Two-Dimensional $Z$-Complementary Array Code Sets Based on Matrices of Generating Polynomials

The unprecedented elevation of wireless technologies produces the ever-increasing requirement for higher-dimensional array sets with preferable correlation properties and more flexible parameters. In this paper, we investigate new two-dimensional Z-complementary array code sets (2D-ZCACSs) with unimodular arrays, which are more preferable in ultra wideband communication system to improve its performance than 2D mutually orthogonal complementary array set. We first introduce a new idea of 2D Z-paraunitary (2D-ZPU) matrices by extending our previous concept of 1D-ZPU matrices. Then, we show that there exists an equivalence between a 2D-ZCACS and 2D-ZPU matrix when the former is expressed as a matrix with 2D generating polynomial entries. In the 2D generating matrix, each column corresponds to a 2D Z-complementary array code and two distinct columns correspond to 2D Z-complementary array mates. Finally, we propose a new construction method of unimodular 2D-ZCACSs with the aid of higher-dimensional z-transforms and the theory of ZPU matrices.