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 2lnN 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 2lnN. Some approaches to coping with the PAPR problem are discussed in light of the obtained results.

The asymptotic behavior of level clipped orthogonal frequency-division multiplexing when its order N approaches infinity is analyzed. It is shown that if the clipping level approaches infinity faster than /spl radic/lnN, then a zero bit-error rate penalty and arbitrarily large peak to-average power ratio (PAPR) gain are asymptotically obtained. Moreover, the expression for the probability of clipping is found, and using it, the upper bound of the probability of error is derived. This upper bound can be used to analyze the tradeoff between PAPR and probability of error.