Arrays over Small Phase Alphabet Having Desirable Correlation Properties

具有所需相关特性的小相位字母表上的阵列

• 批准号: 9814106
• 负责人: Krishnasamy Arasu
• 金额: $ 14.22万
• 依托单位: Wright State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-03-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9814106&HistoricalAwards=false
• 关键词: Arrays; over; Small; Phase; Alphabet

Time-discrete one- and two- dimensional sequences and arrays find applications in signal processing and as aperture functions for electromagnetic and acoustic imaging. Applications of two dimensional perfect binary arrays are found in 2-D synchronization and time-frequency coding. These are also usedin channel coding and cryptographic coding. This research involves the study of perfect arrays and their related mathematical objects. Wide-band digital communications, optical signal processing, radar and audio coding are other disciplines that have applications of these objects.The conventional binary case { +1, -1} as the alphabet. The investigator extends the alphabet to the ternary and quaternary cases: the corresponding alphabets being {0, +1, -1} and {i,-i,+1,-1}. Here i denotes the complex fourth roots of unity. The problems studied pertain to perfect binary arrays, perfect ternary arrays, perfect quaternary arrays, almost perfect arrays and periodic complementary sequences. The investigator studies these via their algebraic formulations viz. difference sets, supplementary difference sets and divisible difference sets. New structural theorems will be proved using character sumsof group ring elements over suitable abelian groups. These results would enable to produce new classes of sequences and arrays with desirable correlation properties.

时间离散的一维和二维序列和阵列在信号处理和作为电磁和声学成像的孔径函数中得到应用。研究了二维完美二进制数组在二维同步和时频编码中的应用。这些也用于信道编码和密码编码。这项研究涉及到对完美数组及其相关数学对象的研究。宽带数字通信、光信号处理、雷达和音频编码是这些对象应用的其他学科。常规二进制{+1，-1}作为字母表。研究者将字母表扩展到三进制和四进制：相应的字母表是{0，+1，-1}和{i，-i,+1,-1}。这里i表示单位的复四次根。研究的问题涉及到完全二进制数组、完全三元数组、完全四元数组、几乎完全数组和周期互补序列。研究了它们的代数表述，即差分集、互补差分集和可分差分集。利用合适的阿贝尔群上群环元素的字符和证明了一些新的结构定理。这些结果将能够产生具有理想相关性的序列和数组的新类别。