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.

中文翻译：

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基于生成多项式矩阵的二维Z-互补数组代码集

无线技术的空前发展产生了对具有更佳相关特性和更灵活参数的更高维阵列集的不断增长的需求。在本文中，我们研究了新的二维$Z$-具有单模阵列的互补阵列码集（2D-ZCACS），在超宽带通信系统中比二维相互正交的互补阵列集更适合提高其性能。我们先介绍一个2D的新思路$Z$-paraunitary (2D-ZPU) 矩阵通过扩展我们之前的 1D-ZPU 矩阵概念。然后，我们证明当 2D-ZCACS 和 2D-​​ZPU 矩阵表示为具有 2D 生成多项式项的矩阵时，2D-ZCACS 和 2D-​​ZPU 矩阵之间存在等价。在二维生成矩阵中，每一列对应一个二维$Z$- 互补数组代码和两个不同的列对应于 2D $Z$-互补阵列配对。最后，我们提出了一种新的单模 2D-ZCACS 构建方法，借助高维$z$- 变换和 ZPU 矩阵理论。