Individual Correlation Properties and Structural Features of Periodic Complementary Sequences

Complementary sequences (CS) were considered to be used in pairs, although their property to reduce the crest factor in OFDM and MC-CDMA systems employing CS-based spreading is widely known. Their individual properties have hardly ever been studied, with one exception for the Golay sequences. In this paper, we study the individual properties of periodic CS (PCS), which are a superclass of Golay sequences. We show that PCS have remarkable correlation characteristics and unique features at their own, acting as single sequences. Although PCS are somewhat inferior to the Gold and Kasami sequences in terms of peak correlations, they are similar, and sometimes even perform better, in terms of RMS correlation values, and outnumber them by orders of magnitude. The structure of PCS enables efficient processing in applications requiring high data rates. We have also identified the unique feature of PCS which is possibility to use them to construct sets of orthogonal signals that lead to processing advantages of both complementary sequences and cyclic codes.