On Cosets of the Generalized First-Order Reed-Muller Code with Low PMEPR

Golay sequences are well-suited for use as codewords in orthogonal frequency-division multiplexing (OFDM) since their peak-to-mean envelope power ratio (PMEPR) in q-ary phase-shift keying (PSK) modulation is at most 2. It is known that a family of polyphase Golay sequences of length 2^m organizes in m!/2 cosets of a generalized first-order Reed-Muller code RM_q(1, m). In this paper a more general construction technique for cosets of RM_q(1, m) with low PMEPR is provided. These cosets contain so-called near-complementary sequences. The application of this result is then illustrated by providing some construction examples. First, it is shown that the m!/2 cosets of RM_q(1, m) comprised of Golay sequences just arise as a special case. Second, further families of cosets of RM_q(1, m) with maximum PMEPR between 2 and 4 are presented, showing that some previously unexplained phenomena can now be understood within a unified framework. A lower bound on the PMEPR of cosets of RM _q(1, m) is proved as well, and it is demonstrated that the upper bound on the PMEPR is tight in many cases