发表机构
California State University, Northridge; University of Nebraska-Lincoln（北岭加州州立大学; 内布拉斯加大学林肯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二元序列互相关劣化因子的矩，提出精确计算任意阶中心矩的方法，并证明其均值为1且高阶中心矩为正。
AI 中文摘要
具有低互不周期互相关的序列族有助于设计多用户异步通信和多输入多输出雷达系统。一对序列的互相关劣化因子定义为：当序列归一化为单位欧几里得范数时，它们在每个移位处的互相关值平方幅度之和；而优值因子是劣化因子的倒数。对于每个正整数$\ell$，我们赋予$2^{2\ell}$对长度为$\ell$的二元序列以均匀概率测度，并研究其互相关劣化因子的分布。Sarwate证明了无论长度$\ell$如何，均值始终为$1$。我们开发了一种方法，用于求出第$p$阶中心矩（对任意正整数$p$）作为$\ell$的函数的精确公式。然后通过手算得到方差和第三中心矩（$p=2$和$3$）的公式，而第四至第六中心矩则通过计算机辅助计算获得。我们的理论还表明，对于$p\geq 2$和$\ell\geq 3$，所有中心矩必须严格为正。
英文摘要
Families of sequences with low mutual aperiodic crosscorrelation assist the design of systems for multi-user asynchronous communications and multiple-input multiple-output radar. The crosscorrelation demerit factor of a pair of sequences is the sum of the squared magnitudes of their crosscorrelation values at every shift when the sequences are normalized to unit Euclidean norm, and the merit factor is the reciprocal of the demerit factor. For each positive integer $\ell$, we endow the $2^{2 \ell}$ pairs of binary sequences of length $\ell$ with uniform probability measure and study the distribution of their crosscorrelation demerit factors. Sarwate showed that the mean value is always $1$ regardless of length $\ell$. We develop a method for finding an exact formula for the $p$th central moment (for any positive integer $p$) as a function of $\ell$. Formulae for the variance and third central moment ($p=2$ and $3$) are then obtained by hand calculations, while the fourth through sixth central moments are obtained by computer-assisted calculations. Our theory also shows that all the central moments must be strictly positive for $p\geq 2$ and $\ell \geq 3$.
Comments32 pages
