A Novel Construction of Two-Dimensional Z-Complementary Array Pairs with Large Zero Correlation Zone

The two-dimensional (2-D) Z-complementary array pair (ZCAP) can be viewed as an extension of the well-known one-dimensional (1-D) Z-complementary pair (ZCP). To date, most constructions of 2-D ZCAPs are indirect and based on existing 1-D sequences or 2-D arrays. In this letter, a new direct construction of 2-D ZCAPs with flexible array sizes based on 2-D generalized Boolean functions is proposed. Compared with the state-of-the-art method, the proposed 2-D ZCAPs have larger 2-D zero correlation zone (ZCZ) sizes and more flexible array sizes. Furthermore, the peak-to-average power ratio of column sequences of the proposed 2-D ZCAPs is analyzed and upper bounded by 2.