Constructions of two-dimensional Z-complementary array pairs with large ZCZ ratio.

Two-dimensional (2-D) Z-complementary array pair (ZCAP) is a pair of 2-D arrays, whose 2-D autocorrelation sum gives zero value at all time shifts in a zone around the (0, 0) time shift, except the (0, 0) time shift. The zone is called a zero correlation zone (ZCZ). 2-D ZCAPs include 2-D Golay complementary array pairs (GCAPs) as special cases, and can be applicable in 2-D synchronization. In this paper, we focus on designing new 2-D ZCAPs by exploring two promising approaches. The first construction of 2-D ZCAPs uses 1-D ZCPs as the initial stage, such that any binary ZCP and q-phase ZCP can produce a q-phase 2-D ZCAP. The second construction of 2-D ZCAPs is based on 2-D generalized Boolean functions (GBFs), and the resulting 2-D ZCAPs can have the largest 2-D ZCZ ratio 6/7, compared with known 2-D ZCAPs but not 2-D GCAPs in the literature. Here the ZCZ ratio is defined as the ratio of the ZCZ size over the array size. [ABSTRACT FROM AUTHOR]