To achieve the extreme high data rate and extreme coverage extension requirements of sixth generation (6G) wireless communication, high-frequency bands such as millimeter wave (mmW) and sub-terahertz (sub-THz) frequencies, and non-terrestrial networks (NTN), are two of the macro trends of 6G candidate technologies, respectively. However, non linearity of power amplifiers (PA) is a critical challenge for both high-frequency bands and NTN. Therefore, low peak to average power ratio (PAPR) waveform and modulation design becomes one of the most significant research topics for 6G. To maintain fifth generation (5G) New Radio (NR) backward compatibility, many waveform and modulation enhancement schemes based on DFT-s-OFDM have been proposed, including frequency domain spectrum shaping with spectrum extension (FDSS + SE), π/4-QPSK, symbol level interleaving, and unified non-orthogonal waveform (uNOW). This paper firstly provides a general description of the waveform and modulation enhancement schemes based on DFT-s-OFDM. To analyze the factors affecting PAPR, the time domain equivalent shaped-pluses of these enhancement schemes are derived and compared. Based on the analysis, three influencing factors that reduce the PAPR of DFT-s-OFDM are analyzed and summarized. Secondly, a low-complexity scheme, asymmetric DFT-s-OFDM, achieving time-domain compression and expansion (TD-CE) based on asymmetric DFT spreading, is proposed and discussed. Thirdly, the optimal constellation rotations for BPSK and QPSK to further improve the PAPR performance of asymmetric DFT-s-OFDM are proposed. Finally, the PAPR and block error rate (BLER) performance of these 6G candidate enhancement schemes for NTN and mmW scenarios are evaluated and compared based on link-level simulation with non-ideal factors (nonlinear PA and phase noise (PN)), which reveals that asymmetric DFT-s-OFDM with QPSK rotation can achieve the best PAPR and BLER performance among all the 6G candidate enhancement schemes for both NTN and mmW scenarios. In addition to its low-complexity and backward compatibility, asymmetric DFT-s-OFDM with QPSK rotation can be considered a promising candidate low-PAPR waveform and modulation scheme for 6G.
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