How do I calculate the peak to average power ratio of an OFDM signal?

The peak-to-average power ratio (PAPR) of an OFDM signal is the ratio of the instantaneous peak power to the average signal power, expressed in dB: PAPR = 10 log(P_peak / P_average). For an OFDM signal with N subcarriers, each modulated independently with random data, the theoretical maximum PAPR is 10 log(N) dB (occurring when all N subcarriers align in phase simultaneously, creating a peak voltage N times the RMS voltage of a single subcarrier). For example: 64 subcarriers: PAPR_max = 18 dB, 256 subcarriers: 24 dB, 1024 subcarriers: 30 dB, 4096 subcarriers (5G NR 100 MHz): 36 dB. However, the probability of all subcarriers aligning exactly is astronomically small. The practical PAPR is described using the complementary cumulative distribution function (CCDF): the probability that the PAPR exceeds a given threshold. For practical system design, the PAPR at 0.01% CCDF (PAPR exceeded only 0.01% of the time) is used: this is typically 10-12 dB for a standard OFDM signal, nearly independent of the number of subcarriers (because the central limit theorem makes the sum of many random phasors approach a Rayleigh-distributed envelope regardless of N). The PAPR matters for PA design because the PA must be able to handle the peak power without clipping: the PA's P1dB must be at least PAPR dB above the required average output power, meaning the PA operates at significant back-off (low efficiency) most of the time.