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.