New Sets of Even-Length Binary Z-Complementary Pairs With Asymptotic ZCZ Ratio of <inline-formula> <tex-math notation="LaTeX">$3/4$</tex-math> </inline-formula>

Abstract

This letter is focused on increasing the zero correlation zone (ZCZ) of even-length binary Z-complementary pairs (EB-ZCPs). Till date, the maximum ZCZ ratio (i.e., ZCZ width over the sequence length) for systematically constructed EB-ZCPs is $2/3$ . In this letter, we give a construction of EB-ZCPs with lengths $2^{\alpha +2} 10^\beta 26^\gamma +2$ (where $\alpha$ , $\beta$ , and $\gamma$ are nonnegative integers) and ZCZ widths $3 \times 2^\alpha 10^\beta 26^\gamma +1$ , thus achieving asymptotic ZCZ ratio of $3/4$ . The proposed EB-ZCPs are constructed via proper insertion of concatenated odd-length binary ZCPs. The ZCZ width is proved by exploiting several newly identified intrinsic structure properties of binary Golay complementary pairs, obtained from Turyn's method. The proposed EB-ZCPs have aperiodic autocorrelation sums (AACS) magnitude of 4 outside the ZCZ region (except for the last time-shift taking AACS value of zero).