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New Sets of Even-Length Binary Z-Complementary Pairs With Asymptotic ZCZ Ratio of 3/4

Authors: Avik Ranjan Adhikary , Sudhan Majhi , Zilong Liu , and Yong Liang Guan

Abstract: This paper 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 paper, we give a construction of EBZCPs with lengths  (where ,  and  are non-negative integers) and ZCZ widths , thus achieving asymptotic ZCZ ratio of 3/4. The proposed EB-ZCPs are constructed via proper insertion of concatenated odd-length binary ZCPs (OB-ZCPs). The ZCZ width is proved by exploiting several newly identified intrinsic structure properties of binary GCPs obtained from Turyn’s method. The proposed EB-ZCPs have aperiodic autocorrelation sum magnitude of 4 outside the ZCZ region (except for the last time-shift taking aperiodic autocorrelation sum value of zero).

Published in: IEEE Signal Processing Letters, Volume: 25, Issue: 7, July 2018.

Link: https://ieeexplore.ieee.org/document/8355785/