and m is an integer. From the central-limit theorem, for large values of NFFT, the real and imaginary values of s(t) (from Equation (9-11) and without the Re{.} operator) would have a Gaussian distribution. Consequently, the amplitude of the OFDM signal has a Rayleigh distribution with zero mean and a variance of NFFT times the variance of one complex sinusoid. Assuming the samples are mutually uncorrelated, the cumulative distribution function for the peak power per OFDM symbol is given by: (9-13) From the above equation, it can be seen that a large PAPR occurs only infrequently due to the relatively large values of NFFT used in practice. The PAPR of an OFDM signal is depicted in Figure 9- 12. Power amplifiers (PA) generally have a non-linear amplitude (AM) response where the output power is saturated for large input powers. Most applications require operation in the linear region of the PA response, where the output power is a linear function of the input. The larger the linear operation region or alternatively the larger the saturation point the more expensive the PA. Therefore, it is imperative to reduce the PAPR of the OFDM signal before processing through the PA. Figures 9-7 and 9-8 illustrate examples of PA AM/AM response and QAM signal constellation fuzziness when the OFDM signal with large PAPR is processed through a PA with low saturation point. In this example, 64 QAM modulation, 256 point IFFT with CP = 1/4T, and PA saturation point of 6 dB are assumed. The modulation accuracy or the permissible signal constellation fuzziness is often measured via the error vector magnitude (EVM) metric. The EVM defines the average constellation error with respect to the farthest constellation point (i.e., the distance between the reference signal and the measured signal points in I-Q plane) and is calculated as follows: [2] "In the tone reservation method, the transmitter and the receiver reserve a subset of tones or sub-carriers for generating PAPR reduction signals. Those reserved tones are not used for data transm