1. A computer-implemented 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; 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 the reserved null tones are no longer null due to the addition of the peak-reducing signal.