Constructions of Z-optimal Type-II quadriphase Z-complementary pairs

Investigating (periodic) and design sequences with good correlation properties have numerous applications in communications. Research on designing sequence pairs with good correlation properties started in the early 1950's thanks to M.J. Golay. Ideally, one of our ultimate aims in this context is to design a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. The so-called Z-complementary pair (ZCP) is one of the suitable candidates. A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). ZCPs have been widely used in different communication systems and are closely related with almost difference families, which are useful in studying partially balanced incomplete block design. Despite remarkable progress in designing ZCPs, only a few constructions of quadriphase ZCPs (QZCPs) have been reported in the literature up to now. Aiming to reducing this gap, we explore in this article several methods to design such sequences. More specifically, we propose a recursive construction based on the concatenation of sequences aimed to design Type-II QZCPs. Also, based on Turyn's construction method, we present another new Type-II QZCPs. The proposed constructions lead to Z-optimal Type-II even-length QZCPs (E-QZCPs) and Type-II odd-length QZCPs (O-QZCPs) with large ZCZ widths. Finally, we derive upper bounds for the peak-to-mean envelope-power ratio (PMEPR) of the proposed ZCPs. It turns out that our constructions lead to ZCPs with low PMEPR. These characteristics allow our QZCPs to be seen as promising for practical uses in some modern communication systems.