Constructions of Two-Dimensional Binary Z-Complementary Array Pairs

One-dimensional (1-D) Z-complementary pair (ZCP) is an extension of 1-D Golay complementary pair (GCP) where the autocorrelations of constituent sequences are complementary within a zero correlation zone (ZCZ). The concept of ZCZ can be applied to two-dimensional (2-D) Golay complementary array pair to obtain the 2-D Z-complementary array pair (ZCAP). In this paper, constructions of ZCAPs are proposed based on concatenations of 1-D ZCPs or existing 2-D ZCAPs. In addition, the construction of 1-D ZCPs based on Kronecker product is modified and extended to 2-D ZCAPs. One potential application of 2-D ZCAPs is 2-D synchronization.