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We address the peak-to-average power ratio (PAPR) of transmission signals in OFDM and consider the performance of tone reservation for reduction of the PAPR. Tone reservation is unique among methods for reducing PAPR, because it does not affect information bearing coefficients and involves no additional coordination of transmitter and receiver. It is shown that if the OFDM system always satisfies a given peak-to-average power ratio constraint, then the efficiency of the system, defined as the ratio of the number of tones used for information to the entire number of tones used, must converge to zero as the total number of tones increases. More generally, we investigate and provide insight into a tradeoff between optimal signal and information properties for OFDM systems and show that it is necessary to use very small subsets of the available signals to achieve PAPR reduction using tone reservation.

PAPR and the Density of Information Bearing Signals in OFDM