g into adjacent channels. Therefore, RF PAs should be operated in a very large linear region. Otherwise, the signal peaks leak into nonlinear region of the PA caus- ing signal distortion. This signal distortion introduces intermodulation among the subcarriers and OOB emission. Thus the PA should be operated with large power back-offs. On the other hand, this leads to very inefficient amplification and an expensive transmitter. Thus, it is highly desir- able to reduce the PAPR. In addition to inefficient operation of the PA, a high PAPR requires larger dynamic range for the receiver analog to digital converter (ADC). To reduce the PAPR, several techniques have been proposed and used such as clipping, channel coding, temporal windowing, tone reservation, 10 and tone injection. However, most of these methods are unable to achieve simultaneously a large reduction in PAPR with low complexity and without perfor- mance degradation. The PAPR & of an OFDM signal is defined as follows: In the above equation E{.} denotes the expectation operator and n is an integer. From the central-limit theorem, for large values of NFFT, the real and imaginary values of OFDM sig- nal x(t) would have 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 to be mutually uncorrelated, the CDF for the peak power per OFDM symbol is given by From the above equation it can be seen that large PAPR occurs only infrequently due to rel- atively large values of NFFT used in practice. The CDF of the real-valued random variable X is defined as X Fx(x) = P(X .x), Axe R, where the right- hand side represents the probability that random variable X takes on a real value less than or equal to X. The CDF of X can be defined in terms of the probability density function f(x) as F(x) = The comple- mentary CDF (CCDF), on the other hand, is defined as P(X (>x)=1-Fx(x). Since the OFDM signal has a high PAPR, it may be cl