tive distribution function (CDF)¹ of the PAPR for 99.0%, 99.9%, and 99.99% are approximately The CDF of the real-valued random variable X is defined as Fx(x) = P(X x), Axei where the right-hand side represents the probability that the 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) = Stoof(x)dx. The Complementary CDF (CCDF), on the other hand, is defined as P(X > x) = 1 Fx(x). 9.3 SC-FDMA and OFDMA principles 8.3, 10.3, and 11.8 dB, respectively. Since the OFDM signal has a high PAPR, it could be clipped in the transmitter power amplifier, because of its limited dynamic range or non-linearity. Higher output back- off is required to prevent performance degradation and inter-modulation products spilling into adjacent channels. Therefore, RF power amplifiers should be operated in a very large linear region. Otherwise, the signal peaks leak into the non-linear region of the power amplifier, causing signal distortion. This signal distortion introduces inter-modulation among the sub-carriers and out-of-band emission. Thus, the power amplifiers should be operated with large power back-offs. On the other hand, this leads to very inefficient amplification and expensive transmitters. Thus, it is highly desirable to reduce the PAPR. In addition to inefficient operation of the power amplifier, a high PAPR requires a larger dynamic range for the receiver analog-to-digital (A/D) converter. To reduce the PAPR, several tech- niques have been proposed and used such as clipping, channel coding, temporal windowing, Tone Reservation, and Tone Injection. However, most of these methods are unable to simultaneously achieve a large reduction in PAPR with low complexity, with low coding overhead, without perfor- mance degradation, and without transmitter receiver symbol handshake. The PAPR w of the OFDM signal defined in Equation (9-11) is defined as follows: (9-12) mT(m+1)T, In the above equation, E{.} denotes the expectation operator 