1. A peak-to-average power ratio reduction method in an orthogonal frequency division multiplexing (OFDM) transmitter, the method comprising the steps of: generating a baseband OFDM symbol while reserving a fixed subset of null tones in random distribution over an available transmission spectrum; increasing the number of reserved tones, thereby improving the peak-to-average power ratio reduction while yielding an improved estimate of a peak-reducing signal at a receiver of an OFDM signal, wherein a Symbol Error Rate is improved; generating a sparse time domain peak-reducing signal; adding the peak-reducing signal to the OFDM signal, thereby annihilating peaks of the OFDM signal exceeding a predetermined clipping threshold; and transmitting the OFDM signal, wherein reserved null tones are no longer null due to the addition of the peak-reducing signal.