Method for reducing the peak-to-average of a multi-carrier waveform

Two new carrier phasing algorithms are presented for reducing the peak-to-average ratio of a multi-carrier waveform. Both of these algorithms are capable of significantly reducing the peak-to-average power ratio for a set of either uniformly spaced or nonuniformly spaced carriers. The algorithms perform this reduction using the lowpass equivalent representation of the bandpass waveform. There, the original system of N bandpass carriers is then converted to a system of N*(N-1)/2 lowpass carriers, typically with multiple lowpass carriers at each lowpass frequency. Peak-to-average reduction is then accomplished by simply setting the phase angles of the original bandpass carriers such that groups of lowpass carriers with the same lowpass frequency are eliminated.