Relationship between Hamming weight and peak-to-mean envelope power ratio of orthogonal frequency division multiplexing

We show that for certain binary codewords, the PMEPR is exactly determined by their Hamming weight or the Hamming distance from the worst-case PMEPR sequences. Consequently, it is relatively easy to devise selection metrics and construct codes that achieve initial PMEPR reductions of 3 to 6 dB without the need to perform high complexity computations. The technique used in this paper applies the metric of Hamming distance of a sequence from a sequence with highest PMEPR. More generally, we consider the metric of Hamming distance from any sequence with known PMEPR. In particular we build code 'clusters' around low PMEPR complementary sequences so as to construct codes with reasonable rate and low PMEPR.