A Novel Construction of Z-Complementary Pairs Based on Generalized Boolean Functions

Abstract

Binary Golay complementary pairs exist for quite limited lengths whereas the binary Z-complementary pairs (ZCPs) are available for more lengths. Therefore, the ZCPs can potentially find more engineering applications. In this letter, we propose a novel construction of binary and nonbinary ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math> </inline-formula> -ary for even <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> ) ZCPs based on generalized Boolean functions. Both even- and odd-length ZCPs can be obtained by the proposed construction. Moreover, the sequence length, the width of zero correlation zone (ZCZ), and the constellation size are all very flexible. A family of ZCPs with large ZCZ widths is presented based on our construction where the width of ZCZ is larger than half of the sequence length. This proposed family includes some previous results on binary ZCPs as special cases.