Algebraic Schemes for Space-Time Modulation in Multiple Transmit Antenna Design

为了这项数学科学的跨学科资助，grant将于2003年8月至2004年7月访问科罗拉多大学博尔德分校的电气与计算机工程系，与他们的数字通信研究小组合作。主要目标是设计具有多个发射天线的系统的调制技术。这种调制也被称为空时编码，需要产生一组复杂的矩阵，这些矩阵达到最大的空间分集（也就是说，任何这些矩阵的差值都具有最大的秩）。对于调制方案，这些矩阵的条目被约束为所谓的星座点。Grant希望在最近使用代数数论的人的工作基础上，建立具有最大空间多样性的矩阵集，这些矩阵集的条目在BPSK， QPSK和矩形QAM调制方案的星座中，并将代数数论应用于其他星座的空时编码设计。该IGMS项目由MPS多学科活动办公室（OMA）和数学科学司（DMS）联合支持。

For this interdisciplinary grant in the mathematical sciences, Grant will spend August 2003-July 2004 visiting the Department of Electrical and Computer Engineering at the University of Colorado atBoulder to collaborate with their research group in digital communications.The primary goal is to design modulation techniques for systems with multiple transmit antennas. This modulation is also referred to as space-time coding, and requires the production of sets of complex matriceswhich achieve maximal spatial diversity (that is, the difference of any of these matrices has maximal rank). The entries of these matrices are constrained to be so-called constellation points for the modulation scheme.Grant hopes to build upon recent work of those who have used algebraic number theory to build sets of matrices with maximal spatial diversity whose entries are in constellations for BPSK, QPSK, and rectangular QAM modulation schemes, and to apply algebraic number theory to the design ofspace-time codes for other constellations.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).