A Novel Construction of Complementary Sets With Flexible Lengths Based on Boolean Functions

Golay complementary sets (GCSs) have been proposed to reduce the peak-to-average power ratios (PAPRs) in orthogonal frequency-division multiplexing (OFDM). They have upper bounds depending on the set sizes. The constructions of GCSs based on generalized Boolean functions have been proposed in the literature. However, most of these constructed GCSs have limited lengths, and hence they are not feasible for practical OFDM communication systems. This letter proposes a new construction of GCSs with flexible lengths. The proposed construction is a direct construction based on generalized Boolean functions. In addition, the constructed GCSs have various constellation sizes, set sizes, and upper bounds on PAPR.