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

对于这项数学科学的跨学科拨款，格兰特将于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和计算机工程系，与他们的研究小组在数字通信方面进行合作。主要目标是为具有多个发射天线的系统设计调制技术。这种调制也称为空时编码，需要产生复矩阵集，以实现最大的空间分集(即，这些矩阵中的任何一个的差值具有最大秩数)。这些矩阵的条目被限制为调制方案的所谓星座点。Grant希望在那些使用代数数论的人的最新工作的基础上，构建具有最大空间分集的矩阵集合，其条目是BPSK、QPSK和矩形QAM调制方案的星座，并将代数数论应用于其他星座的空时码的设计。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).