Cumulative Distribution of the PAPR in a Out-Of-Band Coded OFDM System

An OFDM signal consists of a number of independently modulated SCs, which can give a large peak-to-average power (PAP) ratio when added up coherently. The peak power is defined as the power of a sine wave with amplitude equal to the maximum envelope value. Hence, an unmodulated carrier has a PAP ratio of 0 dB. An alternative measure of the envelope variation of a signal is the Crest factor, which is defined as the maximum signal value divided by the RMS signal value. For an unmodulated carrier, the Crest factor is 3 dB. This 3-dB difference between the PAP ratio and Crest factor also holds for other signals, provided that the center frequency is large in comparison with the signal bandwidth.