A Construction of General QAM Golay Complementary Sequences

A construction of general quadrature amplitude modulation (QAM) Golay complementary sequences based on quadrature phase shift keying Golay-Davis-Jedwab sequences (GDJ sequences) is described. Existing constructions of 16- and 64-QAM Golay sequences are extended to 4^q-QAM sequences of length 2^m, for q ≥ 1, m ≥ 2. This construction gives [(m + 1)4^{2(q - 1)} - (m + 1)4^{(q - 1)} + 2^{q - 1}](m! / 2)4^{(m + 1)} Golay complementary sequences. A previous offset pair enumeration conjecture for 64-QAM Golay sequences is proved as a special case of the enumeration for 4q-QAM Golay sequences. When used for orthogonal frequency-division multiplexing signals, the peak-to-mean envelope power ratio upper bound is shown to be 6(2^q - 1)/ (2^q + 1), approaching 6 as the QAM constellation size increases.