PAPR for OFDM and the proportion of information bearing signals for tone reservation

We consider the performance of tone reservation for reduction of the Peak-to-Average Power Ratio (PAPR) in OFDM signals. 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.