A Symbol vector for RF transmission after multiplexing onto a subset of a set of subcarriers using OFDM is transformed to the time domain. A first time domain cancellation vector is generated from a basis vector that has the same dimensionality as the symbol vector. In the frequency domain the basis vector has a substantially zero value in each of a first subset of sub-carriers of the symbol vector and in the time domain the difference between a first element of the basis vector having the highest value and a second element of the basis vector having the next highest value is maximized. The first cancellation vector is subtracted from the symbol vector to produce modified symbol vector having reduced Peak-to-Average Power Ratio (PAPR). A second cancellation vector is generated using the modified symbol vector and is used to produce a second modified symbol vector having reduced PAPR.