Fractional local peak detection and mitigation for PAR reduction

A method for reducing the peak-to-average ratio of a single-carrier or a multi-carrier modulated signal, the method comprising:

• storing an original signal;
• extending the original signal by adding a suffix to form an original extended signal;
• interpolating and upsampling the original extended signal at a fractional sampling rate to form an extended interpolated signal;
• localizing the extended interpolated signal to form a localized neighborhood;
• setting a threshold for the extended, interpolated signal within the localized neighborhood;
• tracing back across all the signal samples to detect for and mitigate the peaks that exceed the threshold in the localized neighborhood;
• generating sequences basis (Q) by partitioning the available bins into a number of subsets, and taking N-dimensional inverse Fourier transforms of each subset at the rate of T;
• locally generating a PAR lowering sub-sequence (J) at T,
• in the time-domain locally combining the PAR lowering sub-sequence (J) and a highest peak source at the scale of one extended symbol for multi-carrier modulation and at one or more of symbols for single-carrier modulation;
• locally interpolating the combination of the sub-sequences and the highest peak source;
• finding and determining if the PAR for one of the locally combined sub-sequences and the highest peak is a PAR-lowering sequence;
• storing the PAR-lowering, locally combined sub-sequences and the highest peak;
• from the stored, locally combined PAR lowering sub-sequences finding the one that yields the lowest PAR at the local rate of T/K;
• generating the best PAR-lowering sub-sequence for all the samples at the rate of T;
• and
• combining the best PAR-lowering sub-sequence and the originally stored signal and, transmitting the signal.