Generation and correlation algorithms for ternary complementary pairs of sequences of length 3·2n

Abstract

Binary complementary pairs of sequences, which are available for certain even length values (L = 2n · 10m · 26p), are very interesting for applications with high noise levels and/or highly attenuated signals. To extend the range of useful lengths, some authors have defined ternary complementary pairs of sequences. These sequences have been approached from a theoretical perspective, but further research should be conducted regarding the architectures to process them. This letter describes algorithms for generating and performing the correlation of these sequences using a minimum amount of calculations. These algorithms allow to work with sequences of length 3 · 2n, making it possible to attain a wider range of lengths, and, as a consequence, a wider range of noise immunity in some applications. The proposed approach uses a particular delay arrangement that minimizes the memory requirements in hardware applications. The procedure described could also be used in ternary complementary pairs generated from primitives of length different from 3.