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A quaternion-based approach to construct quaternary periodic complementary pairs
IEEE Communications Letters ( IF 4.1 ) Pub Date : 2020-09-01 , DOI: 10.1109/lcomm.2020.2995337
Nitin Jonathan Myers , Robert W. Heath

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.

中文翻译:

一种基于四元数的方法来构建四元周期互补对

如果两个阵列的周期性自相关之和是 delta 函数,则它们形成一个周期性互补对。然而,对于条目受限于小字母表的大型数组,找到这样的对是具有挑战性的。一个这样的字母表是四元组,它包含复杂的四次统一根。在这封信中,我们提出了一种使用完美四元数阵列构造在四元集上定义的周期性互补对的技术。我们展示了如何使用我们的方法构建满足周期性互补性质的新四元序列、矩阵和四维数组对。
更新日期:2020-09-01
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