Constructions of quadriphase Z-complementary sequences

Aperiodic quadriphase Z-complementary sets (QZCS), which include the conventional complementary sets as special cases, are introduced. It is shown that, aperiodic quadriphase Z-complementary pairs are normally better than binary ones of the same length in terms of the number of Z-complementary pairs, and maximum zero correlation zone (Zmax). The new notions of elementary transformations on quadriphase sequences and elementary operations on QZCS are brought forward. In particular, new methods for analyzing the relations among the formulas relative to QZCS and for describing aperiodic Z-complementary sets are proposed. Improved constructions of QZCS and their mates are given.