关于零相关窗互补码理论界的几点讨论

A discussion on theoretical limits of zero correlation window complementary codes

提出了一类新型的零相关窗互补码,这类新型零相关窗互补码可以表示为三个独立的元素:一对相互正交的互补码、一个正交矩阵和一个标号矩阵的组合。本文重点讨论了这类新型零相关窗互补码的副峰平方之和的理论界,证明了几个重要的定理。这些定理包括:副峰的平方之和只是相对偏移的函数、零相关窗互补码集的一致性、列旋转不变性及列排列不变性等。这些定理对零相关窗互补码的设计具有重要的指导意义。

A new set of zero correlation window complementary codes is introduced in this paper, it can be represented by three independent elements which are namely: a pair of complementary orthogonal codes, an orthogonal matrix and a matrix of sequence number. The theoretical limit of the sum of the square of side-lobes of the correlation functions of such zero correlation window complementary codes is discussed in this paper and few very important theorems are also given. These theorems include: sum of square of the side-lobes is the function of relative phase shift only, consistency of the zero correlation window complementary codes and invariance of sum of square of the side-lobes in column rotation or rearrangement. These theorems have strong impact on designing the zero correlation window complementary codes set.