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 4q -QAM sequences of length 2m, for q ≥ 1, m ≥ 2. This construction gives [(m + 1)42(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(2q - 1)/(2q + 1), approaching 6 as the QAM constellation size increases.