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

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Abstract
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.
Funding Information
  • National Key Research and Development Program of China (2020YFA0711301)
  • National Natural Science Foundation of China (61901298, 61771286, 61922049)
  • Natural Science Foundation of Tianjin (20JCQNJC00300)
  • Shanghai Municipal Science and Technology Major Project (2018SHZDZX04)
  • Tsinghua University-China Mobile Communications Group Co., Ltd. Joint Institute
  • EU Marie Sklodowska-Curie Actions Project titled “High-reliability Low-latency Communications with network coding,” and ERA-NET Smart Energy Systems SG+ 2017 Program, “SMART-MLA” (89029 (and SWEA 42811-2))
  • FORMAS Project titled “Intelligent Energy Management in Smart Community with Distributed Machine Learning” (2021-00306)

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