CIF: Small: Algebraic Methods in the Study of Some Problems in Communication Engineering

CIF：小：研究通信工程中一些问题的代数方法

• 批准号: 1016576
• 负责人: Krishnasamy Arasu
• 金额: $ 16.87万
• 依托单位: Wright State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-15 至 2015-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1016576&HistoricalAwards=false
• 关键词: CIF; Small; Algebraic; Methods; Study

This research involves the study of some specific cases of the Correlation Problem, the instances of which are carefully chosen so that advances in any of these cases would constitute dramatic advances, and improve our understanding of the whole Correlation Problem. These cases are also chosen with an eye to practical applications. We would employ algebraic methods to generate block-Hankel weighing matrices, multi dimensional Hadamard matrices, almost difference sets and perfect sequences. Our motivation stems from their usefulness in several areas of communication engineering: quantum computing, MC-CDMA systems , quasi-synchronous CDMA , multiple antenna wireless communication systems , FHSS which are widely used in military radios, CDMA and GSM networks, radars and sonars, and Bluetooth communications - to name a few.Discrete mathematical structures that can be developed using modern algebra, number theory and finite geometry and other combinatorial structures are useful in constructing sequences and arrays with desirable correlation properties. They are systematically studied via their algebraic counterparts. The results obtained will lead to new mathematical theories that are of interest to combinatorial design theorists and communication engineers. We thus investigate sequence design problems, which have a variety of applications in communication engineering. Our methods will be very algebraic and would employ tools from algebra, finite fields, and algebraic number theory.

这项研究涉及对相关性问题的一些具体案例的研究，这些案例都是经过精心选择的，以便这些案例中任何一个的进展都将构成巨大的进步，并提高我们对整个相关性问题的理解。 这些案例的选择也着眼于实际应用。我们将采用代数方法来生成块汉克尔权重矩阵、多维哈达玛矩阵、几乎差集和完美序列。我们的动机源于它们在通信工程的多个领域的有用性：量子计算、MC-CDMA 系统、准同步 CDMA、多天线无线通信系统、FHSS，广泛应用于军用无线电、CDMA 和 GSM 网络、雷达和声纳，可以使用现代代数、数论和有限几何以及其他组合结构开发的离散数学结构可用于构造具有所需相关属性的序列和数组。它们通过代数对应物被系统地研究。获得的结果将产生组合设计理论家和通信工程师感兴趣的新数学理论。因此，我们研究了序列设计问题，这些问题在通信工程中有多种应用。我们的方法将非常代数，并且将使用代数、有限域和代数数论的工具。