One-dimensional (1-D) Golay complementary pair (GCP) and its extension Z-complementary pair (ZCP) with additional zero autocorrelation zone property have been widely studied in the literature. Recently, the investigation of 1-D GCPs have been extended to two-dimensional (2-D) and higher dimensional Golay complementary array pairs (GCAPs). In this article, the concept of zero correlation zone (ZCZ) is applied to 2-D GCAP and the 2-D Z-complementary array pair (ZCAP) is presented. Several constructions of ZCAPs are proposed in this article and the existence of ZCAPs is discussed as well. Based on the proposed constructions, 2-D ZCAPs are shown to exist for all sizes. Furthermore, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived when both dimensions are odd. The proposed constructions can include ZCAPs which achieve the upper bound.

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.