This paper proposes a novel method to reduce the peak-to-average-power-ratio (PAPR) of affine frequency division multiplexing (AFDM) signals without side information (SI). The method is based on circularly shifting the original transmit signal in the affine domain, and selecting the shifted candidate with the lowest PAPR. Next, a maximum-likelihood-based (MLB) receiver is derived, which exploits the position of the AFDM pilot and guard band to detect the shift applied at the transmitter without SI. Simulation results show that the proposed method can achieve 2.5 to 4 dB in PAPR reduction as compared to original AFDM and existing schemes, which can be translated into significantly lower error rate, depending on the quality of power amplifiers.

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