Two constructions of 16-QAM Golay complementary sequences

One of the major issues in deploying OFDM is the high peak to mean envelope power ratio (PMEPR) of uncoded OFDM signals. An important approach to PMEPR reduction is the use of Golay (1961) complementary sequences for OFDM transmission. Davis and Jedwab (see IEEE Trans. Inform. Theory, vol.45, no.7, p.2397-2417, 1999) developed a powerful theory which yields 2^b-PSK Golay sequences as unions of cosets of the classical Reed-Muller codes and new generalizations of them. Given the practical applications of 2^b -PSK Golay sequences and that QAM sequences are widely used in OFDM, it is natural to ask of 16-QAM (and higher) Golay complementary sequences. We present two constructions of 16-QAM Golay complementary sequences from 4-QAM complementary sequences. These sequences can be applied as pilot sequences in future OFDM systems.