On the PAPR of Discrete Zak Transform Based OTFS Modulation

Recently, Zak transform based orthogonal time frequency space (OTFS) waveform has generated new research interest owing to its better robustness to large channel spreads compared to that of the widely researched OTFS waveform based on inverse symplectic finite Fourier transform (ISFFT) and Heisenberg transform (HT). In this paper, we investigate the peak-to-average power ratio (PAPR) characteristics of discrete Zak transform based OTFS (DZT-OTFS), which has not been reported. We derive an upper bound on the PAPR of DZT-OTFS waveform for general transmit pulse shapes and a tighter upper bound for rectangular pulse, using Cauchy-Schwartz inequality. The PAPR upper bound for DZT-OTFS and two-step OTFS (based on ISFFT and HT) are shown to be the same for rectangular pulse, and hence the PAPR of DZT-OTFS with rectangular transmit pulse shape grows linearly in the number of Doppler bins. With non-rectangular transmit pulse, the results on complementary cumulative distribution function (CCDF) of PAPR show that DZT-OTFS can have better PAPR characteristics compared to that of two-step OTFS.