  Integrated sensing and communication improves the design of systems by
combining sensing and communication functions for increased efficiency,
accuracy, and cost savings. The optimal integration requires understanding the
trade-off between sensing and communication, but this can be difficult due to
the lack of unified performance metrics. In this paper, an
information-theoretical approach is used to design the system with a unified
metric. A sensing rate is introduced to measure the amount of information
obtained by a pulse-Doppler radar system. An approximation and lower bound of
the sensing rate is obtained in closed forms. Using both the derived sensing
information and communication rates, the optimal bandwidth allocation strategy
is found for maximizing the weighted sum of the spectral efficiency for sensing
and communication. The simulation results confirm the validity of the
approximation and the effectiveness of the proposed bandwidth allocation.
