Closed-form approximations of the PAPR distribution for Multi-Carrier Modulation systems

The theoretical analysis of the Peak-to-Average Power Ratio (PAPR) distribution for an Orthogonal Frequency Division Multiplexing (OFDM) system, depends on the particular waveform considered in the modulation system. In this paper, we generalize this analysis by considering the Generalized Waveforms for Multi-Carrier (GWMC) modulation system based on any family of modulation functions, and we derive a general approximate expression for the Cumulative Distribution Function (CDF) of its continuous and discrete time PAPR. These equations allow us to directly find the expressions of the PAPR distribution for any particular family of modulation functions, and they can be applied to control the PAPR performance by choosing the appropriate functions.