PAPR in AFDM: Upper Bound and Reduction With Normalized μ-Law Companding

Affine Frequency Division Multiplexing (AFDM) is an advanced waveform technique designed for environments with significant Doppler shifts and time-frequency dispersion. It uses the Discrete Affine Fourier Transform (DAFT) to create flexible waveforms that are resilient to channel variations. Compared to Orthogonal Frequency Division Multiplexing (OFDM), AFDM provides better localization in time and frequency, improved spectral efficiency, and greater robustness, but it suffers due to a high Peak-to-Average Power Ratio (PAPR). To lower it, we applied the normalized μ-law companding transform to the AFDM waveform. Further, we derived an upper bound for PAPR of the AFDM waveform and demonstrated that the maximum PAPR increases with the number of subcarriers (N). We also provided an analytical expression for the Complementary Cumulative Distribution Function (CCDF) of the PAPR of AFDM for all values of N. To know the effectiveness of the AFDM waveform, simulations are carried out with respect to bit error rate (BER) over different channels and the CCDF of PAPR.