New QAM Golay complementary pairs with unequal sequence power

A collection of new length four 16-QAM Golay complementary pairs are presented. Most of the new pairs have pairing sequences with unequal sequence power. These pairs are variations of 13 basic pairs, including ([A A A A], [A B −B −A]), where A is any complex number and B= (1+2j)A. Note that the constant sequence [A A A A] was considered not to be a Golay sequence when PSK alphabets are employed. There are 1440 length four 16-QAM new Golay sequences and 11264 new Golay pairs associated with the 13 basic pairs, in addition to the 2432 Golay sequences and 20480 Golay pairs constructed by Chong, et. al.. These new pairs can be used as primitive pairs to recursively generate longer new QAM Golay sequences and pairs. The construction of Golay pairs/sequences from variations of the basic pair ([A A A A], [A B −B −A]) is discussed. OFDM peak-to-mean envelope power ratio upper bounds for Golay sequences generated from that basic pair is 0.8 for sequence lengths n=2m, m≫1. Constructions and bounds for sequences/pairs associated with the other basic pairs can be derived in a similar manner.