  In this paper, the probability distribution of the peak to average power
ratio (PAPR) is analyzed for the mixed numerologies transmission based on
orthogonal frequency division multiplexing (OFDM). State of the art theoretical
analysis implicitly assumes continuous and symmetric frequency spectrum of OFDM
signals. Thus, it is difficult to be applied to the mixed-numerology system due
to its complication. By comprehensively considering system parameters,
including numerology, bandwidth and power level of each subband, we propose a
generic analytical distribution function of PAPR for continuous-time signals
based on level-crossing theory. The proposed approach can be applied to both
conventional single numerology and mixed-numerology systems. In addition, it
also ensures the validity for the noncontinuous-OFDM (NC-OFDM). Given the
derived distribution expression, we further investigate the effect of power
allocation between different numerologies on PAPR. Simulations are presented
and show the good match of the proposed theoretical results.
