Universal Generator for Complementary Pairs of Sequences Based on Boolean Functions

Abstract: We present a general algorithm for generating arbitrary standard complementary pairs of sequences (including binary, polyphase, M-PSK and QAM) of length 2^N using Boolean functions. The algorithm follows our earlier paraunitary algorithm, but does not require matrix multiplications. The algorithm can be easily and efficiently implemented in hardware. As a special case, it reduces to the non-recursive (direct) algorithm for generating binary sequences given by Golay, to the algorithm for generating M-PSK sequences given by Davis and Jedwab (and later improved by Paterson) and to all published algorithms for generating QAM sequences. However the algorithm does not solve the problem of sequence uniqueness (except for the trivial M-PSK case), which must be treated separately for each QAM constellation.