On the PMEPR of Binary Golay Sequences of Length $2^{n}$

Abstract

In this paper, some questions on the distribution of the peak-to-mean envelope power ratio (PMEPR) of standard binary Golay sequences are solved. For n odd, we prove that the PMEPR of each standard binary Golay sequence of length 2n is exactly 2, and determine the location(s), where peaks occur for each sequence. For n even, we prove that the envelope power of such sequences can never reach 2n+1 at time points t ∈ {(v/2u)|0 ≤ v ≤ 2u, v,u ∈ N}. We further identify eight sequences of length 24 and eight sequences of length 26 that have PMEPR exactly 2, and raise the question whether, asymptotically, it is possible for standard binary Golay sequences to have PMEPR less than 2 - ϵ, where, ϵ > 0.