Integrated sensing and communication (ISAC) has been recognized as a key enabler and feature of future wireless networks. In the existing works analyzing the performances of ISAC, discrete-time systems were commonly assumed, which, however, overlooked the impacts of temporal, spectral, and spatial properties. To address this issue, we establish a unified information model for the band-limited continuous-time ISAC systems. In the established information model, we employ a novel sensing performance metric, called the sensing mutual information (SMI). Through analysis, we show how the SMI can be utilized as a bridge between the mutual information domain and the mean squared error (MSE) domain. In addition, we illustrate the communication mutual information (CMI)-SMI and CMI-MSE regions to identify the performance bounds of ISAC systems in practical settings and reveal the trade-off between communication and sensing performances. Moreover, via analysis and numerical results, we provide two valuable insights into the design of novel ISAC-enabled systems: i) communication prefers the waveforms of random amplitude, sensing prefers the waveforms of constant amplitude, both communication and sensing favor the waveforms of low correlations with random phases; ii) There exists a linear positive proportional relationship between the allocated time-frequency resource and the achieved communication rate/sensing MSE.

翻译：集成感知与通信（ISAC）已被认为是未来无线网络的关键使能技术和重要特征。现有分析ISAC性能的研究通常假设离散时间系统，然而这种假设忽略了时域、频域和空间特性的影响。为解决这一问题，我们为带限连续时间ISAC系统建立了一个统一的信息模型。在该信息模型中，我们采用了一种称为感知互信息的新型感知性能度量指标。通过分析，我们展示了如何将SMI作为互信息域与均方误差域之间的桥梁。此外，我们通过CMI-SMI与CMI-MSE区域刻画了实际场景中ISAC系统的性能边界，揭示了通信与感知性能之间的权衡关系。进一步地，通过理论分析与数值结果，我们为新型ISAC系统设计提供了两个重要启示：i) 通信倾向于随机幅度波形，感知倾向于恒定幅度波形，而通信与感知均偏好具有随机相位的低相关性波形；ii) 所分配时频资源与可达通信速率/感知MSE之间存在线性正比例关系。