A Quaternion-Based Approach to Construct Quaternary Periodic Complementary Pairs
A Quaternion-Based Approach to Construct Quaternary Periodic Complementary Pairs
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DOI：
10.1109/lcomm.2020.2995337
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
Nitin Jonathan Myers;R. Heath
中科院分区：
文献类型：
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作者：
Nitin Jonathan Myers;R. Heath
如果两个数组的周期自相关和是一个函数，则它们形成周期互补对。然而，对于条目被限制为小字母的大型数组来说，找到这样的对是一个挑战。一个这样的字母表是四元集，它包含了单位的复四次根。在这封信中，我们提出了一种技术来构造周期互补对定义在四元集合上使用完美四元数数组。我们展示了如何用我们的方法构造满足周期互补性质的新的四元序列、矩阵和四维数组对。
Two arrays form a periodic complementary pair if the sum of their periodic autocorrelations is a delta function. Finding such pairs, however, is challenging for large arrays whose entries are constrained to a small alphabet. One such alphabet is the quaternary set which contains the complex fourth roots of unity. In this letter, we propose a technique to construct periodic complementary pairs defined over the quaternary set using perfect quaternion arrays. We show how new pairs of quaternary sequences, matrices, and four-dimensional arrays that satisfy a periodic complementary property can be constructed with our method.