Charactering the Peak-to-Average Power Ratio of OTFS Signals: A Large System Analysis

Orthogonal time frequency space (OTFS) system constitutes an effective structure conceived for efficiently utilizing the channel information, which is capable of achieving a promising transmission performance in high-mobility environment. To extract enough channel diversity, a two-dimensional Fourier transformation combined with a pulse shape is designed at the OTFS transmitter. Consequently, the amplitude of OTFS signals may fluctuate drastically, owing to the combined dependency of the OTFS transformation and the pulse shape. To quantify the amplitude fluctuation, we investigate the peak-to-average power ratio (PAPR) of OTFS signals, for a large amount of data in the delay-Doppler domain. We first reveal that when the number of data points approaches to infinity, based on central limit theorems for dependent variables, the complex-valued OTFS signals weakly converge to a Gaussian distribution. Then, according to the extremal theory of the Chi-squared process for stationary OTFS signals, an accurate expression of the PAPR distribution is derived, depending on the transmit pulse and the number of data points. It is also demonstrated that upon modifying the exponential factor, the analytical PAPR expression is applicable for the non-stationary Gaussian distribution caused by the bandlimited pulse with a large roll-off factor. Simulation results confirm the accuracy of the analytical PAPR probability for practical conditions.