Peak-to-average power ratio in high-order OFDM

The problem of peak-to-average power ratio (PAPR) of high-order orthogonal frequency-division modulation (OFDM) is considered. Using results on level crossing of random processes, an upper bound on the probability that the PAPR of an OFDM signal will exceed a given value is derived. Numerical computations are used to show that this bound is tight for low-pass OFDM systems. The central limit theorem is used to find an asymptotic expression for the bound when the number of carriers N grows to infinity. The central limit theorem is also used to find an asymptotic expression for another bound that is based on the envelope of the OFDM signal, and is tighter for bandpass systems. It is shown that, effectively, the PAPR grows as 2 ln N and not linearly with N, and by developing a lower bound on the probability that the PAPR of an OFDM signal will exceed a given value, it is shown that asymptotically most OFDM symbols have a PAPR close to 2 ln N. Some approaches to coping with the PAPR problem are briefly discussed in light of the obtained results.