New Sets of Even-Length Binary Z-Complementary Pairs With Asymptotic ZCZ Ratio of $3/4$
Avik Ranjan Adhikary, Sudhan Majhi, Zilong Liu, Yong Liang Guan · IEEE Signal Processing Letters · 2018
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 2α+210β26γ+ 2 (where α, β, and γ are nonnegative integers) and ZCZ widths 3 × 2α10β26γ+ 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).