  Integrated Sensing and Communication (ISAC) is gradually becoming a reality
due to the significant increase in frequency and bandwidth of next-generation
wireless communication technologies. Therefore it becomes crucial to evaluate
the communication and sensing performance using appropriate channel models to
address resource competition from each other. Existing work only models the
sensing capability based on the mutual information between the channel response
and the received signal, and its theoretical resolution is difficult to support
the high-precision requirements of ISAC for sensing tasks, and may even affect
its communication optimal.
  In this paper, we propose a sensing channel encoder model to measure the
sensing capacity with higher resolution by discrete task mutual information.
For the first time, derive upper and lower bounds on the sensing accuracy for a
given channel. This model not only provides the possibility of optimizing the
ISAC systems at a finer granularity and balancing communication and sensing
resources, but also provides theoretical explanations for classical intuitive
feelings (like more modalities more accuracy) in wireless sensing. Furthermore,
we validate the effectiveness of the proposed channel model through real-case
studies, including person identification, displacement detection, direction
estimation, and device recognition. The evaluation results indicate a Pearson
correlation coefficient exceeding 0.9 between our task mutual information and
conventional experimental metrics (e.g., accuracy).
