Band-Limited Continuous-Time ISAC Systems: Exploring Fundamental Performance Boundaries

Integrated sensing and communication (ISAC) is emerging as a key enabler of future wireless networks. However, existing analyses of ISAC performance commonly assume discrete-time systems, overlooking the impacts of temporal, spectral, and spatial properties. To address this limitation, we establish a unified information model for band-limited continuous-time ISAC systems. In this model, we employ a novel sensing performance metric called the sensing mutual information (SMI). Our analysis demonstrates how SMI serves as a bridge between the mutual information domain and the minimum mean squared error (MMSE) domain. Additionally, we characterize the communication mutual information (CMI)-SMI and CMI-MMSE regions to identify the performance bounds of practical ISAC systems and reveal the trade-off between communication and sensing performances. Moreover, through analysis and numerical results, we derive two valuable insights for the design of ISAC-enabled systems: i) communication prefers waveforms with random amplitude, sensing prefers waveforms with constant amplitude, and both benefit from waveforms with low correlations and random phases; ii) a linear positive proportional relationship exists between allocated time-frequency resources and the achieved communication rate/sensing accuracy.