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 4(q)-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.