For one-dimensional (1-D) sequences, many lower bounds on the maximum cross-correlations have been demonstrated. For example, bounds proposed by Welch, Levenstein, Liu et al., and others are the lower bounds on the maximum cross-correlations of aperiodic 1-D sequence sets or quasi-complementary sequence sets (QCSSs). However, in recent times, two-dimensional (2-D) arrays have emerged with promising applications in wireless communication, such as ultra wide-band (UWB), 2-D synchronization, massive multiple-input multiple-output (MIMO), 2-D multi-carrier code division multiple access (2D-MC-CDMA), etc. Although the construction of a 2-D quasi-complementary array set (QCAS) exists in literature, the lower bound on the maximum cross-correlation \(\delta _{max}\) of such a 2-D QCAS has not been reported previously. In this paper, we propose, for the first time lower bounds on the maximum cross-correlations of 2-D QCASs for both periodic and aperiodic cases. The existing lower bounds on the maximum cross-correlations of 1-D QCSSs and 1-D sequence sets can be deduced from the proposed lower bounds on the maximum cross-correlations of 2-D QCASs and 2-D array sets for certain cases.

对于一维 (1-D) 序列，已证明了最大互相关性的许多下限。例如，Welch、Levenstein、Liu等人提出的界限。，其他是非周期一维序列集或准互补序列集（QCSS）的最大互相关的下界。然而，近年来，二维（2-D）阵列在无线通信中出现了具有前景的应用，例如超宽带（UWB）、2-D同步、大规模多输入多输出（MIMO）、二维多载波码分多址（2D-MC-CDMA）等。虽然文献中存在二维准互补阵列集（QCAS）的构造，但最大互相关的下界\ (\delta _{最大值}\)这种 2-D QCAS 的研究以前从未有过报道。在本文中，我们首次提出了周期性和非周期性情况下二维 QCAS 最大互相关的下界。对于某些情况，1-D QCSS 和 1-D 序列集的最大互相关性的现有下界可以从所提出的 2-D QCAS 和 2-D 阵列集的最大互相关性下界推导出来。