The radar-centric terahertz integrated sensing and communication (THz-ISAC) is identified as a significant application in future wireless access networks. Up to date, previously reported demonstrations regarding radar sensing performance lack sufficient support in a complex environment with a strong target masking effect. This work tacks this problem by proposing a radar-centric waveform combining linear frequency modulation (LFM) waveform and phase shift keying (PSK). We first derive sensing metrics of the LFM-PSK waveform through theoretical analysis, including range resolution, peak sidelobe ratio (PSLR), and Cramér-Rao lower bound (CRLB). Then a proof-of-concept experiment on a photonics-assisted integrated sensing and communication (ISAC) system operating at 330 with 18 GHz bandwidth is conducted to verify the performance of the proposed LFM-PSK waveform. In the experiment, the proposed waveform can reach a PSLR of up to 20.9 dB and a range resolution of 1.3 cm, simultaneously accommodating a data transmission of 6 Gbit/s. In addition, the effect of embedding symbols on sensing metrics is also discussed, and by comparing the range solution and PSLR with various data rates, around $\sim$ 6 dB gain in the PSLR without any deterioration of range resolution is observed.