Nowadays, waveforms of integrated sensing and communication (ISAC) are almost based on conventional communication and sensing signal, which bounds both the communication and sensing performance. To deal with this issue, in this paper, a novel waveform design is presented for the partial-time superimposed (PTS) ISAC system. At the base station (BS), a parameter-adjustable linear frequency modulation (LFM) pulse signal and a continuous communication orthogonal frequency division multiplexing (OFDM) signal are employed to broadcast public information and perform sensing tasks, respectively, using a PTS scheme. Pulse compression gain enhances the system's long-range sensing capability, while OFDM ensures the system's high-speed data transmission capability. Meanwhile, the LFM signal is utilized as superimposed pilot for channel estimation, which has higher time-frequency resource utilization and stronger real-time performance compared to orthogonal pilots. We present an accurate parameter estimation method of multi-path sensing signal for reconstructing and interference cancellation in communication users. Additionally, a cyclic maximum likelihood method is introduced for channel estimation and the Cramer-Rao lower bound (CRLB) of channel estimation is derived. Simulations demonstrate the accuracy and robustness of the proposed parameter estimation algorithm as well as the improved channel estimation performance over traditional methods. The proposed waveform design method can achieve reliable data transmission and accurate target sensing.