Aperiodic autocorrelation properties of sequences and arrays.

二进制序列的非周期自相关特性的研究始于20世纪50年代，并继续在各种数字传输系统中发挥核心重要性，包括雷达信息处理、多载波无线传输的功率控制和光时域反射。非周期自相关性相对于序列或阵列大小总体较小的序列和阵列对应的信号的传输浪费很少的能量，并且可以在接收器有效地恢复。传统上，对自相关性质的分析主要集中在周期情况下，其中存在丰富的数学结构，需要许多理论技术。但非周期情况在实践中更为重要，因为它在许多应用环境中自然出现。尽管传统观点长期以来一直认为，非周期自相关几乎没有显示出什么结构，而且通常唯一现实的分析手段是计算机搜索，但最近有几个迹象表明，情况恰恰相反。该计划的短期目标是研究这一领域的特定经典问题，最近的研究成果开辟了新的研究方向。长期目标是确定新兴的方法，并开发新的方法，用于研究大序列和阵列的非周期自相关。随着现代数字通信系统不太可能局限于使用较小的序列和阵列，这一点变得越来越重要。一般的科学方法将是结合离散数学、计算科学和数字通信工程的工具和见解。在适当的情况下，实验计算将用于揭示模式，识别关键示例，提高直觉，从而为新的理论结果指明道路。

The study of the aperiodic autocorrelation properties of binary sequences began in the 1950s and continues to be of central importance in diverse digital transmission systems, including radar information processing, power control for multicarrier wireless transmission, and optical time domain reflectometry. Sequences and arrays whose aperiodic autocorrelations are collectively small in relation to the sequence or array size correspond to signals whose transmission wastes very little energy and which can be recovered efficiently at the receiver.Traditionally, the analysis of autocorrelation properties has concentrated on the periodic case, where the presence of rich mathematical structure admits many theoretical techniques. But the aperiodic case is much more significant in practice, because it arises naturally in so many application contexts. Although conventional wisdom has long been that aperiodic autocorrelations display little structure, and that often the only realistic means of analysis is computer search, there have been several recent indications to the contrary.The short-term objectives of the program are to study particular classical problems in this area for which recent results have opened up new research directions. The long-term objective is to identify emerging methods, and develop new ones, for studying aperiodic autocorrelations of large sequences and arrays. This is becoming increasingly important as modern digital communications systems are less likely to be restricted to the use of smaller sequences and arrays. The general scientific approach will be to combine tools and insights from discrete mathematics, computing science, and digital communications engineering. Where appropriate, experimental computation will be used to reveal patterns, identify key examples, improve intuition, and so point the way to new theoretical results.