In the disclosed system and method phase (and optionally amplitude) shifts are applied at an OFDM transmitter to resource blocks within a given slot to implement Crest Factor Reduction (CFR). The phase shifts may differ between resource blocks and are selected to reduce the peaks in the OFDM waveform. The resource block phase shifts do not affect the demodulation process when the equalization at the receiver is performed on individual blocks separately. As a result, the crest factor reduction is achieved without increasing the EVM or BER in the received signal. In addition, a computational efficient algorithm for determining the resource block phase shifts needed for CFR is disclosed.