High Code Rate 16-QAM Golay Complementary Set Construction for Communication Systems

This paper presents two direct constructions of 16-QAM Golay complementary sets (GCS) employing generalized Boolean functions (GBFs) aimed at enhancing communication system performance. The initial method facilitates the generation of 16-QAM GCS with a set size of $2^{k+1}$ and the constituent sequence of lengths in the form of $2^{m-1}+2^{t}$, offering advantages in terms of set size. The second methodology enhances the codebook size by utilizing GBFs, resulting in 16-QAM GCS with a sequence length of $2^{m}$. In comparison to existing sequences, new sequences have a bigger family size, which leads to a higher relevant code rate which is beneficial for efficient data transmission. Notably, the construction demonstrates PMEPRs significantly lower than 4, i.e., the set size of GCS. This advancement holds promise for enhancing the OFDM system’s efficiency and performance by exploiting the advantageous properties of Golay complementary sequences.