1 research outputs found
On Cosets of the Generalized First-Order Reed-Muller Code with Low PMEPR
Golay sequences are well suited for the 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 q-ary generalization of the 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 established. These cosets contain so-called
near-complementary sequences. The application of this theory 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. Finally it is shown that
all upper bounds on the PMEPR of cosets of RM_q(1,m) also hold for the
peak-to-average power ratio (PAPR) under the Walsh-Hadamard transform