Polyphase scalable complete complementary sets of sequences

Extended from their biphase counterparts, biphase scalable complete complementary sets of sequences are discovered in this paper. Starting from biphase scalable complete complementary sets of sequences, the notions of Golay-paired matrix, Golay-paired Hadamard matrix and mutually orthogonal Golay-paired matrices are reviewed and extended to their respective polyphase ones. Synthesis methods, including recursive procedure and closed-form formula, for constructing these polyphase scalable complete complementary sets of sequences represented by mutually orthogonal polyphase Golay-paired Hadamard matrices are also proposed accordingly. Finally, the polyphase cover code and its synthesis methods are discussed and illustrated, which provides the linkage between biphase and polyphase scalable complete complementary sets of sequences.