  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.
