Abstract:Traditional Orthogonal Frequency Division Multiplexing(OFDM) signals in terahertz communication systems usually bring about high Peak to Average Power Ratio(PAPR) problems that would seriously degrade the power amplifier efficiency and deteriorate the nonlinear effect of terahertz link. The design of constant-envelope OFDM based Integrated Sensing And Communication(ISAC) waveforms can suppress the harmful effects of high PAPR. The Ambiguity Function is used as the criteria for the range and velocity performance evaluation of three OFDM-based ISAC waveforms in the terahertz bands, namely, OFDM-16QAM(16-Quadrature Amplitude Modulation)-LFM(Linear Frequency Modulation), OFDM-BPSK(Binary Phase Shift Keying)-LFM, OFDM-MSK(Minimum Shift Keying)-LFM. The numerical simulation results demonstrate that, OFDM-16QAM-LFM waveform has excellent range-velocity performance but serious PAPR problems. OFDM-BPSK-LFM, OFDM-MSK-LFM waveforms replace the amplitude-phase modulation with phase modulation, thus maintaining constant-envelope characteristics. The range detection capability of OFDM-BPSK-LFM waveform does not degrade with the increase of subcarriers, while the velocity detection capability is seriously affected. Therefore OFDM-BPSK-LFM waveform is not suitable for the velocity detection of fast-moving objects. OFDM-MSK-LFM waveform can tolerate more subcarriers, making it suitable for multi-carrier radar detection under complex circumstances. This work provides references for the choice of ISAC waveforms in different application scenarios.