Exact Expressions for PAPR Statistics in Low Number Subcarrier Multicarrier Systems

It is shown that the exact expression for the mean of the peak to average power ratio (PAPR) of a multicarrier system can be written straightforwardly as a harmonic number. The expression is valid for a wide range of numbers of subcarriers, including as few as 12 subcarriers, and is therefore useful in the context of narrowband orthogonal frequency division multiplexing (OFDM) systems. To obtain the expression, an exact closed form expression for the cumulative distribution function of the PAPR is derived. Furthermore, exact closed form expressions for the probability density function, mean, and variance of the PAPR across the OFDM symbols are also provided. The expressions are also shown to be asymptotically equal to previous results for large numbers of subcarriers.