Lengths and Alphabet Size of Recursively Constructed Complex Golay Sequences

Golay complementary sequences have been used in synchronization, channel estimation, and peak-to-average power ratio reduction for multicarrier signals. The length and alphabet size of recursively constructed complex Golay complementary sequences are determined by the input Golay pairs used in the construction. The length of the constructed Golay sequence will contain product of the lengths of the input Golay pairs as its factor. The alphabet size will grow when the number of QAM input Golay pairs increases. The growth of the length and alphabet size are analyzed. An alphabet size reduction method is proposed.