赖于感知与通信资源分配的子空间权衡（ST）和依赖于数据调制方案的确定-随机权衡（DRT）。