Golay Complementary Sets and Multiple-Shift Complementary Sets with Non-Power-of-Two Length and Bounded PAPRs

The Golay complementary set (GCS) has been applied in OFDM systems because of its desirable property of low peak-to-average power ratios (PAPRs). A generalization of GCS which is called the multiple-shift complementary set (MSCS) was also introduced to have bounded PAPRs. In addition, the MSCSs can be used to construct GCSs. In this letter, we first provide a more generalized construction of GCSs with non-power-of-two length. Then, a direct construction of MSCSs of non-power-of-two length is proposed based on the generalized Boolean functions. Moreover, a connection between the constructed GCSs and MSCSs is provided and hence the PAPR upper bound of the constructed MSCSs is derived. The proposed GCSs and MSCSs can have various lengths, set sizes, and bounded PAPRs.