A Balancing Method for PMEPR Reduction in OFDM Signals

A relation is established between the strength of a binary code over the alphabet {+1,-1}, and its ability to reduce peak-to-mean envelope power ratio (PMEPR) in n-subcarrier (OFDM) signals. Based on this relation, a method is proposed to deterministically bound PMEPR of such signals using coordinate-wise multiplication by a balancing vector (BV) chosen from a code of given strength. A practical probabilistic scheme considering a small number of candidate codewords is devised. For this scheme, estimates on the PMEPR reduction achievable with arbitrary high probability are derived. In particular, the scheme provides for large n PMEPR of lnn+2.01lnlnn with (ln2)middot(log₂n)²+1 bits of redundancy, the failure probability at most e^-n, and testing n/(lnlnn) candidate BVs. Finally, several practical settings are considered. For example, for quaternary phase-shift keying, n=128, the scheme with 36 bits of redundancy (18 redundant subcarriers), by testing only 4 BVs provides over 2 dB PMEPR reduction, for any failure rate below 10^-2.5