Distribution of PAPR in low order OFDM with non equal amplitudes

It has been widely known that one of the key design parameters in orthogonal frequency division multiplexing (OFDM) systems is the distribution of peak-to-average power ratio (PAPR). Recently some theoretical approaches to determine the PAPR distribution have been proposed based on the assumption that all subcarriers are allocated with equal power, and that number of subcarriers is large. As a result Gaussian approximations may be used. However, these assumptions may not be valid due to the following facts: (i) in all realistic OFDM systems, usually only a subset of subcarriers is used to carry information and the rest are set to zero, (ii) power allocation may not be uniform and may depend on bit and power loading. As a result the Gaussian approximation is not longer valid to compute the PAPR distribution. In this paper we derive an analytical expression of the PAPR distribution of low order OFDM signal having non-equal amplitudes. To validate the analytical results, extensive numerical analysis have been conducted, showing a very good match between the analytically results and that of real OFDM systems.